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# Gilbert Cell

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 Title: Gilbert Cell Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Gilbert Cell

In electronics, the Gilbert cell is an elaborated cascode circuit used as an analog multiplier and frequency mixer. It was invented by Howard Jones in 1963, but usually attributed to Barrie Gilbert (before joining Analog Devices) in 1968.[1]

The properties of the circuit is that the output current is a 4 quadrant multiplication of the differential base voltages of the LO and RF inputs.

## Function

The Gilbert cell consists of two differential amplifier stages formed by emitter-coupled transistor pairs (Q1/Q4, Q3/Q5) whose outputs are connected (currents summed) with opposite phases. The emitter junctions of these amplifier stages are fed by the collectors of a third differential pair (Q2/Q6). The output currents of Q2/Q6 become emitter currents for the differential amplifiers. Simplified, the output current of an individual transistor is given by Ico=Vbe.gm. Its transconductance (gm) is given by gm=40.IDC. Combining these equations gives Ico=40.IDC.Vbe_lo.  However, IDC here is given by Vbe_rf.gm_rf. Hence Ico=40.Vbe_lo. Vbe_rf.gm_rf.  Which is a multiplication of Vbe_lo and Vbe_rf. Combining the two difference stages output currents yields four-quadrant operation.

A functionally equivalent circuit can be constructed using field-effect transistors (JFET, MOSFET) or vacuum tubes.

## Applications

A Gilbert cell can be used as:

• A small signal precise four-quadrant multiplier (with condition that both inputs are small compared with VT (Thermal voltage=0.025V)
• A large signal phase detector (with condition that both inputs are great compared with VT)
• A modulator in a communications application (with condition that only one input is small compared with VT while the other input is greater)
• A pre-processing circuit in a Flash ADC to reduce the number of comparators in this architecture. This is called a folding ADC.

## References

 Electronics portal
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