Consider the following amplifier:

Notice the capacitors \(C_C,\ C_E,\ C_L\).

• \(C_C\) is an input coupling capacitor
• \(C_E\) is an output coupling Capacitor
• \(C_L\) is a bypass capacitor

A bypass capacitor minimizes loss

Corner Frequencies

\[f_L = \frac{1}{2 \pi {\tau}_S}\] \[f_H = \frac{1}{2 \pi {\tau}_P}\] \[{\tau}_S = R_{EQ} C_C\] \[{\tau}_P = R_{EQ} C_L\]

• Low-pass network: low frequency passes, high frequency decays -> bypass capacitor
• High-pass network: high frequency passes, low frequency decays -> coupling capacitor

Low-pass and high-pass network can be analyzed separately: Low frecuency -> bypass = open circuit High frequency -> coupling = short

In mid-band range:

• Coupling, bypass capacitors -> short
• Load, stray, transistor capacitors -> open

Small-signal voltage gain = Mid-band Gain

Voltage transfer function:

\[T(s) = \frac{V_o(s)}{V_i(s)}\]

Use s-domain analysis to get V_o(s) and V_i(s). Then replace s with \(j\omega\).

Amplifier Analysis

Keep capacitors in small-signal model