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.
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