Transistor signal notation convention

The case of a symbol and the case of its subscript tell you whether it’s a DC bias, total instantaneous, or small-signal AC quantity. Every transistor textbook uses this, and getting it wrong means confusing a bias point with a signal.

A transistor in an amplifier carries a small AC signal riding on top of a DC bias. At the gate-source terminal, the total voltage at any instant is

$v_{GS}(t)=V_{GS}+v_{gs}(t)$

the DC bias plus the small wiggle. Three different quantities, three different notations:

Notation	Case pattern	Meaning	Example
$V_{GS}$, $I_D$	UPPER symbol, UPPER subscript	DC (bias / quiescent) value	the operating point
$v_{GS}$, $i_D$	lower symbol, UPPER subscript	total instantaneous value	DC + AC combined, as a function of time
$v_{gs}$, $i_d$	lower symbol, lower subscript	small-signal AC part only	the wiggle alone

So $v_{GS}(t)=V_{GS}+v_{gs}(t)$ reads: total instantaneous = DC + small-signal. The same pattern holds for currents: $i_D=I_D+i_d$.

$V_{GS}$ DC, $v_{gs}(t)$ small AC, $v_{GS}(t)=V_{GS}+v_{gs}(t)$ total.

Why the distinction is load-bearing

Small-signal analysis depends on separating these. You first solve the uppercase circuit (DC only, the Operating point, using the MOSFET large-signal model). Then you solve the lowercase circuit (AC only, DC sources zeroed). The relations differ: the DC current obeys the nonlinear MOSFET square-law $I_D=\frac{1}{2}{k}_n{V}_{OV}^2$, while the AC current obeys the linear $i_d=g_m{v}_{gs}$. Writing $i_D$ when you mean $i_d$, or $V_{GS}$ when you mean $v_{gs}$, silently mixes a nonlinear bias equation with a linear signal one. Read the cases before reading the symbol.