# Gilbert cell mixer / multiplier

### Mixer tutorial includes

The Gilbert cell mixer or Gilbert cell multiplier is a form of RF mixer circuit that is widely used in integrated circuits. Not only does the Gilbert cell mixer lend itself to integrated circuit technology, but it is able to provide a high level of performance. Gilbert cells are often referred to as four-quadrant multipliers

The Gilbert cell mixer or Gilbert cell multiplier is a form of double balanced mixer that is able to exploit the symmetrical topology to remove the unwanted RF & LO output signals from the IF by cancellation. As performance of adjacent components within an integrated circuit is likely to be well matched, the circuit will be well balanced and suppression of the unwanted signal components will be high.

For these reasons the Gilbert cell mixer is the most widely used form of mixer or multiplier found within RF integrated circuits.

## Gilbert cell beginnings

The Gilbert cell mixer topology was first used as a mixer by Barrie Gilbert around 1967 / 68. Although Gilbert himself did not suggest the use of the name, it is widely used to describe this mixer circuit topology.

The same idea had previously been used and patented as a synchronous detector, although not a mixer by H E Jones years earlier.

## Gilbert cell mixer / multiplier basics

The Gilbert cell mixer essentially comprises two differential transistor pairs whose bias current is controlled by one of the input signals. The other input signal drives the base electrodes of the differential pair transistors.

The output that results from the Gilbert cell mixer or multiplier is an accurate multiplication of the two input signals.

Basic Gilbert cell mixer configuration

## Gilbert cell mixer modes

The Gilbert cell mixer can be used in one of two modes:

• Analogue Gilbert cell mixer:   When used as an analogue mixer, the Gilbert cell requires that one of the inputs is "pre-distorted" using a diode circuit. This is used to add a level of distortion equal and opposite to that inherent in the differential pair.
• Switching Gilbert cell mixer:   When the circuit is used as a switching mixer, the local oscillator input to the mixer needs to be a square wav, and there is no need for the pre-distortion circuitry. As a switching mixer, the RF port then serves as the linear input.

When used in the switching mode, the Gilbert cell mixer has a switching signal fed into the local oscillator port. This acts to multiply the signal on the RF port by either +1 or -1 - multiplying it by +1 transfers the RF input level to the output port with no change. Multiplying it by -1 inverts the output (i.e. a 180° phase change).

When used in the switching mode, the LO input of the Gilbert cell mixer does not need to exhibit high linearity (i.e. low intermodulation distortion, and harmonic distortion) as it is purely a switching signal. It does need to provide a fast switching time. It is the RF input for the Gilbert cell mixer that needs to provide the linearity.

## Gilbert cell mixer active device

Although the diagram above shows the use of bipolar transistors, the Gilbert cell mixer can equally well use field effect transistors. The same basic concepts apply - the only real difference is in the biasing arrangements used.

For use of a Gilbert cell mixer within an integrated circuit, the choice of device type will depend to a large degree upon the process used for the IC manufacture. If MOS is applicable then FETs will be used. Similarly if the remainder of the IC is bipolar, then this technology will be used for the devices.

By Ian Poole

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