[time-nuts] Hetrodyning concept

[Gary Chatters]

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.
> 
> 
> 
> ---------------------------------------
> (Mr.) Taka Kamiya
> KB4EMF / ex JF2DKG