# Extensive Definition

Transconductance, also known as mutual conductance, is a property of certain electronic components. Conductance is the reciprocal of resistance and transconductance is the ratio of the current at the output port and the voltage at the input ports and is written as gm:
g_m =
or sometimes defined as simply (if using ac):
g_m =
Note: In the first case we have change of current divided by the change of voltage and in the second case we have ac current iout divided by ac voltage vin.

## Terminology

It is a contraction of "transfer conductance". The old unit of conductance, the mho (ohm spelled backwards), was replaced by the SI (International System) unit, the siemens, with the symbol S (1 siemens = 1 ampere per volt).
The origin of the term transistor is a contraction of "transconductance varistor", proposed at Bell Telephone Laboratories, sometimes incorrectly attributed to a contraction of transresistance. See internal BTL opinion poll .

### Transresistance

Transresistance, infrequently referred to as mutual resistance, is the dual of transconductance. It is a contraction of "transfer resistance". It refers to the ratio between a change of the voltage at two output points and a related change of current through two input points, and is notated as rm:
r_m =
The SI unit for transresistance is simply the ohm, as in resistance.

## Devices

### Vacuum tubes

For vacuum tubes, transconductance is defined as the change in the plate(anode)/cathode current divided by the corresponding change in the grid/cathode voltage, with a constant plate(anode)/cathode voltage. Typical values of gm for a small-signal vacuum tube are 1 to 10 millisiemens.

### Field effect transistors

Similarly, in field effect transistors, and MOSFETs in particular, transconductance is the change in the drain/source current divided by the change in the gate/source voltage with a constant drain/source voltage. Typical values of gm for a small-signal field effect transistor are 1 to 30 millisiemens.
Using the archaic Shichman-Hodges model, the transconductance for the MOSFET can be expressed as (see MOSFET article):
g_m = \begin \frac \end
where ID = DC drain current at the Q-point, and Vov = overdrive voltage, customarily chosen at about 70 - 200 mV for the 65 nm technology node (ID ≈ 1.13 mA/μm of width) for a gm of 11 - 32 mS/μm.

### Bipolar transistors

The gm of bipolar small-signal transistors varies widely, increasing exponentially with the emitter current. It has a typical range of 1 to 400 millisiemens. The input voltage change is applied between the base/emitter and the output is the change in collector current flowing between the collector/emitter with a constant collector/emitter voltage.
The transconductance for the bipolar transistor can be expressed as
g_m = \begin \frac \end
where IC = DC collector current at the Q-point, and VT = thermal voltage, typically about 26 mV at room temperature. For a typical current of 10 mA, gm ≈ 385 mS.

## Amplifiers

### Transconductance amplifiers

A transconductance amplifier (gm amplifier) puts out a current proportional to its input voltage. In network analysis the transconductance amplifier is defined as a voltage controlled current source (VCCS) .

### Transresistance amplifiers

A transresistance amplifier outputs a voltage proportional to its input current. The transresistance amplifier is often referred to as a transimpedance amplifier, especially by semiconductor manufacturers.
The term for a transresistance amplifier in network analysis is current controlled voltage source (CCVS) .
A basic inverting transresistance amplifier can be built from an operational amplifier and a single resistor. Simply connect the resistor between the output and the inverting input of the operational amplifier and connect the non-inverting input to ground. The output voltage will then be proportional to the input current at the inverting input, decreasing with increasing input current and vice versa.
Specialist chip transresistance (transimpedance) amplifiers are widely used for amplifying the signal current from photo diodes at the receiving end of ultra high speed fibre optic links. The MAX3724 and MAX3725 http://pdfserv.maxim-ic.com/en/ds/MAX3724-MAX3725.pdf are examples.

### Operational transconductance amplifiers

Many semiconductor manufacturers produce chips (integrated circuits) which can function as transconductance amplifiers. These are frequently described as operational transconductance amplifiers (OTAs) and normally have an input to allow the transconductance to be controlled. Examples are: CA3080 http://www.intersil.com/data/fn/fn475.pdf, MAX 435 http://pdfserv.maxim-ic.com/en/ds/MAX435-MAX436.pdf, MAX 436 http://pdfserv.maxim-ic.com/en/ds/MAX435-MAX436.pdf, LM13700 http://www.national.com/ds/LM/LM13700.pdf.