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Describe the transfer characteristic of the level-clamp circuit of Fig. 9-16(a) if diode Z2 is shorted. Ans: Let VZ2 0 in Fig. 9-16(b) Find the gain of the inverting ampli er of Fig. 9-33 if the op amp and diodes are ideal. Ans: Av R2 =R1 for vS > 0; Av R3 =R1 for vS 0
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The op amp in the circuit of Fig. 9-34 is ideal. Find an expression for vo in terms of vS , and determine the function of the circuit. Ans: vo 2=R1 C vS dt, a noninverting integrator If the nonideal op amp of the circuit of Fig. 9-35 has an open-loop gain AOL 104 , nd vo . Ans: 0:9999Eb
Eb +
Fig. 9-35
How can the square-wave generator of Problem 9.11 be used to make a triangular-wave generator Ans: Cascade the integrator of Fig. 9-6 to the output of the square-wave generator Describe an op amp circuit that will simulate the equation 3v1 2v2 v3 vo . Ans. The summer of Fig. 9-4, with RF =R1 3; RF =R2 2, and RF =R3 1, cascaded into the inverting ampli er of Fig. 9-2, with RF =R1 1 The circuit of Fig. 9-36 (called a gyrator) can be used to simulate an inductor in active RC lter design. Assuming ideal op amps, nd (a) the s-domain input impedance Z s and (b) the value of the inductance that is simulated if C 1 nF, R1 2 k, R2 100 k, and R3 R4 10 k. Ans: a Z s sR1 R2 R3 C=R4 ; b 200 mH
CHAP. 9]
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Fig. 9-36
For the double integrator circuit of Problem 9.14, if the output is connected to the input so that vi vo , an oscillator is formed. Show that this claim is so, and that the frequency of oscillation is f 1=RC Hz. [Hint: Replace Vo with Vi in (1) of Problem 9.14 to get an expression of the form Vi f s 0: In the logarithmic ampli er circuit of Fig. 9-7, vo must not exceed approximately 0.6 V, or else iD will not be a good exponential function of vD . Frequently, a second-stage inverting ampli er is added as shown in Fig. 0 9-7, so that vo is conveniently large. If the second-stage gain is selected to be Av RF =R1 1=VT , then 0 its output becomes vo ln vi . In the circuit of Fig. 9-7, vD is exponential for 0 iD 1 mA, 0 vi 10 V, 0 and Io 100 pA. Size R, RF , and R1 so that vo is as given above. Ans: R 10 m; arbitrarily select R1 1 k, and then RF 38:46 k In the logarithmic ampli er of Fig. 9-24, let vS 5 V; VR 10 V; R1 1 k; R2 10 k; R3 1 k; and R4 50 k. The matched BJTs are operating at 258C, with VT 0:026 V. Find (a) v2 and (b) vo (see Problem 9.17). Ans: a 41:8 mV; b 2:13 V Having at your disposal a logarithmic ampli er and an exponential ampli er, devise a circuit that will produce the quotient of two numbers. (Hint: x=y eln x ln y .) Ans: See Fig. 9-37
Logarithmic amplifier V1 _ k (ln V ) 1 R R1 V1 V2
C(ln V1 _ ln V2)
+ V2 _ k (ln V ) 2 R R1 Logarithmic amplifier Exponential amplifier
Fig. 9-37
The unity follower of Fig. 9-13 is the noninverting ampli er of Fig. 9-3 if R1 ! 1 and R2 ! 0. (a) Find the output impedance Rout of the noninverting ampli er of Fig. 9-3 subject to the approximation ii 0.
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