Transconductance

Transconductance, also known as mutual conductance, is a property of certain electronic components. It is a contraction of "transfer conductance". conductance is the flow of a current through two points when a voltage is applied as in a resistor, conductance being the reciprocal of resistance. In contrast, transconductance is the control of a current through two output points by a voltage at two input points, as if the conductance is transferred from the input points to the output points. When referring to a value, it is the ratio between these changes in voltage and current, and is written as gm:

[itex]

g_m = {\Delta I_{out} \over \Delta V_{in}} [itex]

or sometimes defined as simply :

[itex]

g_m = {I_{out} \over V_{in}} [itex]

The old unit of conductance, the mho (ohm spelled backwards), was replaced by the SI (Système International) unit, the siemens, with the symbol S (1 siemens = 1 ampere per volt).

In the world of vacuum tubes, transconductance is 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.

Similarly, in field effect transistors, transconductance is the change in the drain/source current divided by the change in the gate/drain voltage with a constant drain/source voltage. Typical values of gm for a small-signal field effect transistor are also 1 to 10 millisiemens.

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.

A transconductance amplifier outputs a current proportional to its input voltage.

In the exacting field of network analysis the transconductance amplifier is defined as a voltage controlled current source (VCIS) .

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).

The origin of the term transistor is a contraction of "transconductance varistor", sometimes incorrectly attributed to a contraction of transresistance.  (http://users.arczip.com/rmcgarra2/namememo.gif)

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:

[itex]

r_m = {\Delta V_{out} \over \Delta I_{in}} [itex]

The SI unit for transresistance is simply the ohm, as in resistance.

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 (ICVS) .

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.

Yet another term, this time coined by National Semiconductor in the early 1970s with the introduction of their LM3900  (http://www.national.com/ds/LM/LM2900.pdf), is the eponymous Norton amplifier. The Norton amplifier produces an output voltage proportional to the difference between the currents flowing into its two inputs.

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. For example, the MAX 3725  (http://pdfserv.maxim-ic.com/en/ds/MAX3724-MAX3725.pdf) operates up to 3.3 gigabits per second and costs about \$3.5 U.S.

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