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Computer programs (such as Matlab, Mathematica, SPICE, etc) are not allowed. Problem #1 Calculate the frequency response of the folded cascode topology shown below. Don't confuse this topology with differential pair, as one of the transistors is an NMOS and the other is a PMOS. (Cox=1.0fF/um², VTN=0.7V, Vrp=0.7V, UnCax=50e-6 A/V², upCox=25e-6 A/V², An=Ap=0, = v=0. L.==.1um). VDD=5V t / bigs=500A Rs Vin 40/2.2 V bias =3.5V in o 80/2.2 (drawn) 1kQ (drawn) V out 10kQ RD Figure 1 a) Find KN, , Kp and Keal for the NMOS, PMOS, and tail NMOS transistors. (L=Ldrawn-2Ld) KN unCoxWN 2 = 2 L b) For an input dc voltage of 1.5V, calculate the transcondunctance and gate-to-source and gate-to-drain capacitances of each transistor. Ignore the fringing effects (Cov=CoxLd. For calculating the capacitors you can use the equations on pages 30-34 of Razavi. Ignore Cdb and Csb. gmn= Cgsn³ Cgdn² gmp= Cgsp Cgdp= c) Draw the small-signal model for the amplifier. Ignore gate-to-bulk and drain-to-bulk capacitors of the MOS transistors d) What is the low frequency voltage gain of the circuit? Av= e) Use the method of zero-value (open circuit) time constant to estimate the bandwidth of the above amplifier. Show all the time constants separately and identify the dominant source (sources) of bandwidth limitation). Tgsn Tgdn Tgsp = Tgdp f-3dB² Problem #2 The frequency response of the cascade topology can be modified by adding a shunt capacitor in parallel with the common-gate stage. Ignore all the transistor's parasitic capacitors and only consider Cx. You can ignore channel length modulation, but take body effect into account. The bulks are connected to ground. V DD R D V out V bias C, X M 2(gm2,gmb2) Vin in M1(gm1,gmb1) Figure 2 a) Draw the small signal equivalent of the above circuit. b) Use the above small signal model to calculate the small signal transfer function of the above circuit (Don't use any approximations beyond those mentioned above). c) Now use the method of zero-value time constants to find the bandwidth of the circuit in terms of circuit parameters. d) Do you see any discrepancy between the result directly obtained by calculating the transfer function in part b) and the result in part c)? In a few lines explain the reason for this discrepancy. Which one is the correct result?

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