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In the context of MOSFETs, small-signal parameters are essential to understanding how a circuit behaves when subject to small, dynamic input variations. For a MOSFET source follower, the two critical small-signal parameters are transconductance (\( g_m \)) and output resistance (\( r_o \)). Transconductance (\( g_m \)) measures how effectively the MOSFET converts a change in input voltage to output current, and is typically expressed in \( \ ext{mA/V} \). In this exercise, \( g_m = 5 \ ext{ mA/V} \), representing robust current control.The second parameter, \( r_o \), the output resistance, indicates the MOSFET's resistance to changes in voltage when the output current changes. Given here as \( 100 \ ext{ k}\Omega \), it illustrates how the MOSFET stabilizes the output under varying load conditions. Understanding these parameters helps in predicting how the follower will respond to different load and signal conditions.

Calculating the voltage gain in a MOSFET source follower requires accounting for the small-signal parameters. The voltage gain is a measure of how much the input signal is amplified at the output. For the no-load condition, the voltage gain \( A_v \) is determined by the formula:\[A_v = \frac{g_m \cdot r_o}{g_m \cdot r_o + 1} \]Given \( g_m = 5 \ ext{ mA/V} \) and \( r_o = 100 \ ext{ k}\Omega \), calculating \( A_v \) gives approximately \( 0.998 \). This high voltage gain close to unity demonstrates the source follower's efficacy in minimal signal attenuation.When a load is introduced, as in this exercise, the voltage gain calculation changes slightly. The modified output resistance (\( R'_\text{out} \)) interacts with the load to affect how much of the original no-load gain is preserved, resulting in a slightly lower voltage gain of about \( 0.960 \).

Output resistance (\( R_\text{out} \)) in a source follower plays a crucial role in determining how the circuit interacts with downstream components. In essence, it defines how much voltage drops across this internal resistance, which affects the signal delivered to the load. For a MOSFET source follower without a load, \( R_\text{out} \) is calculated using:\[R_\text{out} = \frac{r_o}{1 + g_m \cdot r_o}\]Substituting the given values, \( R_\text{out} \) approximates to \( 199.6 \) \( \Omega \). This low resistance is beneficial, characteristic of the high stability conducive for buffering applications.When a load is connected, the output resistance is recalculated considering the parallel effect of the load and \( r_o \), stressing the need for precise calculation to maintain optimal performance in the context of load variations.

In a source follower, load resistance (\( R_L \)) significantly impacts the overall circuit performance, especially its voltage gain and output resistance. The load resistance is the resistance into which the source follower delivers the current, and it acts in parallel with the original output resistance.The effect of \( R_L \) can be visualized through the modified voltage gain formula, which accommodates this load:\[A'_v = \frac{g_m \cdot R'_\text{out}}{1 + g_m \cdot R'_\text{out}}\]Here, \( R'_\text{out} \) depends on both \( r_o \) and \( R_L \), formulated as:\[R'_\text{out} = \frac{R_L \cdot r_o}{R_L + r_o}\]Inclusion of a load modifies the output resistance and consequently lowers the voltage gain from approximately \( 0.998 \) (no-load) to about \( 0.960 \) (with \( R_L = 5 \text{k}\Omega \)). This demonstrates the load's impact, necessitating design considerations for preserving desired performance with expected loads.