chapter 10 operational amplifier theory and performance modeling an operational amplifier feedback...

Chapter 10 Operational Amplifier Theory and Performance

Modeling an Operational Amplifier Feedback Theory oFeedback in the Noninverting Amplifier oNoninverting Input/Output Resistance Frequency Response oStability oThe Gain-Bandwidth Product Slew Rate

FIGURE 10-1 A simple operational amplifier model with three components: differential input resistance, differential gain, and output resistanceBogart/Beasley/RicoElectronic Devices and Circuits, 6e

Copyright ©2004 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

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Modeling an Operational Amplifier

FIGURE 10-2 The noninverting amplifier using the simplified op-amp model

Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Noninverting amplifier model

FIGURE 10-3 A block diagram representation of the noninverting amplifier

FIGURE 10-4 (Example 10-1)




Example 10-1 Find the closed-loop gain of the amplifier when (1) a = (2) A = 106, and (3) A = 103.

FIGURE 10-5 Obtaining the closed-loop input resistance in a noninverting amplifier




ri = vi/ii ii = (vi – βvo)/rid = (vi – βAii rid)/rid

ri = vi/ii = rid (1+A β)

FIGURE 10-6 An external source vo driving the output to obtain the closed-loop output resistance




FIGURE 10-12 Frequency response of the open-loop gain of an operational amplifier; A0 = dc gain, f0 = cutoff frequency, fu = unit-gain frequency




fu = A0 f0 also called gain-bandwidth product or GBP

Closed-loop bandwidth BWCL

BWCL = fuβ = A0f0β = βGBP

Where β is the feedback ratioAny point along the sloped portion of the open-loop gain plot satisfies the relationship

gain x frequency = GBP

Only minimum guaranteed A0 is given f0 is not known, but GBP is always given





Example 10-5 Each of the op-amp has an open-loop GBP equal to 1 x 106 Hz. Find the cutoff frequencies in the closed-loop configurations shown.

BWCL = fuβ = A0f0β = βGBP

FIGURE 10-14 Closed-loop gain vs. frequency for noninverting and inverting amplifiers




2

1

c

CLOCL

ff

AA

where ACLO = 1 + Rf /R1 (noninverting)or ACLO = Rf /R1 (inverting)and fc = β GBP

FIGURE 10-15 Open-loop frequency response for the op-amp in Example 10-6Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Example 10-6 With reference to the op-amp whose open-loop frequency response is shown in the following figure, find1.The unity-gain frequency,2.The open-loop 3-dB frequency,3.The BW when the feedback ration is 0.02, and4.The closed-loop gain at 0.4 MHz when the feedback ration is 0.04

FIGURE 10-17 The rate of change of a linear, or ramp, signal is the change in voltage divided by the change in time




The maximum possible rate at which an amplifier’s output voltage can change, in volts per second, is called its slew rate.





Example 10-7 The op-amp has a slew-rate specification of 0.5 V/µs. If the input is the ramp waveform shown, what is the maximum closed-loop gain that the amplifier can have without exceeding its slew rate?

ConclusionThe maximum frequency at which an amplifier can be operated depends on both bandwidth and the slew rate

The rate change of vo(t) = Vp sin ωt is (Vpω) volts/second

so Vp ω Sor 2πf Vp S

where S is the specified slew rate of an amplifier

fs (max) S/(2πVp)and

f (max) BWCL

FIGURE 10-19 (Example 10-8)Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Example 10-19 The op-amp has a slew rate of 0.5 V/µs. The amp must be capable of amplifying the following input signals:v1 = 0.01 sin (106t),v2 = 0.05 sin (350 x 103t),v3 = 0.1 sin (200 x 103t), andv4 = 0.2 sin (50 x 103t).1.Determine whether the output will be distorted due to slew-rate limitations on any input.2.If so, find a remedy (other than changing the input signals).

FIGURE 10-20 (Example 10-9) Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Example 10-9 The op-amp has a unity-gain frequency of 1 MHz (fu) and a slew rate of 1 V/µs. Find the maximum frequency of a 0.1-V-peak sine-wave input that can be amplified without slew-rate distortion.

chapter 10 operational amplifier theory and performance modeling an operational amplifier feedback...

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