Amplificadores Operacionales

Operational Amplifiers

9.1. INTRODUCTION The name operational amplifier (op amp) was originally given to an amplifier that could be easily modified 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 figure as fundamental building blocks in basic amplification and signal conditioning, in active filters, function generators, and switching circuits.

9.2.

IDEAL AND PRACTICAL OP AMPS

An op amp amplifies the difference vd  v1 À v2 between two input signals (see Fig. 9-1), exhibiting the open-loop voltage gain v ð9:1Þ AOL  o vd In Fig. 9-1, terminal 1 is the inverting input (labeled with a minus sign on the actual amplifier); signal v1 is amplified 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 +

Lo

3

L1 L2

1 + Ld _ 2

_ +

Lo

_ 2 1 + L2 _ +

_

_V 4

CC

_

(a) Complete representation

(b) Simplified representation

Fig. 9-1 Operational amplifier

258

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CHAP. 9]

OPERATIONAL AMPLIFIERS

259

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 amplifier is linear over the range ÀðVCC À 2Þ < vo < VCC À 2 V ð9:2Þ

The ideal op amp has three essential characteristics which serve as standards for assessing the goodness of a practical op amp: 1. The open-loop voltage gain AOL is negatively infinite. 2. The input impedance Rd between terminals 1 and 2 is infinitely 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 ¼ 10 V, an open-loop voltage gain of À105 , and input resistance of 100 k

. Find (a) the value of vd that will just drive the amplifier to saturation and (b) the op amp input current at the onset of saturation. (a) By (9.1), vd ¼ ÆVosat Æ10 ¼ ¼ Æ0:1 mV AOL À105 vd Æ0:1 Â 10À3 ¼ ¼ Æ1 nA Rd 100 Â 103

(b) Let iin be the current into terminal 1 of Fig. 9-1(b); then iin ¼

In application, a large percentage of negative feedback is used with the operational amplifier, 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.

9.3.

INVERTING AMPLIFIER

The inverting amplifier 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 i1 +

LS

R1 + Ld _

iin _

iF

+ +

Lo

_

_

Fig. 9-2 Inverting amplifier Example 9.2. For the inverting amplifier of Fig. 9-2, find the voltage gain vo =vS using (a) only characteristic 1 and (b) only characteristic 2 of the ideal op amp.

260

OPERATIONAL AMPLIFIERS

[CHAP. 9

(a) By the method of node voltages at the inverting input, the current balance is vS À vd vo À vd v þ ¼ iin ¼ d R1 RF Rd where Rd is the differential input resistance. vS À vo =AOL vo À vo =AOL vo =Rd þ ¼ R1 RF AOL In the limit as AOL ! À1, (9.4) becomes vS v þ o ¼0 R1 RF (b) If iin ¼ 0, then vd ¼ iin Rd ¼ 0, and i1 ¼ iF  i. vS ¼ iR1 whence in agreement with (9.5). Av  so that Av  vo R ¼À F vS R1

ð9:3Þ

By (9.1), vd ¼ vo =AOL which, when substituted into (9.3), gives ð9:4Þ

ð9:5Þ

The input and feedback-loop equations are, respectively, and vo ¼ ÀiRF (9.6)

vo R ¼À F vS R1

9.4.

NONINVERTING AMPLIFIER

The noninverting amplifier of Fig. 9-3 is realized by grounding R1 of Fig. 9-2 and applying the input signal at the noninverting op amp terminal. When v2 is positive, vo is positive and current i is positive. Voltage v1 ¼ iR1 then is applied to the inverting terminal as negative voltage feedback.

1 + _ Ld +

L2

+ 3 _ R2 iin 2 i R1 _ 0 Rout

Lo

+

...