* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Homework 9 - Engineering Class s - University of Southern California
Battle of the Beams wikipedia , lookup
Oscilloscope types wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Schmitt trigger wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
Signal Corps (United States Army) wikipedia , lookup
Integrated circuit wikipedia , lookup
Phase-locked loop wikipedia , lookup
Power electronics wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Analog television wikipedia , lookup
Oscilloscope history wikipedia , lookup
Analog-to-digital converter wikipedia , lookup
Transistor–transistor logic wikipedia , lookup
Superheterodyne receiver wikipedia , lookup
Cellular repeater wikipedia , lookup
Valve audio amplifier technical specification wikipedia , lookup
Two-port network wikipedia , lookup
Rectiverter wikipedia , lookup
Operational amplifier wikipedia , lookup
Radio transmitter design wikipedia , lookup
Index of electronics articles wikipedia , lookup
Regenerative circuit wikipedia , lookup
Negative-feedback amplifier wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Power MOSFET wikipedia , lookup
Current mirror wikipedia , lookup
U niversity of S outhern C alifornia School Of Engineering Department Of Electrical Engineering EE 348: Homework Assignment #09 (Due 04/25/2002) Spring, 2002 Choma Problem #35: In the common source feedback amplifier depicted in Fig. (P35), the current sources, IQi and IQo are ideal biasing currents in the sense that their terminal resistances can be taken as infinitely large. In the interest of analytical simplification, the channel resistance, ro, of the transistor can also be viewed as infinitely large. However, bulk-induced modulation of the forward transconductance cannot be ignored. Vdd Rf IQo Rs Vo Rout Vs IQi Rin Rss Rl Fig. (P35) (a). Use the low frequency small signal model of a MOSFET to show that the indicated driving point input resistance, Rin, is given by R R f l Rin , 1 g me Rl where gme represents the effective forward transconductance, g m gme @ . 1 1 g R b m ss (b). Use the low frequency small signal model of a MOSFET to show that the indicated driving point output resistance, Rout, is given by R R f s Rout . 1 g me Rs (c). A match-terminated amplifier, which is commonly exploited in broadband communication EE 348 University of Southern California J. Choma, Jr. system applications, is designed to ensure that Rs = Rl = Rin = Rout R. In terms of resistance R and effective forward transconductance gme, how must the feedback resistance, Rf, be selected to realize match-terminated performance? (d). Show that the small signal voltage gain, Av, of the match-terminated amplifier is V 1 g R me A o . v Vs 2 Problem #36: The transistors in the voltage reference circuit of Fig. (P31) operate in their saturation regimes. All transistors are identical except for the fact that while the gate aspect ratio of transistor M4 is unity, the gate aspect ratios of the remaining three devices are each 4. All transistor substrate terminals are grounded. Derive an expression for the indicated static voltage, Vref. Vdd IQ M3 M4 Vref M1 M2 Rout Fig. (P36) Problem #37: In the current reference circuit of Fig. (P37), transistors M1, M2, and M3 are identical, except for the fact that the gate aspect ration of M2 is k-times larger than that of M1, and the gate aspect ratio of M3 is k-times larger than that of M2. Transistors M4 and M5 are identical, inclusive of identical gate aspect ratios. All transistors operate in saturation, with the substrates of M1, M2, and M3 returned to ground and the substrates of M4 and M5 returned to the positive bus voltage. The drain of transistor M5 is connected to a load that is not shown in the diagram. Derive an expression for the static reference current, Iout. Homework #09 46 Spring Semester, 2002 EE 348 University of Southern California J. Choma, Jr. Vdd M4 M5 Iout Rout R M2 M3 M1 Fig. (P37) Problem #38: Revisit the circuits addressed in the preceding two problems. (a). Derive an expression for the small signal output resistance, Rout, in the circuit of Fig. (P37). (b). Derive an expression for the small signal output resistance, Rout, in the circuit of Fig. (P36). Problem #39: The NMOS transistors in the amplifier of Fig. (P39a) 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. Vdd ML Vo MD Rs CL Rth Vs Vos CL KthVs Vgg Vss (a). (b). Fig. (P39) (a). Reduce the small signal equivalent model of the subject amplifier to the Thévenin equiva- Homework #09 47 Spring Semester, 2002 EE 348 University of Southern California J. Choma, Jr. lent form abstracted in Fig. (P39b). Give “exact” and approximate expressions for the Thévenin parameters, Kth and Rth. (b). What is the time constant associated with the pole established by the load capacitance, CL? Approximate your “exact” result. (c). What is the overall voltage transfer function, Av(s) = Vos(s)/Vs(s)? Give an approximate expression for the voltage gain at zero signal frequency. (d). What are the 3–dB bandwidth and unity gain frequency of the amplifier? Approximate your “exact” results. Problem #40: In the CMOS amplifier of Fig. (P40a), both transistors operate in their saturated domains and do not have identical small signal parameters. Moreover, their channel resistances are not infinitely large. (a). Reduce the small signal equivalent model of the subject amplifier to the Norton equivalent form abstracted in Fig. (P40b). Give “exact” and approximate expressions for the Norton parameters, Gn and Rn. (b). What is the time constant associated with the pole established by the load capacitance, CL? Approximate your “exact” result. (c). What is the overall voltage transfer function, Av(s) = Vos(s)/Vs(s)? Give an approximate expression for the voltage gain at zero signal frequency. (d). What are the 3–dB bandwidth and unity gain frequency of the amplifier? Approximate your “exact” results. Vdd MP Vbb Vo MN Rs CL Vs Vos GnVs Rn CL Vgg Vss (a). (b). Fig. (P40) Problem #41: The NMOS transistors in the buffer of Fig. (P41a) are identical except for the fact that the gate aspect ratio of transistor M2 is k–times smaller than the gate aspect ratio of Homework #09 48 Spring Semester, 2002 EE 348 University of Southern California J. Choma, Jr. 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. Vdd Rs Rin M1 Rout Vs Rth Vo M2 CL Vbb Rout Vos CL KthVs Vgg Vss (a). (b). Fig. (P41) (a). Reduce the small signal equivalent model of the subject amplifier to the Thévenin equivalent form abstracted in Fig. (P41b). Give “exact” and approximate expressions for the Thévenin parameters, Kth and Rth. (b). What is the time constant associated with the pole established by the load capacitance, CL? Approximate your “exact” result. (c). What is the overall voltage transfer function, Av(s) = Vos(s)/Vs(s)? Give an approximate expression for the voltage gain at zero signal frequency. (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 #42: The current source, Idd, in the common gate amplifier of Fig. (P42a) is ideal in the sense that its small signal terminal resistance is infinitely large. On the other hand, Is is a signal current source. The channel resistance of the transistor, which operates in saturated mode, is large, but it is not infinitely large. (a). Reduce the small signal equivalent model of the subject amplifier to the Norton equivalent form abstracted in Fig. (P42b). Give “exact” and approximate expressions for the Norton parameters, Gn and Rn. (b). What is the time constant associated with the pole established by the load capacitance, CL? Approximate your “exact” result. (c). Give “exact” and approximate expressions for the low frequency input resistance, Rin. (d). What is the overall transimpedance function, Zv(s) = Vos(s)/Is? 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. Homework #09 49 Spring Semester, 2002 EE 348 University of Southern California J. Choma, Jr. Vdd Idd Vo MN Rs CL Rin Vs Rout Vos Rs Is GnVs Vgg (a). Rn CL (b). Fig. (P39) Problem #43: In the current amplifier of Fig. (P43), transistors M1, M2, and M3 are identical, save for the fact that the gate aspect ratio of transistor M1 is k–times smaller than that of M2 and M3. The signal is applied as the current, Is. (a). In terms of k, determine the small signal, low frequency current gain, Aio = IL/Is. (b). Give an expression for the 3–dB bandwidth, B, of the circuit. Assume that the capacitances intrinsic to all transistors are negligible. VDD R RL C M3 IL M1 Is M2 Fig. (P43) Homework #09 50 Spring Semester, 2002 EE 348 University of Southern California J. Choma, Jr. U niversity of S outhern C alifornia School Of Engineering Department Of Electrical Engineering EE 348: Homework Assignment #09 (SOLUTIONS: Due 04/25/2002) Spring, 2002 Choma Problem #35: Homework #09 51 Spring Semester, 2002