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The CS JFET ampli er of Fig. 7-2(a) is modeled by the equivalent circuit of Fig. 8-22 for low-frequency operation. Let RG 500 k; RS 500 ; RD 3 k; CS 10 F;  60; and rds 30 k. Use SPICE methods to determine the low-frequency cuto point. (Netlist code available at the author s website.) Ans: fL 40:9 Hz
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Operational Ampli ers
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9.1. INTRODUCTION The name operational ampli er (op amp) was originally given to an ampli er that could be easily modi ed by external circuitry to perform mathematical operations (addition, scaling, integration, etc.) in analog-computer applications. However, with the advent of solid-state technology, op amps have become highly reliable, miniaturized, temperature-stabilized, and consistently predictable in performance; they now gure as fundamental building blocks in basic ampli cation and signal conditioning, in active lters, function generators, and switching circuits.
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IDEAL AND PRACTICAL OP AMPS
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An op amp ampli es the di erence vd  v1 v2 between two input signals (see Fig. 9-1), exhibiting the open-loop voltage gain v 9:1 AOL  o vd In Fig. 9-1, terminal 1 is the inverting input (labeled with a minus sign on the actual ampli er); signal v1 is ampli ed in magnitude and appears phase-inverted at the output. Terminal 2 is the noninverting input (labeled with a plus sign); output due to v2 is phase-preserved.
+ VCC _ 1 + 2 +
Ld L1
5 Rd + _ Ro AOL Ld +
L1 L2
1 + Ld _ 2
_ 2 1 + L2 _ +
_V 4
(a) Complete representation
(b) Simplified representation
Fig. 9-1 Operational ampli er
Copyright 2002, 1988 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
CHAP. 9]
OPERATIONAL AMPLIFIERS
In magnitude, the open-loop voltage gain in op amps ranges from 104 to 107 . The maximum magnitude of the output voltage from an op amp is called its saturation voltage; this voltage is approximately 2 V smaller than the power-supply voltage. In other words, the ampli er is linear over the range VCC 2 < vo < VCC 2 V 9:2
The ideal op amp has three essential characteristics which serve as standards for assessing the goodness of a practical op amp: 1. 2. The open-loop voltage gain AOL is negatively in nite.
The input impedance Rd between terminals 1 and 2 is in nitely large; thus, the input current is zero. 3. The output impedance Ro is zero; consequently, the output voltage is independent of the load.
Figure 9-1(a) models the practical characteristics.
Example 9.1. An op amp has saturation voltage Vosat 10 V, an open-loop voltage gain of 105 , and input resistance of 100 k. Find (a) the value of vd that will just drive the ampli er to saturation and (b) the op amp input current at the onset of saturation. (a) By (9.1), vd Vosat 10 0:1 mV AOL 105 vd 0:1 10 3 1 nA Rd 100 103
(b) Let iin be the current into terminal 1 of Fig. 9-1(b); then iin
In application, a large percentage of negative feedback is used with the operational ampli er, giving a circuit whose characteristics depend almost entirely on circuit elements external to the basic op amp. The error due to treatment of the basic op amp as ideal tends to diminish in the presence of negative feedback.
INVERTING AMPLIFIER
The inverting ampli er of Fig. 9-2 has its noninverting input connected to ground or common. A signal is applied through input resistor R1 , and negative current feedback (see Problem 9.1) is implemented through feedback resistor RF . Output vo has polarity opposite that of input vS .
RF iF _ + Ld _ + +
i1 +
Fig. 9-2 Inverting ampli er Example 9.2. For the inverting ampli er of Fig. 9-2, nd the voltage gain vo =vS using (a) only characteristic 1 and (b) only characteristic 2 of the ideal op amp.
OPERATIONAL AMPLIFIERS
[CHAP. 9
(a) By the method of node voltages at the inverting input, the current balance is vS vd vo vd v iin d R1 RF Rd where Rd is the di erential input resistance. vS vo =AOL vo vo =AOL vo =Rd R1 RF AOL In the limit as AOL ! 1, (9.4) becomes vS v o 0 R1 RF (b) If iin 0, then vd iin Rd 0, and i1 iF  i. vS iR1 whence in agreement with (9.5). Av  so that Av  vo R F vS R1
9:3
By (9.1), vd vo =AOL which, when substituted into (9.3), gives 9:4
9:5
The input and feedback-loop equations are, respectively, and vo iRF (9.6)
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