BJT and MOSFET Amplifiers

Transistors amplify small signals. Design has two steps: set a stable DC operating point (biasing), then find the small-signal gain and impedances.

BJT

• Regions: active (amplifier: BE forward, BC reverse), saturation and cut-off (switch).
• I_C = β I_B, I_E = I_B + I_C, α = β/(1 + β).
• Voltage-divider bias gives the best stability against β changes; stability factor S = ∂I_C/∂I_CO.
• Thermal runaway is prevented by emitter resistance and heat sinks.

Small-signal (hybrid-π) model: g_m = I_C/V_T, r_π = β/g_m, r_o = V_A/I_C.

An unbypassed emitter resistor R_E gives negative feedback: gain ≈ −R_C/R_E, more stable but lower.

MOSFET

• Saturation (amplifier region): I_D = (k/2)(V_GS − V_T)² (k = μC_ox W/L), for V_DS ≥ V_GS − V_T.
• Linear (triode) region: I_D = k[(V_GS − V_T)V_DS − V_DS²/2].
• g_m = k(V_GS − V_T) = √(2k I_D) = 2I_D/(V_GS − V_T).
• Common source gain = −g_m (R_D ∥ r_o). Very high input resistance (insulated gate).
• Enhancement vs depletion; n-channel vs p-channel; CMOS uses both.

Frequency response

• Low-frequency cut-off from coupling and bypass capacitors; high-frequency cut-off from junction capacitances.
• Miller effect: a capacitance C between input and output of an inverting amplifier with gain −A appears at the input as C(1 + A), which limits bandwidth.
• Gain–bandwidth product is roughly constant.
• Cascading n identical stages: overall gain multiplies, bandwidth shrinks.

Worked example

A BJT has I_C = 2 mA (V_T = 25 mV) and R_C = 2 kΩ in a CE stage.

• g_m = 2/25 = 80 mA/V; gain = −80 × 10⁻³ × 2000 = −160.

Practice