A source-follower circuit with a saturated load is shown in Figure P4.57. The transistor parameters are \(V_{T N D}=1 \mathrm{~V}, K_{n D}=1 \mathrm{~mA} / \mathrm{V}^{2}\) for \(M_{D}\), and \(V_{T N L}=1 \mathrm{~V}, K_{n L}=0.1 \mathrm{~mA} / \mathrm{V}^{2}\) for \(M_{L}\). Assume \(\lambda=0\) for both transistors. Let \(V_{D D}=9 \mathrm{~V}\).

(a) Determine \(V_{G G}\) such that the quiescent value of \(v_{D S L}\) is \(4 \mathrm{~V}\).

(b) Show that the small-signal open-circuit \(\left(R_{L}=\infty\right)\) voltage gain about this \(Q\)-point is given by \(A_{v}=1 /\left[1+\sqrt{K_{n L} / K_{n D}}\right]\).

(c) Calculate the small-signal voltage gain for \(R_{L}=4 \mathrm{k} \Omega\). 

VGG +1 VDD Mp Cc Figure P4.57 Mr. VDSL R RL