To calculate the input impedance and voltage gain of a common-drain (CD) MOSFET amplifier, also known as a source follower or voltage follower, you'll need to use the small-signal model of the MOSFET and analyze the circuit. Here are the steps to do so:
Small-Signal Model of the MOSFET:
The small-signal model of a MOSFET includes the transconductance (gm) and output conductance (gds) parameters. For a common-drain configuration, the small-signal model looks like this:
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____Rs____
Vi >---- | |----| | > Vo
| | |
|____| |
In this model:
Rs is the source resistor.
gm is the transconductance of the MOSFET.
gds is the output conductance of the MOSFET.
Vi is the small-signal input voltage.
Vo is the small-signal output voltage.
Calculate Input Impedance (Zin):
The input impedance (Zin) is the impedance seen at the input of the amplifier when a small-signal source is connected. It is given by the following formula:
Zin = Rs + (1/gm)
The first term (Rs) accounts for the resistance due to the source resistor, and the second term (1/gm) is the dynamic input impedance due to the MOSFET's transconductance.
Calculate Voltage Gain (Av):
The voltage gain (Av) of the common-drain amplifier is given by the ratio of the output voltage to the input voltage:
Av = Vo / Vi
To calculate the voltage gain, you need to consider the voltage divider formed by the output impedance (Ro) and the load impedance (RL) attached to the output. The output voltage (Vo) is related to the load voltage (Vload) by the formula:
Vo = Vload * (Ro / (Ro + RL))
Note that the output impedance (Ro) is given by:
Ro = 1 / gds
The load voltage (Vload) is the output voltage across the load resistor (RL) connected to the drain of the MOSFET.
By combining all these formulas, you can calculate the voltage gain of the common-drain MOSFET amplifier.
Keep in mind that these calculations are based on the small-signal model of the MOSFET, which assumes that the variations in the input and output signals are small enough to be approximated linearly. Large signal behavior and nonlinear effects are not considered in this analysis. Additionally, the MOSFET parameters gm and gds depend on the biasing conditions, which should be taken into account for accurate calculations.