To calculate the small-signal output resistance (ro) of a common-drain (CD) MOSFET amplifier, you can follow these steps:
Identify the small-signal equivalent circuit: For small-signal analysis, you need to consider the small-signal equivalent circuit of the MOSFET. The common-drain configuration is also known as the source follower, so the small-signal equivalent circuit will have a similar structure.
Draw the small-signal equivalent circuit: The small-signal equivalent circuit for the common-drain MOSFET amplifier consists of a signal voltage source (Vsig) at the input, the source follower transistor (MOSFET), and the output load resistance (RL).
Apply small-signal model for MOSFET: In the small-signal equivalent circuit, the MOSFET will be represented by a small-signal transconductance (gm) and a small-signal output resistance (ro). The transconductance (gm) is the small-signal counterpart of the MOSFET's transconductance in the large-signal model, and the output resistance (ro) is the small-signal counterpart of the MOSFET's output resistance in the large-signal model.
Short-circuit the input source: For calculating the output resistance (ro), you need to short-circuit the input signal source (Vsig). This is because you are interested in finding the small-signal resistance at the output when there's no input signal.
Apply test voltage: Apply a small test voltage (Vtest) at the output node where the load resistance (RL) is connected. Assume this test voltage causes a small change in output current (ΔIout).
Analyze the circuit: Using the small-signal equivalent circuit with the short-circuited input, analyze the circuit to find the relationship between the small-signal output voltage (Vout) and the small change in output current (ΔIout).
Calculate the output resistance (ro): The small-signal output resistance (ro) can be calculated using the following formula:
ro = ΔVout / ΔIout
Where ΔVout is the small change in output voltage caused by the test current ΔIout.
It's important to note that the MOSFET's small-signal output resistance (ro) is typically quite large, often in the order of tens to hundreds of megaohms, especially for modern MOSFETs with smaller feature sizes.
Remember that the small-signal model assumes that the MOSFET operates in the linear region, where the changes in voltages and currents are small enough to be considered as variations around the DC bias point. Additionally, for more accurate results, parasitic elements (like the channel length modulation effect) should be taken into account in the MOSFET model.