Response to the following problem:
The circuit of Fig. shows an effective way of implementing the resistance Rs needed for the circuit. Here Rs is realized as the series equivalent of two MOSFETs Q3: and Q4: that are operated in the triode region, thus, Rs = rDS3 + rDS4. Assume that Q1: and Q2: are matched and operate in saturation at an overdrive voltage VOV that corresponds to a drain bias current of I/2. Also, assume that Q3: and Q4: are matched.
(a) With vG1 = vG2 = 0 V, what dc voltages appear at the sources of Q1: and Q2: What current flows through Q3: and Q4: At what overdrive voltages are Q3: and Q4: operating?
Find an expression for rDS for each of Q3: and Q4: and hence for Rs in terms of (W/L)1,2, (W/L)3,4, and gm1,2.
(b) Now with vG1 =vid/2 and vG2 =-vid /2, where vid is a small signal, find an expression of the voltage gain Ad ≡vod /vid in terms of gm1,2, RD, (W/L)1,2, and (W/L)3,4.