[ARC5] Product detectors - the name.

Wed May 10 20:39:04 EDT 2017

  Hello Bruce!

  I always find a mathematical dissertation very illuminating.
  It makes me think!   Mathematics takes me beyond a simple verbal
  description.  Mathematics suggests the limit of performance.  

  Mathematics is amazing!  Don't be afraid to put on your funny red cap
  and gown from time to time!
   73 de Les Smith
   vk2bcu at operamail.com

On Thu, May 11, 2017, at 04:59, Bruce Long wrote:
> I agree with Les:
> 
> As an RF design engineer I associate a product detector as a circuit
> block where the output voltage is the product of two input voltages
> hence the name product detector.> 
> It is entirely true that a diode amplitude detector will function as a
> kind of product detector if supplemented with BFO injection.  Here is
> how that works.> 
> Excuse the math
> 
> The diode works because it has a non-linear Iout/Vin curve
> 
> In circuit analysis you deal with the circuit non-linearity by
> representing the non-linearity as an infinate series expansion have
> the form:> 
> Vout = a0 +a1(Vin) + a2(Vin)^2 + a3(Vin)^3 + ............,.
> 
> Where a0, a1 ... an  are coefficients
> 
> Vin is the sum of two sinusoids,  one being the IF frequency signal,
> the other being the BFO injection signal.> 
> If you look up the formula for the square of the sum of two sinusoids
> in a math handbook you will find that expression has a Vif  times Vbfo
> product term and it is that product term that provides SSB an or CW
> detection.   All the other terms generate intermodulation and harmonic
> terms and are undesirable.   Some can be filtered out, others cannot
> be filtered and contribute distortion.> 
> If you have a circuit block that really and truly has an output
> voltage that is the product of the two input voltages and only the
> product of the two input voltages then all the all the unwanted, un-
> filterable  non-product terms go away allowing clean non-distortion
> multiplicative detection.> 
> Communication theorists like product detectors because they are simple
> and easy to represent mathematically.> 
> So in short all SSB CW detectors are product detectors in as much such
> detection and down conversion requires the multiplication of two
> sinusoids  ( looking at the trig section of any math handbook
> multiplication of two sinusoids creates both sum and difference
> frequencies) and any circuit non-linearity will provide a measure  of
> "product" detection becaue of the V, V^2, V^3 etc terms that appear
> when one attempts to define a circuit non-linearity in terms of a
> series expansion.> 
> A true product detector in my way of thinking is a circuit especially
> configured to provide an output that is the product of two input
> signals - and nothing- else to the degree possible.> 
> 
> Sorry for the lecture but I once taught this stuff at the university
> level and they take away my professor membership card if I don't
> occasional make like a professor.]> 
> 
> Bruce
> 
> 
> 
> 
> 
> 
> **From:** Leslie Smith <vk2bcu at operamail.com> **To:** Dennis
> Monticelli <dennis.monticelli at gmail.com>; ARC-5 List
> <arc5 at mailman.qth.net> **Sent:** Wednesday, May 10, 2017 2:59 AM
> **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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> > 
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