Transconductance (fortransfer conductance), also infrequently calledmutualconductance, is the electrical characteristic relating thecurrent through the output of a device to thevoltage across the input of a device. Conductance is the reciprocal of resistance.

Transadmittance (ortransferadmittance) is theAC equivalent of transconductance.

Transconductance is very often denoted as a conductance,g_m, with a subscript,m, formutual. It is defined as follows:

${\displaystyle g_{\text{m}}=\frac{\mathrm{\Delta }{I}_{\text{out}}}{\mathrm{\Delta }{V}_{\text{in}}}}$

Forsmall signalalternating current, the definition is simpler:

${\displaystyle g_{\text{m}}=\frac{i_{\text{out}}}{v_{\text{in}}}}$

TheSI unit for transconductance is thesiemens, with the symbolS, as in conductance.

Transresistance (fortransfer resistance), also infrequently referred to asmutual resistance, is thedual 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 denotated asr_m:

${\displaystyle r_{\text{m}}=\frac{\mathrm{\Delta }{V}_{\text{out}}}{\mathrm{\Delta }{I}_{\text{in}}}}$

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

Transimpedance (or,transferimpedance) is the AC equivalent of transresistance, and is thedual of transadmittance.

Forvacuum tubes, 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 ofg_m for a small-signal vacuum tube are 1 to10 mS. It is one of the three characteristic constants of a vacuum tube, the other two being itsgainμ (mu) and plate resistancer_p orr_a. TheVan der Bijl equation defines their relation as follows:

${\displaystyle g_{\mathrm{m}}=\frac{\mu }{r_{\mathrm{p}}}}$^[1]

Similarly, infield-effect transistors, andMOSFETs 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 ofg_m for a small-signal field-effect transistor are1 to 30 mS.

Using theShichman–Hodges model, the transconductance for the MOSFET can be expressed as (seeMOSFET § Modes of operation)

${\displaystyle g_{\text{m}}=\frac{2I_{\text{D}}}{V_{\text{OV}}},}$

whereI_D is the DC drain current at thebias point, andV_OV is theoverdrive voltage, which is the difference between the bias point gate–source voltage and thethreshold voltage (i.e.,V_OV ≡V_GS –V_th).^{[2]: p. 395, Eq. (5.45)} The overdrive voltage (sometimes known as the effective voltage) is customarily chosen at about 70–200 mV for the65 nm process node (I_D ≈ 1.13 mA/μm × width) for ag_m of 11–32 mS/μm.^{[3]: p. 300, Table 9.2 [4]: p. 15, §0127}

Additionally, the transconductance for the junction FET is given by

${\displaystyle g_{\text{m}}=\frac{2I_{\text{DSS}}}{|V_{\text{P}}|}\left(1-\frac{V_{\text{GS}}}{V_{\text{P}}}\right),}$

whereV_P is the pinchoff voltage, andI_DSS is the maximum drain current.

Theg_m ofbipolar small-signal transistors varies widely, being proportional to the collector current. It has a typical range of1 to 400 mS. 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

${\displaystyle g_{\mathrm{m}}=\frac{I_{\mathrm{C}}}{V_{\mathrm{T}}}}$

whereI_C is the DC collector current at theQ-point, andV_T is thethermal voltage, typically about26 mV at room temperature. For a typical current of10 mA,g_m ≈385 mS. The input impedance is thecurrent gain (β) divided by the transconductance.

The output (collector) conductance is determined by theEarly voltage and is proportional to the collector current. For most transistors in linear operation it is well below100 μS.

Atransconductance amplifier (g_m amplifier) puts out a current proportional to its input voltage. Innetwork analysis, the transconductance amplifier is defined as avoltage controlled current source (VCCS). These amplifiers are commonly seen installed in acascode configuration, which improves the frequency response.

An ideal transconductance amplifier in a voltage follower configuration behaves at the output like a resistor of value1/g_m, between a buffered copy of the input voltage and the output. If the follower is loaded by a single capacitorC, the voltage follower transfer function has a single pole with time constantC/g_m,^[5] or equivalently it behaves as a 1st-order low-pass filter with a−3 dB bandwidth ofg_m/2πC.

Anoperational transconductance amplifier (OTA) is an integrated circuit which can function as a transconductance amplifier. These normally have an input to allow the transconductance to be controlled.^[6]

Atransresistance amplifier outputs a voltage proportional to its input current. The transresistance amplifier is often referred to as atransimpedance amplifier, especially by semiconductor manufacturers.

The term for a transresistance amplifier in network analysis iscurrent controlled voltage source (CCVS).

A basic inverting transresistance amplifier can be built from anoperational 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.

• Transistor
• Vacuum tube
• Electronic amplifier
• Transimpedance amplifier
• Fontana bridge
• Operational transconductance amplifier
• MOSFET

• Horowitz, Paul;Hill, Winfield (1989),The Art of Electronics, Cambridge University Press,ISBN 0-521-37095-7

Look uptransconductance in Wiktionary, the free dictionary.

• Transconductance — SearchSMB.com Definitions
• Transconductance in audio amplifiers: article by David Wright of Pure Music[1]

• Transfer functions
• Electrical resistance and conductance

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