# RF Mixing / Multiplication Basics

### RF mixers and the process of RF mixing or multiplication is key to many RF circuit enabling signal to be converted from one frequency to another as well as providing phase comparison.

RF Mixers & Mixing Tutorial Includes:
RF mixing basics     Theory & math     Specs & data     Transistor mixer     FET mixer     Double balanced mixer     Gilbert cell mixer     Image reject mixer

the process of rf or non-linear mixing or multiplication is used in virtually every radio set these days and also in many other circuits beside. it enables signals to be changed from one frequency to another so that signal processing for example can be undertaken on a low frequency where it is easier to perform, but the signal can be changed to a from a higher frequency where the signal is to be transmitted or received.

## What happens when signals are mixed

it is found that if two signals are passed through a non-linear circuit, then additional signals on new frequencies are formed. these appear at frequencies equal to the sum and difference frequencies of the original signals. in other words if signals at frequencies of f1 and f2 enter the mixer, then additional signals at frequencies of (f1+f2) and (f1-f2) will also be seen at the output.

to give an example if the two original signals are at frequencies of 1 mhz and 0.75 mhz, then the two resultant signals will appear at 1.75 mhz and 0.25 mhz.

## Why RF mixing or multiplication works

the two signals can be considered as sine waves. the instantaneous output level is dependent upon the instantaneous level of signal a multiplied by the instantaneous level of signal b. if points along the curve are multiplied, then the output waveform is more complex as shown below.

the frequencies used to generate the example below for the frequencies mentioned above, i.e. 0.75 mhz and 1.0 mhz. it can be seen that in the output there is a low frequency component (the difference frequency at 0.25 mhz) and high frequency component (the sum frequency at 1.75 mhz).

## RF mixer circuit symbol

the key rf mixer circuit symbol shows the two signals entering circuit block consisting of a circle with a cross or "x" within it.

this circuit symbol indicates the multiplication aspect of the mixer. RF mixer circuit symbol showing the frequency translation scheme that is the goal for good mixers

## RF Mixer applications

rf mixers are used in all areas of rf design, and development. they are used in circuits from radio receivers and transmitters to radar systems, and in fact anywhere that radio frequency signals are used.

• Frequency translation:   The most obvious application for RF mixers is for frequency translation. This technique is used in many areas and in particular in receivers and transmitters to move the frequency of a signal from one band to another. Using the fact that the two input frequencies generate sum and difference frequencies, it is possible to change the signal input to another frequency by taking either the sum or the difference signal. One of the first major applications of this was in the superheterodyne radio receiver.
• Phase comparison:   Using a mixer it is possible to detect the phase difference between two signals. This RF mixer application can be used in many areas, one of which is within phase locked loops.