MOSFET characteristics and the common-source amplifier

Set the bias and watch the Q-point move on the load line. Then feed in a sine: see the gain, the 180° inversion and the moment the output clips as the transistor leaves saturation, with small-signal and exact output side by side.

V_{GS}\text{ bias } V_B

1.5 V

\text{input amplitude } v_{in}

100 mV

R_D

2 kΩ

V_{DD}

5 V

\lambda

0.030 V⁻¹

Device: $V_t = 0.5\,\text{V},\; k_n' \tfrac{W}{L} = 2\,\text{mA/V}^2$

I_D

1.08 mA

V_{DS}

2.83 V

g_m

2.17 mS

r_o

33.3 kΩ

A_v = -g_m(R_D \parallel r_o)

-4.09

Q-point: saturation

Signal through the amplifier

What to notice

Saturation: $g_m = k_n V_{ov} = 2.17 mS$ , so $A_v = -g_m (R_D \parallel r_o) = -4.09$ . The minus sign is the 180° phase inversion you see between input and output.
Still within saturation over the whole cycle, but look closely: the output is no longer a perfect sine. The square law adds second-harmonic distortion as the swing grows.
Swing limits: the bottom of the output is set by entering triode ( $V_{DS} = V_{GS} - V_t$ ), the top by cut-off ( $V_{DS} \to V_{DD}$ ). Bias in the middle of that range for the largest undistorted swing.
Channel-length modulation gives finite $r_o = 1/\lambda I_D = 33.3 k\Omega$ , which caps the gain at the intrinsic gain $g_m r_o = 72.3$ even if $R_D \to \infty$ .

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