What is transconductance?

Hint: It is electrical characteristic relating the current flowing through the output and the voltage arising in the input of electrical circuit/devices. It is also known as mutual conductance. Reciprocal resistance gives the conductance. It is usually used for direct current circuits.

Formula used:
${g_m} = \dfrac{{\Delta {I_{out}}}}{{\Delta {V_{in}}}}$, where ${g_m}$ denotes the transconductance, (m for mutual), $\Delta {I_{out}}$ denotes the current through the output and $\Delta {V_{in}}$ represents the input voltage.

Complete step by step answer:
Transconductance is the ratio of the current flowing through the output and the voltage arising in the input of electrical circuit/devices. Transconductance is calculated using the equation

${g_m} = \dfrac{{\Delta {I_{out}}}}{{\Delta {V_{in}}}}$

It is used in bipolar junction transistors in order to measure its sensitivity. Transconductance shows how sensitive collected current ${I_C}$ is with respect to the base emitter voltage ${V_{BE}}$.

It is represented by the equation ${g_m} = {\left. {\dfrac{{{\text{d}}{{\text{i}}_C}}}{{{\text{d}}{{\text{v}}_{BE}}}}} \right|_{Q - po\operatorname{int} }}$

Substituting ${i_c} = {I_s}{e^{\dfrac{{{v_{BE}}}}{{{v_T}}}}}$, we get

${g_m} = {\left. {\dfrac{{\text{d}}}{{{\text{d}}{{\text{v}}_{BE}}}}\{ {I_s}{e^{\dfrac{{{v_{BE}}}}{{{v_T}}}}}\} } \right|_{Q - po\operatorname{int} }}$
\[{g_m} = \dfrac{1}{{{V_T}}}{I_s}{e^{\dfrac{{{v_{BE}}}}{{{v_T}}}}}\]

${g_m} = \dfrac{{{I_C}}}{{{V_T}}}$, where ${I_C}$ is the DC collector current at the Q-point and ${V_T}$ is the thermal voltage.

This is the transconductance for a bipolar junction transistor (BJT).
For an FET, transconductance is the ratio of change in drain current to the change in gate voltage over an arbitrary small interval on the graph of drain current versus gate voltage curve.

A transconductance amplifier gives current proportional to its input voltage. Transconductance amplifier is generally known as voltage controlled current source.

Note: The SI unit of transconductance is siemens which is usually denoted by the symbol $S$. 1 siemens is equal to 1 ampere per volt. The measure of transconductance is commonly used in reference to vacuum tube ratings as well as some electronic devices.