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Add an inverting ampli er (see Fig. 9-2) to the output for the circuit of Fig. 9-28 to give a positive transfer function. Select the resistor values for this inverting ampli er to adjust the low-
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[CHAP. 9
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Fig. 9-30
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Fig. 9-31
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frequency voltage gain of the complete network to unity. Let C1 C2 0:001 F, R1 500 k, and R2 15 k. Then from Problem 9.21, 1=1 1=R1 C1 2 106 rad=s > 1=2 1=R2 C2 66:7 krad=s, making the circuit a lag-lead network. Use SPICE methods to generate the Bode plot of this circuit over the frequency range from 100 Hz to 10 MHz. The op amp model of Section 9.12 is applicable.
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Netlist code describing the circuit is shown below:
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Prb9_26.CIR vs 1 0 AC 1V R1 1 2 500ohm C1 1 2 0.001uF R2 2 3 15kohm C2 2 3 0.001uF X1 2 0 3 0 OPAMP * Inverting amplifier to set * dc gain to unity R3 3 4 15kohm R4 4 5 500ohm X2 4 0 5 0 OPAMP .SUBCKT OPAMP 1 2 3 * Model Inv NInv Out Rd 1 2 500kohm E 5 4 (1,2) -le5 Ro 5 3 10ohm .ENDS OPAMP .AC DEC 250 100Hz 10MegHz .PROBE .END
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Execute hPrb9_26.CIRi and use the Probe feature of PSpice to generate the gain magnitude plot (Mdb) and the phase plot (Phi) shown in Fig. 9-31. Notice that the phase angle plot begins to lag toward 908 at 0:1=2 and then moves in a leading sense back to 08 at 10=1 . Thus, the lag-lead characteristic is exempli ed.
CHAP. 9]
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Supplementary Problems
9.27 For the noninverting ampli er of Fig. 9-3, (a) nd an exact expression for the voltage-gain ratio, and (b) evaluate it for R1 1 k; R2 10 k; Rd 1 k; and AOL 104 . (c) Compare your result in part b with the value produced by the ideal expression (9.7). Ans: a Av R1 R2 ; b 10:977; R1 R2 R R2 R1 1 AOL Rd AOL c Avideal 11, for a 0:21% difference
In the rst-order low-pass lter of Example 9.9, R 10 k; R1 1 k; and C 0:1 F. Find (a) the gain for dc signals, (b) the break frequency f1 at which the gain drops o by 3 db, and (c) the frequency fu at which the gain has dropped to unity (called the unity-gain bandwidth). Ans: a 10; b 159:2 Hz; c 1583:6 Hz The noninverting ampli er circuit of Fig. 9-3 has an in nite input impedance if the basic op amp is ideal. If the op amp is not ideal, but instead Rd 1 M and AOL 106 , nd the input impedance. Let R2 10 k and R1 1 k. Ans: 1 T Let R1 R2 R3 3RF in the inverting summer ampli er of Fig. 9-4. What mathematical operation does this circuit perform Ans: Gives the negative of the instantaneous average value An inverting summer (Fig. 9-4) has n inputs with R1 R2 R3 Rn R. Assume that the openloop basic op amp gain AOL is nite, but that the inverting-terminal input current is negligible. Derive a relationship that shows how gain magnitude is reduced in the presence of multiple inputs. Ans: An  vo vS1 vS2 vSn RF =R nRF 1 R 1 AOL
For a single input vS1 , the gain is A1 . For the same input vS1 together with n 1 zero inputs vS2 vSn 0, the gain is An . But since AOL < 0; jAn j < jA1 j for n > 1 9.32 The basic op amp in Fig. 9-32 is ideal. Find vo and determine what mathematical operation is performed by the ampli er circuit. Ans: vo 1 R2 =R1 vS2 vS1 , a subtractor
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