From the Foxlist: What is a "true" doppler?

The following LONG discussion was taken from the Foxlist, and concerns
the  topic  of  whether current Doppler direction finders  are  really
"true"  dopplers.    No matter what your own view  on  this  technical
topic,  it  is  nice  to  see  intelligent people have an  intelligent
debate.

----------------------------------------------------------------------
Date: Tue, 5 Mar 1996 08:37:19 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: fox-list <fox-list@netcom.com>
Subject: A Real Doppler
Sender: owner-fox-list@netcom.com

Is anyone  aware  of a direction-finding device that actually uses the
Doppler principle?   There  are  a  lot  of  devices  that  are called
"Doppler" direction finders (e.g., A Dopplescant, The Roanoke Doppler,
etc...) that do not in  fact utilize the Doppler principle;  i.e., the
shift  in frequency resulting from relative  velocity  of  the  signal
source with respect to the signal receiver.

A "real" Doppler DFer working with a circle of switched antennas would
probably require careful attention to the diameter of  the circle, and
the  switching  rate.    Also,  there should be no  restriction  (only
practical  limitations) on the maximum radius about which the antennas
are spaced.  Any design that REQUIRES that the circle of antennas have
a  diameter  not to exceed 1/2 wavelength is probably not operating on
the Doppler principle.

Any leads on a real Doppler DFer would be appreciated!

73,
Charles E. Scharlau, NZ0I
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134 
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam          
-----------------------------------------------------------------------

Date: Thu, 07 Mar 1996 08:15:25 -0600 (CST)
From: schellew@wu1.wl.aecl.ca (Wayne Schellekens)
Subject: Re: A Real Doppler
To: fox-list@netcom.com
Content-length: 2025
Sender: owner-fox-list@netcom.com

> Is anyone aware of a direction-finding device that actually uses the 
> Doppler principle? There are a lot of devices that are called "Doppler" 
> direction finders (e.g., A Dopplescant, The Roanoke Doppler, etc...) that 
> do not in fact utilize the Doppler principle; i.e., the shift in 
> frequency resulting from relative velocity of the signal source with 
> respect to the signal receiver.

The roanoke doppler  design  <does> use the frequency shift principle.
Various experiments have shown that you can get good enough resolution
by using a square of  four  antennas  instead  of a circle of eight or
more.  Personally I would like  to  borrow  my friend's 8 antenna unit
and see if it is any more  precise  than  the  four  antenna  one I am
testing now.

If you examine the circuitry of the roanoke  unit, you can see that it
measures  the phase delay between the reference signal (that  switches
the antennas) and the recieved audio signal.  The nice  thing about FM
is that switching the antennas at 500 Hz will create a  500 Hz tone on
the received audio.

> A "real" Doppler DFer working with a circle of switched antennas would 
> probably require careful attention to the diameter of the circle, and the 
> switching rate. Also, there should be no restriction (only practical 
> limitations) on the maximum radius about which the antennas are spaced. 
> Any design that REQUIRES that the circle of antennas have a diameter not 
> to exceed 1/2 wavelength is probably not operating on the Doppler 
> principle.

The  switching rate should only affect your filters in the electronics
of your  unit.   You would probably want a switching rate in the audio
passband, and try to select a frequency which is not being transmitted
by your 'fox'.

One could argue that  a  "real"  doppler  DF  uses  a  vertical dipole
rotating in a 1/4 wave  circle.    But I think that switching multiple
antennas is more practical.

> 73,
> Charles E. Scharlau, NZ0I

73,
-- 
Wayne Schellekens, VE4WTS
schellew@wu1.wl.aecl.ca | http://www.mbnet.mb.ca/~wschell 
-----------------------------------------------------------------------

Date: Thu, 07 Mar 1996 19:13:17 -0800
From: James Ewen <jewen@oanet.com>
Organization: Strathcona Radio Volunteers
To: fox-list@netcom.com
Subject: Re: A Real Doppler
References: <Pine.SUN.3.91.960305082231.10779A-100000@eskimo.com>
Sender: owner-fox-list@netcom.com

Charles:

I  would  like  to know what your  parameters  for  a  "real  doppler"
direction finder is.  I have a doppler  df  based  on the DoppleScAnt.
It  doesn't rotate the antenna array physically to produce  a  doppler
shift  in  the  received signal, but rather swithes between the  eight
antennas to produce a psuedo-doppler shift.  By swithing between these
antennas, it approximates the rotation of the antenna.

You  say  that "There are a lot of devices that are  called  "Doppler"
direction finders (e.g.,  A  Dopplescant, The Roanoke Doppler, etc...)
that do not in fact utilize the Doppler principle;  i.e., the shift in
frequency resulting from relative velocity  of  the signal source with
respect to the signal receiver." Your  next  paragraph  then  says  "A
"real" Doppler DFer working with a circle  of  switched antennas would
probably require careful attention to the diameter of  the circle, and
the switching rate." 

In  one  sentence  you  say  a real doppler can't  scan  an  array  of
antennas,  then  you say a "real" doppler can.  To  achieve  a  "real"
doppler  shift,  you  have  to  move  ONE  antenna.  The logistics  of
physically rotating one antenna fast enough is impractical.  f(c + vt)
f'  =   -----------  c  Where  f'  =  Doppler-shifted  frequency  f  =
transmitter frequency vt = velocity of antenna toward or away from the
transmitter c = speed of light

To achieve a 1 kHz Doppler shift on a 147 MHz transmitter, you need to
rotate the antenna at 2000 meters/second.  This is about six times the
speed of sound.  (Stolen from  Terrence Rogers article in QST May 1978
pg 24)

What is a "real" doppler system?
-- 
  __
 /_ _/_ __ _//_ __ __ __ __
__/ // /-/ // //_ /_// //-/
    Radio Volunteers        73 de VE6SRV
-----------------------------------------------------------------------

Date: Fri, 8 Mar 1996 10:39:11 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: fox-list <fox-list@netcom.com>
Subject: True Doppler Search
Sender: owner-fox-list@netcom.com

To:  All who have written to  inform  me  that the Roanoke Doppler and
similar Doppler designs do in fact utilize the Doppler frequency shift
effect:

Thank you for your responses. Please understand the following:

1) I  AGREE  that a switched circle of antennas should  approximate  a
   single  antenna  being  rotated  about  a central point, and should
   result in a Doppler shifted signal.

2) I am  NOT saying that the Roanoke Doppler and other "Dopplers" that
   operate on the same  principle  do  not  work.    I've  heard  from
   numerous  "Doppler" owners who sing  their  praises.    I  own  one
   myself.

3) I am NOT saying that a true Doppler system would perform any better
  than the Roanoke or similar "Doppler" systems.   I've  never  seen a
  true  Doppler  system, or even heard of one, so I  have  no  way  of
  knowing.

What I am calling a "true Doppler" system, which would include  a true
Doppler  that operates using a network of switched antennas, must obey
the theory  of the Doppler effect.  The Roanoke and similar systems DO
NOT.  In  fact  they all include very narrow audio filters centered on
the  rotational  frequency  of   the  antenna  system,  and  therefore
effectively remove any trace of the Doppler- effect tone. 

Doppler theory requires that the Doppler-shifted signal conform to the
following equation:  
   
   S = (R*W*Fc)/C where 

   S is the Doppler shift (Hertz)
   R is the radius of antenna rotation (in meters)
   W is the rotational velocity of the antenna system (radians per second)
   Fc is the carrier frequency of the received signal (Hertz)
   C is the speed of light (meters per second)

Notice that the shift depends on  antenna  radius, how fast you switch
among the various antennas, and the frequency  of  the  signal you are
receiving.  Change any one of these variables  and  you  should change
the Doppler shift, and therefore the tone coming from  your DF system.
(The first clue that the Roanoke and similar DF systems  are  not true
Dopplers  is  that  the  tone  they  produce is independent of antenna
Radius or received frequency.)

If  you  apply  the values from a "Doppler" direction finder design to
the  above  equation, you should derive the frequency of the tone that
the system  analyzes  to  determine bearings.  For the Roanoke Doppler
described  in  "Transmitter    Hunting:      Radio  Direction  Finding
Simplified," chapter 9, you get the following: 

Fc = 146,000,000 Hz (choose middle of amateur 2-meter band)
W  = 500 revolutions per second = 1000*pi radians per second = 3142 radians/sec
R  = lambda/(4*sqrt(2)) = 0.363 meters
C  = 300,000,000 meters per second

S  = 555 Hertz

The Roanoke Doppler includes  a series of active low-pass filters with
cut-offs set at 500 Hz.    In  addition  it has a very narrow switched
capacitor band pass filter (a few  Hertz wide) centered at 500 Hz.  So
it is safe to say that very little 555 Hertz Doppler signal ever makes
its way to the zero-cross detector of the  Roanoke  Doppler.   In fact
the Doppler shift is completely ignored.

Anyone who contends that the Roanoke, or by extension any "Doppler" of
similar  design, actually utilizes the Doppler principle, must explain
why such systems don't comply with theory.

I contend  that the operation of such systems is quite simple.  If you
understand the operation  of  a  "Handifinder"  or similar two-antenna
switched phase-difference system, then  you  can extend that principle
to the so-called Doppler direction finders.  For such systems to work,
the antenna separation (diameter of the  circle  of antennas) must not
exceed  one-half  wavelength  at the highest frequency  at  which  the
system is used.  The tone they produce  will  always  be  exactly  the
rotational  frequency of the antenna system, independent of radius  or
received  frequency.    But  they do NOT in fact utilize  the  Doppler
effect. 

It seems that a true Doppler which uses a circle of  switched antennas
should  be  possible,  and  may  very well exist.  Perhaps only a  few
changes to  the  audio filtering circuit of the "Doppler" designs, and
very careful attention  to  the  antenna  layout,  would be all that's
necessary.

If you can point out any substantial errors in the above arguments or,
if you hear of a  switched  antenna  system  which  actually  uses the
Doppler effect, I'd be interested to hear from you. 

73,
Charles E. Scharlau
SEA, A Unit of Datamarine International, Inc.
7030 220th S.W., Mountlake Terrace, WA 98043, USA
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134 
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam          
-----------------------------------------------------------------------

Date: Sat, 9 Mar 1996 00:25:08 -0800 (PST)
From: Jay Hennigan <jay@west.net>
X-Sender: jay@acme.sb.west.net
To: fox-list@netcom.com, Charles Scharlau <cscharl@eskimo.com>
Subject: Re: A Real Doppler
Sender: owner-fox-list@netcom.com

On Tue, 5 Mar 1996, Charles Scharlau wrote:

> Is anyone aware of a direction-finding device that actually uses the 
> Doppler principle? There are a lot of devices that are called "Doppler" 
> direction finders (e.g., A Dopplescant, The Roanoke Doppler, etc...) that 
> do not in fact utilize the Doppler principle; i.e., the shift in 
> frequency resulting from relative velocity of the signal source with 
> respect to the signal receiver.

I beg to differ.  The  dopplescant,  Roanoke,  etc.    indeed  use  an
electrical simulation of a rotating antenna and the shift in frequency
due to the doppler effect as the virtual  receiving antenna approaches
and  recedes from the signal source.  What principle  do  you  suggest
that they actually use?  An actual mechanical rotating antenna  at the
angular velocities required to produce a reasonable shift in frequency
at 144MHz would be impractical. 

> A "real" Doppler DFer working with a circle of switched antennas would 
> probably require careful attention to the diameter of the circle, and the 
> switching rate. 

The two  are  indeed  related,  as  the  diameter  of  the  circle and
switching rate interact  to  generate  the  angular  velocity  of  the
virtual antenna and thus the deviation imposed on the received signal.
The key to the proper  operation is the use of a common clock to drive
the antenna switch and also clock  a  high-Q  switched-capacitor audio
filter  prior  to the zero-crossing detector.   This  ensures  optimum
detection  of the FM signal imposed by the  rotation  of  the  virtual
antenna while rejecting other causes of frequency shift such  as voice
modulation of the carrier. 

> Also, there should be no restriction (only practical 
> limitations) on the maximum radius about which the antennas are spaced. 

True.

> Any design that REQUIRES that the circle of antennas have a diameter not 
> to exceed 1/2 wavelength is probably not operating on the Doppler 
> principle.

This  restriction  has to do with the number of electrically  switched
antennas.   A larger circle of antennas is indeed possible, but  would
require a  larger  number  of  antennas  to  eliminate  aliasing.  The
limitation is really  that  the  distance  between  any  two  adjacent
antennas in the circle  is  a small fraction of a wavelength, not that
the circle itself be so limited. 

I suppose it would be  possible to use a small number of antennas in a
large circle with a very careful  selection of the switching rate with
regard to the carrier frequency to eliminate  aliasing.   Some sort of
synchronous  detector/PLL would probably be required, and it  wouldn't
fit on your car.  :)

> Any leads on a real Doppler DFer would be appreciated!

I question your assumption that the Roanoke, dopplescant, etc. are not 
"real" Doppler DF units.

----
WestNet:  Internet service to Santa Barbara, Ventura and the world. 
          805-892-2133   805-289-1000   805-578-2121
-----------------------------------------------------------------------

Date: Sat, 9 Mar 1996 11:07:45 -0800 (PST)
From: Jay Hennigan <jay@west.net>
X-Sender: jay@acme.sb.west.net
To: fox-list@netcom.com, Charles Scharlau <cscharl@eskimo.com>
Subject: Re: True Doppler Search
Sender: owner-fox-list@netcom.com

On Fri, 8 Mar 1996, Charles Scharlau wrote:

> To: All who have written to inform me that the Roanoke Doppler and similar 
> Doppler designs do in fact utilize the Doppler frequency shift effect:
> 
> Thank you for your responses. Please understand the following:
> 
> 1) I AGREE that a switched circle of antennas should approximate a single
>    antenna being rotated about a central point, and should result in a
>    Doppler shifted signal.

OK.

> 2) I am NOT saying that the Roanoke Doppler and other "Dopplers" that operate
>    on the same principle do not work. I've heard from numerous "Doppler"
>    owners who sing their praises. I own one myself.

OK.

> 3) I am NOT saying that a true Doppler system would perform any better than
>    the Roanoke or similar "Doppler" systems. I've never seen a true Doppler
>    system, or even heard of one, so I have no way of knowing.

You own one yourself. :)

> What I am calling a "true Doppler" system, which would include a true 
> Doppler that operates using a network of switched antennas, must obey 
> the theory of the Doppler effect. The Roanoke and similar systems DO 
> NOT. In fact they all include very narrow audio filters centered on the 
> rotational frequency of the antenna system, and therefore effectively 
> remove any trace of the Doppler- effect tone. 

This is is where you are in error.  The rotational  frequency is equal
to  the  sampling  rate.    The filters remove other artifacts such as
voice and noise. 
 
> Doppler theory requires that the Doppler-shifted signal conform to the 
> following equation:
>                      S = (R*W*Fc)/C
> where 
> 
>    S is the Doppler shift (Hertz)
>    R is the radius of antenna rotation (in meters)
>    W is the rotational velocity of the antenna system (radians per second)
>    Fc is the carrier frequency of the received signal (Hertz)
>    C is the speed of light (meters per second)
> 
> Notice that the shift depends on antenna radius, how fast you switch 
> among the various antennas, and the frequency of the signal you are 
> receiving. Change any one of these variables and you should change the 
> Doppler shift, 

Correct.

> and therefore the tone coming from your DF system. 

Incorrect as to the frequency of the tone.

> (The first clue that the Roanoke and similar DF systems are not true Dopplers 
> is that the tone they produce is independent of antenna Radius or 
> received frequency.)

You are  confusing  the doppler shift (FM deviation) with the rotation
rate.  
 
> If you apply the values from a "Doppler" direction finder design to the above 
> equation, you should derive the frequency of the tone that the system analyzes 
> to determine bearings. For the Roanoke Doppler described in "Transmitter 
> Hunting: Radio Direction Finding Simplified," chapter 9, you get the 
> following: 
> 
> Fc = 146,000,000 Hz (choose middle of amateur 2-meter band)
> W  = 500 revolutions per second = 1000*pi radians per second = 3142 radians/sec
> R  = lambda/(4*sqrt(2)) = 0.363 meters
> C  = 300,000,000 meters per second
> 
> S  = 555 Hertz
> 
> The Roanoke Doppler includes a series of active low-pass filters with cut-offs 
> set at 500 Hz. In addition it has a very narrow switched capacitor band pass 
> filter (a few Hertz wide) centered at 500 Hz. So it is safe to say that very 
> little 555 Hertz Doppler signal ever makes its way to the zero-cross detector 
> of the Roanoke Doppler. In fact the Doppler shift is completely ignored.

The rate of  repetition  of the Doppler shifted signals is 500 Hz., as
that is the rotational  rate of the antennas.  The shift is indeed 555
Hz.!  The 146,000,000 Hz  signal  increases to 146,000,555 Hz.  as the
virtual  antenna  approaches  the  transmitter,  and    decreases   to
145,999,445 Hz.  as the virtual antenna  recedes from the transmitter.
This occurs 500 times per second.  The _deviation_ of the FM signal is
+/- 555 Hz., just like the math says it should be! 

> Anyone who contends that the Roanoke, or by extension any "Doppler" of similar 
> design, actually utilizes the Doppler principle, must explain why such systems 
> don't comply with theory.

I beg to differ.

> I contend that the operation of such systems is quite simple. If you 
> understand the operation of a "Handifinder" or similar two-antenna switched 
> phase-difference system, then you can extend that principle to the so-called 
> Doppler direction finders.

Please so extend the switched phase-difference two antenna theory.  

> For such systems to work, the antenna separation 
> (diameter of the circle of antennas) must not exceed one-half wavelength at 
> the highest frequency at which the system is used.

This  depends  on the number of antennas.  The  distance  between  two
adjacent antennas should be a small fraction of a wavelength  to avoid
aliasing. 

> The tone they produce will 
> always be exactly the rotational frequency of the antenna system, independent 
> of radius or received frequency.

Correct  as to the frequency of the tone.  The _deviation_  (  Doppler
shift:> ) of the tone is dependent on the factors you stated  in  your
formula above. 

> But they do NOT in fact utilize the Doppler effect. 

I beg to differ.
 
> It seems that a true Doppler which uses a circle of switched antennas 
> should be possible, and may very well exist. Perhaps only a few changes to 
> the audio filtering circuit of the "Doppler" designs, and very careful 
> attention to the antenna layout, would be all that's necessary.

No changes necessary.  They work just fine.  

> If you can point out any substantial errors in the above arguments or, if you 
> hear of a switched antenna system which actually uses the Doppler effect, I'd 
> be interested to hear from you. 

Your arguments are  in  error.    The  virtual rotating antenna indeed
Doppler-shifts the received frequency.  The FM _deviation_ in Hertz of
the shifted signal is as  you have stated above.  The sampling rate at
which the zero-crossings are taken to  determine  the  bearing  to the
transmitter is equal to the rotational speed  of  the  virtual antenna
and determines the _frequency_ of the audible tone heard.

----
WestNet:  Internet service to Santa Barbara, Ventura and the world. 
          805-892-2133   805-289-1000   805-578-2121
-----------------------------------------------------------------------

Date: Sat, 09 Mar 1996 12:26:57 -0600
To: Charles Scharlau <cscharl@eskimo.com>
From: geletka@synergetic.com (Tom Geletka)
Subject: Re: True Doppler Search
Cc: fox-list@netcom.com
Sender: owner-fox-list@netcom.com

>Fc = 146,000,000 Hz (choose middle of amateur 2-meter band)
>W  = 500 revolutions per second = 1000*pi radians per second = 3142 radians/sec
>R  = lambda/(4*sqrt(2)) = 0.363 meters
>C  = 300,000,000 meters per second
>
>S  = 555 Hertz
>
>The Roanoke Doppler includes a series of active low-pass filters with cut-offs 
>set at 500 Hz. In addition it has a very narrow switched capacitor band pass 
>filter (a few Hertz wide) centered at 500 Hz. So it is safe to say that very 
>little 555 Hertz Doppler signal ever makes its way to the zero-cross detector 
>of the Roanoke Doppler. In fact the Doppler shift is completely ignored.
>

A  hypothetical  mechanical  doppler  system rotating at  500  rev/sec
(30000  rev/minute)  would produce an FM signal with  a  500  hz  tone
regardless  of  the  diameter  of the antenna path.   The  instanteous
received  RF  frequency  would  change,  but the average would be  the
transmitted  frequency.    The FM detector would only see a change  in
antenna  path  diameter  as  a  change  in the FM modulation deviation
(loudness of derived audio).

One would  still  deduce the direction of the signal by looking at the
phase of the modulation that is produced at the rotation speed.  An FM
detector and a phase  detector  are  equivilant  over a narrow band of
frequencies.

If you cannot agree that a mechanical system rotating at 30000 rpm would
produce a 500 hz tone in an FM receiver, read no further.

>Anyone who contends that the Roanoke, or by extension any "Doppler" of similar 
>design, actually utilizes the Doppler principle, must explain why such systems 
>don't comply with theory.

Measuring the frequency 

>
>I contend that the operation of such systems is quite simple. If you 
>understand the operation of a "Handifinder" or similar two-antenna switched 
>phase-difference system, then you can extend that principle to the so-called 
>Doppler direction finders. For such systems to work, the antenna separation 
>(diameter of the circle of antennas) must not exceed one-half wavelength at 
>the highest frequency at which the system is used.

Dopplar systems are no-way limited  to  1/2 wavelength.  To use bigger
systems  requires  more  elements  to  approximate   the  hypothetical
rotating antenna.  Commercial ship navigation dopplers  often  use  96
elements and are a few wavelengths in diameter.    The  more antennas,
the better the approximation.  The individual antennas should  not  be
spaced too far.

The switched systems are an aproximation of a theoretical system.  The
more antennas, the closer the approximation.

>The tone they produce will 
>always be exactly the rotational frequency of the antenna system, independent 
>of radius or received frequency. But they do NOT in fact utilize the Doppler 
>effect. 

You  could  compare  a  two-element  switched  antennal fed into an FM
detector to the effect of a single element mechanically moved back and
fourth  on  a  straight  line.  One could argue that that system is  a
minimal Dopper.  Would  you  say  that the mechanical in-line movement
system would be using the Doppler principal?

It is true that sometimes  switched  Doppler systems have a mixture of
things going on.  For example,  the amplitude of the signal will often
vary with the rotation.  This is due to the other antennas having some
parasitic effect, and nearby object (a finite ground  plane).   If the
FM receiver does not reject AM, that will figure  into the picture.  A
friend  has  reported that his Dick Smith Doppler works better  on  AM
than FM at frequencies higher than the antenna was designed for.

>
>It seems that a true Doppler which uses a circle of switched antennas 
>should be possible, and may very well exist. Perhaps only a few changes to 
>the audio filtering circuit of the "Doppler" designs, and very careful 
>attention to the antenna layout, would be all that's necessary.

Dopplers are not by any means 

>
>If you can point out any substantial errors in the above arguments or, if you 
>hear of a switched antenna system which actually uses the Doppler effect, I'd 
>be interested to hear from you. 

Well? Do you acknowlege any errors?

Tom N9CBA
==============================================================
Chicago foxhunt schedule is at
http://homepage.interaccess.com/~geletka/foxhunt.html
-----------------------------------------------------------------------

Date: Sat, 9 Mar 1996 19:26:09 -0500
From: Grandrews@aol.com
To: fox-list@netcom.com
cc: cscharl@eskimo.com
Subject: K6BMG Comments on Dopplers. /K6BMG Comments on True Dopplers.
Sender: owner-fox-list@netcom.com

I think I can clear up some points  raised  by  Charles.    I will use
plain English, which is the language I used when I taught myself radio
(long before I became and Engineer - MSEE).  I  will  discuss the True
Doppler first.

For a true Doppler, let us consider a single antenna rotating around a
circle  at  some  high  speed.    The  received  signal will appear to
"wobble" around  the  transmitter  frequency.  For an FM detector, the
receiver output will  be the voltage equivalent of this wobble.  For a
single RF path the wobble will be a sine wave.    

The FREQUENCY of the  sine wave will always be EXACTLY the same as the
spin (the rotation) frequency.   The  PEAK  MAGNITUDE of the sine wave
(the + and - frequency shift  during  the  spin)  is a function of the
velocity towards (or away from) the transmitter.

The equation which Charles gave is:

S  =  (R*W*Fc)/C   

This is the equation used to calculate  the MAGNITUDE of the frequency
wobble.  It does not calculate the tone  frequency.    The value of S,
the magnitude of the Doppler shift in Hz, does not appear in the audio
signal being processed by the Doppler RDF as an audio  FREQUENCY,  but
only as the magnitude of the spin (audio) frequency.  Thus  we see the
basic  error  which  Charles has made.  The FREQUENCY he calculates is
not an  audio  frequency, and does not appear in the audio bandpass at
all!  The  tone  heard in a Doppler RDF (True or Switched type) is the
Doppler Effect tone!  It is the spin frequency.

Please note that theoretically a Doppler RDF would not make use of the
magnitude of the Doppler shift (as calculated by the formula presented
by Charles), even if it were  a  True  Doppler.    The  system is only
interested in the exact timing of when  the  voltage sine wave changes
polarity (i.e.  the zero-volt crossing point;   assume  we  are  using
only  the  positive  to  negative crossing).  This event  is  used  to
"capture"  the  information  that  tells where in the spin circle  the
antenna is at the instant of the zero-volt crossing.  That information
is displayed as the bearing.

Notice that  I  said  that  "theoretically" the Doppler system doesn't
care about the  magnitude  of  the  sine wave.  In practical terms, it
does.  The greater  the  magnitude, the less susceptible the system is
to noise.  If we  have  low  Doppler  magnitude  (poor signal to noise
ratio), the noise fuzzes up the  zero  crossing  so  that it cannot be
determined reliably, and the bearing will jitter all over the compass!

Signal  to  noise  ratio  of  a True  Doppler  would  be  improved  by
increasing  either  the  spin frequency or the spin  diameter.    Both
increase the magnitude of the peak Doppler shift.
--------------

I  wish to make some points regarding the practical  switched  antenna
Doppler.  The basic challenge is to improve the RDF  (audio) signal to
noise ratio.

For the  practical  switched  antenna  Doppler,  increasing  the  spin
frequency does not  (by  itself) make a bigger RDF signal.  The reason
is the switched Doppler  really  is making phase steps in the incoming
signal,  and  these phase steps  are  the  SAME  SIZE  (in  electrical
degrees) no matter what the spin frequency.

Improving  S/N  ratio by making the  narrow  band  synchronous  filter
narrower can have the drawback of slowing  down  the  response time of
the system too much.  It takes "forever"  for  the  bearing to finally
settle down!   

Better S/N ratio can be obtained by taking more samples per spin, with
a  greater  radius.    The rule of thumb here is  to  not  exceed  1/2
wavelength between  ADJACENT  antenna  elements.   (I suspect that not
greater than 1/4  would be better, but I've never done a study on this
- any comments?) There is no theoretical limit on the diameter as long
as there are enough elements to maintain close adjacent spacing.  Thus
one could have a 2 meter  Doppler  12  feet  in  diameter and using 32
elements!  (My Doppler has 8 elements  on  a  38  inch  diameter:    A
practical size for a car.)

Having  more  elements  on  a  larger  diameter  does    provide  some
advantages.  Assume the same spin frequency and the  same bandwidth in
the narrow-band filter.  One gets the same settling time  for a stable
bearing.   But there are now MORE SAMPLES PER SPIN, with  each  sample
producing  the  same  magnitude phase steps as the smaller antenna (in
electrical degrees).    Thus  the  bandpass  filter  is receiving more
information per spin, and the S/N ratio improves!
-----------

Regarding antennas with only two elements, such as my SuperDF.    

These are not  Doppler  systems  by any stretch of the mind.  They are
what I call Phase  Front  Detectors.   They are used to tell when both
dipoles see the same RF phase.  In the case of the SuperDF, it is able
to tell the operator which dipole  is  closer  to the transmitter, and
thus which why to rotate in order to face the signal source.

The filtering used on SuperDF does not  have  the  drawbacks  of those
used  on  the  Doppler.    The  Doppler  narrow   band  filter  has  a
considerable potential of injecting its own noise which is synchronous
to the spin frequency.  Thus it is likely to  have  its  own  floor of
sensitivity  below which it is impossible to go.  (The SuperDF  filter
cannot do this.)

Even  using  the  long time constant filter option of the SuperDF, the
magnitude (by ear) of the switching tone can be used to determine when
bearing has been achieved, even if the filter lags behind.

SuperDF uses other  methods  not  used  in the Doppler (besides narrow
band filters) to improve  S/N  ratio.   SuperDF is able to hear and DF
signals that are 20 dB  BELOW  the  noise!    This  is  VERY much more
sensitive than the Doppler.  That subject is too long to go into here.
See my Web page for a good  discussion  of  how this is possible!  URL
is:

http://members.aol.com/bmgenginc

(Lots of stuff has been added.)

73 de Russ, K6BMG
-----------------------------------------------------------------------

Date: Mon, 11 Mar 1996 20:33:28 -0800
From: James Ewen <jewen@oanet.com>
Organization: Strathcona Radio Volunteers
To: fox-list@netcom.com
Subject: Re: True Doppler Search
References: <Pine.SOL.3.91.960309102542.3216B-100000@acme.sb.west.net>
Sender: owner-fox-list@netcom.com

Well, since we have so many doppler experts  on  here, I need a little
lesson.

Charles  had  me shaking my head about his frequency  problems  for  a
while.    I  knew that the DoppleScAnt and Roanoke were  as  close  to
dopplers  as  possible without physically rotating one antenna, but my
poor old brain was starting to hurt...  Now I don't have to go dig out
the old text books to figure things out again!

Anyway, back to my question.  When I was calibrating my DoppleScAnt, I
came upon a quandary.

The display shows a stepped sine wave consisting of 8 steps for a full
360 wave, corresponding to the  eight antennas in the array.  Watching
the waveform on the oscilloscope, you  can  see  the wave jump to each
step as you circle the array.   The  DoppleScAnt has a 16 LED display,
and steps through two LEDs for every one  step  of the array.  How can
the array trigger each LED when the negative going  zero  crossing can
only  happen when the antenna array switches from one antenna  to  the
next.  The way I figure it, only 8 LEDs should  be  able  to be fired.
Some  Dopplers  have a digital direction readout, should they not only
be able  to read in increments of 360 degrees divided by the number of
antennas?  I would think that an eight element array would give you 45
degree  resolution.  A  four  element  array  should  give  90  degree
resolution.  

max     __              __
      --  --          --  --
  0 --......--......--......--......--
              --__--          --__--
min
* two full rotations of an 8 antenna array shown

max   --      -- 
  0 --..--..--..--..--
min       --      --
* two full rotations of a 4 antenna array shown

Since the antennas do not  physically move (vehicular motion ignored),
there would be no doppler shift  during  the time that each antenna is
selected, the signal can only change frequency  when  the  antenna  is
moved (stepped to the next antenna in the  array).    Therefore, there
should  only be four possible directions indicated by a  four  element
array, and eight directions from an eight element array. 

I have seen all 16 LEDs lit on my display,  so  this  is not the case.
Where in my logic am I wrong?

-- 
  __
 /_ _/_ __ _//_ __ __ __ __
__/ // /-/ // //_ /_// //-/
    Radio Volunteers        73 de VE6SRV
-----------------------------------------------------------------------

Date: Tue, 12 Mar 96 11:17:25 EDT
From: Bruce Paterson <bruce@martin.com.au>
Subject: True Doppler Search (fwd)
To: sleipnir!fox-list%netcom.com@sleipnir.iaccess.com.au (Foxhunt Mailing List)
Mailer: Elm [revision: 70.85]
Sender: owner-fox-list@netcom.com

I'm sure others will reply to this also so I'll keep it short...

*To: All who have written to inform me that the Roanoke Doppler and similar 
*Doppler designs do in fact utilize the Doppler frequency shift effect:
...bits cut out....

*Doppler theory requires that the Doppler-shifted signal conform to the 
*following equation:
*                     S = (R*W*Fc)/C
*where 
*
*   S is the Doppler shift (Hertz)
*   R is the radius of antenna rotation (in meters)
*   W is the rotational velocity of the antenna system (radians per second)
*   Fc is the carrier frequency of the received signal (Hertz)
*   C is the speed of light (meters per second)
*
*to determine bearings. For the Roanoke Doppler described in "Transmitter 
*Hunting: Radio Direction Finding Simplified," chapter 9, you get the 
*following: 
*
*Fc = 146,000,000 Hz (choose middle of amateur 2-meter band)
*W  = 500 revolutions per second = 1000*pi radians per second = 3142 radians/sec
*R  = lambda/(4*sqrt(2)) = 0.363 meters
*C  = 300,000,000 meters per second
*
*S  = 555 Hertz

Haven't you just (correctly) calculated the FM deviation of the signal
?  The tone you hear after FM demodulation will still be  500Hz.   The
only effect FM deviation will have on an FM reciever is how "loud"  it
sounds.   With a doppler system the "louder" the better to improve the
S/N ratio prior to the zero crossing or phase detector up to the limit
of the FM receivers  capabilities.  Since FM amateur rigs are normally
used they are designed for deviations up to about 3kHz or so.

As an aside:
Of course as you increase  the  diameter  to  increase  the  deviation
either  your  approximation of a single  rotating  antenna  gets  more
dubious, or, if you use more antennas,  your  problems  with  resonant
structures  (the  OFF antennas) seen by the currently  active  antenna
(the ON antenna) gets worse.  It also gets  physically harder to mount
on  a  vehicle.    So,  as  with  all engineering systems,  there  are
compromises to be made.

*of  the  Roanoke  Doppler.   In fact the Doppler shift is  completely
ignored.    No  No  !   The instantaneous doppler phase shift from the
arbitarily set  origin  is what the zero crossing detector (hopefully)
picks up. 

The reliability of information I got from our doppler was usually such
that it wasn't worth  fitting  to  the  car,  and  it  has fallen into
disuse.  I'm sure many improvements can be made, and they are good for
short  duration  signals,  but  the  relative    deafness,  multi-path
problems,  signal polarity sensitivity and the fact  that  it's  quite
tricky to get working on many different bands  well  all  work against
it.

Cheers, Bruce

--
    /\  /\  /\  /   /                        EMAIL: bruce@martin.com.au
   /  \/  \/  \/   /  MARTIN COMMUNICATIONS
  /   /\  /\  /\  /       Bruce Paterson
 /   /  \/  \/  \/  Electronics Design Engineer       Callsign: VK3TJN
-----------------------------------------------------------------------

Date: Tue, 12 Mar 1996 22:24:58 -0800 (PST)
From: Jay Hennigan <jay@west.net>
X-Sender: jay@acme.sb.west.net
To: James Ewen <jewen@oanet.com>
cc: fox-list@netcom.com
Subject: Re: True Doppler Search
Sender: owner-fox-list@netcom.com

On Mon, 11 Mar 1996, James Ewen wrote:

> Anyway, back to my question. When I was calibrating my DoppleScAnt, I 
> came upon a quandary.
> 
> The display shows a stepped sine wave consisting of 8 steps for a full 
> 360 wave, corresponding to the eight antennas in the array. Watching the 
> waveform on the oscilloscope, you can see the wave jump to each step as 
> you circle the array. The DoppleScAnt has a 16 LED display, and steps 
> through two LEDs for every one step of the array. How can the array 
> trigger each LED when the negative going zero crossing can only happen 
> when the antenna array switches from one antenna to the next. The way I 
> figure it, only 8 LEDs should be able to be fired. 

[bobbitt]

The stepped  waverform  is smoothed into a sinewave approximation by a
low-pass active filter following the switched-capacitor filter (U7B in
the original QST Dopplescant).  Thus the actual zero-crossing point of
this waveform can vary linearly.  If the previous step is barely above
zero and the following step substantially below, the gate will trigger
earlier. 

Also consider that while the number of  antennas indeed contributes to
the  resolution, the design of the switched-capacitor filter  does  as
well.  There is nothing to prevent using the  eight-step filter of the
Dopplescant with a four-antenna array.  

Adjusting the Q of the switched-capacitor filter can have a noticeable
effect on the operation of the unit.  A higher Q  will give less jumpy
readings, but a lower Q will give an indication to a practiced user of
the reliability  of  the  signal  in  weak-signal  areas or those with
reflections, as a  good  bearing  will be a single LED as opposed to a
"fuzzy" indication of several  adjacent  LEDs.  Too low of a Q results
in interference from voice and tone modulation of the signal. 

A good antenna-mounted preamp is  very  helpful,  and  I've  had  good
results with just the doppler on  weak  signals.    Even with a signal
down in the noise, the doppler tone  is perceptible and it is possible
to get at least a left/right/front/back reading out of a fuzz of LEDs. 

Best is a combination of a beam and doppler if you have the room.  The
doppler  performs  best  when  the  vehicle  is  in  motion,   as  the
reflections will tend to average out.  The beam performs best when the
vehicle   is  stopped,  as  the  signal  strength  will  vary  due  to
reflections with the vehicle moving, giving erratic readings. 

>From a practical  standpoint  eight  indicators are probably adequate
for most T-hunt situations,  though 16 are better.  The numeric degree
readout isn't too useful for  mobile  hunts other than as an input for
high tech computer-aided T-hunting. 

----
WestNet:  Internet service to Santa Barbara, Ventura and the world. 
          805-892-2133   805-289-1000   805-578-2121
----------------------------------------------------------------------------

Date: Wed, 13 Mar 1996 08:15:00 -0600 (CST)
From: schellew@wu1.wl.aecl.ca (Wayne Schellekens)
Subject: Re: True Doppler Search
To: jewen@oanet.com (James Ewen)
Cc: fox-list@netcom.com
Content-length: 2978
Sender: owner-fox-list@netcom.com

Hi James,
> The display shows a stepped sine wave consisting of 8 steps for a full 
> 360 wave, corresponding to the eight antennas in the array. Watching the 
> waveform on the oscilloscope, you can see the wave jump to each step as 
> you circle the array. The DoppleScAnt has a 16 LED display, and steps 
> through two LEDs for every one step of the array. How can the array 
> trigger each LED when the negative going zero crossing can only happen 
> when the antenna array switches from one antenna to the next. The way I 
> figure it, only 8 LEDs should be able to be fired. Some Dopplers have a 
> digital direction readout, should they not only be able to read in 
> increments of 360 degrees divided by the number of antennas? I would 
> think that an eight element array would give you 45 degree resolution. A 
> four element array should give 90 degree resolution.  

Think of the antenna switching signal and the recieved doppler (audio)
signal  as two different signals.  If  you  pass  the  received  audio
through a low-pass filter, you will filter the  step  waveform  into a
sine wave (more or less).

The bearing to the source is the phase delay  (0..359 degrees) between
the  reference  signal  (which switches the antennas) and the received
signal  (filtered).    You  can compare the maximum of the two  'sine'
waves,  or  look  at  one  of the zero crossings (say the positive  to
negative zero crossing).

The LED  display  just  converts  this  0..359  degrees  into a visual
indication.  It  doesn't matter how may LEDs are in the display, or if
you use a digital indication.

> Since the antennas do not physically move (vehicular motion ignored), 
> there would be no doppler shift during the time that each antenna is 
> selected, the signal can only change frequency when the antenna is moved 
> (stepped to the next antenna in the array). Therefore, there should only 
> be four possible directions indicated by a four element array, and eight 
> directions from an eight element array. 

You are correct that  there  is  no doppler shift during the time each
antenna is selected, but by filtering the doppler signal you can get a
waveform closer to a sine wave to extrapolate the zero crossings.

> I have seen all 16 LEDs lit on my display, so this is not the case. Where 
> in my logic am I wrong?

The dopplers I am familiar with  (Roanoke)  clock  the  display at the
antenna  switching rate and will freeze the  display  at  the  correct
moment  to  display  the bearing.  If the  zero-crossing  detector  is
having problems (weak signal, audio at 500 Hz, etc)  then the lock may
be off and the display will rotate or show multiple  LEDs lit.  When I
say 'lock' I probably should say 'latch the current counter value'.

If anyone can point out errors in my logic, feel free  to do so.  I am
just  writing  this  from memory, and it's been about a month since  I
last looked at the schematics for the doppler.

-- 
Wayne Schellekens, VE4WTS
schellew@wu1.wl.aecl.ca | http://www.mbnet.mb.ca/~wschell 
----------------------------------------------------------------------------

Date: Wed, 13 Mar 1996 19:43:11 -0800
From: James Ewen <jewen@oanet.com>
Organization: Strathcona Radio Volunteers
To: fox-list@netcom.com
Subject: Doppler lessons...
Sender: owner-fox-list@netcom.com

Wow, I hit a jackpot!  Ask a simple little question, and  you  get  10
answers.

I haven't played with my doppler for quite a while, and the last  time
I  had  it hooked up to the scope was when I built it, about  June  of
1993.  I  understand that I wasn't looking at the recieved audio after
filtering.  What signal was I looking at then?  I got this beautiful 8
step sinewave that shifted in  phase  as  I rotated the array.  (I had
the array sitting on a swivel  chair) I had everything all figured out
when I built it, but I obviously have forgotten a lot.

Thanks to everyone that answered my question.
-- 
  __
 /_ _/_ __ _//_ __ __ __ __
__/ // /-/ // //_ /_// //-/
    Radio Volunteers        73 de VE6SRV
------------------------------------------------------------------------

Date: Thu, 14 Mar 1996 09:26:11 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: Grandrews@aol.com
cc: fox-list <fox-list@netcom.com>
Subject: Re: K6BMG Comments on Dopplers. K6BMG Comments on True Dopplers.
Sender: owner-fox-list@netcom.com

Dear Russ (and others following these discussions),

Thank  you  for  your  clear reply to my cluttered ideas on Doppler DF
operation.  Your response shows considerable knowledge on the subject,
and a great deal of patience.  Thank you for taking the time to set me
straight.

I think my confusion was brought about,  in  part,  by  my familiarity
with  two-antenna  switched  direction  finders similar (in theory  of
operation) to the SuperDF you mention.  Doppler's seemed  like nothing
more than a natural extension of that concept.  Now  it  seems that it
is the other way around.  Some things you mention bring  to  mind more
questions.    If  you  feel  inclined  to  reply,  it  would  be  much
appreciated.

> Regarding antennas with only two elements, such as my SuperDF.    
> 
> These are not Doppler systems by any stretch of the mind.   They are what I
> call Phase Front Detectors.   They are used to tell when both dipoles see the
> same RF phase.    In the case of the SuperDF, it is able to tell the operator
> which dipole is closer to the transmitter, and thus which why to rotate in
> order to face the signal source.

Understanding the concept a little better now, it seems to me that the
phase shift between  just two antennas could just as rightly be called
the Doppler effect.   Aren't  you  getting  a shift in phase resulting
from the apparent motion from  one  antenna to the next?  When the two
antennas  are equidistant from the transmitter  there  is  no  Doppler
shift, since there is no motion toward  or  away from the transmitter.
The  shift is maximum when the two antennas  lie  on  a  line  passing
through the transmitter.

Of course with only two antennas you are sampling  the  phase  at just
two  points,    so   the  half-wavelength  maximum  separation  holds.
Exceeding it would  mean  that  you  are  not  satisfying  the Nyquist
sampling rate, and would get ambiguous bearings.  Am I all wet on this
concept too?

Here's another idea this topic  brings  to  ming.   It seems one might
make a Doppler with three or  more  antennas  which  all lie along the
same line, equidistant from one another.   With more than two antennas
(more than 2 sample points) it would seem  that  you  could  then make
your  antenna  system  stretch beyond 1/2 wavelength, so long  as  you
don't  exceed  1/2  wavelength  separation  between  adjacent  antenna
elements.  Of  course you would still only have a left-right direction
indication,  and  a  larger  antenna  to  lug  around.    But  from  a
theoretical standpoint it would seem  possible, and it would appear to
improve your S/N in the same  manner  as if the antennas were arranged
in a circle. 

Your two-element DFer sounds like a much  more  elegant solution.  But
am I still not getting Doppler theory straight?

73,
Charles E. Scharlau
SEA, A Unit of Datamarine International, Inc.
7030 220th S.W., Mountlake Terrace, WA 98043, USA
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134 
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam          
-----------------------------------------------------------------------

Date: Thu, 14 Mar 96 13:12:52 EDT
From: Bruce Paterson <bruce@martin.com.au>
Subject: Re: True Doppler Search (fwd)
To: sleipnir!fox-list%netcom.com@sleipnir.iaccess.com.au (Foxhunt Mailing List)
Mailer: Elm [revision: 70.85]
Sender: owner-fox-list@netcom.com


*Well, since we have so many doppler experts on here, I need a little 
*lesson.
*
*Anyway, back to my question. When I was calibrating my DoppleScAnt, I 
*came upon a quandary.
*
*The display shows a stepped sine wave consisting of 8 steps for a full 
*360 wave, corresponding to the eight antennas in the array. Watching the 
*waveform on the oscilloscope, you can see the wave jump to each step as 

I assume you mean the waveform output from your FM receiver ?

*you circle the array. The DoppleScAnt has a 16 LED display, and steps 
*through two LEDs for every one step of the array. How can the array 
*trigger each LED when the negative going zero crossing can only happen 
*when the antenna array switches from one antenna to the next. The way I 
*figure it, only 8 LEDs should be able to be fired. Some Dopplers have a 
*digital direction readout, should they not only be able to read in 
*increments of 360 degrees divided by the number of antennas? I would 
*think that an eight element array would give you 45 degree resolution. A 
*four element array should give 90 degree resolution.  
*
*max     __              __
*      --  --          --  --
*  0 --......--......--......--......--
*              --__--          --__--

Ah, but put this waveform through the very  narrow  commuative  filter
you have in your DoppleScAnt and the steps are no longer visible.  All
you  should  be  left with is the fundamental sinewave component.    A
sinewave   of  best  fit  through  your  diagram  above  will  have  a
zero-crossing point which is again variable down to any resolution you
wish to  pretend you have.  Therefore you can have as many LEDs as you
want.  There  is little point in adding more display resolution beyond
what you have, however, as other inaccuracies in the system will swamp
it. 

Hope this helps,
Cheers, Bruce

--
    /\  /\  /\  /   /                        EMAIL: bruce@martin.com.au
   /  \/  \/  \/   /  MARTIN COMMUNICATIONS
  /   /\  /\  /\  /       Bruce Paterson
 /   /  \/  \/  \/  Electronics Design Engineer       Callsign: VK3TJN
----------------------------------------------------------------------

Date: Thu, 14 Mar 1996 23:05:07 -0500
From: Grandrews@aol.com
To: cscharl@eskimo.com
cc: fox-list@netcom.com
Subject: The "Doppler" isn't a Doppler.
Sender: owner-fox-list@netcom.com

Dear Charles, and others

I contend that  the RDF antenna that most people call a Doppler is not
a Real Doppler.   The  SuperDF  and  other similar 2 element phase RDF
systems are not Two Element Dopplers.

The Doppler antenna only APPEARS to produce the same DFing result as a
true Doppler (a single antenna spinning  around  a  circle).    I will
explain why I think it isn't.

Assume you have a true Doppler (a  single  antenna  spinning  around a
circle)  spinning  at  some  fixed  angular  rate (X  revolutions  per
second).   Measure the frequency deviation of the carrier  and  record
that value.  Now spin it twice as fast and  measure  deviation  again.
It will be twice what you measured before, just as expected  from  the
Doppler effect.   

Similarly,  assume  you  have  a single element that you move back and
forth between two positions, moving at some fixed velocity between the
two positions.   If  the  RF is coming in parallel to this motion, you
will measure some value  of  + & - deviation of the carrier.  Now move
the element twice as fast, and you will measure twice the deviation as
before.

In both of the above thought  experiments  the deviation exists at the
operating frequency.  Also note that as  it  goes  though  the  IF and
reaches the discriminator, that same deviation is present,  regardless
of the bandwidth of the receiver.

Now,  take  the  SuperDF (or similar antenna) that switches  back  and
forth between 2 elements.  We will use it, rather than the Doppler, in
order  to  simplify  the following discussion.  Keep in mind that  the
same thinking applies to both the Doppler and SuperDF.   

When  you  look  at the output of the receiver with a 'scope  you  see
narrow  blips  of  voltage  (pulses),  first + then - polarity, as the
antenna switches  back and forth.  Between these blips is no RDF info,
just "noise" as far as the RDF is concerned.  

How are these  pulse  generated?    Remember  that  one  antenna stays
selected for about 1250 microseconds.  This is a long time compared to
the  time-constant associated with the  Q  of  the  IF  strip  of  the
receiver.    As  far  as  it  is  concerned,  it  is  listening  to  a
steady-state RF signal.  Because of this,  the  discriminator  sees  a
steady  amplitude,  constant  frequency constant phase RF signal,  and
there  is no output from the discriminator (discounting any  component
from the signal being off frequency).  The resonant circuits of the IF
strip have stored a lot of energy at this RF phase.

Suddenly  (within  about  1  microseconds) the antenna switches to the
other dipole.    The RF feeding into the receiver has an instantaneous
phase  shift to  a  new  steady-state  phase  value.    (Instantaneous
compared to the time constant due to the Q of the IF tanks.)

This  signal  has  to    go  through  the  IF  strip  to  get  to  the
discriminator.  But remember that just a very few microseconds earlier
there was the earlier carrier present which had pumped up the IF tuned
circuits with a lot of sine wave  energy  at  that old RF phase.  That
energy is still in the tank circuits, sloshing  back and forth.  There
hasn't been enough time for much energy to build  up at the new phase,
so the old energy is still dominant.  But the  old  energy  is  slowly
dying  out  while  the new phase energy is slowly building up.    They
combine by the law of superposition of sine waves.  The RF phase being
delivered to the discriminator is shifting (not stepping, as it did at
the antenna!) from the old phase to the new phase.    

Now think  about  that  last statement.  In order to "slowly" change a
sine wave from  one  phase to a new phase (let us assumed to a lagging
phase), each individual sine  wave must be made longer (to move to the
"later"  or  "lagging"  phase  position.)    That    means   that  the
instantaneous frequency of EACH cycle of sine wave must decrease.  Now
consider what happens if the amount of  time  available  for  the same
shift is changed.  If the time available  for  shifting  the  phase is
shorter,  then  each  individual sine wave must be stretched  MORE  (a
lower  frequency).  If the time is longer, then each  individual  sine
wave  must be stretched LESS (not as low a frequency).   The  apparent
deviation  is  respectively MORE or LESS, depending upon the amount of
time allowed for the the phase shift to take place.    

What does  that mean in the real world of radios and RDFs?  The amount
of time it  takes  for  the  transition  from the old phase to the new
phase is a function  of  the  Q  (read bandwidth) of the IF amplifier!
(Remember that higher Q =  narrower  bandwidth  =  longer time for the
system to change from one steady  state to a different steady state of
phase and / or amplitude.)

What's this we have now?  A "Doppler like" system whose deviation is a
function of the receiver bandwidth!  Strange!

The amount of time it takes for this  transition from the old phase to
the new phase is short compared to the antenna  switching  time  (1250
microseconds).    The  discriminator  puts out a voltage spike exactly
like it  would if the carrier frequency had actually just gone through
a momentary frequency  deviation and back to normal carrier frequency.
Lets look at the  output signal with a 'scope, and assume this voltage
spike is exactly 0.100 volts  peak.    The  pulse takes about 60 to 80
microseconds.

Now  lets do this same thought  experiment,  but  double  the  antenna
switching rate.  What happens?  The 'scope shows the exact same output
voltage  pulse,  0.100  volts  peak,  but  occurring twice  as  often.
Remember,  the  voltage pulse is produced by the transition  from  one
phase to another phase.  It doesn't matter how long  we  were  in  the
steady state period between antenna switchings!  And since the SuperDF
filter capacitor  charges  to  peak  pulse  value, the DC error signal
doesn't change.

Inside the SuperDF,  the  voltage  pulses  are  synchronously detected
(every other one is  inverted).    Now  all  the  pulses  are the same
polarity (either all + or  all  -),  rather than alternating polarity.
These pulses charge an RC filter.  The discharge time constant is very
much longer than the time between pulses  and  also  very  much longer
than the charge time constant, so the capacitor charges up to the peak
voltage,  0.100  volts.    It is the same as  it  was  at  the  slower
switching rate!  But wait!  If it were a  Doppler,  it  should  now be
0.200  volts.    It  isn't.    It  doesn't respond to changes  in  the
switching speed  by  changing  the "apparent Doppler shift." Hummm.  A
"Doppler RDF" that  doesn't change its Doppler shift when you speed it
up.  Strange!

Exactly the same thing  happens  in  a  "Doppler"  system.    The main
difference is that the capacitor  being charged changes as the antenna
"steps" around its circle.

There is another difference between a  Doppler  and  the SuperDF.  The
SuperDF throws away about 97% of the  radio's  audio  output.    It is
absolutely stone deaf 97% of the time.   It  listens to the radio only
3% of the time.   

Why  would  I want to do a "dumb" think  like  that?    Remember,  the
switching event at the antenna causes a narrow voltage pulse  to  come
out  of  the  radio.    SuperDF  opens its ears just long  enough  (40
microseconds)  to hear the PEAK of that pulse.  That is where  the  DF
information is.  Most of the rest of the time the stuff coming  out of
the radio has no DF information.  It is noise!  40/1250 = 0.032 (3.2%)
is the  listening duty cycle.  That's a dramatic improvement in signal
to noise ratio!  (By the way, this selective listening done by SuperDF
is protected by a U.S.  Patent.)

The Doppler does not  do  this.  It listens ALL the time and hears ALL
the noise.  Even if  you were to apply this technique to a Doppler you
would  not  reach  the  same  sensitivity   because  of  the  inherent
synchronous noise made by the commutating capacitor filter (the narrow
band filter) of the Doppler.   

(Hummm.  It may LOOK like a duck, but it doesn't walk like a duck, and
it doesn't quack like a duck.  I guess it ISN'T a duck after all!)

The "Doppler" doesn't act like a real Doppler and  it  does not follow
the  equation for calculating Doppler shift, therefore, I say that  it
is not a Doppler.  The only common aspect is that  they both produce a
sine  wave  error signal.  At first glance from the outside it  "looks
like" a Doppler.  What it is is a device that is able  to  measure the
relative phase differences at  several  point  in  space,  and convert
these to a sine wave.

What is SuperDF?  I call it a Phase Front Detector.  SuperDF by itself
does not measure the direction of  arrival.    The human operator does
that by manually rotating until the phase  front  is  found (the point
where both antennas see the same RF phase).  

<<<Aren't  you getting a shift in phase resulting  from  the  apparent
motion from one antenna to the next?  >>>

No.  The apparent motion of the antenna is  very  fast, lasting only a
micro  second  or  so to cover a distance of nearly  two  feet.    The
apparent  velocity  would be something like 2,000,000 feet per second!
Put THAT in the Doppler equation and turn the crank!

The general formula for Doppler Shift is:
Fr = Ft (1 + Vd/C)    
(Where Vd is minus for movement away from each other)
C = (300,000,000 meters/sec)*(39.34 inches/meter)*(1 foot/12 inches)
C = 986,000,000

We have: Fr = Ft * (1 + Vd/C) = Ft * (1 + 2,000,000/986,000,000) 

Fr =  Ft(1+  0.00203) = 146,000,000 (1.00203) = 146,297,000, a Doppler
shift of 297 kHz!

The frequency deviation that one would have from such high speed would
be very much more  than  the  bandwidth of the receiver and be present
for  only  about  1 microsecond.    It  could  never  even  reach  the
discriminator!   The shift in phase  seen  is  the  result  of  merely
switching  between one source of one phase  to  another  source  of  a
different phase.  

<<<When the two antennas are equidistant from the transmitter there is
no Doppler shift>>> This should read "....no phase shift...."

<<<Of course with only two antennas you are sampling the phase at just
two  points,    so   the  half-wavelength  maximum  separation  holds.
Exceeding it would  mean  that  you  are  not  satisfying  the Nyquist
sampling rate, and would get ambiguous bearings.  Am I all wet on this
concept too?>>>

K6BMG Responds:

When the two antennas are  sampling  RF  phases  that  are 180 degrees
different  (1/2  wavelength  between  antenna elements)  the  behavior
inside the IF strip would be as follows.

The two energy levels of the two  phases  decay  and  build  just as I
described earlier.  But the behavior of the  superposition  of the two
changing amplitude sine waves does NOT produce a slow  phase  shift as
seen at the discriminator.  Instead, the RF magnitude drops to zero at
the time when both magnitudes are the same.  As the  magnitude  builds
back  up,  the  phase  is  180  degrees  different.    Notice that the
instantaneous cycle time never changed.  Sketch out two sine waves 180
degrees apart and  do the thought exercise examining the magnitude and
phase  of the resulting  combined  wave  as  the  relative  magnitudes
change.

This behavior was illustrated one evening when I was demonstrating the
SuperDF to our local FCC.   Sitting on top of a hill where we had good
DF  visibility,  we  DFed signals all over  the  spectrum.    When  we
exceeded the frequency specification of the antenna, we  got very good
nulls  when  the  antenna elements were seeing the same  phase  (equal
distant from the transmitter, but we also got phantom nulls  at  other
positions, roughly  corresponding  to 1/2 wavelength difference to the
transmitter.  These  nulls  were  not  good  and  deep  like the equal
distant one.  What  I  believe  was  happening  was that at this phase
difference (180 degrees) there was a DF null because of the phenomenon
I described earlier (no phase shift  to produce a frequency blip), but
because  there  was  100% AM modulation, that  modulation  was  coming
through.  (Remember, that a discriminator WILL respond to AM if the IF
amplifiers are not FULLY limiting.  Also remember that  I  said the AM
would be 100%;  that is the carrier will COMPLETELY disappear when you
have  exactly equal magnitude and exactly 180 degree phase difference.
There will  always  be  a  position  of  the  antenna  above its upper
frequency  limit where  both  conditions  happen  at  the  same  time.
Therefore, no amount of limiting can protect the discriminator against
this effect, because the signal  AM  modulation will always drop below
the limiting threshold, and get through  to  the  discriminator, which
detects it!)

*************

<<<Here's another idea this topic brings to  mind.  It seems one might
make a Doppler with three or more antennas  which  all  lie  along the
same line, equidistant from one another.  With more  than two antennas
(more  than 2 sample points) it would seem that you  could  then  make
your  antenna  system  stretch  beyond  1/2 wavelength, so long as you
don't  exceed  1/2  wavelength  separation  between  adjacent  antenna
elements.  Of course you  would still only have a left-right direction
indication,  and  a  larger  antenna  to  lug  around.    But  from  a
theoretical standpoint it would seem possible, and  it would appear to
improve your S/N in the same manner as  if  the antennas were arranged
in a circle.  >>>

K6BMG responds.

I have done some thinking about this kind of long linear multi-element
antenna.  It would be a very good antenna to  mount  on  a  rotor at a
base station.  You see, the SuperDF is VERY accurate when it is mobile
in  motion.   It is taking its samples over a distance, covering  many
cycles of the multipath standing waves in space pattern, and averaging
them.  The  longer  this  path  (the  faster you are driving) the more
accurate the bearing on the strongest path.

If one were to  build  a very long array of elements, covering several
wavelengths, and then swept back  and  forth along them all, and had a
appropriate detector circuit, the accuracy at  a base station would be
much  better than the present 2 element  SuperDF  (WHEN  MULTIPATH  IS
PRESENT).  Sensitivity would be about the same.    I  never built one.
Very little incentive.  

I had (it died) a really nice beam system  up.    A very unusual beam.
It was 2 six element Yagis of unusual design, with  unusual horizontal
stacking.  Each antenna had balanced line feed.  I brought  the 2 feed
lines (300 Ohm twin line) to the center where they joined in parallel.
But  one  line went though a relay which was able to invert only  that
feed  line.    With the relay off, the two antennas were in phase, and
acted like  an  ordinary  beam.    With  the relay activated, they fed
together out of  phase.   The combined feed line was then fed though a
balance matching device into  a  balanced to unbalanced 4:1 balun, and
then to the shack via  RG-8  coax.    The  stacking  did  not have the
antenna booms parallel to each other, as would normally be done.  They
were out of parallel by 22.5 degrees.  Thus, the two beams front lobes
were pointing in two directions different by this  22.5 degrees.  With
this configuration there would always be a point where  the  two front
lobes overlapped at EXACTLY the same Gain.

This was an interesting DF antenna.  First I would  start out with the
two beams in phase.  I got my rough bearing as  anyone  would  with  a
beam.   

Then  I  switch  to  out  of  phase.    The  system  then  became   an
interferometer, with gain.  Then I would rotate to find the null point
of the  interferometer.    On a signal with no multipath, the null was
extremely deep and  extremely  narrow  at  the  bottom.    Its maximum
capability is illustrated by the following.

I adjusted the antenna phasing by  adjusting  a  short  parallel  stub
connected to one Yagi feed point while listening to a 2 meter repeater
of 1 KW ERP 8 miles away, looking  right  down  my  throat from a 5000
foot mountain.  STRONG signal!  When I finished  adjusting, moving the
end  of the 8 foot long cross-boom only 1/8 of  an  inch  in  rotation
caused  the  signal to pass through the bottom of the null,  where  it
fell into the noise and DISAPPEARED!  When I would bring this  antenna
to  rest  on  a signal, the tiny torsion oscillations of the tower and
rotor  system  (too  small to see!) was enough to cause the S-meter to
bounce up and down most of its scale, until the system finally came to
rest after three or four oscillations.  AWESOME ANTENNA! 

73 de Russ, K6BMG
-----------------------------------------------------------------------

Date: Mon, 18 Mar 1996 11:25:55 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: fox-list <fox-list@netcom.com>
Subject: A Doppler's a Doppler, NOT!
Sender: owner-fox-list@netcom.com

Dear Russ et al,

OK,  I   think  I  finally  get  it.    Russ's  points  are  valid.    A
switched-Doppler could be  built from a series of separate antennas, but
it would not operate  the  same  way  that most (all?) Doppler direction
finders work.  The differences  are kind of subtle, but very real.  I've
done a full 360-degree phase shift in my beliefs of Doppler operation. 

To  explain  the  concepts I'd like  to  propose  a  series  of  thought
experiments similar to Russ's illustrations, but simpler. 

Let's try something as simple as possible,  but  still illustrative of a
Doppler shift:  a single antenna moving along  a  straight  line.  We'll
start it from rest, accelerate it to a constant  velocity,  and  let  it
continue  to move frictionlessly along a straight line toward a  distant
transmitter sending a carrier. 

As the antenna begins to move, the frequency that it receives  from  the
distant transmitter  begins  to  increase.   The frequency of the signal
received by the moving antenna is given by the now familiar formula: 

f = fo -  fo * v/c

where fo = distant transmitter's carrier frequency
      f  = frequency of signal observed by the moving antenna
      v  = velocity of the moving antenna
           v < 0 when the antenna is moving toward distant transmitter
      c = speed of light

[Note:  the formula above is only an approximation.  It gives reasonable
results only for antenna  velocities that are much slower than the speed
of light.] 

Once the antenna reaches its  maximum  velocity,  the received frequency
also  reaches its maximum value.   From  that  point  on,  the  received
frequency does not change. 

The output of an FM discriminator connected  to the moving antenna would
give an output signal indicating a shift in  the  phase  of the received
signal  so  long  as  the antenna was accelerating.   Once  the  antenna
reaches  its  maximum  velocity, and stays there, the output of  the  FM
discriminator  would  go  to  zero.    So  there  would  be  an  initial
discriminator output  "blip" as the antenna accelerates, and zero output
from then on. 

Now suppose we  want  to  build  a  system  of  discrete  antennas  that
approximates the behavior of  the  single  antenna  thought  experiment.
Imagine that we replace the continuously moving antenna by a long series
of  discrete antennas spaced evenly along  a  line  leading  toward  the
distant transmitter.  The antennas are separated  from  one another by a
very  small  distance,  much less than one-half the  wavelength  of  the
distant transmitter's signal. 

Let's keep things REALLY simple.  Let's assume that  our antennas can be
placed  as close together as we wish without mutual coupling  (parasitic
effects) among the antennas.  Let's further assume that we have  a phase
measuring  device that has infinite bandwith, that our entire system has
no noise,  and that the signal strength is full quieting at each antenna
along the line. 

We simulate the  motion  of  a  moving  antenna  by  switching our phase
measuring device from one antenna to the next adjacent antenna, starting
from the antenna farthest from  the distant transmitter.  We will remain
connected to each antenna only for an infinitessimal period of time, but
we will wait for a longer period  of  time  before switching to the next
antenna.  Our phase measuring device will have  to  be extremely fast so
that  we  can  measure  the  phase of the received  signal  in  the  few
nanoseconds that the antenna is connected to it. 

By  using  more  and more antennas, and placing them closer  and  closer
together,  our    system   of  discrete  antennas  should  more  closely
approximate  the continuous  movement  of  the  single  antenna  thought
experiment.  In fact,  it does.  If we switch to each successive antenna
in such a way that  we  mimick the acceleration of a single antenna to a
steady velocity, we will get an  initial  pulse from our phase measuring
device, and a zero output thereafter. 

This then is a model for the  Doppler  effect using a series of discrete
antennas.  Is this the way Doppler direction finders (e.g.  the Roanoke,
the DoppleScant, etc) work?  The answer is an emphatic NO.

As Russ pointed out, if you built an antenna that worked like the series
of  switched  antennas  described  above, amateur FM receivers would not
have the bandwidth and S/N to make it work.  (Is  there  any  device out
there  that  would?)  The fact that Doppler direction finders do work is
proof  that  they  do  not  operate like the system of switched antennas
described above. 

All right.    So  how  do  they work then?  As Russ pointed out, Doppler
direction finders switch  quickly from one antenna to the next, but then
they spend a relatively  long  period of time connected to each antenna.
(Note:  that is just  the  reverse  of  the  situation  for the discrete
Doppler  system  described above!) The long  time  (approximately  0.001
seconds) spent at each antenna is necessary  to allow the system to work
within the bandwidth constraints of practical FM receivers. 

To  understand  how Doppler direction finders really work,  I  found  it
instructive  to  consider  the analogous single-antenna system that such
antennas approximate.  Have you ever seen an analog clock  with a minute
hand  that moves in steps?  The minute hand remains stationary  for  one
minute,  then  it  clicks  over  to  the next minute position.  Consider
placing a  single antenna on the end of the minute hand of such a clock.
(You could modify  to  the clock so that it makes eight steps instead of
60 to make this  thought  experiment  more like common Doppler direction
finders.) The antenna would stand  still  for a long period of time, and
then suddenly make a quick movement  to  the next position.  There would
be no Doppler frequency shift while the  minute  hand stood still.  Once
the hand begins to click to the next  position  a brief spurt of Doppler
shift occurs, and then stops abruptly as the hand comes to a rest again. 

The single antenna on a jerking clock hand is  just what the Roanoke and
similar  Doppler  designs approximate.  One antenna is connected to  the
receiver  for  a  hundred  thousand oscillations of the incoming carrier
signal (0.001  seconds).   During this time there is no frequency shift.
Then suddenly, over  a  period of a hundred oscillations of the incoming
carrier signal (1 microsecond),  the  receiver  is connected to the next
antenna.  The receiver detects a sudden shift in the phase of the signal
received  at  the  switched-to antenna relative  to  the  phase  at  the
switched-from antenna.  The phase shift is  a result of the two antennas
residing at two different locations. 

Any Doppler frequency shift would have occured during  the  switch,  and
would be too sudden to be detected by the  FM  receiver.  Once the shift
is complete the receiver is given time to detect the phase of the signal
at  the  switched-to  antenna.   The discriminator gives a pulse with  a
polarity  that  indicates  the  direction  of  the  phase  shift that it
detects, if  any.   The polarity of the phase shift is determined by the
relative positions of  the  two  antennas  involved  in  the switch with
respect to the source  of the received signal.  If the switch results in
the FM receiver being connected  to  an  antenna  that is 1/4 wavelength
closer to the transmitter then a -90 degree phase shift is detected.  If
a switch results in the FM receiver  being  connected to an antenna that
is 1/4 wavelength farther from the transmitter then  a  +90 degree phase
shift  is  detected.   The Doppler effect doesn't even  enter  into  the
theory of operation.  

Any periodic function can be broken down into a series  of  sine  waves,
and the periodic pulses coming from a "Doppler" direction finder are  no
exception.  A circular arrangement of discrete antennas will result in a
series of  pulses  with  a  strong  sinusoidal  component at the antenna
rotation frequency.   If  you  pass  these  pulses through a very narrow
filter centered at the  frequency  of  antenna  rotation, you will get a
nice clean sinusoidal waveform with  zero crossings corresponding to the
points at which the pulses change in polarity from positive to negative,
or from negative to positive.  So  Dopplers  work,  but  they just ain't
Dopplers. 

So here I am again at the same  spot  I was at a little over a week ago,
asking the question:  Are there any TRUE Doppler  direction  finders out
there?    If  you  can  point out any substantial errors  in  the  above
arguments  or,  if you hear of a switched antenna system which  actually
uses the Doppler effect, I'd be interested to hear from you. 

73,
Charles E. Scharlau
SEA, A Unit of Datamarine International, Inc.
7030 220th S.W., Mountlake Terrace, WA 98043, USA
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134 
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam          
-----------------------------------------------------------------------

Date: Tue, 19 Mar 96 10:33:45 EDT
From: Bruce Paterson <bruce@martin.com.au>
Subject: Re: Real Dopplers
To: sleipnir!fox-list%netcom.com@sleipnir.iaccess.com.au (Foxhunt Mailing List)
Mailer: Elm [revision: 70.85]
Sender: owner-fox-list@netcom.com

Ooops.   I  stand  corrected  on  my  statement  about  the  DoppleScant
commutative filter.  Yes of course the waveform will look stepped out of
this filter.  I  was  getting  confused with the doppler I've built most
recently that had a switched  cap  filter  (MF10)  like the Tricky Dicky
design.  Since this filter is  clocked  at  100* the Fo centre frequency
it's output does indeed look like a  sinewave.    A  low pass after this
sort of filter is still a good idea  however to get rid of the low level
clock  feedthrough which can lower the S/N ratio at  the  zero  crossing
detector.

On  another  note,  I guess the use of sinusoidal switching  of  doppler
elements  (using  dual  gfate FETS or whatever and lookup tables) is  to
better simulate the  continueously  rotating  antenna.   This would also
mean the FM receiver  will  not  be hit with sudden phase changes it may
not be able to respond  to  quickly.   Has anyone tried this ?  How well
does it work ?  Does it result in significantly better performance ?  --
/\  /\  /\  /  /  EMAIL:   bruce@martin.com.au  /  \/  \/  \/  /  MARTIN
COMMUNICATIONS / /\ /\ /\ / Bruce Paterson  /  /  \/  \/  \/ Electronics
Design                Engineer           Callsign:                VK3TJN
-----------------------------------------------------------------------

Date: Wed, 20 Mar 1996 14:34:42 -0800
From: "Chuck Grant" <grant@aretha.llnl.gov>
References: <960314230506_168920829@emout09.mail.aol.com>
To: Grandrews@aol.com
Subject: Re: The "Doppler" isn't a Doppler.
Cc: fox-list@netcom.com
Sender: owner-fox-list@netcom.com

On Mar 14, 11:05pm, Grandrews@aol.com wrote:

refering  to    the   magnitide  of  the  pulses  from  the  FM  radio's
discriminator not changing as the switching frequency changes:

> Exactly the same thing happens in a "Doppler" system.   The main difference
> is that the capacitor being charged changes as the antenna  "steps" around
> its circle.

Actually no, what  you say is true, but there is more to what happens in
the doppler system.  The antenna and switcher do not simulate a rotating
antenna very well, as you  point  out.    But  the antenna, switcher, FM
radio, and audio bandpass filter do  simulate  a rotating antenna and FM
radio system quite well.

The amplitude of the signal out of  the  audio bandpass filter increases
as the switching frequency increases, even though the  amplitude  of the
pulses out of the FM radio do not increase.   And the narrow bandpass of
the audio filter increases the signal to noise ratio from what comes out
of  the  FM  radio,  gaining  back  much  of what was lost  by  the  low
information duty cycle from the FM radio.

As with any sampled data system simulating a continuous system, you must
include the  reconstruction  filter in the analysis.  If you examine the
signal out of  the  bandpass filter as you change the sampling rate, you
will see that it  acts just like the signal out of an FM radio connected
to a spinning antenna.

Chuck, KE6CIL
-----------------------------------------------------------------------

Date: 22 Mar 96 02:11:02 EST
From: Joe Moell <75236.2165@compuserve.com>
To: Fox-list <fox-list@netcom.com>
Subject: K0OV Throws Log on True Doppler Fire
Message-ID: <960322071101_75236.2165_HHB53-1@CompuServe.COM>
Sender: owner-fox-list@netcom.com
Precedence: list

Is a switched-antenna doppler a  "true  doppler?"  Sure!  It does indeed
walk and quack like a doppler  duck,  so it's fair to call it a doppler.
Consider the following:

Johann Doppler didn't write the oft-discussed doppler DF equation:

S = (R*W*Fc)/C        Equation (1)

He didn't even create this classic:  

f' = f*[(1- u/c)/((1-(u/c)^2)^0.5]       Equation (2)

Equation (2) predicts observed doppler frequency (f') of electromagnetic
waves  in  receding  cases, given source frequency (f), radial  velocity
(u), and speed of light (c), based on Einstein's theory  of  relativity.
Doppler  couldn't  do this because when he died in 1853, the  theory  of
relativity was still over 50 years away and the best measurement of  the
speed of  light  (Fizeau's  toothed  wheel  experiment in France) was in
error by almost 5%.

All Johann Doppler  did  was  predict  that the apparent frequency of an
emitted wave will shift higher when source and observer are approaching,
and vice versa.  I  think  we  can  all  agree  that Doppler's principle
predicts if we physically move a  vertical  whip  antenna  in a circular
track at constant tangential velocity, the observed  frequency of the RF
signals received by that whip MUST rise and  fall in a sinusoidal manner
on  each  rotation as the whip approaches and recedes  relative  to  the
source.    If  we  had  instrumentation sensitive enough to measure  the
instantaneous received frequency accurately enough, we could detect this
doppler-induced carrier shift even at a rotation rate of 1 RPM.

But if we  want  to  use the discriminator in an ordinary FM receiver to
sense the sinusoidal doppler-induced carrier shift, Equation (1) reveals
that  much higher whip rotation  speeds  are  required,  to  get  enough
frequency  deviation  of  the  carrier  shift    to   provide  a  useful
signal-to-noise ratio at the discriminator output.   If we could somehow
physically move the whip at 30,000 RPM and then detect the instantaneous
phase  of  the  doppler-induced sine wave at discriminator output,  with
respect  to  the  moving whip's instantaneous position, we would have  a
"true doppler" RDF indicator.  Everyone agree so far?

If we accept that a "true doppler" set would indeed be  achieved  with a
theoretical 30,000 RPM physically rotating whip, we must also accept the
premise that  we  can  substitute an INFINITE number of individual whips
and a PERFECT  commutation  (switching)  system  in  place of the single
moving whip.  This  is  based  on  the classical piecewise approximation
technique used in the Calculus.    This  substitution  still  gives us a
hypothetical "true doppler" RDF set, because  Johann Doppler's frequency
shift prediction still exactly describes the apparent  frequency changes
that  the receiver perceives.  The receiver discriminator  output  would
contain a sinusoidal doppler-induced carrier shift identical to that  of
the physically rotating whip case.

It  is  harder for hams to accept the premise that  we  can  reduce  the
number of whips from infinity to 16, 8, 4 or even  3  and  still  have a
"true doppler" RDF set.  But all that has been done by  this  step is to
reduce the  number  of  pieces  in  the  piecewise  approximation of one
rotation  from  infinity    to  the  number  of  whips.    The  receiver
discriminator  output  still  includes   the  induced  frequency  change
information, but it is "encoded" as phase jumps corresponding to antenna
switching  steps.    The  single-audio-frequency  (at    rotation  rate)
sinusoidal  carrier shift from the infinite number  of  whips  has  been
replaced by a stepped sine wave that can  be described mathematically by
a Fourier series.  The phase information that we  need  to determine our
RDF bearing is still present in the fundamental frequency term  of  this
series.  

In  a  practical  doppler,  a very narrow (about 2 Hz bandwidth  in  the
Roanoke) audio  filter  strips out the upper Fourier components, leaving
the  fundamental  term    with    phase    information   intact,  nearly
indistinguishable from what would be achieved with an infinite number of
whips.  Because it is  synchronized  to  the  antenna rotation rate, the
filter  is  locked to the fundamental  frequency  of  the  series.    In
addition to eliminating the upper terms of  the series (the "steps"), it
filters out the unwanted noise and modulation components on the incoming
signal.

In summary, reducing the number of whips from infinity  to  4  does  not
change  the  fact  that relative motion of RDF antenna versus  hidden  T
antenna causes phase/frequency changes which can be detected to give the
RDF bearing.    Therefore,  a 4-whip doppler depends on Johann Doppler's
principle just as  much as if it had a physically moving antenna system,
Q.E.D.

It may well be  true  that  one can make use of some other principles of
physics to help explain the  operation  of  a practical doppler RDF set.
But that doesn't negate the fact  that  the  operation  of a doppler RDF
does indeed depend on Johann's discovery.   Look  at  it this way:  What
would happen if the laws of physics suddenly changed and relative motion
of source/observer no longer resulted in apparent phase/frequency shifts
of acoustical and electromagnetic waves?  Train whistles would no longer
appear  to rise in pitch when approaching and Equation (2) would  become
invalid.    I  contend  that  Equation (1) would also become invalid and
every form  of  doppler  RDF  set,  switched-antenna  or not, would stop
working.  If you disagree, please explain why.

In a separate  post,  I'll  take  on  K6BMG's assertion that the doppler
signal at the receiver's discriminator does not follow Equation (1).

73 de Joe K0OV
Homingin@aol.com
------------------------------------------------------------------------

Date: Fri, 22 Mar 1996 08:11:57 -0800 (PST)
From: Jay Hennigan <jay@west.net>
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To: fox-list@netcom.com
Subject: Re: A Doppler's a Doppler, NOT!
In-Reply-To: <Pine.SUN.3.91.960318112046.28079A-100000@eskimo.com>
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Precedence: list

On Thu, 21 Mar 1996, Charles Scharlau wrote:
> Let's try something as simple as possible, but still illustrative of a Doppler 
> shift: a single antenna moving along a straight line. We'll start it from 
> rest, accelerate it to a constant velocity, and let it continue to move 
> frictionlessly along a straight line toward a distant transmitter sending a 
> carrier. 

Okay.
> 
> As the antenna begins to move, the frequency that it receives from the distant 
> transmitter begins to increase. The frequency of the signal received by the 
> moving antenna is given by the now familiar formula: 

[snip]

Okay.

> Once the antenna reaches its maximum velocity, the received frequency also 
> reaches its maximum value. From that point on, the received frequency does not 
> change. 

Correct.

> The output of an FM discriminator connected to the moving antenna would give 
> an output signal indicating a shift in the phase of the received signal so 
> long as the antenna was accelerating. Once the antenna reaches its maximum 
> velocity, and stays there, the output of the FM discriminator would go to 
> zero. So there would be an initial discriminator output "blip" as the antenna 
> accelerates, and zero output from then on. 

To pick a nit, a true Foster/Seeley _discriminator_  has a response down
to DC, and will continue to show a frequency above the reference carrier
as long as the antenna is in motion toward the transmitter.  This is the
basis of zero-center tuning meters.  The quadrature detector more common
in modern receivers will behave as you describe.  However, this isn't of
real consequence in the operation of a doppler DF.

> Now suppose we want to build a system of discrete antennas that approximates 
> the behavior of the single antenna thought experiment. Imagine that we replace 
> the continuously moving antenna by a long series of discrete antennas spaced 
> evenly along a line leading toward the distant transmitter.  The antennas are 
> separated from one another by a very small distance, much less than one-half 
> the wavelength of the distant transmitter's signal. (Actually this should 
> be less than one-half the wavelength of the shifted frequency, but this 
> difference is small.)
> 
> Let's keep things REALLY simple. Let's assume that our antennas can be placed 
> as close together as we wish without mutual coupling (parasitic effects) among 
> the antennas. Let's further assume that we have a phase measuring device that 
> has infinite bandwith, that our entire system has no noise, and that the 
> signal strength is full quieting at each antenna along the line. 

Well,  you really  want  a  frequency  measuring  device,  not  a  phase
measuring device, to look  at  the  doppler  shift.    Minor nit, can be
calibrated out when aligning the  unit  as we're concerned with a narrow
band of frequencies. 

> We would simulate the motion of a moving antenna by switching our phase 
> measuring device from one antenna to the next adjacent antenna, starting 
> from the antenna farthest from the distant transmitter. Each antenna 
> remains connected to the phase shift detector connected to only for an 
> infinitessimal period of time, but we will wait for a longer period of 
> time before switching to the next antenna. Our phase measuring device 
> will have to be extremely fast so that we can measure the phase of the 
> received signal in the few nanoseconds that the antenna is connected to it. 
> 
> By using more and more antennas, and placing them closer and closer together, 
> our system of discrete antennas should more closely approximate the continuous 
> movement of the single antenna thought experiment. In fact, it does. If we 
> switch to each successive antenna in such a way that we mimick the 
> acceleration of a single antenna to a steady velocity, we will get an initial 
> pulse from our phase measuring device, and a zero output thereafter. 

And  you'll  also  get a steady-state  upward  frequency  shift  with  a
frequency-measuring device.

> This then is a model for the Doppler effect using a series of discrete 
> antennas. Is this the way Doppler direction finders (e.g. the Roanoke, the 
> DoppleScant, etc) work? The answer is an emphatic NO.
 
I say yes.

> As Russ pointed out, if you built an antenna that worked like the series of 
> switched antennas described above, amateur FM receivers would not have the 
> bandwidth and S/N to make it work. (Is there any device out there that would?) 
> The fact that Doppler direction finders do work is proof that they do not 
> operate like the system of switched antennas described above. 

The sudden shift indeed has components that  extend  above the bandwidth
of the detector.  Of course, any FM  signal has sidebands that extend to
infinity,  but  that  doesn't  require  an  infinitely wide receiver  to
recover  useful  information.  A narrow-band receiver is a _good  thing_
here, as it by nature filters out much of the switching noise.
 
> All right. So how do they work then? As Russ pointed out, Doppler direction 
> finders switch quickly from one antenna to the next, but then they spend a 
> relatively long period of time connected to each antenna. (Note: that is just 
> the reverse of the situation for the discrete Doppler system described above!) 
> The long time (approximately 0.001 seconds) spent at each antenna is necessary 
> to allow the system to work within the bandwidth constraints of practical FM 
> receivers. 
> 
> To understand how "Doppler" direction finders really work, I found it 
> instructive to consider the analogous single-antenna system that such antennas 
> approximate. Have you ever seen an analog clock with a minute hand that moves 
> in steps? The minute hand remains stationary for one minute, then it clicks 
> over to the next minute position. Consider placing a single antenna on the end 
> of the minute hand of such a clock. (You could modify to the clock so that it 
> makes eight steps instead of 60 to make this thought experiment more like 
> common Doppler direction finders.) The antenna would stand still for a long 
> period of time, and then suddenly make a quick movement to the next position. 
> There would be no Doppler frequency shift while the minute hand stood still. 
> Once the hand begins to click to the next position a brief spurt of Doppler 
> shift occurs, and then stops abruptly as the hand comes to a rest again. 
> 
> The single antenna on a jerking clock hand is just what the Roanoke and 
> similar Doppler designs approximate. One antenna is connected to the receiver 
> for a hundred thousand oscillations of the incoming carrier signal (0.001 
> seconds). During this time there is no frequency shift. Then suddenly, over a 
> period of a hundred oscillations of the incoming carrier signal (1 
> microsecond or less), the receiver is connected to the next antenna. The 
> receiver detects a sudden shift in the phase of the signal received at 
> the switched-to antenna relative to the phase at the switched-from 
> antenna. The phase shift is a result of the two antennas residing at two 
> different locations. 
> 
> Any Doppler frequency shift would have occured during the switch, and would be 
> too sudden to be detected by the FM receiver. Once the shift is complete the 
> receiver is given time to detect the phase of the signal at the switched-to 
> antenna. The discriminator gives a pulse with a polarity that indicates the 
> direction of the phase shift that it detects, if any. The polarity of the 
> phase shift is determined by the relative positions of the two antennas 
> involved in the switch with respect to the source of the received signal. If 
> the switch results in the FM receiver being connected to an antenna that is 
> 1/4 wavelength closer to the transmitter then a -90 degree phase shift is 
> detected. If a switch results in the FM receiver being connected to an antenna 
> that is 1/4 wavelength farther from the transmitter then a +90 degree phase 
> shift is detected. The Doppler effect doesn't even enter into the theory of 
> operation.  

I beg to differ.  The stepped antenna approximates a mechanically moving
antenna, and is aided by the fact that the bandwidth of the  receiver is
not capable of reacting fast enough to capture the steps.  Going back to
your clock  analogy,  consider  the same thing much more apparent with a
quartz watch, you  see  the  second-hand move in jerky movements because
your eye can resolve them, like a very large bandwidth receiver. 

However, the minute-hand of  that  same  watch  is  also moving in jerky
movements, but your eye doesn't  have the bandwidth to receive them, snd
so the 3600 jerky movements of  the minute-hand per hour are interpreted
as a continuous mechanical sweep.

Don't forget that there is a very  narrow  filter  associated with these
units.  Take your watch example.  Apply  a  theoretical  narrow-bandpass
optical filter with a center frequency of 1/60 hz  (one  minute)  to the
movement of the second-hand.  The jerkiness is far above the bandpass of
the  filter,  and  lost  in the noise.  Likewise, the filter  helps  the
electrical stepping of  the  antennas  approximate a smooth mechanically
moving antenna. 

> Any periodic function can be broken down into a series of sine waves, 
> and the periodic pulses coming from a "Doppler" direction finder are no 
> exception. A circular arrangement of discrete antennas will result in a 
> series of pulses with different amplitudes and a period equal to the 
> rotation frequency. This waveform has a strong sinusoidal component at 
> the antenna rotation frequency. If you pass these pulses through a very 
> narrow filter centered at the frequency of antenna rotation, you will 
> get a nice clean sinusoidal waveform with zero crossings corresponding 
> to the points at which the pulses change in polarity from positive to 
> negative, or from negative to positive. So Dopplers work, but they just 
> ain't Dopplers. 

But, if you look at the unfiltered output of the receiver's FM detector,
you don't see pulses returning  to zero at each antenna step.  You see a
stepped sinewave at the rotation frequency, regardless of whether a true
FM (discriminator) or phase (quadrature) detector is  used.  The doppler
effect is there.  The imperfect narrow-band nature  of the receiver's IF
strip    also   helps.    The  model  also  follows  the    mathematical
representations  of  a  mechanical  doppler.    Move the antennas closer
together, and  the  deviation  (doppler shift) decreases.  The amount of
the shift varies  with the antenna diameter precisely in accordance with
the formula. 

In  a mechanically-rotated doppler,  every  cycle  of  the  received  RF
carrier would be a part  of  the  sampling to determine frequency shift.
In the case of a switched-antenna  doppler,  only  a few hundred samples
are  taken  per second, either four or  eight  per  revolution  in  most
designs depending on the number of antennas.

Suppose you are a kid on a fast merry-go-round and you have a microphone
and a very accurate audio frequency meter.  There  is a loudspeaker some
distance away producing a 1 KHz tone.  You continuously sample the tone,
and  note when its frequency passes through 1KHz with a negative  slope.
At  that instant, the loudspeaker is directly in front of you if  you're
facing away  from  the axis of the merry-go-round.  Definitely a doppler
DF. 

Now do the same thing, but you're only allowed to take eight samples per
revolution.  The results  are  the  same,  the  math  is the same.  
----
WestNet:  Internet service to  Santa  Barbara,  Ventura  and  the world.
805-892-2133 805-289-1000 805-578-2121
-----------------------------------------------------------------------

Date: Fri, 22 Mar 1996 10:13:45 -0500 (EST)
From: Bob Bruninga <bruninga@nadn.navy.mil>
To: Charles Scharlau <cscharl@eskimo.com>
cc: fox-list <fox-list@netcom.com>
Subject: Re: A Doppler's a Doppler, NOT!
Sender: owner-fox-list@netcom.com

Im not following this closely, but wouldnt the output of a discriminator 
on an antenna moving toward the transmitter in a straight line be a 
CONSTANT?   NOT ZERO.

You say it would be an initial value, and then ZERO thereafter...  This 
doesnt seeem correct to me.  THe received frequency will be higher, ergo 
the discriminator will be an unchaniging CONSTANT, NOT ZERO....?
-----------------------------------------------------------------------

Date: Fri, 22 Mar 1996 17:41:32 GMT
From: kd6lza@quick.net (David W. Hess)
To: fox-list@netcom.com
Subject: The Doppler Effect and PFDs
Reply-To: kd6lza@quick.net
Message-Id: <3152e649.6577102@mail.quick.net>
X-Mailer: Forte Agent .99d/32.182
Sender: owner-fox-list@netcom.com
Precedence: list

I'm going  to address the reasons that I believe these types of antennas
are correctly called doppler antennas.  Hopefully the netcom list server
won't eat my message...

On Thu, 14 Mar 1996 23:05:07 -0500, Grandrews@aol.com wrote:

>Assume you have a true Doppler (a single antenna spinning around a circle)
>spinning at some fixed angular rate (X revolutions per second).    Measure
>the frequency deviation of the carrier and record that value.    Now spin it
>twice as fast and measure deviation again.    It will be twice what you
>measured before, just as expected from the Doppler effect.

   Yes.  This can be usefully used to raise the signal to noise ratio on
the detecting FM receiver.

>Similarly, assume you have a single element that you move back and forth
>between two positions, moving at some fixed velocity between the two
>positions.    If the RF is coming in parallel to this motion, you will
>measure some value of + & - deviation of the carrier.    Now move the element
>twice as fast, and you will measure twice the deviation as before.

   The deviation will be proportional  to  the  velocity  of  the single
antenna element.

>In both of the above thought experiments the deviation exists at the
>operating frequency.   Also note that as it goes though the IF and reaches
>the discriminator, that same deviation is present, regardless of the
>bandwidth of the receiver.

   I don't agree.  If the instantaneous frequency goes outside of the IF
passband, the discriminator is going to have  a  hard  time  hearing the
signal and noise will dominate during this time.

>When you look at the output of the receiver with a 'scope you see narrow
>blips of voltage (pulses), first + then - polarity, as the antenna switches
>back and forth.   Between these blips is no RDF info, just "noise" as far as
>the RDF is concerned.

   The  phase  detector  or  phase frequency detector in  the  radio  is
designed to recover only an AC signal.  DC  signal  information can't be
easily  recovered  because  the  phase  of the local oscillators in  the
receiver  and  the  phase  of  the  transmitter  doesn't  come  close to
remaining  constant.    If we use a DC accurate phase detector (a  phase
locked loop detector can do this easily) and arrange for there to be  no
phase drift in  the receiver local oscillators and the transmitter, then
we CAN measure absolute  phase.  This is more than a thought experiment.
You could reference the transmitter  and  receiver  oscillators  to  the
atomic clocks on the GPS satellites  easily.    As  the antenna switches
back an forth, a shifting DC signal will be present at the output of the
DC phase detector and it will look a  lot  like  a square wave.  In this
case,  phase  information is contained during and between the  switching
operations.

   As   a  side  note,  I  now  better  understand  your  RDF    system.
Synchronously  detecting the pulses from the AC phase detector to ignore
the  noise  is  an  excellent  idea.  When the system noise exceeds  the
signal  level  after  the  pulse settles near zero, there is no point in
measuring anymore.

On  Mon,  18  Mar    1996    11:25:55   -0800  (PST),  Charles  Scharlau
<cscharl@eskimo.com> wrote:

>Dear Russ et al,
>
>OK, I think I finally get it. Russ's points are valid. A switched-Doppler 
>could be built from a series of separate antennas, but it would not operate 
>the same way that most (all?) Doppler direction finders work. The differences 
>are kind of subtle, but very real. I've done a full 360-degree phase shift 
>in my beliefs of Doppler operation.

   I hope I don't make you too dizzy! <grin>

>To explain the concepts I'd like to propose a series of thought experiments 
>similar to Russ's illustrations, but simpler. 
>
>Let's try something as simple as possible, but still illustrative of a Doppler 
>shift: a single antenna moving along a straight line. We'll start it from 
>rest, accelerate it to a constant velocity, and let it continue to move 
>frictionlessly along a straight line toward a distant transmitter sending a 
>carrier. 
>
>As the antenna begins to move, the frequency that it receives from the distant 
>transmitter begins to increase. The frequency of the signal received by the 
>moving antenna is given by the now familiar formula: 
>
>f = fo -  fo * v/c
>
>where fo = distant transmitter's carrier frequency
>      f  = frequency of signal observed by the moving antenna
>      v  = velocity of the moving antenna
>           v < 0 when the antenna is moving toward distant transmitter
>      c = speed of light
>
>[Note: the formula above is only an approximation. It gives reasonable results 
>only for antenna velocities that are much slower than the speed of light.] 
>
>Once the antenna reaches its maximum velocity, the received frequency also 
>reaches its maximum value. From that point on, the received frequency does not 
>change. 
>
>The output of an FM discriminator connected to the moving antenna would give 
>an output signal indicating a shift in the phase of the received signal so 
>long as the antenna was accelerating. Once the antenna reaches its maximum 
>velocity, and stays there, the output of the FM discriminator would go to 
>zero. So there would be an initial discriminator output "blip" as the antenna 
>accelerates, and zero output from then on.

   I agree completely.  See  above however where I talk about DC capable
phase  detection.   A DC phase  detector  would  maintain  a  DC  output
proportional to antenna velocity.

>Now suppose we want to build a system of discrete antennas that approximates 
>the behavior of the single antenna thought experiment. Imagine that we replace 
>the continuously moving antenna by a long series of discrete antennas spaced 
>evenly along a line leading toward the distant transmitter.  The antennas are 
>separated from one another by a very small distance, much less than one-half 
>the wavelength of the distant transmitter's signal. 
>
>Let's keep things REALLY simple. Let's assume that our antennas can be placed 
>as close together as we wish without mutual coupling (parasitic effects) among 
>the antennas. Let's further assume that we have a phase measuring device that 
>has infinite bandwith, that our entire system has no noise, and that the 
>signal strength is full quieting at each antenna along the line.

   If we also assume a DC phase detector we get different results.

>We simulate the motion of a moving antenna by switching our phase measuring 
>device from one antenna to the next adjacent antenna, starting from the 
>antenna farthest from the distant transmitter. We will remain connected to 
>each antenna only for an infinitessimal period of time, but we will wait for a 
>longer period of time before switching to the next antenna. Our phase 
>measuring device will have to be extremely fast so that we can measure the 
>phase of the received signal in the few nanoseconds that the antenna is 
>connected to it. 
>
>By using more and more antennas, and placing them closer and closer together, 
>our system of discrete antennas should more closely approximate the continuous 
>movement of the single antenna thought experiment. In fact, it does. If we 
>switch to each successive antenna in such a way that we mimick the 
>acceleration of a single antenna to a steady velocity, we will get an initial 
>pulse from our phase measuring device, and a zero output thereafter. 
>
>This then is a model for the Doppler effect using a series of discrete 
>antennas. Is this the way Doppler direction finders (e.g. the Roanoke, the 
>DoppleScant, etc) work? The answer is an emphatic NO.
>
>As Russ pointed out, if you built an antenna that worked like the series of 
>switched antennas described above, amateur FM receivers would not have the 
>bandwidth and S/N to make it work. (Is there any device out there that would?) 
>The fact that Doppler direction finders do work is proof that they do not 
>operate like the system of switched antennas described above.

   The  FM  receiver  system  doesn't  have the  bandwidth  to  show  an
instantaneous antenna shift because the effective doppler speed  is very
high and the phase detector has limitations on it's  bandwidth  and slew
rate.  The value that the phase detector settles to  does  represent the
phase difference.  If it is an AC phase detector, it  will then decay to
zero according to it's time constant.  A DC phase detector would not.

> ...

   A lot of stuff I don't need to address here.

>Any Doppler frequency shift would have occured during the switch, and would be 
>too sudden to be detected by the FM receiver. Once the shift is complete the 
>receiver is given time to detect the phase of the signal at the switched-to 
>antenna. The discriminator gives a pulse with a polarity that indicates the 
>direction of the phase shift that it detects, if any. The polarity of the 
>phase shift is determined by the relative positions of the two antennas 
>involved in the switch with respect to the source of the received signal. If 
>the switch results in the FM receiver being connected to an antenna that is 
>1/4 wavelength closer to the transmitter then a -90 degree phase shift is 
>detected. If a switch results in the FM receiver being connected to an antenna 
>that is 1/4 wavelength farther from the transmitter then a +90 degree phase 
>shift is detected. The Doppler effect doesn't even enter into the theory of 
>operation.

   Insofar  as  the  detector  we  are using is actually measuring phase
changes and  not  frequency  changes,  you  could  say  that  we are not
measuring doppler frequency  shift  and  we  are  therefore  not using a
doppler antenna.  The  same  reasoning  applies  to receiving a FM voice
signal though.  If I  only  have a phase detector (a quadrature detector
in this case which measures phase),  then  I can not claim to be using a
FM receiver.

   The  error here is that phase changes  are  equivalent  to  frequency
changes and the reverse.  If we were  to use a frequency detector in all
of the above statements, nothing would change!  We  could also apply the
mechanism that generates the doppler effect to just as easily  say  that
the phase is continuously changing at a rate that is proportional to the
velocity between a transmitter and a receiver.

>Any periodic function can be broken down into a series of sine waves, and the 
>periodic pulses coming from a "Doppler" direction finder are no exception. A 
>circular arrangement of discrete antennas will result in a series of pulses 
>with a strong sinusoidal component at the antenna rotation frequency. If you 
>pass these pulses through a very narrow filter centered at the frequency of 
>antenna rotation, you will get a nice clean sinusoidal waveform with zero 
>crossings corresponding to the points at which the pulses change in polarity 
>from positive to negative, or from negative to positive. So Dopplers work, but 
>they just ain't Dopplers.

   The  only  difference  when we use AC phase detectors with a discreet
antenna switching system is that the time constant of the phase detector
causes it's output to be a series of pulses.  The average value of these
pulses is proportional  to the phase change over the period of time that
you measure it.   If  the  time constant is long enough, then the output
from the detected signal from  the  circular  doppler  array  will  be a
stepped sine wave.  If the  time  constant  is  not long enough, then we
will have a series of pulses with the area under each pulse proportional
to the value of a sin wave at that point.

>So here I am again at the same spot I was at a little over a week ago, asking 
>the question: Are there any TRUE Doppler direction finders out there? If you 
>can point out any substantial errors in the above arguments or, if you hear of 
>a switched antenna system which actually uses the Doppler effect, I'd be 
>interested to hear from you. 

   I here ask for forgiveness if I have only confused this subject more.
------------------------------------------------
Contradictions do not exist.  Whenever you think
that you are facing a contradiction, check your
premises.  You will find that one of them is wrong.
   - Francisco d'Anconia
-----------------------------------------------------------------------

Date: Mon, 25 Mar 1996 07:14:32 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: fox-list <fox-list@netcom.com>
Subject: Rest of Doppler Story
Message-ID: <Pine.SUN.3.91.960325071151.22573C-100000@eskimo.com>
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Sender: owner-fox-list@netcom.com
Precedence: list

Doppler Discussers,

I have  communicated  with several individuals who espouse the idea that
the Roanoke Doppler direction finder, and switched DF devices of similar
design,  operate  because  of   the  Doppler  effect.    Most  of  these
individuals identify the point of  transition  from  one  antenna to the
next as the critical point where frequency shift information is obtained
from the antenna system. 

As I understand their arguments, they go something like this:  each time
we switch from antenna (A) to antenna (B)  we  get  a pulse, or step, of
some  kind  that  is  proportional to the Doppler shift  we  would  have
observed  had  we  moved a single antenna continuously from point  A  to
point B.  Or, some maintain, we get a signal that  our  FM receiver uses
to produce a pulse, or step, of some kind that is proportional  to  that
Doppler  shift.    Others   hasten  to  add  that  this  Doppler-induced
step/pulse may be distorted or  clipped  by the bandwidth limitations of
amateur FM receivers. 

So far, no one has been  able to explain to me the source of this pulse,
or step, and why it should have  any  relationship  to the Doppler shift
observed using a continuously moving antenna.  It  doesn't  seem that it
should  be  too  difficult to provide such an explanation,  provided  of
course that such a frequency-shift-induced pulse/step exists. 

Let's  try  an  experiment.    Consider  an  FM  radio  connected  to  a
two-antenna  system  receiving  a  carrier.  We wish to switch from  one
antenna (A) to the next antenna (B).  We can do this  in  one  of  three
ways:   break  before  make, make before break, or simultaneous make and
break.  Let's look at each possibility individually. 

1) BREAK BEFORE MAKE

Our FM receiver  is  connected to antenna A:  The FM receiver detects no
frequency change. 

The antenna connection with  antenna  A  is  broken:    The  FM receiver
detects no carrier signal, and  no  frequency  change.  This state lasts
for 1 or 2 microseconds. 

Our FM receiver is connected to  antenna B:  The FM receiver detects the
carrier arriving from antenna B.  The  FM  receiver detects no frequency
change.  (It might however detect a sudden  phase  shift  if  it remains
connected to antenna B long enough.)

2) MAKE BEFORE BREAK

Our FM receiver is connected to antenna A:   The  FM receiver detects no
frequency change.

Antenna  B  is  connected  to  the  FM receiver, and antenna  A  remains
connected to it as well:  The FM receiver receives the same carrier from
the two antennas.  The two carrier signals differ in phase by  an amount
determined  by  the  distance  from  antenna  A  to  antenna  B, and any
difference  in   feedline  lengths.    There  is  some  constructive  or
destructive interference between  the  two  signals  arriving  at the FM
receiver.  The signal strength that the FM receiver detects is affected,
but no frequency change is  detected.    This  state  lasts  for  1 or 2
microseconds. 

Our FM receiver is connected only to antenna B:  The FM receiver detects
the  carrier  arriving  from antenna B.   The  FM  receiver  detects  no
frequency change.  (It might however detect a  sudden  phase shift if it
remains connected to antenna B long enough.) 

3) MAKE AND BREAK SIMULTANEOUSLY

Our FM receiver is connected to antenna A:   The  FM receiver detects no
frequency change.

Antenna B is connected to the FM receiver, and antenna A is disconnected
from the FM receiver at the exact same instant.

Our FM receiver is connected to antenna B:  The FM  receiver detects the
carrier  arriving  from antenna B.  The FM receiver detects no frequency
change.   (It  might  however  detect a sudden phase shift if it remains
connected to antenna B long enough.)

There you have  it.  At no time does Doppler frequency shift information
sneak into the radio.    There's  no subtle Doppler effect observed, and
nothing magical happens.  You might get a phase shift but nothing more. 

Suppose you want to build  a  switched  antenna  system  that can detect
Doppler- shifted carrier signals.  Shouldn't it be possible? 

You bet it should be.   But  the detected Doppler shift will result from
the signal detected while the FM receiver  is connected to each antenna,
not while the transition is being made.   Also,  the switching will have
to be accomplished much more rapidly than in a  Roanoke,  DoppleScant or
pseudo-Dopplers of similar design. 

Sampled  signal  theory tells us that if you want to  recover  frequency
information from a sampled signal then you need to sample fast enough so
that  you can reconstruct the original signal from the samples you take.
The  minimum  sampling  rate is refered to as the Nyquist sampling rate,
and it  is  twice the frequency of the highest frequency signal you wish
to reconstruct.   That is the theoretical minimum.  In practice you will
probably need to sample at several times the Nyquist rate.

To construct a switched  antenna  system that can detect Doppler-shifted
2-meter band signals would require  a  sampling  rate somewhere near 2 x
146,000,000 samples per second (S/s), minimum.   That's 292 million S/s,
or one sample every 3.4 nanoseconds.  That is fast.  Too fast.  Standard
PIN diode switching schemes probably aren't going to cut it.

Just for comparison, let's look at how fast  pseudo-Dopplers  sample  an
incoming signal.  Say we have eight antennas on the roof of our vehicle,
and we switch among them so that we complete 500 revolutions per second.
That  comes  to  8  samples/revolution  x  500 revolutions/second = 4000
samples per  second.  That is one 73,000th as fast as our minimum sample
rate for recovering Doppler frequency shift information. 

Say we want  to  build a "true" Doppler from switched antennas.  Suppose
we want to keep  the  rotation rate at 500 Hz so that we can continue to
use the same audio filtering  circuit as our pseudo-Doppler.  That would
mean that we have to increase  the  number  of antennas until we satisfy
the Nyquist sampling rate.  In other  words we need 73,000 x 8 = 584,000
antennas (minimum) arranged in a circle.  That's  a  lot of wire.  Also,
the spacing between antennas might be a tad cozy. 

I  said  building  such  antennas  should  be possible, not  necessarily
practical.  My guess is that "true" Doppler direction finders that use a
system of switched antennas are used only at low frequencies, where  the
minimum sampling rate would be much lower.  They would probably take  up
a  great  deal  of  real  estate, and have many many antennas.  I  would
expect that some kind of anti- aliasing low-pass filter would need to be
attached to  each  antenna.    If  you ever hear of one I'd love to hear
about it. 

73,
Charles E. Scharlau
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134 
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam          
----------------------------------------------------------------------

Date: Mon, 25 Mar 1996 12:57:54 -0800
To: cscharl@eskimo.com
From: grant@hooked.net (Chuck Grant)
Subject: Re: (Fwd) Re: A Real Doppler
Cc: fox-list@netcom.com
Sender: owner-fox-list@netcom.com

>
>Let's try something as simple as possible, but still illustrative of a Doppler
>shift: a single antenna moving along a straight line. We'll start it from
>rest, accelerate it to a constant velocity, and let it continue to move
>frictionlessly along a straight line toward a distant transmitter sending a
>carrier.
>

Doppler shift is  nothing  more  than  phase  modulation.   Changing the
position of either antenna  changes  the  distance between them and thus
the phase of the received  signal.    The  phase::position  relation  is
fundamental.  If you take the  derivative  of  this equation you get the
commonly taught Doppler effect (the derivative of  position is velocity,
and the derivative of phase is frequency) velocity::frequency.  But this
is not the fundamental relation.

>As the antenna begins to move, the frequency that it receives from the distant
>transmitter begins to increase. The frequency of the signal received by the
>moving antenna is given by the now familiar formula:
>
>f = fo -  fo * v/c
>
>where fo = distant transmitter's carrier frequency
>      f  = frequency of signal observed by the moving antenna
>      v  = velocity of the moving antenna
>           v < 0 when the antenna is moving toward distant transmitter
>      c = speed of light
>
>[Note: the formula above is only an approximation. It gives reasonable results
>only for antenna velocities that are much slower than the speed of light.]
>
>Once the antenna reaches its maximum velocity, the received frequency also
>reaches its maximum value. From that point on, the received frequency does not
>change.
>
>The output of an FM discriminator connected to the moving antenna would give
>an output signal indicating a shift in the phase of the received signal so
>long as the antenna was accelerating. Once the antenna reaches its maximum
>velocity, and stays there, the output of the FM discriminator would go to
>zero. So there would be an initial discriminator output "blip" as the antenna
>accelerates, and zero output from then on.
>

The  output  you  describe  is  not  what  you  would  get  from  an  FM
descriminator, thus the rest of your thought experiment is invalid.

There are many kinds of FM descriminators.  What you  describe  is not a
true  FM  descriminator,  but  a  kind  of  phase  detector.    A   true
descriminator outputs  a DC voltage proportional to the frequency shift,
not the phase,  over a small range of frequencies.  A true descriminator
is not a difficut  circuit.    You  probably  have one in your two meter
radio.

The audio amplifier in your radio is probably not DC coupled, so this DC
signal does not make it out  of  your  radio.  But at the descriminator,
direct  measurements  of  constant frequencies, relative to  the  center
frequency of the descriminator, are possible by measuring DC voltages.

>Now suppose we want to build a system of discrete antennas that 
 approximates  
>the  behavior  of  the single antenna thought experiment. Imagine  that  
 we  replace  
>the  continuously moving antenna by a  long series  of  discrete 
 antennas spaced 
>evenly along a line leading toward the distant  transmitter.   
 The antennas are 
>separated from one another by a very small distance, much less 
 than one-half 
>the wavelength of the distant transmitter's signal.   (Actually  
 this  should  
>be  less  than one-half the wavelength of the  shifted  frequency, 
 but this 
>difference is small.) 
> 
>Let's keep things  REALLY  simple.   Let's assume that our antennas 
 can be placed 
>as close together  as  we  wish  without  mutual coupling (parasitic 
 effects) among 
>the antennas.  Let's  further assume that we have a phase measuring 
 device that 
>has  infinite bandwith, that our entire system has no noise, and 
 that the 
>signal  strength  is  full quieting  at  each  antenna  along the 
 line.  
> 
>We would  simulate  the motion of a moving antenna by switching our phase 
>measuring device from one antenna  to  the  next  adjacent antenna, starting 
>from the antenna farthest from the  distant transmitter.  Each antenna 
>remains connected to the phase shift  detector  connected  to  only for an 
>infinitessimal period of time, but we  will  wait  for  a longer period of 
>time before switching to the next antenna.  Our phase measuring device 
>will have to be extremely fast so that we can  measure  the  phase  of  the 
>received signal in the few nanoseconds that the antenna is connected to it.  
>

Ok now you are talking about a "phase  measuring  device" which you have
not defined.  If you are going to make  phase  measurements, you need to
have two signals to get a phase difference.  If  your signal samples are
seperated widely in time, as you suggest, then you need a  very accurate
and fast locking reference oscilator of some kind.  In any case,  it  is
questionable how  accurate  a  phase  measurement you can make during an
interval much less  than  a  single  period,  as  you suggest, even with
nearly ideal conditions.

So now we are  comparing  an  invalid  continuous  model  with an overly
idealized and unrealizable sampled model.   I think there is very little
similarity or relevance to real RDF equipment left.

>By using more and more antennas, and placing them closer and closer together,
>our system of discrete antennas should more closely approximate the continuous
>movement of the single antenna thought experiment. In fact, it does. If we
>switch to each successive antenna in such a way that we mimick the
>acceleration of a single antenna to a steady velocity, we will get an initial
>pulse from our phase measuring device, and a zero output thereafter.
>

Not true.  The output from  a continous phase detector would be a series
of steps, the output from an FM  descriminator  would  be  a  series  of
pulses.  In neither case would it be  a short pulse followed by nothing,
but then this does not happen in the moving antenna and FM descriminator
case either.  Why bother accelerating anyway?  It is  not  necessary for
the  switched  antenna  case,  and  the  effect  is  based  on a  flawed
assumption in the continuous case.

>This then is a model for the Doppler effect using a series of discrete
>antennas. Is this the way Doppler direction finders (e.g. the Roanoke, the
>DoppleScant, etc) work? The answer is an emphatic NO.
>

Your  understanding  of  the  model  is flawed, so you can not make  the
judgement if the two effects are "the same".  They are infact the same.

>As Russ pointed out, if you built an antenna that worked like the series of
>switched antennas described above, amateur FM receivers would not have the
>bandwidth and S/N to make it work. (Is there any device out there that would?)
>The fact that Doppler direction finders do work is proof that they do not
>operate like the system of switched antennas described above.
>

You  do not have to have full bandwidth and infinite S/N for the  system
to work.    Infact  the  way  typical  dopplers  are built and used, the
represent about a  10db loss to the incoming signal.  That is, you can't
get a direction out  of  them  until the signal is 10db higher than what
you need to hear the  signal  clearly  without  the  doppler.  This loss
represents several things including the narrow  bandwidth  of  the radio
and the signal to noise ratio.   This  loss  is consistant with assuming
that we are using the "swtiched antenna doppler effect".

Dopplers do work, obviously many people use them.

>All right. So how do they work then? As Russ pointed out, Doppler direction
>finders switch quickly from one antenna to the next, but then they spend a
>relatively long period of time connected to each antenna. (Note: that is just
>the reverse of the situation for the discrete Doppler system described above!)
>The long time (approximately 0.001 seconds) spent at each antenna is necessary
>to allow the system to work within the bandwidth constraints of practical FM
>receivers.
>
>To understand how "Doppler" direction finders really work, I found it
>instructive to consider the analogous single-antenna system that such antennas
>approximate. Have you ever seen an analog clock with a minute hand that moves
>in steps? The minute hand remains stationary for one minute, then it clicks
>over to the next minute position. Consider placing a single antenna on the end
>of the minute hand of such a clock. (You could modify to the clock so that it
>makes eight steps instead of 60 to make this thought experiment more like
>common Doppler direction finders.) The antenna would stand still for a long
>period of time, and then suddenly make a quick movement to the next position.
>There would be no Doppler frequency shift while the minute hand stood still.
>Once the hand begins to click to the next position a brief spurt of Doppler
>shift occurs, and then stops abruptly as the hand comes to a rest again.
>
>The single antenna on a jerking clock hand is just what the Roanoke and
>similar Doppler designs approximate. One antenna is connected to the receiver
>for a hundred thousand oscillations of the incoming carrier signal (0.001
>seconds). During this time there is no frequency shift. Then suddenly, over a
>period of a hundred oscillations of the incoming carrier signal (1
>microsecond or less), the receiver is connected to the next antenna. The
>receiver detects a sudden shift in the phase of the signal received at
>the switched-to antenna relative to the phase at the switched-from
>antenna. The phase shift is a result of the two antennas residing at two
>different locations.
>
>Any Doppler frequency shift would have occured during the switch, and would be
>too sudden to be detected by the FM receiver. Once the shift is complete the

It is not true that it is too sudden to be detected by an FM receiver.

>receiver is given time to detect the phase of the signal at the switched-to
>antenna. The discriminator gives a pulse with a polarity that indicates the
>direction of the phase shift that it detects, if any. The polarity of the
>phase shift is determined by the relative positions of the two antennas
>involved in the switch with respect to the source of the received signal. If
>the switch results in the FM receiver being connected to an antenna that is
>1/4 wavelength closer to the transmitter then a -90 degree phase shift is
>detected. If a switch results in the FM receiver being connected to an antenna
>that is 1/4 wavelength farther from the transmitter then a +90 degree phase
>shift is detected. The Doppler effect doesn't even enter into the theory of
>operation.
>

The Doppler effect is just phase modulation.  Weather it enters into the
theory of operation or not depends entirely on how you think about it.

>Any periodic function can be broken down into a series of sine waves, and the

Almost  any  function  can be broken down into sine  functions  (Fourier
transform).  Almost any periodic function can be broken down  onto  sine
functions with frequencies that are integer multiples of the fundamental
frequency of  the periodic signal (the Fourier series, a special case of
the Fourier transform).   Some functions do not have a Fourier transform
representation if they do not meet particular integrability constraints.
Just  being  periodic  is  not    a  guarantee  that  a  Fourier  series
representation  exists, although they exist for  most  signals  you  are
likely to encounter.

>periodic pulses coming from a "Doppler" direction finder are no exception. A
>circular arrangement of discrete antennas will result in a series of pulses
>with different amplitudes and a period equal to the rotation frequency.
>This waveform has a strong sinusoidal component at the antenna rotation
>frequency. If you pass these pulses through a very narrow filter
>centered at the frequency of antenna rotation, you will get a nice clean
>sinusoidal waveform with zero crossings corresponding to the points at
>which the pulses change in polarity from positive to negative, or from
>negative to positive. So Dopplers work, but they just ain't Dopplers.
>

The  fundamental  component of this signal is  not  as  strong  as  your
comments indicate, which is one of the reasons  why  you get such a loss
through a "Doppler".

The reasoning that "this is not a Doppler" is not valid.  A Doppler uses
phase modulation, you use phase modulation, any differences are subtile.
Also  you are comparing a sampled system with a continuous system.    In
order  to  make  such  a  comparison you must include the reconstruction
filter used to turn the sampled signal back into a continuous one.  This
is the narrow bandpass filter at the switching frequency, The need for a
narrow band filter does not invalidate anything, it is expected.

>So here I am again at the same spot I was at a little over a week ago, asking
>the question: Are there any TRUE Doppler direction finders out there? If you

Yes they all are.

>can point out any substantial errors in the above arguments or, if you hear of

Done.

>a switched antenna system which actually uses the Doppler effect, I'd be
>interested to hear from you.
>
>I can provide a better description of how a "true" Doppler direction
>finder might operate, if that might be of help in identifying such a beast.
>

Please do.  I think that  may  help identify where your misunderstanding
is, if nothing else.
------------------------------------------------------------------------

Date:  Tue,  26  Mar  1996  08:15:39 -0800 (PST) From:  Charles Scharlau
<cscharl@eskimo.com>  Reply-To:  Charles  Scharlau  <cscharl@eskimo.com>
To:  Chuck Grant <grant@hooked.net>  cc:    fox-list@netcom.com Subject:
Re:  (Fwd) Re:  A Real Doppler Sender:  owner-fox-list@netcom.com

On Mon, 25 Mar 1996, Chuck Grant wrote:

> Doppler shift is nothing more than phase modulation.  Changing the position
> of either antenna changes the distance between them and thus the phase of
> the received signal.  The phase::position relation is fundamental.
> If you take the derivative of this equation you get the commonly taught
> Doppler effect (the derivative of position is velocity, and the derivative
> of phase is frequency) velocity::frequency.  But this is not the fundamental
> relation.

Exactly right.  The Doppler frequency shift  results  from  a continuous
shift in phase that occurs when an antenna  is  moving  with  a  certain
VELOCITY.  A phase shift occurs when you switch  from  an antenna at one
location to an antenna at another location:  POSITION.  The relationship
between  these  two  effects  is  analogous  to the relationship between
position and velocity:  a derivative with respect to time.

> >The output of an FM discriminator connected to the moving antenna would give
> >an output signal indicating a shift in the phase of the received signal so
> >long as the antenna was accelerating. Once the antenna reaches its maximum
> >velocity, and stays there, the output of the FM discriminator would go to
> >zero. So there would be an initial discriminator output "blip" as the antenna
> >accelerates, and zero output from then on.
> >
>
> The output you describe is not what you would get from an FM descriminator,
> thus the rest of your thought experiment is invalid.

You are  right  and wrong here.  I have incorrectly described the output
from an FM  discriminator.    What  I  have  described is more like a PM
discriminator.  My apologies.    However, whether the output is constant
or whether that constant is zero, the rest of my argument holds.

You see, both FM and  PM  discriminators  will  respond  to  a change in
phase, provided that it is of  sufficient  duration  to  be  within  the
bandwidth of the discriminator.

> There are many kinds of FM descriminators.  What you describe is not a true
> FM descriminator, but a kind of phase detector.  A true descriminator outputs
> a DC voltage proportional to the frequency shift, not the phase, over a small
> range of frequencies.  A true descriminator is not a difficut circuit. You
> probably have one in your two meter radio.
>
> The audio amplifier in your radio is probably not DC coupled, so this DC
> signal does not make it out of your radio.  But at the descriminator,
> direct measurements of constant frequencies, relative to the center
> frequency of the descriminator, are possible by measuring DC voltages.

Provided  that  the signal which the FM  discriminator  is  tracking  is
changing at some non-DC rate then an AC  coupled circuit should pass the
AC output of an FM discriminator.  A pulse is such an AC signal.

> >We would simulate the motion of a moving antenna by switching our phase
> >measuring device from one antenna to the next adjacent antenna, starting
> >from the antenna farthest from the distant transmitter. Each antenna
> >remains connected to the phase shift detector connected to only for an
> >infinitessimal period of time, but we will wait for a longer period of
> >time before switching to the next antenna. Our phase measuring device
> >will have to be extremely fast so that we can measure the phase of the
> >received signal in the few nanoseconds that the antenna is connected to it.
> >
>
> Ok now you are talking about a "phase measuring device" which you have not
> defined.  If you are going to make phase measurements, you need to have
> two signals to get a phase difference.  If your signal samples are seperated
> widely in time, as you suggest, then you need a very accurate and fast
> locking reference oscilator of some kind.
> In any case, it is questionable how accurate a phase measurement you can
> make during an interval much less than a single period, as you suggest,
> even with nearly ideal conditions.

The undefined "phase measuring device" could be either an  FM  or  a  PM
discriminator of sufficient bandwidth to detect the shift in phase.    I
can  see  that  my  example here is flawed, however.  It  does  seem  to
suggest that you might get some kind of Doppler shift from merely taking
shorter  samples,  when  the  real  problem is the need for both shorter
samples and a much more frequent sample period.  Again, my apologies.

> So now we are comparing an invalid continuous model with an overly idealized
> and unrealizable sampled model.  I think there is very little similarity or
> relevance to real RDF equipment left.

True.   The  real pseudo-Dopplers I've heard about don't come very close
to detecting a true Doppler frequency shift.

> >By using more and more antennas, and placing them closer and closer together,
> >our system of discrete antennas should more closely approximate the continuous
> >movement of the single antenna thought experiment. In fact, it does. If we
> >switch to each successive antenna in such a way that we mimick the
> >acceleration of a single antenna to a steady velocity, we will get an initial
> >pulse from our phase measuring device, and a zero output thereafter.
> >
>
> Not true.  The output from a continous phase
> detector would be a series of steps, the output from an FM descriminator
> would be a series of pulses. In neither case would it be a short pulse
> followed by nothing, but then this does not happen in the moving antenna
> and FM descriminator case either.  Why bother accelerating anyway?  It is
> not necessary for the switched antenna case, and the effect is based on
> a flawed assumption in the continuous case.

Hold on a  second.  If a Doppler works by detecting a shift in frequency
due to velocity, then what difference should it make whether the antenna
is traveling in a circle  or  a  straight  line?  If you get a series of
pulses from the above system then  you  aren't  doing a very good job of
mimicking the continuous case with a series  of  switched  antennas.  In
fact it violates the whole principle of the single-antenna model.

> >This then is a model for the Doppler effect using a series of discrete
> >antennas. Is this the way Doppler direction finders (e.g. the Roanoke, the
> >DoppleScant, etc) work? The answer is an emphatic NO.
> >
>
> Your understanding of the model is flawed, so you can not make the judgement
> if the two effects are "the same".  They are infact the same.

Sorry, you've failed to prove your point.  In what way are they the same
if  one  results  in one pulse and the other  results  in  a  series  of
pulses??

> >As Russ pointed out, if you built an antenna that worked like the series of
> >switched antennas described above, amateur FM receivers would not have the
> >bandwidth and S/N to make it work. (Is there any device out there that would?)
> >The fact that Doppler direction finders do work is proof that they do not
> >operate like the system of switched antennas described above.
>
> You do not have to have full bandwidth and infinite S/N for the system to
> work.  Infact the way typical dopplers are built and used, the represent
> about a 10db loss to the incoming signal.  That is, you can't get a direction
> out of them until the signal is 10db higher than what you need to hear the
> signal clearly without the doppler.  This loss represents several things
> including the narrow bandwidth of the radio and the signal to noise ratio.
> This loss is consistant with assuming that we are using the "swtiched
> antenna doppler effect".
>
> Dopplers do work, obviously many people use them.

The issue was never whether pseudo-Dopplers work, it was HOW they work.

> >All right. So how do they work then? As Russ pointed out, Doppler direction
> > (more missing text)
> >Any Doppler frequency shift would have occured during the switch, and would be
> >too sudden to be detected by the FM receiver. Once the shift is complete the
>
> It is not true that it is too sudden to be detected by an FM receiver.

I'm pretty sure that my receiver doesn't have 1 MHz frequency response.

> The Doppler effect is just phase modulation.  Weather it enters into the
> theory of operation or not depends entirely on how you think about it.

I  think  you  are pretty close to the target here.    But  why  try  to
describe a  change-in-position  effect using a velocity explanation?  It
doesn't make sense.    Why  obscure  the operation of pseudo-Dopplers by
comparing their operation with  a  smoothly rotating single antenna when
pseudo-Dopplers in no way approximate such a model?

> >Any periodic function can be broken down into a series of sine waves, and the
>
> Almost any function can be broken down into sine functions (Fourier transform).
> Almost any periodic function can be broken down onto sine functions with
> frequencies that are integer multiples of the fundamental frequency of
> the periodic signal (the Fourier series, a special case of the Fourier
> transform).  Some functions do not have a Fourier transform representation
> if they do not meet particular integrability constraints.  Just being
> periodic is not a guarantee that a Fourier series representation exists,
> although they exist for most signals you are likely to encounter.

Yup.

> >periodic pulses coming from a "Doppler" direction finder are no exception. A
> >circular arrangement of discrete antennas will result in a series of pulses
> >with different amplitudes and a period equal to the rotation frequency.
> >This waveform has a strong sinusoidal component at the antenna rotation
> >frequency. If you pass these pulses through a very narrow filter
> >centered at the frequency of antenna rotation, you will get a nice clean
> >sinusoidal waveform with zero crossings corresponding to the points at
> >which the pulses change in polarity from positive to negative, or from
> >negative to positive. So Dopplers work, but they just ain't Dopplers.
> >
>
> The fundamental component of this signal is not as strong as your comments
> indicate, which is one of the reasons why you get such a loss through a
> "Doppler".

Again, I think you are correct.

> The reasoning that "this is not a Doppler" is not valid.  A Doppler uses
> phase modulation, you use phase modulation, any differences are subtile.
> Also you are comparing
> a sampled system with a continuous system.  In order to make such a
> comparison you must include the reconstruction filter used to turn the
> sampled signal back into a continuous one.  This is the narrow bandpass
> filter at the switching frequency, The need for a narrow band
> filter does not invalidate anything, it is expected.

It seems that the front  end  of your radio would probably fill the bill
of  a  "reconstruction  filter."  You  would,   however,  probably  want
anti-aliasing  filter(s) to avoid having higher frequency  signals  fool
your system.  You would also want to  satisfy the Nyquist sampling rate,
which pseudo-Dopplers do not.

I  agree  with  you  about the narrow bandpass filter  not  invalidating
anything.    Extracting  the rotation rate frequency component is simply
one method  of  detecting  the  point  where  switching between antennas
results in a phase shift from positive to negative, or vice versa.

> >So here I am again at the same spot I was at a little over a week ago, asking
> >the question: Are there any TRUE Doppler direction finders out there? If you
>
> Yes they all are.
>
> >can point out any substantial errors in the above arguments or, if you hear of
>
> Done.

Thanks for your input!

> Please do.  I think that may help identify where your misunderstanding is,
> if nothing else.

Please see "The  Rest of the Doppler Story" coming to a list server near
you.

73,
Charles E. Scharlau
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam
--------------------------------------------------------------------

Date: Wed, 27 Mar 1996 00:34:34 -0800
From: Charles Grant <grant@mailhost.hooked.net>
To: <cscharl@eskimo.com>
Cc: fox-list@netcom.com, grant@hooked.net
Subject: Re: A Real Doppler
Sender: owner-fox-list@netcom.com

On Tue, Mar 26, 1996 8:15:39 AM  at Charles Scharlau wrote: 
 
> Sorry, you've failed to prove your point. In what way are they the same
if 
> one results in one pulse and the other results in a series of pulses?? 
 
The moving antenna and  FM  descriminator  result in a DC level output -
not one pulse.  The pulse is an artifact of acceleration not relevant to
this problem.  The system is  already  so  idealized, there is no reason
involve acceleration.  You must compare the  steady state output of both
systems.   Not the initialization of one system  and  the  steady  state
output of the other. 
 
The switched antenna system and FM descriminator result in  a  series of
pulses  -  ALL  OF  THE  SAME  VALUE (unless of course  you  go  to  the
unnecessary

trouble  of  simulating some startup acceleration, then you would have a
blip  in  the  first  few  samples  EXACTLY like the moving antenna when
accelerating). 
 
A  series of samples, all of the same value, is the sampled data  domain
equivalent  of  a DC signal in the continuous domain.  They are the same
thing.  The same signal expressed in different domains. 
 
They  are  the  same.    One  is  the  sampled  representation,  one  is
continuous. 
 
Chuck Grant, KE6CIL
------------------------------------------------------------------------

From: kd6lza@quick.net (David W. Hess)
To: fox-list@netcom.com
Cc: kd6lza@quick.net
Subject: The Doppler Effect and PFDs
Date: Wed, 27 Mar 1996 01:58:21 GMT
Reply-To: kd6lza@quick.net
Sender: owner-fox-list@netcom.com

   I'm going to  address  the  reasons  that  I  believe  these types of
antennas are correctly called  doppler  antennas.   Hopefully the netcom
list server won't eat my message...

   I sent this message originally on 3-22-96.  Here it goes again...

On Thu, 14 Mar 1996 23:05:07 -0500, Grandrews@aol.com wrote:

>Assume you have a true Doppler (a single antenna spinning around a circle)
>spinning at some fixed angular rate (X revolutions per second).    Measure
>the frequency deviation of the carrier and record that value.    Now spin it
>twice as fast and measure deviation again.    It will be twice what you
>measured before, just as expected from the Doppler effect.

   Yes.  This can be usefully used to raise the signal to noise ratio on
the detecting FM receiver.

>Similarly, assume you have a single element that you move back and forth
>between two positions, moving at some fixed velocity between the two
>positions.    If the RF is coming in parallel to this motion, you will
>measure some value of + & - deviation of the carrier.    Now move the element
>twice as fast, and you will measure twice the deviation as before.

   The deviation will be proportional to  the  velocity  of  the  single
antenna element.

>In both of the above thought experiments the deviation exists at the
>operating frequency.   Also note that as it goes though the IF and reaches
>the discriminator, that same deviation is present, regardless of the
>bandwidth of the receiver.

   I don't agree.  If the instantaneous frequency goes outside of the IF
passband, the discriminator is going to have a  hard  time  hearing  the
signal and noise will dominate during this time.

>When you look at the output of the receiver with a 'scope you see narrow
>blips of voltage (pulses), first + then - polarity, as the antenna switches
>back and forth.   Between these blips is no RDF info, just "noise" as far as
>the RDF is concerned.

   The  phase  detector  or  phase  frequency detector in the  radio  is
designed to recover only an AC signal.  DC signal  information  can't be
easily  recovered  because  the  phase  of  the local oscillators in the
receiver  and  the  phase  of  the  transmitter  doesn't  come  close to
remaining constant.    If  we  use a DC accurate phase detector (a phase
locked loop detector  can do this easily) and arrange for there to be no
phase drift in the  receiver local oscillators and the transmitter, then
we CAN measure absolute phase.   This is more than a thought experiment.
You  could reference the transmitter and  receiver  oscillators  to  the
atomic clocks on the GPS satellites easily.    As  the  antenna switches
back an forth, a shifting DC signal will be present at the output of the
DC phase detector and it will look a lot  like  a  square wave.  In this
case,  phase  information  is contained during and between the switching
operations.

   As    a   side  note,  I  now  better  understand  your  RDF  system.
Synchronously  detecting the pulses from the AC phase detector to ignore
the noise  is  an  excellent  idea.    When the system noise exceeds the
signal level after  the  pulse  settles  near zero, there is no point in
measuring anymore.

On  Mon,  18  Mar    1996    11:25:55   -0800  (PST),  Charles  Scharlau
<cscharl@eskimo.com> wrote:

>Dear Russ et al,
>
>OK, I think I finally get it. Russ's points are valid. A switched-Doppler 
>could be built from a series of separate antennas, but it would not operate 
>the same way that most (all?) Doppler direction finders work. The differences 
>are kind of subtle, but very real. I've done a full 360-degree phase shift 
>in my beliefs of Doppler operation.

   I hope I don't make you too dizzy! <grin>

>To explain the concepts I'd like to propose a series of thought experiments 
>similar to Russ's illustrations, but simpler. 
>
>Let's try something as simple as possible, but still illustrative of a Doppler 
>shift: a single antenna moving along a straight line. We'll start it from 
>rest, accelerate it to a constant velocity, and let it continue to move 
>frictionlessly along a straight line toward a distant transmitter sending a 
>carrier. 
>
>As the antenna begins to move, the frequency that it receives from the distant 
>transmitter begins to increase. The frequency of the signal received by the 
>moving antenna is given by the now familiar formula: 
>
>f = fo -  fo * v/c
>
>where fo = distant transmitter's carrier frequency
>      f  = frequency of signal observed by the moving antenna
>      v  = velocity of the moving antenna
>           v < 0 when the antenna is moving toward distant transmitter
>      c = speed of light
>
>[Note: the formula above is only an approximation. It gives reasonable results 
>only for antenna velocities that are much slower than the speed of light.] 
>
>Once the antenna reaches its maximum velocity, the received frequency also 
>reaches its maximum value. From that point on, the received frequency does not 
>change. 
>
>The output of an FM discriminator connected to the moving antenna would give 
>an output signal indicating a shift in the phase of the received signal so 
>long as the antenna was accelerating. Once the antenna reaches its maximum 
>velocity, and stays there, the output of the FM discriminator would go to 
>zero. So there would be an initial discriminator output "blip" as the antenna 
>accelerates, and zero output from then on.

   I agree completely.  See  above however where I talk about DC capable
phase  detection.   A DC phase  detector  would  maintain  a  DC  output
proportional to antenna velocity.

>Now suppose we want to build a system of discrete antennas that approximates 
>the behavior of the single antenna thought experiment. Imagine that we replace 
>the continuously moving antenna by a long series of discrete antennas spaced 
>evenly along a line leading toward the distant transmitter.  The antennas are 
>separated from one another by a very small distance, much less than one-half 
>the wavelength of the distant transmitter's signal. 
>
>Let's keep things REALLY simple. Let's assume that our antennas can be placed 
>as close together as we wish without mutual coupling (parasitic effects) among 
>the antennas. Let's further assume that we have a phase measuring device that 
>has infinite bandwith, that our entire system has no noise, and that the 
>signal strength is full quieting at each antenna along the line.

   If we also assume a DC phase detector we get different results.

>We simulate the motion of a moving antenna by switching our phase measuring 
>device from one antenna to the next adjacent antenna, starting from the 
>antenna farthest from the distant transmitter. We will remain connected to 
>each antenna only for an infinitessimal period of time, but we will wait for a 
>longer period of time before switching to the next antenna. Our phase 
>measuring device will have to be extremely fast so that we can measure the 
>phase of the received signal in the few nanoseconds that the antenna is 
>connected to it. 
>
>By using more and more antennas, and placing them closer and closer together, 
>our system of discrete antennas should more closely approximate the continuous 
>movement of the single antenna thought experiment. In fact, it does. If we 
>switch to each successive antenna in such a way that we mimick the 
>acceleration of a single antenna to a steady velocity, we will get an initial 
>pulse from our phase measuring device, and a zero output thereafter. 
>
>This then is a model for the Doppler effect using a series of discrete 
>antennas. Is this the way Doppler direction finders (e.g. the Roanoke, the 
>DoppleScant, etc) work? The answer is an emphatic NO.
>
>As Russ pointed out, if you built an antenna that worked like the series of 
>switched antennas described above, amateur FM receivers would not have the 
>bandwidth and S/N to make it work. (Is there any device out there that would?) 
>The fact that Doppler direction finders do work is proof that they do not 
>operate like the system of switched antennas described above.

   The  FM  receiver  system  doesn't  have the  bandwidth  to  show  an
instantaneous antenna shift because the effective doppler speed  is very
high and the phase detector has limitations on it's  bandwidth  and slew
rate.  The value that the phase detector settles to  does  represent the
phase difference.  If it is an AC phase detector, it  will then decay to
zero according to it's time constant.  A DC phase detector would not.

> ...

   A lot of stuff I don't need to address here.

>Any Doppler frequency shift would have occured during the switch, and would be 
>too sudden to be detected by the FM receiver. Once the shift is complete the 
>receiver is given time to detect the phase of the signal at the switched-to 
>antenna. The discriminator gives a pulse with a polarity that indicates the 
>direction of the phase shift that it detects, if any. The polarity of the 
>phase shift is determined by the relative positions of the two antennas 
>involved in the switch with respect to the source of the received signal. If 
>the switch results in the FM receiver being connected to an antenna that is 
>1/4 wavelength closer to the transmitter then a -90 degree phase shift is 
>detected. If a switch results in the FM receiver being connected to an antenna 
>that is 1/4 wavelength farther from the transmitter then a +90 degree phase 
>shift is detected. The Doppler effect doesn't even enter into the theory of 
>operation.

   Insofar  as  the  detector  we  are using is actually measuring phase
changes and  not  frequency  changes,  you  could  say  that  we are not
measuring doppler frequency  shift  and  we  are  therefore  not using a
doppler antenna.  The  same  reasoning  applies  to receiving a FM voice
signal though.  If I  only  have a phase detector (a quadrature detector
in this case which measures phase),  then  I can not claim to be using a
FM receiver.

   The  error here is that phase changes  are  equivalent  to  frequency
changes and the reverse.  If we were  to use a frequency detector in all
of the above statements, nothing would change!  We  could also apply the
mechanism that generates the doppler effect to just as easily  say  that
the phase is continuously changing at a rate that is proportional to the
velocity between a transmitter and a receiver.

>Any periodic function can be broken down into a series of sine waves, and the 
>periodic pulses coming from a "Doppler" direction finder are no exception. A 
>circular arrangement of discrete antennas will result in a series of pulses 
>with a strong sinusoidal component at the antenna rotation frequency. If you 
>pass these pulses through a very narrow filter centered at the frequency of 
>antenna rotation, you will get a nice clean sinusoidal waveform with zero 
>crossings corresponding to the points at which the pulses change in polarity 
>from positive to negative, or from negative to positive. So Dopplers work, but 
>they just ain't Dopplers.

   The  only  difference  when we use AC phase detectors with a discreet
antenna switching system is that the time constant of the phase detector
causes it's output to be a series of pulses.  The average value of these
pulses is proportional  to the phase change over the period of time that
you measure it.   If  the  time constant is long enough, then the output
from the detected signal from  the  circular  doppler  array  will  be a
stepped sine wave.  If the  time  constant  is  not long enough, then we
will have a series of pulses with the area under each pulse proportional
to the value of a sin wave at that point.

>So here I am again at the same spot I was at a little over a week ago, asking 
>the question: Are there any TRUE Doppler direction finders out there? If you 
>can point out any substantial errors in the above arguments or, if you hear of 
>a switched antenna system which actually uses the Doppler effect, I'd be 
>interested to hear from you. 

   I here ask for forgiveness if I have only confused this subject more.
------
Contradictions do not exist.  Whenever you think
that you are facing a contradiction, check your
premises.  You will find that one of them is wrong.
   - Francisco d'Anconia
---------------------------------------------------------------------------

From: stevew@netcom.com (Steve Wilson)
Subject: Some observerations
To: fox-list@netcom.com
Date: Fri, 29 Mar 1996 09:11:33 -0800 (PST)
Content-Length: 790       
Sender: owner-fox-list@netcom.com

Okay...I've been watching this "Is it a Doppler?   Is it not a Doppler?"
discussion going on for awhile now and I've kept  my mouth shut...(those
who know me should be truly amazed at that ;-)

I've got a couple of observations I'd like to add to the fire.

First...with all  these  arguements about hard-switched systems everyone
has ignored the  soft-switched systems like those available from Doppler
systems!  Their system  is  essentially  continuous!  Please explain how
this isn't a Doppler the  same way that the hard switched systems aren't
a Doppler.

Remember also that the main difference  between the Doppler Systems unit
and  a  Roanoke  is  this  antenna system.    The  basic  timing  chain,
filtering, and display are functionally the same!

Lucy...you've got some splainin to do!

Steve KA6S 
------------------------------------------------------------------------

Date: Wed, 27 Mar 1996 07:34:44 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: Charles Grant <grant@mailhost.hooked.net>
cc: fox-list@netcom.com, grant@hooked.net
Subject: Re: A Real Doppler
Sender: owner-fox-list@netcom.com

On Wed, 27 Mar 1996, Charles Grant wrote:

> On Tue, Mar 26, 1996 8:15:39 AM  at Charles Scharlau wrote:
>
> > Sorry, you've failed to prove your point. In what way are they the same
> if
> > one results in one pulse and the other results in a series of pulses??
>
> The moving antenna and FM descriminator result in a DC level output - not
> one pulse.  The pulse is an artifact of acceleration not relevant to this
> problem.

It may  not  be relative to any of my problems but it certainly pertains
to the problem  that  one faces in trying to rationalize the behavior of
pseudo-Dopplers.

> The system is already so idealized, there is no reason involve
> acceleration.

Say what?

> You must compare the steady state output of both systems.  Not the
> initialization
> of one system and the steady state output of the other.

Exactly right.  The  steady  state  of  one  system is a constant output
value,  assuming  an  FM  discriminator.     The  steady  state  of  the
pseudo-Doppler is a series of pulses.  Is the difference just imaginary?

> The switched antenna system and FM descriminator result in a series of
> pulses - ALL OF THE SAME VALUE  (unless of course you go to the unnecessary
> trouble of simulating some startup acceleration, then you would have a blip
> in
> the first few samples EXACTLY like the moving antenna when accelerating).
>
> A series of samples, all of the same value, is the sampled data domain
> equivalent
> of a DC signal in the continuous domain.  They are the same thing.  The
> same signal
> expressed in different domains.

Imagine taking one sample of ten  thousand  oscillations of the incoming
carrier signal, then quickly moving to another  sample  point and taking
another  sample  of  10,000  oscillations,  and  repeating.     This  is
essentially what a pseudo-Doppler does.  What kind of  sampled signal do
you get?  You get 10,000 oscillations at the carrier frequency, a sudden
phase  shift,  and another 10,000 oscillations at the carrier frequency.
Put this  signal  into  an  FM  discriminator  capable of locking onto a
signal pulse that is 10,000 oscillations long and see what comes out:  a
constant value, pulse due  to  detected  phase  step,  back  to original
constant value, pulse due to detected phase step, etc, etc.

Now imagine taking ten thousand  samples during every oscillation of the
incoming carrier signal.  You would  take a sample that is 1/10,000th of
a cycle, move quickly to the another  point and take another sample that
is  1/10,000th  of a cycle long.  This  is  essentially  what  a  "true"
Doppler using switched antennas would do.  What kind  of  sampled signal
do  you  get?   You get something that looks a  lot  like  the  original
carrier  signal,  but  with  10,000 tiny phase shifts inside each cycle.
The phase shifts either lengthen or shorten each cycle, depending on the
size  of  the  shifts.  Apply this sampled signal to an FM discriminator
capable of  locking  onto  a  continuous  signal at the frequency of the
sampled signal.   What  do  you  get?    A  constant  value from your FM
discriminator.  The constant  value  will be different from the constant
value obtained when receiving the unshifted carrier.  We've approximated
the Doppler effect.

You have two extremes of signal  sampling.   Each one gives results that
depend  on a different effect:  the  first  one  is  the  position-phase
effect,  the second the velocity-frequency effect.  The  Doppler  effect
and  the  equation S = fRw/c play absolutely no  roll  inexplaining  the
operation of pseudo-Dopplers.

There. Have we cleared up my misconceptions yet?

73,
Charles E. Scharlau
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam
------------------------------------------------------------------------

Date: Wed, 27 Mar 1996 15:28:26 -0800
To: Charles Scharlau <cscharl@eskimo.com>
From: grant@hooked.net (Chuck Grant)
Subject: Re: A Real Doppler
Cc: grant@hooked.net, fox-list@netcom.com
Sender: owner-fox-list@netcom.com

At 7:34 AM 3/27/96, Charles Scharlau wrote:

>Imagine taking one sample of ten thousand oscillations of the
>incoming carrier signal, then quickly moving to another sample point and
>taking another sample of 10,000 oscillations, and repeating. This is
>essentially what a pseudo-Doppler does. What kind of sampled signal do
>you get? You get 10,000 oscillations at the carrier frequency, a sudden
>phase shift, and another 10,000 oscillations at the carrier frequency. Put
>this signal into an FM discriminator capable of locking onto a signal
>pulse that is 10,000 oscillations long and see what comes out: a constant
>value, pulse due to detected phase step, back to original constant value,
>pulse due to detected phase step, etc, etc.
>
>Now imagine taking ten thousand samples during every oscillation of the
>incoming carrier signal. You would take a sample that is 1/10,000th of a
>cycle, move quickly to the another point and take another sample that is
>1/10,000th of a cycle long. This is essentially what a "true" Doppler
>using switched antennas would do. What kind of sampled signal do you get?
>You get something that looks a lot like the original carrier signal, but
>with 10,000 tiny phase shifts inside each cycle. The phase shifts either
>lengthen or shorten each cycle, depending on the size of the shifts. Apply
>this sampled signal to an FM discriminator capable of locking onto a
>continuous signal at the frequency of the sampled signal. What do you get?
>A constant value from your FM discriminator. The constant value will be
>different from the constant value obtained when receiving the unshifted
>carrier. We've approximated the Doppler effect.
>
>You have two extremes of signal sampling. Each one gives results that
>depend on a different effect: the first one is the position-phase effect,
>the second the velocity-frequency effect. The Doppler effect and the
>equation S = fRw/c play absolutely no roll inexplaining the operation of
>pseudo-Dopplers.
>

The position/phase effect and the velocity/frequency effect are the same
effect.  If you think the Doppler effect is only the  velocity/frequency
formulation and not  the  position/phase  formulation,  then (aside from
being wrong) this would  lead  you  believe  that  there is some kind of
fundamental difference between switched and  moving  antenna  Doppler DF
units.  This seems to be  your  basic misconception.  The position/phase
formulation  is  the  more  basic  formulation,  the  velocity/frequency
formulation is just the time derivative of the  position/phase  equation
in the continuous domain.  They are different forms of the same equation
and they are the same effect.

You  always have a valid position/phase formulation in either continuous
or sampled domains.

The velocity/frequency formulation  is  merely a convienient formulation
when  working  with simple  motions  in  the  continuous  domain.    The
velocity/ frequency formulation must be  expressed  differently  in  the
sampled data domain because continuous differentiation  is  not possible
in the sampled domain, that is only  a continuous domain operation.  You
must work with differences, summations, Z-transforms, DFTs, etc.

Any  first  year  course in digital signal processing  would  make  this
distinction  clear.    The  Doppler  DF units are exactly  sampled  data
versions  of  the  moving  antenna model.  The differential equation  is
modeled  with  a  difference  equation.  This point can not be  "proven"
unless you  have the mathematical background to understand operations in
the sampled data domain, and then it is quite simple.

>There. Have we cleared up my misconceptions yet?

I hope so.

But in your  examples  you  are still comparing apples and oranges which
probably adds to your  confusion.    This example is not two extremes of
sampling, they are two complely different systems.

In the first case, you  are  sampling  the discriminator output (and you
must do so).  What you  really  trying  to  do is sample the phase every
10,000 cycles, so an FM discriminator is  really  the wrong circuit, but
it will sort of work by giving a  pulse with a magnitude proportional to
the phase shift.  The only value that matters  is  a  single  number for
each sample.  That is why it is a sampled data system.  The shape of the
pulses  representing  the  samples, an artifact of using a particular FM
descriminator type of a particular bandwidth, is irrelevant.  If you had
a sample  and  hold circuit which held the peak value of the pulse, or a
low pass filter,  you would get the same signal output as the continuous
case, without changing the  discrete domain mathematics at all.  This is
the reconstruction filter, which is  necessary  to  transform  a sampled
signal into a continuous one.

In the second case as you  describe  it, you are not sampling the output
of the discriminator at all, you are  not  sampling  the  phase, you are
sampling  the  RF and then reconstructing a continuous  RF  signal  then
feeding it to a discriminator to determine the continuous  domain  phase
of the reconstructed signal.

However, if you were able to switch the antennas and  sample  the phase,
10,000  times  in  every  RF  cycle, you would get a sequence  of  phase
samples  which were the same as the phase samples taken every 10,000  RF
cycles, execpt  there  would  be 100,000,000 times as many samples.  But
there would be  no  fundamental  difference.  Both sets of samples would
describe the same DC  (for  the  linear antenna) or audio frequency (for
the round array) phase signal.    The  output  would  still  be a set of
samples and not a continuous signal,  unless some kind of reconstruction
filter was applied.  

There is no real difference.

Anyway I think this dead horse has probbly been kicked enough for now.

Chuck Grant, KE6CIL
------------------------------------------------------------------------

Date: Thu, 28 Mar 1996 18:53:32 -0800
To: fox-list@netcom.com
From: grant@hooked.net (Chuck Grant)
Subject: How to supercharge your Doppler
Sender: owner-fox-list@netcom.com

Well, I  don't  think there is any huge potential for making money here,
so I'll just  present  this  to the world so amyone can implement it and
vendors can even put  it  in  their  products.  I am planning on writing
this up for one of  the  ham  mags.    Until  that is done, please don't
publish anything about this without my permission.

Why do Dopplers work so poorly?   It seems that there is at least a 10db
loss between what it takes to hear  the signal and what it takes o get a
good direction out of the Doppler.  The  same  goes  for the >simple two
switched antenna "time-of-arrival" direction finder.

The problem is the type of switching waveform generated by the switching
circuit,  the  type  of  signal generated by the switched antenna  as  a
result of this switching waveform, and what kind of a signal an FM radio
expects for good performance.

1,  The  worst  switching  waveform to use is one where there is  a  gap
between the  "on"  periods  of adjacent antennas.  This is probably what
you have in your Doppler unless the switch was designed carefully.


 |-------|                                          |--------|
-|       |------------------------------------------|        |-------

            |--------|                                         |-----
------------|        |-----------------------------------------|

The FM descriminator  will  lose  the signal and be unable to detect any
phase shift if the  off  period  is longer than the settling time of the
tuned circuits in the IF strip of the radio.

2 If the switching waveform  has  no  gap  between  the  "on" pulses for
adajcent antennas, then there will be  a sharp phase shift at the moment
of switching, which will result in a  wide  bandwidth,  narrow  duration
pulse of frequency modulation.  Most of the bandwidth of this pulse will
be outside the bandpass of the radio, and thus  most  of the signal will
be lost.  The output of the FM radio will  be  rich  in harmonics of the
switching frequency.

The  bandwidth of the signal (out of the antenna) is controlled  by  how
fast  the  signal  diodes  in  the  antenna  array  can  switch which is
controlled by how fast the switching current is changed.

 |----------|                                       |----------|
-|          |---------------------------------------|          |-----

            |----------|                                       |-----
------------|          |---------------------------------------|


3,  If  the  on  pulses  overlap then there will be twice as many  phase
transitions (of half  the  magnitude) in the antenna signal.  The signal
will have half the  bandwitdh  and  twice  the energy at the fundamental
frequency.

 |-----------|                                      |-----------|
-|           |--------------------------------------|           |----

            |-----------|                                      |-----
------------|           |--------------------------------------|

This is a 3db improvement over the previous case, but most of the signal
is still outside the bandpass of  the  radio and most of the information
is still lost.  There is still a lot of harmonics in the audio output.

4, Instead of switching the antennas on  and  off  as fast as we can, we
can  slowly  change  the  switching  current so that  signals  from  the
adajcent antenna slowly transition from one to another.   This  gives  a
much  slower  phase transition, which results in a much lower  frequency
shift.  This will give a low bandwidth PM signal with most of the signal
within  the passband of the FM radio, and the result, interpreted as  an
FM  signal,  is  an  audio  signal  with  a  much  stronger  fundamental
component.

This assumes that  the  interaction  between  the  antennas is not major
effect.

     /-----\                                           /-----\        
    /       \                                         /       \     
   /         \                                       /         \    
  /           \                                     /           \   
-/             \-----------------------------------/             \----


               /-----\                                           /-----\      
              /       \                                         /       \     
             /         \                                       /         \    
            /           \                                     /           \   
-----------/             \-----------------------------------/             \--

5, Rounding out and overlapping our switching signals has now produced a
dramatic improvement in the signal  quality  from the antenna and out of
the FM radio.  The signals  now are very similar to those that you would
get with a single rotating antenna.   It is a small step from this point
to see that the optimum switching waveforms, which  would  give the SAME
signals  as  the  rotating antenna, with ALL the signal  energy  at  the
fundamental  frequency,  would  be  where  the transfer functions of the
antenna  switches  were  properly  phased  half  wave  sine  pulses  (in
quadrature for the four antenna case).

Since the  diode switches commonly used are very non-linear with respect
to switching current vs.  AC resistance, the switching current waveforms
are not sine functions,  but  must  be  compensated so that the transfer
functions  are  sine functions.   However,  anything  close  to  a  sine
function is probably pretty good, and  vastly  better  than the old way,
especially if a narrow bandpass audio filter is used.

This scheme can be considerend an analog  approximation  of the rotating
antenna Doppler.  The signal of the rotating  antenna  is  simulated  by
using weighted combinations of signals from fixed antennas, and changing
the weighting in a smooth continuous way so that the  effective location
of the antenna moves in a smooth circle.

This scheme can also be considered a refinement of the sampled, switched
antenna Doppler, where  the  antenna switching characteristics have been
optimized for use with  an  FM  radio.    This would be the antialiasing
prefilter in a sampled data system.

This technique can be used  with  existing  switched antenna Dopplers by
building  an  outboard switching waveform controller.    The  controller
would  use  the  Doppler's  antenna switch outputs  to  phase  lock  the
waveform generators.  The output of the waveform generators is then used
to  swtich/blend  the antenna signals.  No modification in  the  Doppler
logic is required, although you may have to turn down  the  audio  gain,
since you will have a much stronger signal now.  Something  as simple as
a  quad  op-amp  with  a  few  resistors and capacitors to generate four
overlapped trapazoidal  current  waveforms  (such as #4) will give you a
big improvement over rapid switching.

Good luck Dopplering...

Chuck Grant, KE6CIL

PS.  I  guess  this  would  make  it  a "true Doppler" now by just about
anyone's definition.  :-)

------------------------------------------------------------------------

Date: 30 Mar 96 02:09:58 EST
From: Joe Moell <75236.2165@compuserve.com>
To: Fox-list <fox-list@netcom.com>
Subject: Respectful disagreement with K6BMG
Sender: owner-fox-list@netcom.com

I  submitted  this  message  to the list  on  3/22  and  looks  like  it
evaporated, so here goes again.  This list  is  less  reliable  than ten
meters!

==========SNIP=============

A RESPECTFUL REBUTTAL TO RUSS'S RECENT WRITINGS

My recent post "defending" the Roanoke and other ring-of-whips  RDF sets
as "true dopplers" puts me at odds with two recent  scholarly  posts  by
Russ K6BMG.  First I must say that I have the  highest  regard  for Russ
and  his work.  The SuperDF is by far the best dual-antenna  phase-front
RDF  set of the half dozen or so that I have tested.   It's  synchronous
detector does indeed  give it superior sensitvity and rejection of other
modulation on the T's  signal.    (Whether  it's better than a 4-element
quad for RDF on two meters is a debate for another time.)  

However, when K6BMG says that  his  patented  processing techniques give
the SuperDF many times better sensitivity  than  a doppler set, and that
ham  doppler sets don't follow the doppler  equations  and  thus  aren't
"true dopplers," I have to respectfully disagree.  

K6BMG describes doppler RDF processing by explaining how  a SuperDF does
processing   and  he  compares  the  response  of  receiver  IF's    and
discriminators  to  the switched antenna outputs of the two as  if  they
were the same.  But the filtering and data extraction techniques  of the
two are quite dissimilar and must be considered separately.  He writes:

<<SuperDF opens  its ears just long enough (40 microseconds) to hear the
PEAK of that  pulse.   That is where the DF information is.  Most of the
rest  of  the time  the  stuff  coming  out  of  the  radio  has  no  DF
information.  It is noise!  40/1250 = 0.032 (3.2%) is the listening duty
cycle.  That's a dramatic improvement in signal to noise ratio!>>

Agreed.   The time-domain filter in the SuperDF is what makes it  better
than other dual-antenna units.  But then he says:

<<The Doppler does not do this.    It listens ALL the time and hears ALL
the noise.>>

Whoa!  K6BMG acknowledges the presence of the doppler's narrow filter in
a later paragraph  but  ignores  its function here.  The reason that the
SuperDF commutating filter is  useful  is that it rejects wideband noise
and voice/tone/whatever modulation on the  received  signal.  Fine.  But
the narrow-band filter in the doppler achieves exactly the same result.

K6BMG explains the SuperDF's filter operation  in the time domain.  It's
easier to understand the doppler filter's function  by  looking  in  the
frequency domain.  The receiver's discriminator output contains a signal
that  represents  the  doppler-induced  frequency  modulation  from  the
antenna.   We  use  the  phase  of  this  "doppler  tone" to extract the
bearing.  The  discriminator  output  also  contains the noise and other
modulation on the target  signal.    Audio frequency response out of the
discriminator goes from below 50  Hz (so CTCSS can be detected) to above
5 KHz (so the noise-operated squelch  circuit  will work).  The receiver
filters much of this, so the speaker  output  (which goes to the doppler
processor) response ranges from 200 Hz to 3KHz  or  so.  Then a low-pass
filter  in  the  doppler unit further limits the range,  followed  by  a
narrow synchronous filter that limits audio bandwidth to as low  as 2 Hz
(a practical compromise between noise/modulation rejection and indicator
settling time).  The result is a sine wave at the bandpass filter output
with just the DF information  we  want  (relative  phase)  on  it.   The
reduction in audio bandwidth to 0.044%  (5KHz  to  2 Hz) is much greater
than  the reduction of duty cycle to  3.2%  in  the  SuperDF.    So  the
processing method does NOT force a doppler to have inferior sensitivity.
Quite the contrary.

<<Even if you were to apply this  technique  to  a Doppler you would not
reach  the  same sensitivity because of the inherent  synchronous  noise
made by the commutating capacitor filter (the narrow band filter) of the
Doppler.>>

The  SuperDF has a commutating filter, too.  Doesn't  it  have  its  own
noise  floor,  based  on  the noise specs of the audio  switching  IC's?
Isn't that one reason why there is a "dithering" circuit in the SuperDF?

<<SuperDF is able to hear and DF signals that are 20 dB BELOW the noise!
This is VERY much more sensitive than the Doppler.  >>

I don't usually try to use my doppler to track signals I can't hear.  (I
prefer  a  quad and GaAsFET preamp for weak signal work).  But  from  my
correspondence,  I know  there  are  some  experienced  hams  that  will
disagree with the contention that SuperDF is "VERY much more sensitive."
They tell me a doppler  display  also gives reliable bearings on signals
whose voice modulation cannot be understood.    This  is especially true
with the new Roanoke Doppler antenna system,  which  puts  far  less  RF
switching hash into the receiver than the original  antenna switcher.  I
hope these folks will speak out for themselves.   (How  about  it, Jerry
and Tom?)

Now on to the claim that doppler sets don't follow S = (R*W*Fc)/C, which
predicts the peak FM deviation induced by a rotating doppler whip  array
on incoming RF signals.  K6BMG writes:

<<t  doesn't  respond to changes in the switching speed by changing  the
"apparent Doppler  shift."  Hummm.   A "Doppler RDF" that doesn't change
its Doppler shift  when  you  speed it up.  Strange!  ...  The "Doppler"
doesn't act like a  real Doppler and it does not follow the equation for
calculating  Doppler  shift,  therefore,  I    say  that  it  is  not  a
Doppler....For  the practical switched antenna Doppler,  increasing  the
spin frequency does not (by itself) make  a  bigger  RDF  signal.    The
reason  is  the switched Doppler really is making  phase  steps  in  the
incoming signal, and these phase steps are the SAME  SIZE (in electrical
degrees) no matter what the spin frequency.>>

Well, I had to mull that over for a bit.  Then  I realized that K6BMG is
describing the discriminator  output  in terms of Phase Modulation (PM),
whereas S = (R*W*Fc)/C  gives  Frequency  Modulation (FM) deviation.  FM
and  PM are similar forms  of  angular  modulation,  but  they  are  not
identical.  As the latest ARRL  Handbook  says  on  page  15.10,  "An FM
signal deviates according to the amplitude of  its  modulating waveform,
independely  of  the  modulating waveform's frequency;  the  higher  the
modulating  wave's  amplitude  the greater the deviation.  A  PM  signal
deviates  according  to  the  amplitude  and frequency of its modulating
waveform;   the higher the modulating wave's amplitude and/or frequency,
the greater the deviation."

A quick bit  of  history:  Before modern direct-FM modulating techniques
were developed, VHF-FM transmitters used to have an oscillator, followed
by a phase modulator, then  followed  by  several  frequency multiplying
stages.  Armstrong developed this "indirect"  method  of producing FM in
1936.  It was the basis of  the  "serrasoid modulation" scheme that gave
me a lot of grief in the transmitter  of  an FM broadcast station that I
worked for in college.  The indirect method varies  the  phase of the RF
signal,  not  the  frequency.  However, by integrating the audio  to  be
transmitted  (i.e.  putting it through the 6 dB per octave  slope  of  a
low-pass  filter beyond Fc) prior to applying it to the phase modulation
stage, the transmitter's output becomes indistinguishable from that of a
true-FM transmitter.

So as the switched  doppler  antenna  "rotates"  around,  it does indeed
produce  discrete  phase  jumps,  and  this  can  be  thought  of  as  a
phase-modulation process, as K6BMG does.   If  we  double  the switching
speed, the phase delta and thus the  voltage  delta in the discriminator
output does indeed remain the same for each jump in a cycle of rotation.
All that means is that the PM level on  the signal has not changed.  But
since  we  have  doubled  the  rotation frequency and hence doubled  the
frequency of all tone components coming out of the discriminator, the FM
signal  being detected does indeed have twice the deviation, because the
frequency deviation of a phase-modulated signal is directly proportional
to the frequency of the audio signal.  

Voila!  The  doppler  equation  is indeed being followed!  It is a "true
doppler" RDF set after all.

73 de Joe K0OV
Homingin@aol.com
------------------------------------------------------------------------

Date: Mon, 1 Apr 1996 07:54:27 -0800 (PST)
From: Charles Scharlau <cscharl@eskimo.com>
To: Steve Wilson <stevew@netcom.com>
cc: fox-list@netcom.com
Subject: Re: Some observerations
Sender: owner-fox-list@netcom.com

On Fri, 29 Mar 1996, Steve Wilson wrote:

> Okay...I've been watching this "Is it a Doppler? Is it
> not a Doppler?" discussion going on for awhile now and
> I've kept my mouth shut...(those who know me should be
> truly amazed at that ;-)
>
> I've got a couple of observations I'd like to add to the fire.
>
> First...with all these arguements about hard-switched systems
> everyone has ignored the soft-switched systems like those
> available from Doppler systems!  Their system is essentially
> continuous!  Please explain how this isn't a Doppler the
> same way that the hard switched systems aren't a Doppler.
>
> Remember also that the main difference between the Doppler Systems
> unit and a Roanoke is this antenna system.  The basic timing chain,
> filtering, and display are functionally the same!
>
> Lucy...you've got some splainin to do!
>
> Steve KA6S
>

Steve,

Actually I think it is Doppler systems that has some explaining to do.

Keep in mind, I'm not saying that pseudo-Dopplers don't work.    I'm not
saying that a true Doppler would work any better.

I  do  not  own  a  Doppler Systems DF antenna, nor have  I  examined  a
schematic,  nor  have  I  read their literature.  The most I've done  is
explore a partially  disected  Doppler  Systems  controller.  So I can't
speak with authority on  just  what  principle they use.  However, I can
speak to the physics of the problem.

The "soft" switching you are  talking  about  is  not, in principle, any
different from a hard switch.   You  are  going  from one antenna to the
next with no antennas in between.   You  can't get away from the physics
of the the problem just by making your  transition  from  one antenna to
the next more gradual.

I  understand  that the so called "soft" switching results  in  improved
accuracy,  though  at this point I haven't heard a coherent  explanation
for  the  improvement.    It is pretty safe to say, however,  that  such
improvement is NOT because a soft-switched system more closely resembles
a true Doppler.

Doppler Systems DFers usually seem to have four antennas.  (I don't have
a Doppler Systems catalog,  so  perhaps  some of their systems have more
than four antennas.) To sample  at  the  Nyquist rate with four antennas
will  require that the simulated rotation  rate  be  approximately  36.5
million rotations per second.  So unless you hear a 36.5 MHz tone coming
from  your  radio  when  your  four-antenna Doppler Systems  antenna  is
connected to it, it probably is not operating on the Doppler principle.

Doesn't anyone from Doppler Systems subscribe to this list?   Can we get
an explanation from the horse's mouth?  Anyone there named Lucy?

73,
Charles E. Scharlau
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam
------------------------------------------------------------------------

Date: Mon, 1 Apr 1996 08:36:40 -0800 (PST)
From: stevew@netcom.com (Steve Wilson)
Subject: Re: Some observerations
To: fox-list@netcom.com

> 
> On Fri, 29 Mar 1996, Steve Wilson wrote:
> 
> Steve,
> 
> Actually I think it is Doppler systems that has some explaining to do.
> 
> Keep in mind, I'm not saying that pseudo-Dopplers don't work. I'm not
> saying that a true Doppler would work any better.
> 
> I do not own a Doppler Systems DF antenna, nor have I examined a
> schematic, nor have I read their literature. The most I've done is
> explore a partially disected Doppler Systems controller. So I can't speak
> with authority on just what principle they use. However, I can speak to
> the physics of the problem.

Uhm...I've  got  schematics and a technical article from the early  80's
describing  how  the  system  works.  First, there opinion would suggest
they believe it is a true doppler.

As I  said  in  my  post,  the  timing  chain and filters are similar in
function to the  Roanoke,  so  they  don't  bear  any  examination.  The
"patented" part of the  Doppler  Systems  unit  is  the antenna rotation
scheme.  The article describes  a  system  for  generating  a quadrature
modulation system where 4 sinusoids generated  90  degrees out of phase.
These modulation signals are fed to variable gain amplifiers attached to
the antennas.  So, for a good part of the time, more than one antenna is
on.

The basic "improvement" over the hard switching design is  the  lack  of
square wave modulation!  You get rid of all those  nasty  harmonics into
the  receiver  this  way,  and thus alot of the Roanoke Doppler's  cross
modulation  problems.    It  is  said  to give you the sensitivity of  a
dipole(getting rid of the 10db figure people have been tossing around..)
I  believe  that   there  have  been  significant  improvements  in  the
system...now they actually have gain better than a dipole...  

> The "soft" switching you are talking about is not, in principle, any
> different from a hard switch. You are going from one antenna to the next
> with no antennas in between. You can't get away from the physics of the
> the problem just by making your transition from one antenna to the next
> more gradual.
> 
> I understand that the so called "soft" switching results in improved
> accuracy, though at this point I haven't heard a coherent explanation for

Actually, no...it improves the system noise figure significantly.

> the improvement. It is pretty safe to say, however, that such improvement
> is NOT because a soft-switched system more closely resembles a true
> Doppler.
 
Well, here we differ..I'm  of  the opinion that all of these systems ARE
true dopplers.

> Doppler Systems DFers usually seem to have four antennas. (I don't have a
> Doppler Systems catalog, so perhaps some of their systems have more than
> four antennas.) To sample at the Nyquist rate with four antennas will
> require that the simulated rotation rate be approximately 36.5 million
> rotations per second.

WHAT!?!  No!  The  rotation rate of these systems is usually in the area
of  500  rotations/sec.    corresponding  to    an  area  of  reasonable
performance within the audio pass-band of the  radio.  Nyquist says 1000
samples  per  second  minimum....usually it is considerably better  than
this...  like 1000 samples per cycle!  (Depends on the filter design...)

The act of rotating the antenna is what creates  the  modulation  we are
trying to detect(whether roanoke or DF systems or single antenna  moving
in  a  circle.)  There is NO correlation to the received frequency(where
DID  you  come  up with 36.5 million rotations per second???) Except for
some reality  details within the Roanoke system(how I turn the antenna's
off), these systems are receive frequency independent.  Note:  there are
antenna systems that ARE  frequency  independent  available...it is just
that the Roanoke system depends  on  a  1/4  wavelength  to put the feed
point of the antenna into infinite impedence.

> So unless you hear a 36.5 MHz tone coming from your
> radio when your four-antenna Doppler Systems antenna is connected to it,
> it probably is not operating on the Doppler principle.

So, until you understand the above (HOW we are creating  the  modulation
we are trying to detect..) you don't understand nor can argue  correctly
about whether it is a "true" doppler or not.

Steve KA6S
------------------------------------------------------------------------

Date: 06 Apr 96 01:22:19 EST
From: Joe Moell <75236.2165@compuserve.com>
To: Charles Scharlau <cscharl@eskimo.com>, Fox-list <fox-list@netcom.com>
Subject: Re: A respectful disagreement with Joe
Sender: owner-fox-list@netcom.com

Charles Scharlau, INTERNET:cscharl@eskimo.com wrote:
<<A RESPECTFUL DISAGREEMENT WITH JOE MOELL>>
<<There are  two  periods  that  are of interest in the switched antenna
system you are  discussing:   The time we spend completing a switch from
one antenna to the  next,  and  the time that we spend connected to each
antenna.  All simulated movement  occurs during the former, wouldn't you
agree?  The time we spend  sitting at each antenna simulates a period of
no motion.>>

No,  the  COMBINATION  of both the jumps  and  plateaus  (switching  and
sitting times) simulates the motion.  Try this  analogy:  When you watch
a movie, you are seeing a series of still  photos  (frames)  which  snap
from one to another with rapid transitions.  Using your  logic, it would
be  correct  to  say,  "All  the  simulated  movement  occurs during the
transition  time  and  the  time spent setting on each frame simulates a
period of no motion."

In  reality,  of  course,  that  is  incorrect.    It  is  actually  the
COMBINATION of transitions and still frames that the viewer perceives as
smooth motion.  The  eye and brain act as a filter much as the filtering
in the doppler processor.   If  you eliminate either the still frames or
the transitions, the simulation of smooth  motion on the screen will not
occur.

<<In pseudo-Dopplers the amount of time spent  switching is on the order
of  10  microseconds  per  "rotation"  of  the  antenna  (assuming  a  1
microsecond  between-antenna switch period, and eight antennas).  If  we
cut this time in half...>>

Stop!  Are you referring to something in my post?   When I wrote, "If we
double  the  switching  speed..."  I  was  not referring to doubling the
transition rate  (e.g.  going from 1 uS between-antenna switching period
to 0.5 uS).    I  meant  doubling the overall rotation rate (e.g.  going
from 500 revs per  second  to  1000  revs  per second) while keeping the
number of whips the same.  That's also what K6BMG was talking about when
he wrote the following:

<<Now  lets do this same thought  experiment,  but  double  the  antenna
switching rate.  What happens?  The  'scope  shows the exact same output
voltage  pulse,  0.100  volts  peak,  but  occurring  twice   as  often.
[remainder deleted for brevity]>>

And that is what I was responding to when  I  wrote  my  message.  I was
pointing  out  that  the same voltage at twice the frequency  out  of  a
discriminator  does    indeed  represent  twice  the  FM  deviation,  in
accordance with both FM modulation theory and the true doppler equation.
But anyway, back to your interpretation.  You said:

<<...If we cut this  [transition]  time  in  half the rotation rate of a
pseudo-Doppler "rotating" at 500 Hz will appear to rotate at 501 Hz.>>

Yes.    If there are  8  antennas,  there  will  be  8  transitions  per
revolution times 1 uS per transition  = 8 uS total transition time.  The
revolution  rate  is 500 Hz, giving 2000  uS  total  time  per  complete
revolution,  including  all  transition  time,  no matter how  long  the
transition times are.  The total "sitting" time is  2000  - 8 = 1992 uS.
You want to cut the transition time in half without changing the sitting
time.  That will make the total revolution time 1992 uS  setting  + 4 uS
transitions = 1996 uS, corresponding to 501 revs/second.

Fine,  but  keep  in  mind that the only way to achieve this  end  in  a
practical clock-controlled doppler is  to  somehow sharpen the rise/fall
times (which are determined primarily  by  the  characteristics  of  the
driver ICs and stray inductance/capacitance in  a hard-switched doppler)
while simultaneously raising the clock frequency to get 501 rev/sec.

<<The frequency of all tone components coming  out  of the discriminator
has doubled, as you say, but our rotation  rate  has  scarcely  changed.
Strange.>>

No,  I  said the frequency components would double if  you  doubled  the
number of revs/second.  But if you just raise the  revs/second  from 500
to  501,  the  predominant  frequency component out of the discriminator
will change  from  500 Hz to 501 Hz.  (That's the doppler whine you hear
in the receiver  speaker.)  The higher (in frequency) Fourier components
(harmonics) will change from  being  centered  around  1  MHz  to  being
centered around 2 MHz (the  recriprocal  of  the  transition  time pulse
width).  The higher order stuff  is  quite  unimportant, however.  It is
weaker  than the fundamental to begin with  and  is  eliminated  by  the
receiver audio stages and the doppler filter.  The phase detector in the
doppler  processor (the stage that determines incoming signal direction)
receives a nice sine wave at 500 (or 501) Hz from the filters.

One  can  calculate  the  levels  of  the  discriminator  output Fourier
spectral  components  using  sinc  factors,  but  I'll  leave that as an
"exercise for the reader."

73 de Joe K0OV
------------------------------------------------------------------------

Date: Mon, 8 Apr 1996 08:13:04 -0700 (PDT)
From: Charles Scharlau <cscharl@eskimo.com>
To: Joe Moell <75236.2165@compuserve.com>
cc: fox-list <fox-list@netcom.com>
Subject: A Dopplerian Thank You
Sender: owner-fox-list@netcom.com

Dear Joe Moell and all Doppler Discussers,

I just want to thank you for your thoughtful reply to my  remarks.    It
was kind of you to take the time to compose your response.  I owe a debt
of  thanks  to  you  and to all the 20+ people who have responded to  my
queries and comments,  with  70+  replies.   I have learned a great deal
through these discussions.

It appears to me that the is-a-Doppler and the aint-a-Doppler crowds are
in  complete  agreement on most  aspects  of  Doppler  direction  finder
operation.  The points of contention  seem  to  be more pedagogical than
technical.

It  has  become  plain  that  pseudo-Doppler  operation   can  be  shown
mathematically to provide an audio signal which approximates  what would
be  obtained from an FM receiver connected to a  single  antenna  moving
continuously about a circle.  The way a pseudo-Doppler accomplishes this
is indirect;  that is, through the integration of discrete phase shifts,
rather  than  by direct FM detection of a frequency-varying carrier.  To
the engineer,  who  is accustomed to thinking in the frequency domain as
easily as in  the  time  domain,  this  is  no  big distinction.  To the
neophyte attempting to comprehend  the  inner workings of these devices,
it can be a stumbling block.

A time domain (i.e., phase  shift  due to position) explanation would be
less mathematical, but no less correct.    Many  who  have written to me
have  made  this  point,  even if they  prefer  to  call  these  devices
"Dopplers".

Regarding the name:  many folks I've heard  from  place  a great deal of
importance  on  the  name.   "Doppler" and "pseudo-Doppler" both  elicit
emotional   responses  from  certain  individuals.    May  I  suggest  a
compromise?   How  about  calling the common devices "Phase Dopplers?" A
"Frequency Doppler" would then be either a single antenna moving through
space, or a switched  Doppler  system  which samples at greater than the
Nyquist rate.  Just a thought.

Thank you Joe, for all  you have brought to the art and science of radio
direction  finding;  and a big  THANK  YOU  to  everyone  else  who  has
educated me on this topic.

73,
Charles E. Scharlau
E-mail:     cscharl@eskimo.com
Telephones: Office 206-771-2182 ext 134
            Fax    206-771-2650
            Home   206-353-9277
Packet:     nz0i@n7oqn.#nwwa.wa.usa.noam
------------------------------------------------------------------------

Date: 10 Apr 96 01:52:29 EDT
From: Joe Moell <75236.2165@compuserve.com>
To: Fox-list <fox-list@netcom.com>
Subject: Hard vs. Soft Switching
Sender: owner-fox-list@netcom.com

Well, it happened again.  I sent  a  message  to  the list and it hasn't
shown up after a week.  I'm trying  again,  not  to  beat a dead doppler
horse but to encourage y'all to share your experiences:

grant@hooked.net (Chuck Grant) wrote:
<<Instead of switching the antennas on and off as fast as we can, we can
slowly  change  the switching current so that signals from the  adajcent
antenna slowly transition from one to another.  >>

Just  like  Doppler  Systems  has  been  doing  for 15 years.   See  "DF
Breakthrough" in 73 Magazine for June 1981.

<<Well, I don't think there is any huge potential for making money here>>

Dave Cunningham of Doppler Systems has been doing OK.  :-)

<<I am planning on writing this up for one of the ham  mags.  Until that
is  done,  please    don't   publish  anything  about  this  without  my
permission.>>

Before you publish, please read the above-mentioned article and US Patent
4,041,496.

This  topic seems to  come  up  regularly.    Over  the  years,  I  have
corresponded  with  several  hams  who    have    experimented  and  are
experimenting with various ways to "soften"  doppler  antenna  switching
waveshapes.  What's interesting is that when  all is said and done, most
people tell me the effort doesn't seem to  make  a  big  improvement  on
practical mobile dopplers!  

If you agree that a 2 Hz bandwidth filter  synchronized  with  the  whip
rotation  rate  will  eliminate  all higher-order terms in the piecewise
representation  of  the  doppler  antenna  rotation by a small number of
whips, then the only thing that should keep a hard-switched doppler from
performing  as well as a soft-switched doppler is RF noise caused by the
rise-fall times of  the switching logic waveforms.  (i.e.  if you switch
hard enough, the circuit  puts  out  hash  at  two  meters.) That can be
minimized by small R-C or L-C filters on the logic lines far more easily
(circuit-wise) than the method suggested by  Chuck  and  used by Doppler
Systems.

So here is a call for regular  doppler  users  to give us the benefit of
your experiences.  I'd like to hear from  T-hunters  who have experience
with  BOTH  the  Doppler  Systems  soft-switched  doppler  and  a   good
hard-switched  model  such  as  the  Roanoke  Doppler  with  new 8-diode
switcher (which is definitely less noisy than the switcher in the book).
How  about  A/B  comparisons on weak signals and signals in multipath to
see which system is better, how much better, or even if a difference can
be determined.

No theories, please, just hard data from real hunts.

73 de Joe K0OV
Homingin@aol.com
------------------------------------------------------------------------

Date: Tue, 16 Apr 1996 01:24:27 -0700
To: Joe Moell <75236.2165@compuserve.com>
From: grant@hooked.net (Chuck Grant)
Subject: Re: Hard vs. Soft Switching
Cc: Fox-list <fox-list@netcom.com>, grant@hooked.net
Sender: owner-fox-list@netcom.com

Sent April 16 -- let's see how long this one takes to get through the fox-list.

At 1:52 AM 4/10/96, Joe Moell wrote:
>Well, it happened again.  I sent a message to the list and it hasn't shown up
>after a week.  I'm trying again, not to beat a dead doppler horse but to
>encourage y'all to share your experiences:
>
>grant@hooked.net (Chuck Grant) wrote:
><<Instead of switching the antennas on and off as fast as we can, we can slowly
>change the switching current so that signals from the adajcent antenna slowly
>transition from one to another.  >>
>
>Just like Doppler Systems has been doing for 15 years.  See "DF Breakthrough" in
>73 Magazine for June 1981.

I don't claim to be the first one to think it up.  I don't even mean to
claim that it isn't common knowledge to those in the field.  I just claim
that I thought it up myself.

><<Well, I don't think there is any huge potential for making money here>>
>
>Dave Cunningham of Doppler Systems has been doing OK.  :-)

Your comment supports my analysis.
One guy running a  small business is not my idea of a huge potential for
making money.  The entire  world  market for Dopplers isn't even near my
idea of a huge potential for  making money, and this market is currently
cut up between several very small manufacturers (and this is soon to get
much worse).  So I don't mind giving  away  any  ideas I may have on the
subject since they will not make me rich.

Thank  you  for  the  information  on the patent and  the  name  of  the
engineer.  I had been looking for the patent or  patent number, based on
rumors, without luck so far.  If this thing was patented  in  1981, then
it will expire in just a couple of years and it's open  season  for  the
other manufacturers.  Maybe I have two years to prepare an article to be
released at a timely moment.

>This topic seems to come up regularly.  Over the years, I have corresponded with
>several hams who have experimented and are experimenting with various ways to
>"soften" doppler antenna switching waveshapes.  What's interesting is that when
>all is said and done, most people tell me the effort doesn't seem to make a big
>improvement on practical mobile dopplers!  

I'm  sure  it  depends  on  how well the switching was done in the first
place.  I have  been  involved in modifying three different Dopplers and
the results were variable.   However  in one case there was about a 10db
improvement  and  we  haven't went the  whole  way  to  the  sine/cosine
transfer function yet.  I think the  most  important  thing  to note is:
just don't design your switcher in the absolutely worst way and you will
get most of the performance possible.  So it is useful to know:  what is
the absolutely worst way.

>If you agree that a 2 Hz bandwidth filter synchronized with the whip rotation
>rate will eliminate all higher-order terms in the piecewise representation of
>the doppler antenna rotation by a small number of whips, then the only thing
>that should keep a hard-switched doppler from performing as well as a
>soft-switched doppler is RF noise caused by the rise-fall times of the switching
>logic waveforms.  (i.e. if you switch hard enough, the circuit puts out hash at
>two meters.)  That can be minimized by small R-C or L-C filters on the logic
>lines far more easily (circuit-wise) than the method suggested by Chuck and used
>by Doppler Systems.

No this is not true.  Reduced RF noise from  the  switching circuitry is
not  the  only  reason  for improved performance, even with using a  2Hz
bandwidth audio filter (Although RF switching noise can be a significant
problem.) The  soft  switching, by smoothly changing the phase of the RF
signal  between  antennas,  provides  more  energy  at  the  fundamental
switching  frequency and less  energy  at  harmonics  of  the  switching
frequency (measured either in the  RF  sidebands or in the descriminator
audio output).  The result is  that  the audio signal at the fundamental
frequency going into the audio filter is louder, and thus, with the same
amount of background noise, has a higher signal  to noise ratio, even if
we assume there is no RF switching noise in  either case.  A narrow band
audio  filter  improves  the S/N ratio in both cases by  reducing  noise
outside the passband, but the final S/N ratio for a soft  switched, weak
signal after the filter is better than the S/N ratio of a hard switched,
weak  signal  after  the audio filter.  Of course the difference is only
with weak signals, which are the only interesting signals anyway.

>So here is a call for regular doppler users to give us the benefit of your
>experiences.  I'd like to hear from T-hunters who have experience with BOTH the
>Doppler Systems soft-switched doppler and a good hard-switched model such as the
>Roanoke Doppler with new 8-diode switcher (which is definitely less noisy than
>the switcher in the book).  How about A/B comparisons on weak signals and
>signals in multipath to see which system is better, how much better, or even if
>a difference can be determined.
>
>No theories, please, just hard data from real hunts.

One needs  both  theory and experiment to form a complete understanding.
I build equipment  which  I  use in real hunts.  I wouldn't know that to
try to build if  I  didn't  theorize and test.  To get around one of the
biggest problems with Dopplers, multipath,  I  am  currently designing a
system which should be able to  identify the directions and strengths of
several signals on the same frequency, say  a direct signal and a couple
of reflections, at the same time, with no  moving  parts  and no antenna
switching, hard or soft.  If this works, I'll probably spill the details
here for the same reason, the DF market is probably  not large enough to
support a reasonable sized business.

Oh,  here  is another free tip for Doppler builders and hopeful  Doppler
builders.  You can get a fairly reasonable measure of how much multipath
you  are  receiving  by measuring the strength of the second harmonic of
the switching frequency out of the descriminator.  This works quite well
in the field  (ie.    tested  in  real  T-hunts)  as a direction quality
indicator.    Also, 8-antenna  arrays  seem  to  be  more  sensitive  to
multipath than 4-antenna arrays, but  it  varies  a lot depending on the
exact  configuration  and  situation.   Being  able  to  switch  between
8-antenna and 4-antenna modes is probably best.

Happy hunting,

Chuck
------------------------------------------------------------------------

Date: Tue, 16 Apr 1996 14:52:17 -0700
To: Joe Moell <75236.2165@compuserve.com>
From: grant@hooked.net (Chuck Grant)
Subject: Re: Hard vs. Soft Switching
Cc: Fox-list <fox-list@netcom.com>, mike@documentum.com
Sender: owner-fox-list@netcom.com

BTW.  US Patent 4,041,496 granted in 1977 is now expired. US patents
are good for 17 years.  I'll probably post the interesting parts to
the list.

Chuck
------------------------------------------------------------------------

Date: 20 Apr 96 00:22:45 EDT
From: Joe Moell <75236.2165@CompuServe.COM>
To: Chuck Grant <grant@hooked.net>
Cc: Fox-list <fox-list@netcom.com>
Subject: Re: Hard vs. Soft Switching
Sender: owner-fox-list@netcom.com

(sent direct 4/19/96, with copy to the list)

Hope you didn't think I was being too hard on you.  You wrote:
<<I don't  claim to be the first one to think it [soft switching] up.  I
don't even mean  to claim that it isn't common knowledge to those in the
field.  I just claim that I thought it up myself.>>

Fine, but you also  wrote:  "I am planning on writing this up for one of
the ham mags.  Until  that  is done, please don't publish anything about
this without my permission."  

That implied that you thought you  had an "exclusive." I just wanted you
to be aware of the "prior art."

<<One guy running a small business is  not  my  idea of a huge potential
for making money.  The entire world market  for Dopplers isn't even near
my  idea  of  a  huge potential for making money,  and  this  market  is
currently cut up between several very small manufacturers...>>

Don't  forget  the  military  and  "spook"  market.  Big companies  like
Watkins-Johnson  have  added to their financial bottom line with doppler
technology and created quite a few jobs.  But I don't know if anyone got
rich.  :-)

<<One  needs  both    theory    and    experiment  to  form  a  complete
understanding.>>

Of course.  I like a good theoretical discussion as well as anyone.  But
I think the recent debate  has  "scared  off" some list members who have
useful doppler experiences to tell.   I  would  like  them  to  speak up
without  feeling  that they must have a  theoretical  justification  for
their observations.

<<just don't design your switcher in the absolutely  worst  way  and you
will get most of the performance possible.  So  it  is  useful  to know:
what is the absolutely worst way.>>

So what do you think is the absolute worst way?  

I  believe that a hard-switched doppler with enough logic-line filtering
to  prevent  VHF noise will give RDF performance in the same  league  as
Doppler Systems soft-switching equipment,  maybe better.  That's because
I believe that mutual RF coupling in the array is the biggest limitation
to a practical doppler's performance, not hard-vs-soft switching.

As I  showed  in  my  Homing  In  column for April 1995, mutual coupling
between the individual  whips  causes variations in the amplitudes of RF
outputs from the whips  as  pseudorotation  takes  place.   Some of this
imposed  periodic  AM on the  incoming  signal  is  converted  to  PM/FM
variations in the nonlinear stages of  the  receiver (e.g.  the limiting
stages of the IF chain) and is  detected  along with the desired doppler
tone.  The deleterious effect is greatest on weak signals and signals in
multipath, which you stated are "the only interesting signals anyway."

To minimize these  AM  fluctuations, switched-off whips must "look into"
an open circuit at  their  bases.  The must NOT be shorted to the ground
plane and NOT loaded with  50 ohms if minimum AM is to be achieved.  The
difference can be over 10 dB!    Roanoke PIN switchers (both new and old
versions) provide an open circuit, either with  a  PIN diode at the whip
base in the case of the new switching  system  or  a  quarter-wavelength
coax transformer between the base and the shorting PIN diode in the case
of  the  antenna  switcher  in  the book.  On the  other  hand,  Doppler
Systems'  RF  soft-summer loads all whips with 50 ohms.  If  the  50-ohm
loads were removed, the non-controlled equal coax lengths from summer to
whips would  present  an  indeterminate  complex  impedance  at the whip
bases, which is just as undesirable.

Both the theory  and  my own experiments seem to support my conclusions,
and I am looking  for  input  from  others.  Even your own experience is
relevant.  You wrote:

<<I have been involved in  modifying  three  different  Dopplers and the
results were variable.>>

And also:

<<8-antenna arrays seem to be more sensitive to multipath than 4-antenna
arrays, but it varies a lot depending  on  the  exact  configuration and
situation.  Being able to switch between 8-antenna  and  4-antenna modes
is probably best.>>

I  think  variations  in loading of switched-off whips (which  could  be
affected by different coax lengths on your different models) will  go  a
long way  toward explaining your "variable" performance experiences.  In
an 8-whip array, the adjacent whips are closer than in a 4-whip array of
the same radius-of-rotation, giving  greater coupling and thus a greater
potential for multipath degradation.

<<You can get a fairly  reasonable measure of how much multipath you are
receiving  by  measuring the strength of  the  second  harmonic  of  the
switching frequency out of the discriminator.>>

Right.  It can be shown mathematically  that the doppler tone out of the
receiver discriminator induced by a single signal source in the clear is
symmetrical, i.e.  the waveform for one-half period is  the  inverse  of
the waveform during the other half-period.  The Fourier spectrum of such
a  symmetrical  waveform  has  only  odd-order harmonics (3, 5, 7, etc).
Multipath  and mutual coupling corrupt the doppler tone waveform so that
it is  not  symmetrical, creating the even-order harmonics.  So presence
of second harmonic is a good indicator of multipath.  I pointed this out
on page 136 of the T-hunt book.

<<I am currently designing a system which should be able to identify the
directions and strengths of several signals on the same frequency, say a
direct signal and a couple of  reflections,  at  the  same time, with no
moving parts and no antenna switching...>>

You'll have no trouble finding folks on  the list ready to help test and
refine it, myself included.

<<The soft switching, by smoothly changing the phase  of  the  RF signal
between  antennas,  provides  more  energy  at the fundamental switching
frequency  and  less  energy  at  harmonics  of  the switching frequency
(measured  either  in  the  RF  sidebands  or in the discriminator audio
output)...the final S/N ratio for a soft switched, weak signal after the
filter  is  better  than  the  S/N ratio of a hard switched, weak signal
after the audio filter.>>

A very good  point.   But exactly how much signal/noise improvement will
be gotten by soft  switching?   I'm going way out on a limb here and I'm
sure you folks who use  your  communications  math  skills  every day (I
don't) will tell me if you  think there are errors in my analysis.  Here
goes:

A  physically  rotating  whip produces ALL of  its  rotation-induced  FM
energy  at  the  fundamental rotation frequency.  (This  analysis  deals
strictly  with  the fundamental/harmonic issue and assumes no corruption
by   multipath,  no  antenna  summing  losses,  and  no  switching-noise
degradation.) An  ideal  soft-switching  system  would  produce the same
result

In a 4-whip  doppler, the rotation-induced FM is a symmetrical (i.e.  no
even-order harmonics) rectangular waveform.    An  easy-to-analyze  (and
probably worst-case) square wave waveform  occurs  when the target is at
0, 90, 180, or 270 degrees.

Calculation  of  Fourier  series  coefficients and  the  application  of
Parseval's Theorem to this square wave gives  us  the  percentage of the
total power in each of the low-order components, as follows:

"Zero frequency"  50.0 %
Fundamental       39.0 %
3rd harmonic       4.5 %
5th harmonic       1.6 %
7th harmonic       0.85%

>From the above, fundamental power in a hard-switched  doppler output is
39% of the fundamental power output of a perfect  doppler.    Therefore,
the    best  signal/noise  improvement  one  could  get  by  going  from
hard-switching  to  perfect soft-switching is 4.1 dB, assuming all other
components contribute to the noise floor.

But  wait---that    zero-frequency    component  doesn't  contribute  to
signal/noise degradation because  it is at DC.  With elimination of zero
frequency, the signal/noise ratio  degradation  due  to  the presence of
odd-order harmonics is less than 1.1 dB!

We can make up for  the  zero-frequency energy loss in our hard-switched
doppler by doubling the rotation frequency,  which  doubles  the doppler
tone deviation and thus doubles the fundamental  component.    Does this
explain why Doppler Systems uses 300 Hz rotation  frequency  instead  of
the 500 Hz and higher rotation rates used by hard-switched designs?  

Does  a  mere  1.1  dB  signal/noise  improvement  make  the  additional
complexity of a soft switching system worthwhile, when you consider  the
potentially  much  greater  effect  of  mutual  coupling, as I described
earlier?  Decide for yourself.

By the way, the difference in signal/noise between an 8-whip doppler and
a perfect doppler  will be even less, because its 4-step waveform (worst
case) has more power  at  the  fundamental  than  the  worst-case 2-step
(square wave) waveform of the 4-whip doppler.

<<Thank you for the information  on  the  patent  and  the  name  of the
engineer.  I had been looking  for the patent or patent number, based on
rumors, without luck so far.  >>

My source of the number is a  follow-up  to  the 1981 article in 73.  It
may  not  be the right patent covering Doppler  Systems'  soft-switching
technique,  nor the only one.  More than one  knowledgeable  person  has
told me that there are dozens if not hundreds of  patents  issued  about
doppler RDF.  Doppler Systems claims to have at least one of them.

<<US  Patent  4,041,496  granted in 1977 is now expired.  I'll  probably
post the interesting parts to the list.>>

Please do.  I tried to get copies of some doppler patents  back  in  the
early 80's when the only way to get them was to send cash  to Washington
and wait.    My  order  came back as "unavailable." Now that patents are
coming online, it's time to compile the best ones and make 'em available
to the list.

73 de Joe K0OV
------------------------------------------------------------------------
