The following list is the table of contents for the text:
Active Filters
for Integrated-Circuit Applications



(Chapter) No./(Section) Title/Beginning Page No.

Preface ix
Acknowledgments xiii
1 Introduction 1
1.1 Filter Terminology 2
1.1.1 Filter Component Values 8
1.1.2 An Active Filter Definition 9
1.1.3 Conclusion 11
1.2 Problems 12
2 Review of Circuit Analysis Concepts 15
2.1 Network Parameter Matrices 15
2.2 Network Scale Factors 19
2.3 Frequency Transformations of Passive Filters 24
2.3.1 LP to LP 24
2.3.2 LP to HP 25
2.3.3 LP to BP 27
2.3.4 LP to BP Network Functions 31
2.3.5 BP Filter Element Values 34
2.3.6 LP to BS 38
2.4 Impedance Transformations of Passive Filters 40
2.4.1 The Internal Loop Scaling Procedure 41
2.4.2 The Double Terminated Network and Its Dual 47
2.5 Summary 49
2.6 Problems 51
3 Frequency Effects in Feedback Circuits 57
3.1 The Operational Amplifier 58
3.1.1 Some Application Procedures 64
3.1.2 Single-Pole Open-Loop Gain 66
3.1.3 Double-Pole Open-Loop Gain 67
3.1.4 Triple-Pole Open-Loop Gain 70
3.2 An Operational Amplifier Dual 72
3.2.1 Invariant Frequency Response Example 74
3.3 Summary 75
3.4 Problems 76
References 80
4 Some Opamp Design Considerations 81
4.1 The Current Mirror 81
4.1.1 The Widlar Mirror 84
4.2 The Differential Amplifier Input Stage 87
4.2.1 A Single Transistor Amplifier 90
4.2.2 Small-Signal Frequency Response 93
4.2.3 Signal Representation 97
4.2.4 Second-Order Effect on Amplifier Model 99
4.3 The Second Stage 101
4.4 The Third Stage 108
4.4.1 Complementary Emitter Follower Output Stage 113
4.5 All Together Now---A Three-Stage Opamp 119
4.5.1 Temperature Compensation of Output Offset 121
4.5.2 Case Study---A Current Controlled Opamp 124
4.6 Conclusion 126
4.7 Problems 127
References 134
Appendix 4A Matlab and Transistor Modeling 135
4A.1 Modeling BJT Static Response 135
4A.2 Modeling Dynamic Response 143
4A.3 Summary 149
5 Operational Design of Active Filters 153
5.1 The Opamp as a Signal Processor 154
5.1.1 The Buffer Voltage Follower 154
5.1.2 The Noninverting Multiplying Buffer 155
5.1.3 The Noninverting Summing Multiplier 155
5.1.4 The Inverting Summing Multiplier 156
5.1.5 The Inverting Integrator 157
5.2 Analog Operational Circuit Example 158
5.2.1 Adding Transmission Zeros 164
5.3 State Variable Filters 166
5.4 Cascade Methods 169
5.4.1 The Cascade Concept 170
5.4.2 A Single-Amplifier Quadratic Factor Circuit 183
5.4.3 The Twin-T Circuit 186
5.4.4 The Biquad Circuit 191
5.5 Problems 200
Reference 215
6 Network Sensitivity and Leapfrog Filters 217
6.1 A Filter Sensitivity Definition 217
6.1.1 A Sensitivity Property for Terminated Passive Filters 222
6.2 The Leapfrog Filter Architecture 223
6.2.1 Leapfrog Example of Sensitivity Performance 231
6.2.2 The Elliptic Filter LP Topology 236
6.2.3 The All-Pole BP Filter Topology 239
6.2.4 Topology for BP Filters with Finite Transmission Zeros 244
6.3 Summary 247
6.4 Problems 248
Reference 257
7 Switched Capacitor Concepts 259
7.1 The CMOS Switch or Transmission Gate 259
7.1.1 The Switch Clock Rate and Sampling 262
7.1.2 Switch Configurations and Parasitic Capacitance 264
7.1.3 The Equivalent Resistance Concept 267
7.1.4 Typical Resistance and Clock Frequencies 271
7.2 Switched Capacitors and Analog Operations 274
7.2.1 Switched Capacitor s-Plane Distortion 287
7.2.2 Precompensated Network Functions 294
7.2.3 Scale Factors and Bandpass Filter Considerations 298
7.3 Problems 304
References 311
8 The Approximation Problem 313
8.1 Traditional Methods 313
8.1.1 Ideal LP Filter Characteristics 313
8.1.2 Critical Frequencies and Steady-State Response 317
8.1.3 The Butterworth Polynomials 319
8.1.4 The Chebyshev Polynomials 324
8.1.5 Inverted Chebyshev Polynomials 330
8.1.6 A General Form for the LP Transmission Function 333
8.2 General Methods 337
8.2.1 A Fourier Series Solution 338
8.2.2 Finding Polynomial Ratio Network Functions 353
8.2.3 Network Function Phase Versus Loss Function Phase 362
8.2.4 Obtaining Polynomials from a Phase Response 364
8.2.5 Optimizing Polynomial Parameters 374
8.3 Problems 385
References 390
Appendix 8A Approximation Details 390
8A.1 Derivation of the Hilbert Transform 390
8A.2 Program Description 393
8A.3 Code Listing 395
About the Author 403
Index 405