Operational amplifiers

This is a totally revised edition of one of the first operational amplifier books published. It presents the basic principles underlying the use of these important circuits and provides many applications of their use in system design. The extensive revisions made to the text reflect new developments since the first edition was published in 1971. These include substantial technological advances that took place, especially in operational amplifiers with high gain, low input currents and offset voltages, and high speed. In addition, the chapters on stability, frequency response and transient response have been considerably expanded and completely rewritten. Over 300 problems are included and there are many worked examples and figures OPERATIONAL AMPLIFIERS 2 Preface 3 Contents 4 CHAPTER 1 Operational Amplifiers 6 1.1 Properties 7 1.2 Applications 7 PROBLEMS 7 CHAPTER 2 Ideal Operational Amplifiers 8 2.1 Noninverting Amplifiers 8 2.2 Inverting Amplifiers 9 2.3 Dibreotial Amplifiers 9 2.4 Floating-Input Differential Amplifiers 9 PROBLEMS 10 CHAPTER 3 Feedback 11 3.1 Noninverting Feedback Amplifiers 11 3.2 Inverting Feedback Amplifiers 12 3.3 Differential Feedback Amplifiers 13 3.4 Voltage Followers 15 3.5 Instrumentation Amplifiers 15 PROBLEMS 16 CHAPTER 4 Accuracy of the Amplification 19 4.1 Small Variations in Operational Amplifier Amplification 20 4.2 Small Variations in the Feedback Resistor 21 4.3 Small Variations in the Input Resistor 22 4.4 Several Sources of Variations 22 PROBLEMS 23 CHAPTER 5 Frequency Response and Transient Response of Operational Amplifiers, Part I 25 5.1 Lag Networks 25 5.1.1 Frequeocy Response of Lag Networks 26 5.1.2 Transient Response of Lag Networks 27 5.2 Bode Plots 28 5.3 Cascaded Lag Networks 28 5.3.1 Frequency Response of Cascaded Lag Networks 28 5.3.2 Transient Response of Cascaded Lag Networks 30 PROBLEMS 33 CHAPTER 6 Frequency Response and Transient Response of Operational Amplifiers, Part I1 35 6.1 Modified Lag Networks 35 6.1.1 Frequency Response of Modified Lag Networks 35 6.1.2 Transient Response of Modified Lag Networks 37 6.2 Lead Networks 37 6.2.1 Frequency Response of Lead Networks 37 6.3 Voltage Divider Network 39 6.3.1 Frequency Response of Voltage Divider Networks 39 6.3.2 Transient Response of Voltage Divider Networks 40 6.4 Compouod Lag Networks 41 6.4.1 Laplace Transforms for Compouod Lag Networks 41 6.4.2 Frequency Response of Compound Lag Networks 42 6.4.3 Transient Response of Compound Lag Networks 44 6.5 Series RLC Circuits 44 PROBLEMS 46 CHAPTER 7 Stability of Feedback Amplifiers 47 7.1 The Nyquist Criterion 47 7.2 Lag Networks 49 7.3 Lag Compensation 53 7.4 Lad-Lag Compensation 54 7.5 Conditional Stability 55 7.6 Phase Margins 55 7.6.1 Two Lag Networks 56 7.6.2 Three Lag Networks 60 7.7 Inverting Feedback Amplifiers 63 PROBLEMS 63 CHAPTER 8 Frequency Response and Transient Response of Feedback Amplifiers 65 8.1 Operational Amplifiers with A = A& = 65 8.1.1 Frequency-Independent Feedback 65 8.1.2 Lead-Lag Compensation 66 8.1.3 Lag-Lead Compensation 66 8.2 Operational Amplifiers with A = Ad,/(l + j f / fi) 67 8.2.1 Frequency-Independent Feedback 67 8.2.2 Lag-Lead Compensation 68 8.3 Operational Amplifiers with A = Ad,/l(l + j f 1 f ,)(I + j f / j z ) l 73 8.3.1 Frequeocy-Indepeodent Feedback 74 8.3.2 Lead-Lag Compensation 76 8.3.2.1 LEAD-LAG COMPENSATION WITH fL = f2 77 8.3.2.2 LEAD-LAG COMPENSATION WlTH fL fL ffi 78 8.3.2.3 LEAD-LAG COMPENSATION WITH fL f, 93 8.4.4 Transient Response with Lag-Lead Compensation 96 8.5 Inverting Feedback Amplifiers 97 8.6 Computer-Aided Design 98 PROBLEMS 98 CHAPTER 9 Properties of Real Operational Amplifiers, Part I 104 9.1 Common-Mode Amplification and Common-Mode Rejection 104 9.2 Input Impedances 107 9.3 Output Impedance 108 9.4 Supply-Voltage Rejection 109 PROBLEMS 110 CHAPTER 10 Properties of Real Operational Amplifiers, Part I1 110 10.1 Input Currents 110 10.2 Input Offset Voltage 111 10.3 Limitations and Ratings 112 10.4 Slew Rate 113 10.5 Noise 113 PROBLEMS 114 CHAPTER 11 Other Circuits 115 11.1 Current Source Inputs 115 11.1.1 dc Characteristics 116 11.1.2 Transient Response and Frequency Response 116 11.2 Adder Circuits 117 11.2.2 Transient Response and Frequency Response 118 11.3 Integrator Circuits 118 11.3.1 Integration 120 11.3.2 Response at High Frequencies and Short Times 122 11.3.3 The Overall Response 123 11.4 Differentiator Circuits 124 11.5 Nonlinear Circuits 125 PROBLEMS 126 CHAPTER 12 Internal Structure 128 12.1 Input Stages 128 12.2 Current Mirrors 129 12.3 Output Stages 132 PROBLEMS 132 APPENDIX A Mathematical Equations 133 A.l Quadratic Equations 133 A.2 Cubic Equations 133 A.3 Laplace Transform Pairs 134 APPENDIX B Derivations 135 B.l Proof of Equations 6.31a-e 135 APPENDIX C Properties of Operational Amplifiers Used in the Examples and Problems 139 Answers to Selected Problems 140 Index 141 OPERATIONAL AMPLIFIERS......Page 2 Preface......Page 3 Contents......Page 4 CHAPTER 1 Operational Amplifiers......Page 6 PROBLEMS......Page 7 2.1 Noninverting Amplifiers......Page 8 2.4 Floating-Input Differential Amplifiers......Page 9 PROBLEMS......Page 10 3.1 Noninverting Feedback Amplifiers......Page 11 3.2 Inverting Feedback Amplifiers......Page 12 3.3 Differential Feedback Amplifiers......Page 13 3.5 Instrumentation Amplifiers......Page 15 PROBLEMS......Page 16 CHAPTER 4 Accuracy of the Amplification......Page 19 4.1 Small Variations in Operational Amplifier Amplification......Page 20 4.2 Small Variations in the Feedback Resistor......Page 21 4.4 Several Sources of Variations......Page 22 PROBLEMS......Page 23 5.1 Lag Networks......Page 25 5.1.1 Frequeocy Response of Lag Networks......Page 26 5.1.2 Transient Response of Lag Networks......Page 27 5.3.1 Frequency Response of Cascaded Lag Networks......Page 28 5.3.2 Transient Response of Cascaded Lag Networks......Page 30 PROBLEMS......Page 33 6.1.1 Frequency Response of Modified Lag Networks......Page 35 6.2.1 Frequency Response of Lead Networks......Page 37 6.3.1 Frequency Response of Voltage Divider Networks......Page 39 6.3.2 Transient Response of Voltage Divider Networks......Page 40 6.4.1 Laplace Transforms for Compouod Lag Networks......Page 41 6.4.2 Frequency Response of Compound Lag Networks......Page 42 6.5 Series RLC Circuits......Page 44 PROBLEMS......Page 46 7.1 The Nyquist Criterion......Page 47 7.2 Lag Networks......Page 49 7.3 Lag Compensation......Page 53 7.4 Lad-Lag Compensation......Page 54 7.6 Phase Margins......Page 55 7.6.1 Two Lag Networks......Page 56 7.6.2 Three Lag Networks......Page 60 PROBLEMS......Page 63 8.1.1 Frequency-Independent Feedback......Page 65 8.1.3 Lag-Lead Compensation......Page 66 8.2.1 Frequency-Independent Feedback......Page 67 8.2.2 Lag-Lead Compensation......Page 68 8.3 Operational Amplifiers with A = Ad,/l(l + j f 1 f ,)(I + j f / j z ) l......Page 73 8.3.1 Frequeocy-Indepeodent Feedback......Page 74 8.3.2 Lead-Lag Compensation......Page 76 8.3.2.1 LEAD-LAG COMPENSATION WITH fL = f2......Page 77 8.3.2.2 LEAD-LAG COMPENSATION WlTH fL fL ffi......Page 78 8.3.2.3 LEAD-LAG COMPENSATION WITH fL f,......Page 93 8.4.4 Transient Response with Lag-Lead Compensation......Page 96 8.5 Inverting Feedback Amplifiers......Page 97 PROBLEMS......Page 98 9.1 Common-Mode Amplification and Common-Mode Rejection......Page 104 9.2 Input Impedances......Page 107 9.3 Output Impedance......Page 108 9.4 Supply-Voltage Rejection......Page 109 10.1 Input Currents......Page 110 10.2 Input Offset Voltage......Page 111 10.3 Limitations and Ratings......Page 112 10.5 Noise......Page 113 PROBLEMS......Page 114 11.1 Current Source Inputs......Page 115 11.1.2 Transient Response and Frequency Response......Page 116 11.2 Adder Circuits......Page 117 11.3 Integrator Circuits......Page 118 11.3.1 Integration......Page 120 11.3.2 Response at High Frequencies and Short Times......Page 122 11.3.3 The Overall Response......Page 123 11.4 Differentiator Circuits......Page 124 11.5 Nonlinear Circuits......Page 125 PROBLEMS......Page 126 12.1 Input Stages......Page 128 12.2 Current Mirrors......Page 129 PROBLEMS......Page 132 A.2 Cubic Equations......Page 133 A.3 Laplace Transform Pairs......Page 134 B.l Proof of Equations 6.31a-e......Page 135 APPENDIX C Properties of Operational Amplifiers Used in the Examples and Problems......Page 139 Answers to Selected Problems......Page 140 Index......Page 141 A revised and updated edition of one of the first operational amplifier books published. It presents the basic principles underlying the use of these important circuits and provides many applications of their use in system design.