[time-nuts] Hetrodyning concept

[jimlux]

On 4/27/20 7:39 AM, Gary Chatters wrote:
> Your basic error is that you are adding the two sine wave signals.  Get 
> that idea out of your head.
> 
> When mixing two signals (heterodyne) you multiply them:
> 
>          Vout = Asin(2pi*f1*t + p1) * Bsin(2pi*f2*t + p2)
>                                     ^-- Multiply, not add
>          Where:
>            A, B are amplitude
>            f1, f1 frequencies
>            p1, p2 phase offset
> 
> Work out this formula (so you have sum of sines instead of products) 
> using some trigonometric identities and you'll get your sum and 
> difference signals.
> 
> Javier's earlier email shows you the results for the case for f1 = f2.
> 
> Gary
> WA9ZZZ
> 
> On 4/27/20 4:08 AM, Taka Kamiya via time-nuts wrote:
>> I have a question on heterodyining concept.
>> Say you have f1 and f2.  Say you have f1 <> f2.  Then the product is 
>> |f1+f2| and |f1-f2|.  (fundamental is not considered here)
>> What would happen f1 = f2?  If phase is the same, it will be 
>> 2sin(omega t).  (amplitude doubles)  If phase is an odd multiple of pi 
>> radian different, result is zero.  (cancels out each other)
>> What I am trying to do is to first, understand this in case where f1 = 
>> f2, and second, mix f1 and f2 and get f3, which is a sum of f1 and 
>> f2.  Doubling won't do.
>> Can someone help me understand this?  I haven't seen discussion of 
>> cases where source frequencies are equal anywhere.




And to extend a bit - you can get the mixer intermod table (NxLO,MxFin) 
by running the signal through a nonlinearity with "easy to compute" 
terms (like a Nth order polynomial) and the writing out all the cross 
products for all the terms of the series expansion

One way is to assume that your signal has A0+ A1*cos(omega*t + B1) + A2 
*cos(2*omega*t + B2) + A3*cos(3*omega*t * B3)....

And then cross multiply all those terms with the other signal, 
represented as the same kind of series.



Also:
http://www.rfcafe.com/references/articles/wj-tech-notes/Mixers_in_systems_part1.pdf

http://www.rfcafe.com/references/articles/wj-tech-notes/Mixers_in_systems_part2.pdf

And a more recent
https://www.markimicrowave.com/assets/appnotes/mixer_basics_primer.pdf

(Ferenc Marki came from WJ, where he designed mixers back when WJ made 
mixers)

https://www.eeweb.com/featured-engineers/interview-with-ferenc-marki-and-christopher-marki

Interesting comments on noise sources.