[ARC5] Product detectors - the name.

Thu May 11 01:12:04 EDT 2017

I just got home and checked my email and stopped upon seeing this one.

  My brain seems to be tiring out so I hope I did not make any slip ups.

I thought I would add some further explanation.

I have always told my students to use cosines with "real signals" and it makes the math easier.

One student who went on to University of California at Berkeley emailed me back when started a class called complex variables and said I get it now!!!

  That will get you there and is the correct answer. I am going to expand it using all cosines.

The 2*pi* F=angular frequency,and is symbolized by  Greek letter uppercase Omega.

A=cos (2*pi*Fa)  and B=2*pi*Fb   Fa is lets say your signal frequncy and Fb is you BFO frequency

cos(A)*cos(B) = cos (A+B)/2   +  cos (A-B)/2)  This will produce distortionless tone, cos( 2*pi*cos(Fa-Fb))/2

cos(A+B)  is a very high frequency and is removed by the following low-pass filter.

Note: cosine of a positive number is exactly the same as cosine of an negative number. So don't worry about which of the two frequencies is higher.

In using a Taylor series for the diode's , i=Ko+K1*V+K2*V^2+K3*V^3......

take at K2^2 and if V is simply two different added together cos(A) + cos (B) .

Remember (x+y)^2= x^2+2xy+y^2 ?          x^2  doubles one frequency as does y^2 the other

the middle term of this is the product detector.

If you replace xy with cos(A)*cos(B)  You get 2*(cos (A+B)/2   +  cos (A-B)/2) )= cos (A+B)  + cos (A-B)

All of the other terms account for the DC and distortion in the audio and for the RF harmonics.

Also, if the BFO level much greater than the signal level into a diode detector the distortion will be reduced.

cos(A+B)  is a very high frequency and is filtered out by the following low-pass filter.

That is one of the reasons you reduce the RF gain when receiving cw and ssb using a older radio. You also must turn off the AGC in most because it works against the reduced input and also in most radios will over drive the AGC circuit which will reduce the gain even further.

________________________________
From: ARC5 <arc5-bounces at mailman.qth.net> on behalf of Leslie Smith <vk2bcu at operamail.com>
Sent: Wednesday, May 10, 2017 2:59 AM
To: Dennis Monticelli; ARC-5 List
Subject: [ARC5] Product detectors - the name.

Hello Dennis,
I always believe a product detector followed the trig function:

sin(A) * cos(B) = 1/2[sin(A+B) + sin(A-B)].

It's the PRODUCT of two trig functions to give the sum and difference.
I have no idea why I believe this, but I suspect it's true (for a
product detector, or product mixer)
Put in two signal and get the sum and difference.  Isn't maths amazing!!
Isn't electronics amazing!!  If anyone knows more than this - I'm
interested!

   73 de Les Smith
   vk2bcu at operamail.com

On Wed, May 10, 2017, at 03:43, Kenneth G. Gordon wrote:
> On 9 May 2017 at 9:38, Dennis Monticelli wrote:
>
> >
> > Guys,
> >
> > I feel compelled to contribute to this discussion on the impact of the detector upon the AGC.
>
> Good. Thank you.
>
> > First of all, the detectors we are discussing are just special purpose mixers and like all mixers they
> > generate the mathematical products of their inputs.  Regardless of what we call them....detectors,
> > product detectors, converters, etc.....the math is the same.
>
> Yes. I completely agree with you and I have been saying the exact same
> thing for years.
>
> > Now, we don't want all of those math products because some of them can cause trouble.  If we
> > put a strong BFO signal into a simple detector in order to extract a relatively low distortion CW or
> > SSB demodulated output then the BFO energy must be substantially stronger than the incoming
> > signal and that energy can easily overwhelm any downstream AGC pickoff point
>
> Correct.
>
> > When SSB came into being the linearity of the detector became more important than ever
> > because even small amounts of voice distortion are irritating.   To overcome this problem the
> > detector was made balanced with respect to the incoming BFO.  Properly executed this balance
> > reduced the amount of BFO energy bleeding into the signal path by a lot.... about 40dB.  Now one
> > could pump in lots of BFO, enjoy low distortion, and not mess up the AGC.
>
> Well, yes, but in addition, the AGC voltage was taken from some place in
> the circuit OTHER
> THAN the detector. Separating the two makes a huge difference.
>
> >  For some historical
> > reason unknown to me this type of detector became widely known as the product detector.
>
> Supposedly because the output was the "product" of the two inputs, and
> not a straight simple
> addition. Supposedly also if the BFO signal is missing, output is zero,
> so an AM signal
> applied to the input of a true "product" detector would result in zero
> output.
>
> However, I have never believed that.
>
> One of the simplest product detectors, first used by Collins in the
> KWM-2, a simple triode,
> demodulates AM just fine.
>
> Heathkit used that PD in almost all of their rigs.
>
> I also wonder about the term, "linear mixer": how can any "mixer" be
> "linear" since it must be
> "un-linear" in order to work?
>
> Even so, the so-called "product detector" is about the best detector
> available for SSB and
> CW.
>
> Ken
>
> ---
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