Question

How do you calculate the input impedance and voltage gain of a common-drain MOSFET amplifier?

Answer 1

To calculate the input impedance and voltage gain of a common-drain MOSFET amplifier, also known as a source follower or voltage follower, we need to analyze its small-signal equivalent circuit. The small-signal model of a common-drain MOSFET amplifier consists of a small-signal resistance and a voltage source.

Small-Signal Equivalent Circuit:
The small-signal equivalent circuit for a common-drain MOSFET amplifier is shown below:
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Vin -- Rs --|+|-- ID --|D|-- Rd -- Vout
          |-|          |
           |-gm*Vgs---|


Where:

Vin is the small-signal input voltage.
Rs is the small-signal source resistance (usually the internal resistance of the signal source).
ID is the small-signal drain current (varies with the input voltage).
Rd is the small-signal drain resistance (output load resistance).
Vout is the small-signal output voltage.
gm is the transconductance of the MOSFET (dI_D/dV_gs).
Vgs is the small-signal gate-source voltage.
Calculate the Transconductance (gm):
The transconductance (gm) is given by the equation:

gm = 2 * sqrt(ID * k' * (W/L))

Where:

ID is the DC bias drain current (quiescent operating point).
k' is the MOSFET transconductance parameter (a technology-dependent constant).
W/L is the width-to-length ratio of the MOSFET.
Input Impedance (Zin):
The input impedance of the common-drain amplifier is calculated at the gate terminal with the output (Vout) open. It is given by:

Zin = Rs + (1 + gm * Rd) / gm

Voltage Gain (Av):
The voltage gain of the common-drain amplifier is defined as the ratio of the change in output voltage (ΔVout) to the change in input voltage (ΔVin) at a certain frequency. Since the output voltage (Vout) follows the input voltage (Vin) directly, the voltage gain is approximately 1.

Av ≈ ΔVout / ΔVin ≈ 1

Keep in mind that the voltage gain is close to 1 due to the nature of the common-drain amplifier, which is used mainly for impedance matching and voltage buffering rather than voltage amplification.

Remember that the calculations above are based on the small-signal model, which assumes small variations in the input and output voltages around the DC operating point. For a more accurate analysis, you should also consider other non-idealities such as channel-length modulation, early effect, and finite output resistance.