Transcript slew rate
Chapter 10 Operational Amplifier Theory and Performance Modeling an Operational Amplifier Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance Frequency Response o Stability o The Gain-Bandwidth Product Slew Rate Chapter 10 Operational Amplifier Theory and Performance Modeling an Operational Amplifier Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance Frequency Response o Stability o The Gain-Bandwidth Product Slew Rate Modeling an Operational Amplifier FIGURE 10-1 A simple operational amplifier model with three components: differential input resistance, differential gain, and output resistance Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 10 Operational Amplifier Theory and Performance Modeling an Operational Amplifier Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance Frequency Response o Stability o The Gain-Bandwidth Product Slew Rate Noninverting amplifier model FIGURE 10-2 The noninverting amplifier using the simplified op-amp model Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 10-3 A block diagram representation of the noninverting amplifier Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 10-1 Find the closed-loop gain of the amplifier when (1) a = (2) A = 106, and (3) A = 103. FIGURE 10-4 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e (Example 10-1) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 10-5 ri = vi/ii Obtaining the closed-loop input resistance in a noninverting amplifier ii = (vi – βvo)/rid = (vi – βAii rid)/rid ri = vi/ii = rid (1+A β) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 10-6 An external source vo driving the output to obtain the closed-loop output resistance Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 10 Operational Amplifier Theory and Performance Modeling an Operational Amplifier Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance Frequency Response o Stability o The Gain-Bandwidth Product Slew Rate FIGURE 10-12 Frequency response of the open-loop gain of an operational amplifier; A0 = dc gain, f0 = cutoff frequency, fu = unitgain frequency fu = A0 f0 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e also called gain-bandwidth product or GBP Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Closed-loop bandwidth BWCL BWCL = fuβ = A0f0β = βGBP Where β is the feedback ratio Any 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 10-13 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e (Example 10-5) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 10-14 Closed-loop gain vs. frequency for noninverting and inverting amplifiers A ACL CLO f 1 fc 2 where ACLO = 1 + Rf /R1 (noninverting) or ACLO = Rf /R1 (inverting) and fc = β GBP Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 10-6 With reference to the op-amp whose open-loop frequency response is shown in the following figure, find 1. The unity-gain frequency, 2. The open-loop 3-dB frequency, 3. The BW when the feedback ration is 0.02, and 4. The closed-loop gain at 0.4 MHz when the feedback ration is 0.04 FIGURE 10-15 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Open-loop frequency response for the op-amp in Example 10-6 Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 10 Operational Amplifier Theory and Performance Modeling an Operational Amplifier Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance Frequency Response o Stability o The Gain-Bandwidth Product Slew Rate The maximum possible rate at which an amplifier’s output voltage can change, in volts per second, is called its slew rate. FIGURE 10-17 The rate of change of a linear, or ramp, signal is the change in voltage divided by the change in time Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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? FIGURE 10-18 (Example 10-7) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. The rate change of vo(t) = Vp sin ωt is (Vpω) volts/second so Vp ω S or 2πf Vp S where S is the specified slew rate of an amplifier Conclusion The maximum frequency at which an amplifier can be operated depends on both bandwidth and the slew rate fs (max) S/(2πVp) and f (max) BWCL 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), and v4 = 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). Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 10-19 (Example 10-8) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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-Vpeak sine-wave input that can be amplified without slew-rate distortion. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 10-20 (Example 10-9) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.