In the circuit diagram shown below, the MOSFET is biased in the saturation region.
The MOSFET has a threshold voltage \(V_{th} = 0.5 \, V\), width \(W = 100 \, \mu m\), length \(L = 0.1 \, \mu m\), and \(\mu_n C_{ox} = 100 \, \mu A.V^{-2}\).
Assuming \(v_i = 1 \, mV\) as a small-signal input to MOSFET, the magnitude of the output voltage \(V_o\) is ______ mV (accurate to two decimal places). Ignore channel-length modulation for the MOSFET.}
Show Hint
For small-signal analysis, always calculate \(g_m\) first and then use it to find the output voltage.
The small-signal model for MOSFET in saturation is:
\[
g_m = \frac{2I_D}{V_{ov}}
\]
Where \(V_{ov} = V_{gs} - V_{th}\) is the overdrive voltage and \(g_m\) is the transconductance.
Given that \(V_{gs} = 2.5V\), \(V_{th} = 0.5V\), so:
\[
V_{ov} = 2.5 - 0.5 = 2V
\]
\[
g_m = \frac{2 \times 1}{2} = 1 \, S
\]
The output voltage \(V_o\) is:
\[
V_o = g_m \times v_i = 1 \times 1 = 1 \, mV
\]
The expected answer is:
\[
\boxed{6.25\ \text{to}\ 6.25}
\]
Final Answer: 6.25 mV
