For the DC analysis, the capacitors can be replaced by open circuits.
Since \(I_G \simeq 0\ A\) and \(I_D = I_S\)
\(\boxed{V_G = 0\ V}\)
\(V_{GS} + V_{R_S} = 0\) \(V_{GS} = - I_S R_S\)
\(\boxed{V_{GS} = - I_D R_S}\)
Substituting \(V_{GS}\) to Shockley’s equation:
\(I_D = I_{DSS} \left( 1 - V_{GS} / V_P \right) ^ 2\)
\(\boxed{I_D = I_{DSS} \left( 1 + \frac{I_D R_S}{V_P} \right) ^ 2}\)
\(-V_{DD} + I_D R_D + V_{DS} + I_S R_S = 0\) \(-V_{DD} + V_{DS} + I_D \left( R_D + R_S \right) = 0\)
\(\boxed{V_{DS} = V_{DD} - I_D \left( R_D + R_S \right)}\)
\(\boxed{V_D = V_{DD} - I_D R_D}\)
\(\boxed{V_S = I_D R_S}\)