Foreword by Robert Adams  xi
Preface. xix
1 Introduction1
1.1 Conventional Continuous-Time Integrated Filters.... 2
1.1.1 MOS-C Filters. 2
1.1.2 Transconductance-C (gm-C) Filters.... 3
1.2 Introducing Log-Domain Filters: Adams’s 1979 Discovery 6
1.2.1 An Exact First-Order Log-Domain Lowpass Filter.... 6
1.2.2 Discussions...... 9
1.3 Some Recent Developments and Our Approach.... 11
1.4 Nonlinear Signal Processing in Log-Domain 12
1.4.1 Translinear Principle 13
1.4.2 Translinear Circuit Examples 15
1.4.3 LOG and EXP Operators....... 18
1.4.4 Linearization of Log-Domain System. 19
vi Design and Analysis of Integrator-Based Log-Domain Filter Circuits
1.4.5 Potential Advantages of Log-Domain Filters.. 22
1.5 An Integrator-Based Design and Analysis Approach 24
1.6 Summary...... 25
2 Log-Domain Integrators.27
2.1 A Basic Log-domain Integrator....... 27
2.1.1 Detailed Analysis.... 27
2.1.2 Highlights of Intriguing Features ....... 30
2.2 Input and Output Stages ... 31
2.3 Further Log-Domain Integrator Examples... 33
2.3.1 High-Speed Log-Domain Integrators. 34
2.3.2 Low-Power Log-Domain Integrators 37
2.3.3 High-Speed Low-Power Log-Domain Integrators... 43
2.4 Summary...... 45
3 Log-Domain Filter Synthesis-I: Operational
Simulation of LC Ladders......49
3.1 Traditional Active Filter Synthesis by LC Ladder Signal Flow Graph..... 49
3.2 Log-Domain Ladder Filter Synthesis.. 54
3.2.1 Log-Domain Lowpass Biquadratic Filter...... 56
3.2.2 Log-Domain Bandpass Biquadratic Filter..... 65
3.2.3 High-Order Log-Domain Lowpass Filter...... 65
3.2.4 High-Order Log-Domain Bandpass Filter.... 72
3.2.5 Comments on the Designs..... 76
3.3 Simulation: Large-Signal vs. Small-Signal Analysis 78
3.4 Electronic Tunability of Log-Domain Filters. 81
3.5 High-Order Filter Sensitivity-Comparative Studies 82
3.6 Approximate Realization of Elliptic Filter Response 85
3.7 Summary...... 92
4 Log-Domain Filter Synthesis-II: State-Space
Formulation......93
4.1 Frey’s Exponential State-Space Synthesis ... 94
4.2 Towards a State-Space Log-Domain Filter Realization...... 96
4.2.1 State-Space Formulation Revisited.... 96
4.2.2 Design of Low-Noise Low-Sensitivity Filters.. 99
4.2.3 A Collection of Log-Domain Functional Blocks .... 105
4.3 State-Space Synthesis of Log-Domain Filters...... 106
4.3.1 A General N-th Order Log-Domain State-Space Filter...... 106
4.3.2 3rd-Order Elliptic Lowpass Filter..... 119
4.3.3 3rd-Order Elliptic Highpass Filter.... 121
4.3.4 6th-Order Elliptic Bandpass Filter.... 124
4.4 Summary..... 126
5 Nonideality Analysis of Biquadratic Log-Domain
Filters....129
5.1 Effects of Transistor Parasitics & Compensation Methods. 130
5.1.1 Parasitic Emitter Resistances (RE)... 130
5.1.2 Finite Beta.... 136
5.1.3 Parasitic Base Resistances (RB)....... 140
5.1.4 Early Voltages...... 142
5.1.5 Combined Effects 144
5.2 Extension to Bandpass Biquad Filters....... 147
5.3 Comments on Distortion 147
5.4 Transistor Area Mismatches. 150
5.4.1 Statistical Analysis Of Area Mismatches.... 153
5.5 Summary.... 155
viii Design and Analysis of Integrator-Based Log-Domain Filter Circuits
6 Extending the Nonideality Analysis to High-Order
Ladder Filters.157
6.1 Relationship to Classical Filter Theory...... 157
6.2 Study of Nonideal High-Order Log-Domain Filters........ 159
6.2.1 Nonideal LC Ladder Behavior........ 161
6.2.2 Applications to Log-Domain Filters 163
6.3 Compensation of High-Order Log-Domain Filters. 167
6.3.1 Parasitic Emitter Resistances (RE).. 167
6.3.2 Finite Beta.... 169
6.3.3 Early Voltages ..... 174
6.3.4 Extension to High-Order Bandpass Log-Domain Ladder Filters.. 176
6.4 Implementation Considerations Under Finite Beta. 177
6.5 Summary.... 185
7 Experimental IC Prototypes ...187
7.1 Test Chip #1: Lowpass Biquadratic Filter 187
7.1.1 The Test Set-Up.. 188
7.1.2 Frequency Performance...... 188
7.1.3 Linearity And Noise Measurements 191
7.2 Test Chip #2: Fifth-Order Chebyshev Lowpass Filter.... 195
7.2.1 Frequency Performance....... 196
7.2.2 Linearity Measurements..... 199
7.2.3 Approximating an Elliptic Filter Response 201
7.3 Test Chip #3: High-Speed Bandpass Biquadratic Filter... 202
7.3.1 The Test Set-Up.. 203
7.3.2 Frequency Performance....... 203
7.3.3 Linearity And Noise Measurements 205
7.4 Test Chip #4: Balanced High-Speed Fourth-Order Bandpass Filter....... 207
7.4.1 The Test Set-Up.. 208
7.4.2 Frequency Performance....... 211
7.4.3 Linearity And Noise Measurements 211
7.5 Test Chip #5: Low-Voltage 3rd-Order Chebyshev Filter. 212
7.5.1 The Test Set-Up... 213
7.5.2 Frequency Performance....... 213
7.5.3 Linearity and Noise Measurements. 214
7.6 Test Chip #6: Third-Order State-Space Filter...... 215
7.6.1 The Test Set-Up... 216
7.6.2 Demonstration of Filter Programmability.. 216
7.7 Test Chip #7: Fifth-Order State-Space Filter ....... 217
7.7.1 Measured Elliptical Behavior. 219
7.8 Summary.... 221
Appendix. A
Seevinck’s Companding Current-Mode Integrator....... 223
Appendix. B
Multitone Testing Using SPICE.. 229
B.1 Review of the Discrete Fourier Transform. 230
B.2 The SPICE File..... 231
B.2.1 The Signal Sources... 231
B.2.1.1 Frequency. 231
B.2.1.2 Phase. 235
B.2.1.3 Amplitude. 235
B.2.1.4 A Complete SPICE Current Source. 235
B.2.2 Analysis Requests..... 235
B.3 An Example using the Log-Domain Biquad........ 236
Appendix. C
Synthesis of High-Order Log-Domain Filters by a
Cascade of Biquads..239
x Design and Analysis of Integrator-Based Log-Domain Filter Circuits
Appendix. D
Derivation of Equation (5.16) - Compensation of Emitter
Resistance, RE.. 243
Appendix. E
Goodness of Fit Test 245
References.. 247
Index  253