To calculate the input impedance and voltage gain of a common-drain MOSFET amplifier (also known as a source follower), you'll need to analyze its small-signal model. This involves using small-signal equivalent circuits and applying basic circuit analysis techniques. Here are the steps:
Small-Signal Model of the MOSFET:
The small-signal model of a MOSFET typically includes the following components:
rds: Drain-source resistance (output resistance)
gm: Transconductance (small-signal transconductance)
rd: The internal resistance between the gate and the source (reverse-biased pn-junction)
Cgs: Gate-source capacitance
Cgd: Gate-drain capacitance
Input Impedance (Zin):
The input impedance is the impedance seen at the input terminals of the amplifier when a small AC signal is applied. To calculate the input impedance (Zin) of the common-drain MOSFET amplifier, you can ignore the gate-drain capacitance (Cgd) in most cases, assuming it's relatively small. The formula for Zin is:
Zin ≈ Rd || (1/gm)
Where:
Rd is the drain resistance (load resistor connected to the drain).
Voltage Gain (Av):
The voltage gain is the ratio of the small-signal output voltage to the small-signal input voltage. For the common-drain amplifier, the voltage gain is less than unity (less than 1). The voltage gain can be calculated using the formula:
Av ≈ 1
The reason the voltage gain is close to 1 for a common-drain amplifier is because it acts as a voltage buffer. It has a high input impedance and low output impedance, making it an ideal buffer to provide isolation between the input and output signals.
It's important to note that these are approximate calculations and assume ideal transistor behavior. In practical applications, additional factors such as channel length modulation, early effect, and non-ideal capacitances should be considered for accurate analysis. Moreover, the biasing of the MOSFET also plays a crucial role in determining the small-signal parameters.
For more accurate calculations, you would need to know specific transistor parameters from the datasheet or measure them in the laboratory using test equipment.