# Frequency Mixer Concept?

#### crazyengineer

Joined Dec 29, 2010
156
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?

#### w2aew

Joined Jan 3, 2012
219
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?
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...

#### Brownout

Joined Jan 10, 2012
2,390
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.