MOSFET Amplifiers

Small-Signal Model

As MOSFETs have no gate current, their small signal model is much simpler than that of a BJT.

Between the gate and the source is an open circuit, but the voltage between the two sets the dependant current source $i_D=g_m\times V_{GS}$. The MOSFET also has infinite input impedance.

Common-Source Amplifier

Similar to a BJT common emitter amplifier, can construct a MOSFET common source amp:

Using the small signal model of the MOSFET, this amplifier looks like this:

Drain current $i_D=g_m{V}_{GS}$, so:

$$V_{out}=-g_m{V}_{DS}{R}_D$$

$$V_{in}=V_{GS}+g_m{V}_{GS}{R}_S$$

$$A_v=\frac{-g_m{V}_{DS}{R}_D}{V_{GS}+g_m{V}_{GS}{R}_S}=\frac{-g_m{R}_D}{1+g_m{R}_S}\approx \frac{-R_D}{R_S}$$

Note that transconductance in a MOSFET is:

$$g_m=\frac{2i_{DQ}}{V_{GS}-V_{TN}}$$

This is much lower than transconductance in a BJT, hence the gain is much lower/

Bypass Capacitors

Adding a bypass capacitor to the amplifier increases the gain, while keeping the DC Q-point stable. Remember that capacitors act as short circuits in AC, and open circuits in DC.

$$A_v=\frac{-g_m{R}_D{V}_{GS}}{V_{GS}}=-g_m{R}_D$$

The gain of the amplifier with a bypass capacitor is much higher.

Input and Output Impedance

• The input impedance of a MOSFET is infinite, as no current flows between gate and source.
• The overall input impedance of a common source MOSFET amp is $R_{in}=R_{TH}=R_1||R_2$, as the two gate bias resisisors will act as impedances to input signals
• The output impedance of the bypassed amplifier above is just $R_D$, as that's the only impedance in the model.
  • If $R_D=0$, like in a common drain/source follower, then this becomes $1/g_m$
• MOSFETs have higher input impedances for this reason, so MOSFET amplifiers are used over BJTs where high impedance is required.