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Unformatted text preview: University of Southern California Ming Hsieh Department of Electrical Engineering EE 202L  Linear Circuits Homework Set #2 Due in class, Thursday, 6 October Problems 1.40, 1.45, 1.55, 1.59 Problems A, B, C, and D (from old exams) These problems and others (for practice) are attached. Extra notes regarding comparators are attached. PROBLEMS 47 1.38 Consider the circuit of Fig. P1.38. (a) Determine node voltages v a and v b in terms of node voltage v x , then find voltage v and the output current i out . (b) Complete a design such that i out = 1 mA when v 1 = 2 V. + R R R v 1 1 1 1 + + R L + i out R 2 v ` R 3 v x v b R 2 v a Figure P1.38 Special Operations 1.39 Consider the circuit of Fig. P1.39. (a) Show that the circuit is an integrator with v out ( t ) = 1 RC Z t v in ( t ) dt . (b) Suppose v in is a square wave that alternates be tween 2 V and +2 V with a 1ms period, and let C = 0 . 1 F. Find R such that v out has a 2V amplitude, then sketch the output waveform. Chapters 13 and 15 examine applications for the op amp integrator. + v out + + v in R C Figure P1.39 1.40 Consider the circuit of Fig. P1.40. (a) Show that the circuit is a differentiator with v out ( t ) = RC dv in dt . (b) Suppose v in = sin(2000 t ), and let C = 0 . 1 F. Determine R such that v out has a 5V amplitude, then sketch the output waveform. + v out + + v in R C Figure P1.40 1.41 The circuit of Fig. P1.41 has periodic output. Specify the functional form of the output as well as the output frequency. Note: This textbook circuit is not very practical since the output voltage amplitude is undetermined. Extreme v out excursions near the powersupply levels add nonlinear distortion to the idealized waveform. (You may want to build the circuit to observe the actual output characteristic.) c 2010 Edward W. Maby All Rights Reserved 48 CHAPTER 1 BLACKBOX ELECTRONICS v out + R C + R C + R 1 2 2 3 1 R 3 Figure P1.41 1.42 Consider the circuit of Fig. P1.42. (a) Show that the circuit functions as an negative impedance converter with Z in = R 1 R 2 Z . (b) Let R 1 = R 2 , Z = R , and connect a capacitor ( C ) and inductor ( L ) in series with defined Z in . Describe the behavior of this new circuit. + Z R 1 R 2 Z in Figure P1.42 1.43 A cascade of two negative impedance converters (see Problem 1.42) yields the Riordan circuit of Fig. P1.43. (a) Show that Z in = Z 1 Z 2 Z 3 Z 4 Z . (b) Show that Z in takes the form of an inductive impedance when the Riordan circuit contains four resistors and one capacitor. + Z 1 Z 2 Z in + Z Z 3 Z 4 Figure P1.43 1.44 A gyrator is a twoport network (Fig. P1.44a) with the terminal relations v 1 = R 1 i 2 , i 1 = 1 R 2 v 2 . (a) Show that the circuit of Fig. P1.44b conforms to the gyrator relations....
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