# Frequency Mixer Concept?

Discussion in 'General Electronics Chat' started by crazyengineer, Jan 16, 2012.

1. ### crazyengineer Thread Starter Member

Dec 29, 2010
156
2
I was looking up schematics for a gibert cell,but I have no idea what's the underlying concept for it. Can anyone explain how this and other frequency mixers work?

2. ### w2aew Member

Jan 3, 2012
219
64
Briefly - a mixer involves combining two waveforms in some non-linear way, usually via multiplication (as opposed to addition which IS linear). The non-linear combination of signals at two different frequencies results in creating a product that contains energy at the sum and difference frequencies of the inputs and the harmonics thereof. Refresh yourself on the trigonometric identities of multiplying sine waves, and you'll see that sum and difference frequencies are created.

A Gilbert cell multiplies the signal applied at the inputs to the cross coupled differential pair by the signal that is modulating the tail current of that pair (via another diff-pair) - if I recall correctly...

3. ### Brownout Well-Known Member

Jan 10, 2012
2,375
998
Non-lenear function is the key. All non-lenear functions can by described by a Taylor series: F(x)= 1 + Ax + Bx^2 + ... The important term is the x^2 term. Consder a signal described by SinA + SinB, then the squared term becomes:

(SinA + SinB)^2 = SinA^2 + 2SinA*SinB + SinB^2. Now, we examine the middle term:

SinA*SinB = 1/2Cos(A-B)) + 1/2Cos(A+B). Now, the modulation has produced a sum and difference frequency, A-B and A+B. IE if A=w1t and B=w2t, then we have, for the sum and difference: (w1-w2)t and (w1+w2)t. Filtering is now used to select the desired frequency.