# RF Mixer & RF Mixing / Multiplication Tutorial

### - RF mixers provide one of the key building blocks in RF design, enabling frequencies to be translated from one band to another by multiplying two signals together.

RF mixing is one of the key processes within RF technology and RF design. RF mixing enables signals to be converted to different frequencies and thereby allowing the signals to be processed more effectively.

In view of the importance of RF mixing, there are many basic RF mixer circuits available, but in addition to this there are many high performance RF mixers that are available on the market. These RF mixers have very high levels of specification and perform to very high standards.

## RF mixing basics

RF mixing is not like audio mixing where several signals are added together in a linear fashion to give several sounds together. Radio frequency, or RF mixing is a non-linear process that involves the instantaneous level of one signal affecting the level of the other at the output. This process involves the two signal levels multiplying together at any given instant in time and the output is a complex waveform consisting of the product of the two input signals.

**The result of two signals mixed together**

In the diagram, the top two traces show the input signals to the RF mixer, and the bottom trace shows the output from the RF mixer. Looking at a plot or oscilloscope trace of the output it can be imagined that signals on different frequencies are produced, and this is in fact the case.

When two signals enter an RF mixer and are mixed together, new signals are seen at frequencies that are the sum and difference of the two input signals, i.e. if the two input frequencies are f1 and f2, then new signals are seen at frequencies of (f1+f2) and (f1-f2). To take an example, if two signals, one at a frequency of 5 MHz and another at a frequency of 6 MHz are mixed together then new signals at frequencies of 11 MHz and 1 MHz are generated.

**The RF mixing process**

When added to a circuit diagram, an RF mixer is often denoted by a circle with a cross in it as shown below. As can be seen, there are the two inputs and one output as shown.

**Circuit symbol for an RF mixer**

## RF mixer mathematics

It is possible to easily represent the action of an RF mixer mathematically. The two input waveforms are represented by simple sine waves, and these are multiplied together. By expanding the resulting waveform using standard trignometrical processes, it is possible to deduce what the output is.

If the input waveforms are taken as:

**V1 = A sin ( 2 pi f1 t)**

**V2 = B sin ( 2 pi f2 t)**

Then it is necessary to use the trignometrical expression:

**sin (a) x sin (b) = 1/2 [cos (A - B) - cos (A + B)]**

Applying this to the input waveforms, i.e. multiplying them together in the RF mixer, the output is then:

**V1 x V2 = (A x B) / 2 [cos (2 pi {f1 - f2} t ) - cos ( 2 pi {f1 + f2} t )]**

From this it can be seen that the two terms: (f1 - f2) and (f1 + f2) can be seen, and these represent the sum and difference frequencies that are seen on the traces above.

## RF mixer summary

RF mixers are particularly useful components for any RF design or item of RF equipment. RF mixers are widely used as either circuits built using discrete components, or they may be bought as circuit items ready for inclusion in an RF circuit or RF design. These RF mixer block are normally high performance items and may save considerable amounts of time designing and constructing an RF mixer to an equivalent level of performance.

* By Ian Poole*

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• Modulation overview | • Amplitude mod'n | • Frequency mod'n | • Phase mod'n |

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