University of Southern C alifornia School Of Engineering Department Of Electrical Engineering

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1 University of Southern C alifornia School Of Engineering Department Of Electrical Engineering EE 348: Homework Assignment #08 Spring, 2001 (Due 04/26/2001) Choma Problem #35: The NMOS transistors in the amplifier of Fig. (P35a) are identical except for the fact that the gate aspect ratio of the driver transistor, MD, is k times larger than the gate aspect ratio of the load device, transistor ML. The drain-source channel resistances of both transistors are large, but they are not infinitely large. Transistor MD is saturated. V dd ML MD KV th s R th s s Fig. (P35) Reduce the small signal equivalent model of the subject amplifier to the Thévenin equivalent form abstracted in Fig. (P35b). Give exact and approximate expressions for the Thévenin parameters, K th and R th. What is the time constant associated with the pole established by the load capacitance,? (c). What is the overall voltage transfer function, A v (s) = s (s)/ (s)? Give an approximate (d). What are the 3 db bandwidth and unity gain frequency of the amplifier? Approximate your exact results.

2 Problem #36: In the CMOS amplifier of Fig. (P36a), both transistors operate in their saturated domains and do not have identical small signal parameters. Moreover, their channel resistances are not infinitely large. Reduce the small signal equivalent model of the subject amplifier to the Norton equivalent form abstracted in Fig. (P36b). Give exact and approximate expressions for the Norton parameters, G n and R n. What is the time constant associated with the pole established by the load capacitance,? (c). What is the overall voltage transfer function, A v (s) = s (s)/ (s)? Give an approximate (d). What are the 3 db bandwidth and unity gain frequency of the amplifier? Approximate your exact results. MP V dd V bb MN s GV n s R n s Fig. (P36) Problem #37: A capacitance,, terminates the output port of the differential -to- single ended converter depicted in Fig. (4.26) of Lecture Supplement #4. Transistors M1 and M2 are identical, as are transistors M3 and M4, but the transistor pair, M1 M2, does not have small signal parameters identical to those of the M3 M4 pair. Assume that all transistors operate in their saturated regimes and that the common mode rejection ratio of the converter is infinitely large. What is the time constant associated with the pole established by the load capacitance,? What is the overall voltage transfer function, A v (s) = s (s)/ (s)? Give an approximate Homework #08 55 Spring Semester, 2001

3 (c). What are the 3 db bandwidth and unity gain frequency of the amplifier? Approximate your exact results. (d). In order for the circuit at hand to achieve a very large common mode rejection ratio, would you advocate a long or a short channel length for transistor M5? Briefly explain your conclusion. Problem #38: The NMOS transistors in the buffer of Fig. (P38a) are identical except for the fact that the gate aspect ratio of transistor M2 is k times smaller than the gate aspect ratio of the driver device, transistor M1. The drain-source channel resistances of both transistors are large, but they are not infinitely large. All transistors are saturated. V dd R in M1 V bb M2 R out KV th s R th R out s s Fig. (P38) Reduce the small signal equivalent model of the subject amplifier to the Thévenin equivalent form abstracted in Fig. (P38b). Give exact and approximate expressions for the Thévenin parameters, K th and R th. What is the time constant associated with the pole established by the load capacitance,? (c). What is the overall voltage transfer function, A v (s) = s (s)/ (s)? Give an approximate (d). What is the 3 db bandwidth of the amplifier? Approximate your exact results. Why is finding the unity gain frequency of the circuit inappropriate? Problem #39: The current source, I dd, in the common gate amplifier of Fig. (P39a) is ideal in the sense that its small signal terminal resistance is infinitely large. On the other hand, I s is a signal current source. The channel resistance of the transistor, which operates in saturated mode, is large, but it is not infinitely large. Homework #08 56 Spring Semester, 2001

4 Reduce the small signal equivalent model of the subject amplifier to the Norton equivalent form abstracted in Fig. (P39b). Give exact and approximate expressions for the Norton parameters, G n and R n. What is the time constant associated with the pole established by the load capacitance,? (c). Give exact and approximate expressions for the low frequency input resistance, R in. (d). What is the overall transimpedance function, Z v (s) = s (s)/i s? Give an approximate relationship for this transimpedance at zero signal frequency. (e). What are the 3 db bandwidth and unity transimpedance gain frequency of the amplifier? Approximate your exact results. V dd I dd R out MN R in I s GV n s R n s Fig. (P39) Problem #40: As discussed in class, that static output -versus- input characteristic of the NMOS common source amplifier depicted in Fig. (P35a) assumes the first order form provided herewith in Fig. (P40). For analytical simplification, the indicated curve is drawn for the special case of s = 0. Moreover, the threshold voltage, V H, of each transistor is presumed identical, while the indicated maximum output voltage is max = V dd - V H. Homework #08 57 Spring Semester, 2001

5 max MD Off MD Saturated min MD Ohmic 0 V H Fig. (P40) If? dl represents the ratio of the driver gate aspect ratio -to- the load gate aspect ratio, show that the minimum output voltage for s = 0 is Vdd - V V H omax V = =. omin 1 λ 1 λ dl dl Show that for s = 0, the optimum input bias voltage,, which results in maximum possible output signal swing is given by Vdd - VH Vgg = V H. 2 λdl ( 1 λdl ) (c). For V dd = 2.2 V, s = 0 V, V H = 750 mv, and a small signal voltage gain magnitude of 5, evaluate max, min, and the optimum input biasing voltage,. V imax V i Homework #08 58 Spring Semester, 2001

6 University of Southern C alifornia School Of Engineering Department Of Electrical Engineering EE 348: Homework Assignment #08 Spring, 2001 (SOLUTIONS: Due 04/26/2001) Choma Problem #35: Homework #08 59 Spring Semester, 2001