For BJT, the term "gm" refers to base-emitter conductance. But when we are talking about FETs and MOSFETs, where is this "gm"? Between gate-source junction for JFET? Drain to source conductance for MOSFET?
And what "gmb" means when talking about MOSFETs?
Answer
In general $g_m$ in simple term is a "gain" for any transconductance amplifier. And because transconductance amplifier is nothing more then a voltage controlled current source (VCCS) the gain expression is $g_m = \frac{I_{out}}{V_{in}}$.
For example if is $g_m = 1\:Siemens$ any change in the input voltage by $1V$ will change the output current by $1A$ (1 Ampere per Volt).
For BJT the transistor $I_C$ current is a controlled via input$V_{BE}$ voltage.
So, you plot $I_C$ vs $V_{BE}$
The $g_m$ is the slope of this curve
In MOSFET & JFET we have the same situation.
The output current $I_D$ is controlled via $V_{GS}$ voltage.
Hence again the slope of a $I_D = f(V_{GS})$ is a $g_m =\frac{dI_D}{dV_{GS}} $
The MOSFET in general is a 4 terminal device. The Gathe, Soure, Drain and the Body. And we can control the $ I_D $ via the gate terminal or via the Body. And this is why you have $ g_{mb} $
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