*9.21 The resistance R s in the circuit of Fig. P9.20 can be implemented by using a MOSFET operated in the triode region, as shown in Fig. P9.21. Here Q3 implements Rs, with the value of R s determined by the voltage VC at the gate of Q3.(a) With vG1 = vG2 = 0 V, and assuming that Q1 and Q2 are operating in saturation, what dc voltages appearat the sources of Q1 and Q2? Express these in terms of the overdrive voltage VOV at which each of Q1 and Q2 operates, and Vt. (b) For the situation in (a), what current flows in Q3? What overdrive voltage VOV3 is Q3 operating at, in terms of VC, V OV, and Vt? (c) Now consider the case vG1 = +vid/2 and vG2 = −vid/2, where v id is a small signal. Convince yourself that Q3 now conducts current and operates in the triode region with a small v DS. What resistance rDS does it have, expressed in terms of the overdrive voltage VOV3 at which it is operating? This is the resistance Rs. Now if all three transistors have the same W/L, express Rs in terms of V OV, VOV3, and gm1,2. (d) Find VOV3 and hence VC that result in (i) Rs = 1/gm1,2; (ii) R s = 0.5/gm1,2.

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images - *9.21 The resistance R s in the circuit of Fig. P9.20 can be implemented by using a MOSFET operated in the triode region, as shown in Fig. P9.21. Here Q3 implements Rs, with the value of R s determined by the voltage VC at the gate of Q3.(a) With vG1 = vG2 = 0 V, and assuming that Q1 and Q2 are operating in saturation, what dc voltages appearat the sources of Q1 and Q2? Express these in terms of the overdrive voltage VOV at which each of Q1 and Q2 operates, and Vt. (b) For the situation in (a), what current flows in Q3? What overdrive voltage VOV3 is Q3 operating at, in terms of VC, V OV, and Vt? (c) Now consider the case vG1 = +vid/2 and vG2 = −vid/2, where v id is a small signal. Convince yourself that Q3 now conducts current and operates in the triode region with a small v DS. What resistance rDS does it have, expressed in terms of the overdrive voltage VOV3 at which it is operating? This is the resistance Rs. Now if all three transistors have the same W/L, express Rs in terms of V OV, VOV3, and gm1,2. (d) Find VOV3 and hence VC that result in (i) Rs = 1/gm1,2; (ii) R s = 0.5/gm1,2.

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