The parameters of an ideal n-channel MOSFET are \(W / L=8\), \(\mu_{n}=400 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}, C_{\mathrm{ox}}=6.9 \times 10^{-7} \mathrm{~F} / \mathrm{cm}^{2}\), and \(V_{T N}=0.4 \mathrm{~V}\).

(a) Determine the maximum source resistance such that the transconductance \(g_{m}\) is reduced by no more that 20 percent from its ideal value when \(V_{G S}=3 \mathrm{~V}\).

(b) Using the results of part (a), find how much \(g_{m}\) is reduced from its ideal value when \(V_{G S}=1 \mathrm{~V}\).