Transconductance - AbsoluteAstronomy.com

Transconductance, also known as mutual conductance, is a property of certain electronic

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

components. Conductance is the reciprocal of resistance; transconductance, meanwhile, is the ratio of the current change at the output port to the voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

change at the input port. It is written as g_m. For direct current

Direct current

Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...

, transconductance is defined as follows:

For small signal alternating current

Alternating current

In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

, the definition is simpler:

Terminology

It is a contraction of "transfer conductance".
The old unit of conductance, the mho (ohm spelled backwards), was replaced by the SI

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

(International System) unit, the siemens
Siemens (unit)
The siemens is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term...

, with the symbol S (1 siemens = 1 ampere per volt).

The origin of the term transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

is a contraction of "transconductance varistor

Varistor

A varistor is an electronic component with a "diode-like" nonlinear current–voltage characteristic. The name is a portmanteau of variable resistor...

", 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 r_m:

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

Vacuum tubes

For vacuum tube

Vacuum tube

In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

s, 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 g_m for a small-signal vacuum tube are 1 to 10 millisiemens.

Field effect transistors

Similarly, in field effect transistors, and MOSFET

MOSFET

The metal–oxide–semiconductor field-effect transistor is a transistor used for amplifying or switching electronic signals. The basic principle of this kind of transistor was first patented by Julius Edgar Lilienfeld in 1925...

s 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 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 article):

where I_D is the DC drain current at the bias point, and V_eff is the effective voltage, which is the difference between the bias point gate–source voltage and the threshold voltage

Threshold voltage

The threshold voltage of a MOSFET is usually defined as the gate voltage where an inversion layer forms at the interface between the insulating layer and the substrate of the transistor. The purpose of the inversion layer's forming is to allow the flow of electrons through the gate-source junction...

(i.e., V_eff := V_GS - V_th). The effective voltage (otherwise known as the overdrive voltage) is customarily chosen at about 70–200 mV for the 65 nm

65 nanometer

The 65 nm process is an advanced lithographic node used in volume CMOS semiconductor fabrication. Printed linewidths can reach as low as 25 nm on a nominally 65 nm process, while the pitch between two lines may be greater than 130 nm.. For comparison, cellular ribosomes are...

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.

Traditionally, the transconductance for the FET and MOSFET as given in the equations above is derived from the transfer equation of each device, using calculus. However, Cartwright has shown that this can be done without calculus.

Bipolar transistors

The g_m of bipolar

Bipolar junction transistor

|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

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, and V_T = thermal voltage, typically about 26 mV at room temperature. For a typical current of 10 mA, g_m ≈ 385 mS.

Transconductance amplifiers

A transconductance amplifier (gm amplifier) puts out a current proportional to its input voltage. In network analysis
Network analysis (electrical circuits)
A network, in the context of electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, every component in the network. There are a number of different techniques for achieving this...

, the transconductance amplifier is defined as a voltage controlled current source (VCCS) . It is common to see these amplifiers installed in a cascode

Cascode

The cascode is a two-stage amplifier composed of a transconductance amplifier followed by a current buffer. Compared to a single amplifier stage, this combination may have one or more of the following characteristics: higher input-output isolation, higher input impedance, high output impedance,...

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

Operational amplifier

An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...

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 amplifier
Operational transconductance amplifier
The operational transconductance amplifier is an amplifier whose differential input voltage produces an output current. Thus, it is a voltage controlled current source . There is usually an additional input for a current to control the amplifier's transconductance...

s (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, OPA860 http://focus.ti.com/lit/ds/symlink/opa860.pdf, OPA861 http://focus.ti.com/lit/ds/symlink/opa861.pdf.

Further exploration

Transconductance — SearchSMB.com Definitions
Transconductance in audio amplifiers: article by David Wright of Pure Music http://www.beauhorn.com/articles/TC_amps_&_SD_horns.html

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.