Transconductance (for transfer conductance), also infrequently called mutual
conductance, is the electrical characteristic relating the
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
through the output of a device to the
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
across the input of a device. Conductance is the reciprocal of resistance.
Transadmittance (or transfer
admittance
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance ...
) is the
AC equivalent of transconductance.
Definition
Transconductance is very often denoted as a conductance, ''g''
m, with a subscript, m, for ''mutual''. It is defined as follows:
:
For
small signal
Small-signal modeling is a common analysis technique in electronics engineering used to approximate the behavior of electronic circuits containing nonlinear devices with linear equations. It is applicable to electronic circuits in which the AC ...
alternating current
Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
, the definition is simpler:
:
The
SI unit for transconductance is the
siemens
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
, with the symbol S, as in conductance.
Transresistance
Transresistance (for transfer resistance), also infrequently referred to as mutual resistance, is the
dual of transconductance. 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 ''r''
m:
:
The SI unit for transresistance is simply the
ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (b ...
, as in resistance.
Transimpedance (or, transfer
impedance) is the AC equivalent of transresistance, and is the
dual of transadmittance.
Devices
Vacuum tubes
For
vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied.
The type kn ...
s, transconductance is defined as the change in the plate (anode) current divided by the corresponding change in the grid/cathode voltage, with a constant plate(anode) to cathode voltage. Typical values of g
m for a small-signal vacuum tube are 1 to 10 millisiemens. It is one of the three characteristic constants of a vacuum tube, the other two being its
gain
Gain or GAIN may refer to:
Science and technology
* Gain (electronics), an electronics and signal processing term
* Antenna gain
* Gain (laser), the amplification involved in laser emission
* Gain (projection screens)
* Information gain in de ...
''μ'' (mu) and plate resistance ''r''
p or ''r''
a. The
Van der Bijl equation defines their relation as follows:
:
[Blencowe, Merlin (2009). "Designing Tube Amplifiers for Guitar and Bass".]
Field effect transistors
Similarly, in
field effect transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs (JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs control ...
s, and
MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
s in particular, transconductance is the change in the drain current divided by the small change in the gate/source voltage with a constant drain/source voltage. Typical values of ''g''
''m'' for a small-signal field effect transistor are 1 to 30 millisiemens.
Using the
Shichman–Hodges model, the transconductance for the MOSFET can be expressed as (see
MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
article):
:
where ''I
D'' is the DC drain current at the
bias point
In electronics, biasing is the setting of DC (direct current) operating conditions (current and voltage) of an active device in an amplifier. Many electronic devices, such as diodes, transistors and vacuum tubes, whose function is processing ...
, and ''V''
''OV'' is the
overdrive voltage, which is the difference between the bias point gate–source voltage and the
threshold voltage
The threshold voltage, commonly abbreviated as Vth or VGS(th), of a field-effect transistor (FET) is the minimum gate-to-source voltage (VGS) that is needed to create a conducting path between the source and drain terminals. It is an important s ...
(i.e., ''V''
''OV'' ≡ ''V''
''GS'' - ''V''
''th'').
[
] The overdrive voltage (sometimes known as the effective voltage) is customarily chosen at about 70–200 mV for the
65 nm
The 65 nm process is an advanced lithographic node used in volume CMOS ( MOSFET) semiconductor fabrication. Printed linewidths (i.e. transistor gate lengths) can reach as low as 25 nm on a nominally 65 nm process, while the pitc ...
technology node (''I
D'' ≈ 1.13 mA/μm of width) for a ''g''
''m'' of 11–32 mS/μm.
[
][
]
Additionally, the transconductance for the junction FET is given by
, where V
P is the pinchoff voltage and I
DSS is the maximum drain current.
Bipolar transistors
The g
m of
bipolar small-signal transistors varies widely, being proportional to the collector 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
:
where ''I
C'' = DC collector current at the
Q-point
In electronics, biasing is the setting of DC (direct current) operating conditions (current and voltage) of an active device in an amplifier. Many electronic devices, such as diodes, transistors and vacuum tubes, whose function is processin ...
, and ''V
T'' =
thermal voltage
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
, typically about 26 mV at room temperature. For a typical current of 10 mA, ''g
m'' ≈ 385 mS. The input impedance is the current gain
() divided by the transconductance.
The output (collector) conductance is determined by the
Early voltage
The Early effect, named after its discoverer James M. Early, is the variation in the effective width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage. A greater reverse bias across ...
and is proportional to the collector current. For most transistors in linear operation it is well below 100 µS.
Amplifiers
Transconductance amplifiers
A transconductance amplifier (''g'' amplifier) puts out a current proportional to its input voltage. In
network analysis Network analysis can refer to:
* Network theory, the analysis of relations through mathematical graphs
** Social network analysis, network theory applied to social relations
* Network analysis (electrical circuits)
See also
*Network planning and ...
, the transconductance amplifier is defined as a ''voltage controlled current source'' (''VCCS'') . It is common to see these amplifiers installed in a
cascode
The cascode is a two-stage amplifier that consists of a common-emitter stage feeding into a common-base stage.
Compared to a single amplifier stage, this combination may have one or more of the following characteristics: higher input–output ...
configuration, which improves the frequency response.
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
An operational amplifier (often op amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative to c ...
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.
Operational transconductance amplifiers
An
operational transconductance amplifier
The operational transconductance amplifier (OTA) is an amplifier whose differential input voltage produces an output current. Thus, it is a voltage controlled current source (VCCS). There is usually an additional input for a current to control t ...
(OTA) is an integrated circuit which can function as a transconductance amplifier. These normally have an input to allow the transconductance to be controlled.
See also
*
Transistor
upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink).
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
*
Vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied.
The type kn ...
*
Electronic amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a Signal (information theory), signal (a time-varying voltage or Electric current, current). It may increase the power (physics ...
*
Transimpedance amplifier
In electronics, a transimpedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multipli ...
*
Fontana bridge
A Fontana bridge is a type of bridge circuit that implements a wide frequency band voltage-to-current converter. The converter is characterized by a combination of positive and negative feedback loops, implicit in this bridge configuration. This f ...
*
Operational transconductance amplifier
The operational transconductance amplifier (OTA) is an amplifier whose differential input voltage produces an output current. Thus, it is a voltage controlled current source (VCCS). There is usually an additional input for a current to control t ...
*
MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
References
*
External links
{{Wiktionary, transconductance
Transconductance— SearchSMB.com Definitions
* Transconductance in audio amplifiers: article by David Wright of Pure Music
Transfer functions
Electrical resistance and conductance