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Model the op amp with the practical equivalent circuit of Fig. 9-1(a). (b) Let R1 ! 1 and R2 ! 0 in your answer to part a, to nd the output impedance of the unity follower. Ans: a Rout Ro R1 R2 = Ro R2 R1 1 AOL ; b Rout % Ro = 1 AOL 9.45 The circuit of Fig. 9-28 is to be used as a high-pass lter having a gain of 0.1 at low frequencies, unity gain at high frequencies, and a gain of 0.707 at 1 krad/s. Arbitrarily select C1 C2 0:1 F, and size R1 and R2 . Ans: R1 100 k; R2 10 k Find the transfer function for the circuit of Fig. 9-38, and explain the use of the circuit. Ans: T s 1= sRC 1 , a low-pass lter with zero output impedance
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For the circuit of Fig. 9-39, show that Io 1 R1 =R2 Ii , so that the circuit is a true current ampli er. (Note that Io is independent of RL .)
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If the noninverting terminal of the op amp in Fig. 9-29 is grounded, nd the transfer function vo =vi . (Compare with Problem 9.22.) Ans: vo =vi 1
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Devise a method for using the inverting op amp circuit of Fig. 9-2 as a current source. Ans: Let IF be the output current; then iF i1 vS =R1 regardless of the value of RF
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A noninverting ampli er with gain Av 21 is desired. Based on ideal op amp theory, values of R1 10 k and R2 200 k are selected for the circuit of Fig. 9-3. If the op amp is recognized as nonideal in that AOL 104 and CMRRdb 40 db, nd the actual gain Av vo =v2 . Ans: Av 21:17
Use SPICE methods to simulate the di erential ampli er of Fig. 9-12. Let R1 R 10 k for a unity gain. Use the op amp model of Section 9.12. Apply signals vS1 sin 2000t V and vS2 2 sin 2000t V to show that the circuit is indeed a di erential ampli er yielding vo vS2 vS1 sin 2000t V. (Netlist code available from author s website.)
Use SPICE methods to simulate the circuit of Fig. 9-36 with values of Problem 9.39. Apply a 1-kHz sinusoidal source and verify that the input impedance Z 1256:7 908 j2 1000 0:200 ; thus, the circuit does, in fact, simulate a 200-mH inductor as predicted by Problem 9.39. (Netlist code available from author s website.)
Switched Mode Power Supplies
10.1. INTRODUCTION A switched mode power supply (SMPS) is a dc dc converter with an unregulated input dc voltage and a regulated output voltage. The converter circuitry consists of arrangements of inductor, capacitors, diodes, and transistors. The transistors are switched between the ON state (saturation) and the OFF state (cuto ) at rates that typically range from 10 kHz to 40 kHz. Regulation of the output voltage is realized by control of the percentage of time that the transistor is in the ON state. The SMPS e ciency is signi cantly higher than that of the so-called linear power supplies that realize output voltage control by active region operation of the transistors. The material of this chapter will be limited to steady-state operation covering the common case of continuous inductor current.
ANALYTICAL TECHNIQUES
Although numerous circuit topologies exist for SMPS, certain analysis techniques are universally applicable. Clear understanding of the results signi cantly simpli es analysis of the various SMPS arrangements. Notation adopted for analysis uses lowercase v and i for instantaneous values and upper case V and I for average values (dc quantities). Inductor Voltage and Current Consider the current i owing through the inductor L of Fig. 10-1(a). If vC changes insigni cantly over an interval of interest (good approximation of C is su ciently large) so that vC t VC , then vL t VB VC L Whence, i t di
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