Introduction to Small Signal Model

Q1: How can I analyze real amplifier circuits?
A1: You can divide the amplifier circuit into its signal circuit and bias circuit. For now, we will consider the signal circuit.

Q2: How do I map real circuit elements to their signal circuit counterparts?
A2: By using their small signal models (SSM):

Resistors and capacitors behave the same in signal circuits

Independent voltage sources mapped to short circuits while
independent current sources are mapped to open circuits

Things change a bit with nonlinear elements.
The diode maps to a resistor of $r_d=\frac{nV_T}{I_D}$

$r_\pi=\frac{V_T}{I_B}$
$g_m=\frac{I_C}{V_T}=\frac{\beta}{r_\pi}$
$r_o\approx \frac{V_A}{I_C}$

Both the NPN and PNP map to the same SSM

$g_m=\frac{2I_D}{V_{OV}}$
$r_o\approx \frac{1}{\lambda I_D}$
Both the NMOS and PMO map to the same SSM