Current version: version 1.8.1. Partially completed text (12M PDF file).
You may temporarily keep one copy of these PDF files for personal use. Please don't distribute copies of the pre-version-2.0 file.
Copyright © 1975, by James K. Roberge.
Copyright © 2007, by James K. Roberge and Kent H. Lundberg. All rights reserved.No part of this work may be copied, reproduced, stored in a retrieval system, or transmitted in any form or by any means (including, but not limited to, electronic or mechanical copying, photocopying, scanning, or recording) without the prior written permission of the copyright holder.
You are allowed to keep one local copy of the PDF file for personal use until 1 May 2007. After this date, the PDF file must be deleted (you are invited to return to this page for an updated version). No other uses are permitted (including, but not limited to, copying [not even for backup or archival purposes], printing, or distribution of any kind). None. Nada. Zip.
This work was originally Copyright © 1975, by John Wiley & Sons Inc. The copyright was returned to the author in 1995.
We know that the above copyright statement sounds ridiculously strict for a PDF file posted on the web. It is our intention and expectation (but not our promise or obligation) to make version 2.0 of this work available under some sort of Creative Commons license. However, until that time, this work is licensed only under the above statement. You must observe these draconian terms. (If you do not agree to these terms, then the default Copyright Laws apply, which stipulate that you cannot make any copies. At all.)Our purpose is to limit distribution of this document until the second edition is completely finished, proofread, and corrected. We ask for your indulgence and understanding. We will continue to increment the version number as we get closer to our goal. Please don't distribute copies of the pre-version-2.0 file.
Please link to this page. This page ishttp://web.mit.edu/klund/www/books/op2e.htmlDo not link directly to the PDF file. The filename will occasionally change and break direct links.
- Version 1.8.1 (19 April 2007): Bug fixes.
- Version 1.8 (23 Jan 2006): Oscilloscope scans complete (special thanks to Timothy Denision, for providing a copy of the first edition with a broken binding for scanning).
- Version 1.7 (10 Jan 2006): Where were we? 6.331 coming soon! Some bugs fixed.
- Version 1.6 (01 Apr 2005): Text complete (special thanks to Isaac Dancy, speed-racer typist).
- Version 1.5 (09 Aug 2004): OP2E project started.
- Of course, the first edition (pictured above), as published by John Wiley & Sons in 1975, is Version 1.0.
1 Background and Objectives
1.1 Introduction
1.2 The Closed-Loop Gain of an Operational Amplifier
1.2.1 Closed-Loop Gain Calculation
1.2.2 The Ideal Closed-Loop Gain
1.2.3 Examples
1.3 Overview
2 Properites and Modeling of Feedback Systems
2.1 Introduction
2.2 Symbology
2.3 Advantages of Feedback
2.3.1 Effect of Feedback on Changes in Open-Loop Gain
2.3.2 Effect of Feedback on Nonlinearities
2.3.3 Disturbances in Feedback Systems
2.3.4 Summary
2.4 Block Diagrams
2.4.1 Forming the Block Diagram
2.4.2 Block-Diagram Manipulations
2.4.3 The Closed-Loop Gain
2.5 Effects of Feedback on Input and Output Impedance
3 Linear System Response
3.1 Objectives
3.2 Laplace Transforms
3.2.1 Definitions and Properties
3.2.2 Transforms of Common Functions
3.2.3 Examples of the Use of Transforms
3.3 Transient Response
3.3.1 Selection of Test Inputs
3.3.2 Approximating Transient Responses
3.4 Frequency Response
3.5 Relationships Between Transient Response and Frequency Response
3.6 Error Coefficients
3.6.1 The Error Series
3.6.2 Examples
4 Stability
4.1 The Stability Problem
4.2 The Routh Criterion
4.2.1 Evaluation of Stability
4.2.2 Use as a Design Aid
4.3 Root-Locus Techniques
4.3.1 Forming the Diagram
4.3.2 Examples
4.3.3 Systems With Right-Half-Plane Loop-Transmission Singularities
4.3.4 Location of Closed-Loop Zeros
4.3.5 Root Contours
4.4 Stability Based on Frequency Response
4.4.1 The Nyquist Criterion
4.4.2 Interpretation of Bode Plots
4.4.3 Closed-Loop Performance in Terms of Loop-Transmission Parameters
5 Compensation
5.1 Objectives
5.2 Series Compensation
5.2.1 Adjusting the D-C Gain
5.2.2 Creating a Dominant Pole
5.2.3 Lead and Lag Compensation
5.2.4 Example
5.2.5 Evaluation of the Effects of Compensation
5.2.6 Related Considerations
5.3 Feedback Compensation
6 Nonlinear Systems
6.1 Introduction
6.2 Linearization
6.2.1 The Approximating Function
6.2.2 Analysis of an Analog Divider
6.2.3 A Magnetic-Suspension System
6.3 Describing Functions
6.3.1 The Derivation of the Describing Function
6.3.2 Stability Analysis with the Aid of Describing Functions
6.3.3 Examples
6.3.4 Conditional Stability
6.3.5 Nonlinear Compensation
7 Direct-Coupled Amplifiers
7.1 Introduction
7.2 Drift Referred to the Input
7.3 The Differential Amplifier
7.3.1 Topology
7.3.2 Gain
7.3.3 Common-Mode Rejection Ratio
7.3.4 Drift Attributable to Bipolar Transistors
7.3.5 Other Drift Considerations
7.4 Input Current
7.4.1 Operation at Low Current
7.4.2 Cancellation Techniques
7.4.3 Compensation for Infinite Input Resistance
7.4.4 Use of a Darlington Input
7.5 Drift Contributions from the Second Stage
7.5.1 Single-Ended Second Stage
7.5.2 Differential Second Stage
7.6 Conclusions
8 Operational-Amplifier Design Techniques
8.1 Introduction
8.2 Amplifier Topologies
8.2.1 A Design with Three Voltage-Gain Stages
8.2.2 Compensating Three-Stage Amplifiers
8.2.3 A Two-Stage Design
8.3 High-Gain Stages
8.3.1 A Detailed Low-Frequency Hybrid-Pi Model
8.3.2 Common-Emitter Stage with Current-Source Load
8.3.3 Emitter-Follower Common-Emitter Cascade
8.3.4 Current-Source-Loaded Cascode
8.3.5 Related Considerations
8.4 Output Amplifiers
9 An Illustrative Design
9.1 Circuit Description
9.1.1 Overview
9.1.2 Detailed Considerations
9.2 Analysis
9.2.1 Low-Frequency Gain
9.2.2 Transfer Function
9.2.3 A Method for Compensation
9.3 Other Considerations
9.3.1 Temperature Stability
9.3.2 Large-Signal Performance
9.3.3 Design Compromises
9.4 Experimental Results
10 Integrated-Circuit Operational Amplifiers
10.1 Introduction
10.2 Fabrication
10.2.1 NPN Transistors
10.2.2 PNP Transistors
10.2.3 Other Components
10.3 Integrated-Circuit Design Techniques
10.3.1 Current Repeaters
10.3.2 Other Connections
10.4 Representative Integrated-Circuit Operational Amplifiers
10.4.1 The LM101 and LM101A Operational Amplifiers
10.4.2 The µA776 Operational Amplifier
10.4.3 The LM108 Operational Amplifier
10.4.4 The LM110 Voltage Follower
10.4.5 Recent Developments
10.5 Additions to Improve Performance
11 Basic Applications
11.1 Introduction
11.2 Specifications
11.2.1 Definitions
11.2.2 Parameter Measurement
11.3 General Precautions
11.3.1 Destructive Processes
11.3.2 Oscillation
11.3.3 Grounding Problems
11.3.4 Selection of Passive Components
11.4 Representative Linear Connections
11.4.1 Differential Amplifiers
11.4.2 A Double Integrator
11.4.3 Current Sources
11.4.4 Circuits which Provide a Controlled Driving-Point Impedance
11.5 Nonlinear Connections
11.5.1 Precision Rectifiers
11.5.2 A Peak Detector
11.5.3 Generation of Piecewise-Linear Transfer Characteristics
11.5.4 Log and Analog Circuits
11.5.5 Analog Multiplication
11.6 Applications Involving Analog-Signal Switching Problems
12 Advanced Applications
12.1 Sinusoidal Oscillations
12.1.1 The Wien-Bridge Oscillator
12.1.2 Quadrature Oscillators
12.1.3 Amplitude Stabilization by Means of Limiting
12.1.4 Amplitude Control by Parameter Variation
12.2 Nonlinear Oscillators
12.2.1 A Square- and Triangle-Wave Generator
12.2.2 Duty-Cycle Modulation
12.2.3 Frequency Modulation
12.2.4 A Single-Amplifier Nonlinear Oscillator
12.3 Analog Computation
12.3.1 The Approach
12.3.2 Amplitude and Time Scaling
12.3.3 Ancillary Circuits
12.4 Active Filters
12.4.1 The Sallen and Key Circuit
12.4.2 A General Synthesis Procedure
12.5 Further Examples
12.5.1 A Frequency-Independent Phase Shifter
12.5.2 A Sine-Wave Shaper
12.5.3 A Nonlinear Three-Port Network
13 Compensation Revisited
13.1 Introduction
13.2 Compensation When the Op-Amp Transfer Function is Fixed
13.2.1 Input Compensation
13.2.2 Other Methods
13.3 Compensation By Changing the Amplifier Transfer Function
13.3.1 General Considerations
13.3.2 One-Pole Compensation
13.3.3 Two-Pole Compensation
13.3.4 Compensation That Includes a Zero
13.3.5 Slow-Rolloff Compensation
13.3.6 Feedforward Compensation
13.3.7 Compensation to Improve Large-Signal Performance
13.3.8 Summary