Gilbert cell

Lore & Background

The Gilbert cell is a generalized case of an earlier circuit first used by Howard Jones in 1963, invented independently and greatly augmented by Barrie Gilbert in 1967. It is a specific example of translinear design, a current-mode approach to analog circuit design. The cell's differential output current is a precise algebraic product of its two differential analog current inputs. In the Jones topology, two differential amplifier stages are formed by emitter-coupled transistor pairs whose outputs are connected with opposite phases, and the emitter junctions of these stages are fed by the collectors of a third differential pair. The output currents of that third pair become emitter currents for the differential amplifiers. Combining the two different stages' output currents yields four-quadrant operation. The Jones topology can be generalized by stacking any number of pairs of differential pairs on top of a conventional Jones cell, but this generalization is limited in practical microelectronics due to the large voltage headroom needed. In the cells later invented by Gilbert, two additional diode-connected transistors generate the logarithm of the associated differential input current, so that the exponential characteristics of the following transistors result in an ideally perfect multiplication of these input currents with the remaining pair of currents. This additional diode cell topology is typically used when a low distortion voltage-controlled amplifier is required, but is rarely used in RF mixer/modulator applications because the linearity advantage is minimal due to near-square wave drive signals.

Reader's Guide

The Gilbert cell's significance lies in its ability to provide an accurate multiplication of differential input currents, making it a foundational building block for frequency conversion in radio systems. Its balanced operation cancels many unwanted mixing products, yielding a cleaner output compared to simpler mixers. The cell's translinear design approach allows precise analog multiplication in current mode. While the earlier Jones topology can be generalized to handle multiple inputs, practical limitations from voltage headroom restrict its use. Gilbert's addition of diode-connected transistors improved linearity for voltage-controlled amplifier applications, though this variant is less common in RF mixers due to the nature of drive signals at high frequencies. The cell's legacy continues in modern CMOS or BiCMOS implementations, which can construct functionally similar circuits. Its role as a variable-gain amplifier further extends its utility beyond mixing, demonstrating versatility in analog signal processing.

Did You Know?

• Barrie Gilbert independently invented and greatly augmented the cell in 1967.
• Gilbert's later cells added two diode-connected transistors to generate the logarithm of input current for perfect multiplication.