Basic Principles (7.1)

MOSFET (the BJT) as an amplifier: when the transistor is operated in the active region, $V_{GS}$ controls $i_D$ ($V_{BE}$ controls $i_C$) in the manner of a voltage-controlled current source.

• When the device is DC biased in the active region, and the signal $V_{gs}$($V_{be}$) is kept small, the operation becomes almost linear, with $i_d = g_m v_{gs}$ ($i_c = g_mv_{be}$)

Small-Signal Operation (7.2)

Fundamental parameter is characterizing the small-signal linear operation is transconductance $g_m$

• For a MOSFET:

  $$ g_m = \mu n C{ox} (W/L) V_{ov} \newline = \sqrt{2 \mu n C{ox}(W/L)I_D} \newline = \frac{2I_D}{V_{ov}} $$

• For the BJT:

  $$ g_m = \frac{I_C}{V_T} $$

• Transconductance $(g_m)$: represents the control of the gate-source voltage $V_{GS}$ has on the drain current $I_D$ in a MOSFET, or the base-emitter voltage $V_{BE}$ on the collector current $I_C$ in a BJT

  • Depicted as a controlled current source

• Output resistance $(r_o)$: ****Models effect of channel-length modulation in MOSFETs or Early effect in BJTs

  • Variation of current flow with changes in the voltage across the transistor
  • Appears as a resistor in the output part of the models

• Input resistance $(r_{\pi})$ or $(r_{in})$: ****For BJTs, $r_{\pi}$ is the dynamic resistance at the base-emitter junction, and is derived as $r_{\pi} = \frac{\beta}{g_m}$

  • In MOSFETs, the gate is insulated, so input resistance is typically infinite, and there is no direct counterpart of $r_{\pi}$ in the MOSFET models

Analysis Procedure of Transistor Amplifier Circuits

1. Eliminate the signal source and determine the DC operating point of the transistor
2. Calculate the values of the parameters of the small-signal model
3. Eliminate the DC sources:
   1. Replace each DC voltage by a short circuit
   2. Replace each DC current source by an open circuit
4. Replace the transistor with one of its small-signal, equivalent-circuit models
   1. Although any of the models can be
5. Analyze the resulting circuit to determine the required quantities (i.e., voltage gain, input resistance)

Small-Signal Models of the MOSFET

• Hybrid-$\pi$ model: transconductance $g_m$ as a current source $g_mv_{gs}$, which models the control of the drain current by the gate-source ($v_{gs}$)