Q.What is trans conductance? write the relation between g_m, g_mo, V_GS and V_P.

Transconductance measures how strongly the gate voltage controls the drain current, and its value at any bias is tied to its zero-bias value by a simple linear relation. …

[!TLDR]

Transconductance $g_m = \Delta I_D/\Delta V_{GS}$ (at constant $V_{DS}$); it varies with bias as $g_m = g_{mo}\left(1 - \tfrac{V_{GS}}{V_P}\right)$.

Transconductance (or forward transconductance) $g_m$ describes the control the gate voltage has over the drain current. It is defined as $g_m = \Delta I_D/\Delta V_{GS}$ at constant $V_{DS}$ and is measured in siemen (S). Its value is largest when the gate bias is zero, this maximum value being $g_{mo}$, and it decreases as the reverse $V_{GS}$ increases. Obtained by differentiating Shockley's equation, the dependence is

$g_m = g_{mo}\left(1 - \frac{V_{GS}}{V_P}\right)$ …