Operational Amplifiers: Theory and Practice, Second Edition

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Copyright © 1975, by James K. Roberge.
Copyright © 2007, by James K. Roberge and Kent H. Lundberg. All rights reserved.

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Table of Contents

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

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Last updated: 18 April 2007 by Kent Lundberg.