Trans-conductance, trans-impedance and gain

An amplifier or two-port network is described by the ratio of an output quantity to an input quantity. The name depends on which quantities are used.

Trans-conductance (gm)

The ratio of output current to input voltage:

gm = I_out / V_in

• Unit: siemens (S), or mA/V.
• "Trans" means the two quantities are at different ports.
• Example: for a MOSFET or JFET, gm = ΔI_D / ΔV_GS at constant V_DS. A device with gm = 2 mA/V gives a 2 mA drain current change for a 1 V gate voltage change.
• An amplifier described this way is a trans-conductance amplifier (voltage in, current out).

Trans-impedance (Rm or Zm)

The ratio of output voltage to input current:

Rm = V_out / I_in

• Unit: ohm (Ω), or V/mA.
• Example: a photodiode amplifier converts a small diode current into an output voltage; with Rm = 100 kΩ, 10 µA input gives 1 V output.
• An amplifier described this way is a trans-impedance (trans-resistance) amplifier.

Gain

The ratio of an output quantity to the same kind of input quantity, so it has no unit:

Gain is often expressed in decibels: Av(dB) = 20 log₁₀ Av, Ap(dB) = 10 log₁₀ Ap. Example: Av = 100 means 40 dB.