Question

In the small signal circuit shown, the enhancement mode n-channel MOSFET is biased in saturation with transconductance \( g_m \). If channel length modulation is ignored, the small signal impedance looking into the node P is given by _________

• A. ( R_S \parallel R_L \parallel g_m^{-1} \)
• B. ( R_S \parallel g_m^{-1} \)
• C. ( (R_S + R_L) \parallel g_m^{-1} \)
• D. ( \frac{R_L g_m}{1 + R_S g_m} \parallel (R_L \parallel g_m^{-1}) \)

Hint:

For MOSFET small signal analysis, the impedance looking into the source is often dominated by \( R_S \parallel g_m^{-1} \), which is the inverse of the transconductance.

Answer 1

The Correct Option is B

Step 1: Analyzing the circuit.
The small signal impedance looking into the node P of the MOSFET can be calculated by considering the impedance looking into the gate and the transistor’s transconductance. Since the source degeneration resistor \( R_S \) is in parallel with the intrinsic MOSFET impedance, the overall impedance is dominated by \( R_S \) in parallel with the output impedance defined by \( g_m^{-1} \), the inverse of the transconductance. Step 2: Analyzing the options.
- (A) Incorrect, while this expression is a valid form for some circuits, it does not match the given setup here.
- (B) Correct, the small signal impedance looking into node P is dominated by \( R_S \parallel g_m^{-1} \), since the intrinsic impedance \( g_m^{-1} \) and \( R_S \) are in parallel.
- (C) Incorrect, this expression represents the impedance for a different configuration where both \( R_S \) and \( R_L \) are in series with the transconductance.
- (D) Incorrect, this expression is more complex than needed and is not the appropriate form for the given configuration. Step 3: Conclusion.
Thus, the correct answer is (B) \( R_S \parallel g_m^{-1} \).