Foreword by Robert Adams xiPreface. xix1 Introduction11.1 Conventional Continuous-Time Integrated Filters.... 21.1.1 MOS-C Filters. 21.1.2 Transconductance-C (gm-C) Filters.... 31.2 Introducing Log-Domain Filters: Adams’s 1979 Discovery 61.2.1 An Exact First-Order Log-Domain Lowpass Filter.... 61.2.2 Discussions...... 91.3 Some Recent Developments and Our Approach.... 111.4 Nonlinear Signal Processing in Log-Domain 121.4.1 Translinear Principle 131.4.2 Translinear Circuit Examples 151.4.3 LOG and EXP Operators....... 181.4.4 Linearization of Log-Domain System. 19vi Design and Analysis of Integrator-Based Log-Domain Filter Circuits1.4.5 Potential Advantages of Log-Domain Filters.. 221.5 An Integrator-Based Design and Analysis Approach 241.6 Summary...... 252 Log-Domain Integrators.272.1 A Basic Log-domain Integrator....... 272.1.1 Detailed Analysis.... 272.1.2 Highlights of Intriguing Features ....... 302.2 Input and Output Stages ... 312.3 Further Log-Domain Integrator Examples... 332.3.1 High-Speed Log-Domain Integrators. 342.3.2 Low-Power Log-Domain Integrators 372.3.3 High-Speed Low-Power Log-Domain Integrators... 432.4 Summary...... 453 Log-Domain Filter Synthesis-I: OperationalSimulation of LC Ladders......493.1 Traditional Active Filter Synthesis by LC Ladder Signal Flow Graph..... 493.2 Log-Domain Ladder Filter Synthesis.. 543.2.1 Log-Domain Lowpass Biquadratic Filter...... 563.2.2 Log-Domain Bandpass Biquadratic Filter..... 653.2.3 High-Order Log-Domain Lowpass Filter...... 653.2.4 High-Order Log-Domain Bandpass Filter.... 723.2.5 Comments on the Designs..... 763.3 Simulation: Large-Signal vs. Small-Signal Analysis 783.4 Electronic Tunability of Log-Domain Filters. 813.5 High-Order Filter Sensitivity-Comparative Studies 823.6 Approximate Realization of Elliptic Filter Response 853.7 Summary...... 924 Log-Domain Filter Synthesis-II: State-SpaceFormulation......934.1 Frey’s Exponential State-Space Synthesis ... 944.2 Towards a State-Space Log-Domain Filter Realization...... 964.2.1 State-Space Formulation Revisited.... 964.2.2 Design of Low-Noise Low-Sensitivity Filters.. 994.2.3 A Collection of Log-Domain Functional Blocks .... 1054.3 State-Space Synthesis of Log-Domain Filters...... 1064.3.1 A General N-th Order Log-Domain State-Space Filter...... 1064.3.2 3rd-Order Elliptic Lowpass Filter..... 1194.3.3 3rd-Order Elliptic Highpass Filter.... 1214.3.4 6th-Order Elliptic Bandpass Filter.... 1244.4 Summary..... 1265 Nonideality Analysis of Biquadratic Log-DomainFilters....1295.1 Effects of Transistor Parasitics & Compensation Methods. 1305.1.1 Parasitic Emitter Resistances (RE)... 1305.1.2 Finite Beta.... 1365.1.3 Parasitic Base Resistances (RB)....... 1405.1.4 Early Voltages...... 1425.1.5 Combined Effects 1445.2 Extension to Bandpass Biquad Filters....... 1475.3 Comments on Distortion 1475.4 Transistor Area Mismatches. 1505.4.1 Statistical Analysis Of Area Mismatches.... 1535.5 Summary.... 155viii Design and Analysis of Integrator-Based Log-Domain Filter Circuits6 Extending the Nonideality Analysis to High-OrderLadder Filters.1576.1 Relationship to Classical Filter Theory...... 1576.2 Study of Nonideal High-Order Log-Domain Filters........ 1596.2.1 Nonideal LC Ladder Behavior........ 1616.2.2 Applications to Log-Domain Filters 1636.3 Compensation of High-Order Log-Domain Filters. 1676.3.1 Parasitic Emitter Resistances (RE).. 1676.3.2 Finite Beta.... 1696.3.3 Early Voltages ..... 1746.3.4 Extension to High-Order Bandpass Log-Domain Ladder Filters.. 1766.4 Implementation Considerations Under Finite Beta. 1776.5 Summary.... 1857 Experimental IC Prototypes ...1877.1 Test Chip #1: Lowpass Biquadratic Filter 1877.1.1 The Test Set-Up.. 1887.1.2 Frequency Performance...... 1887.1.3 Linearity And Noise Measurements 1917.2 Test Chip #2: Fifth-Order Chebyshev Lowpass Filter.... 1957.2.1 Frequency Performance....... 1967.2.2 Linearity Measurements..... 1997.2.3 Approximating an Elliptic Filter Response 2017.3 Test Chip #3: High-Speed Bandpass Biquadratic Filter... 2027.3.1 The Test Set-Up.. 2037.3.2 Frequency Performance....... 2037.3.3 Linearity And Noise Measurements 2057.4 Test Chip #4: Balanced High-Speed Fourth-Order Bandpass Filter....... 2077.4.1 The Test Set-Up.. 2087.4.2 Frequency Performance....... 2117.4.3 Linearity And Noise Measurements 2117.5 Test Chip #5: Low-Voltage 3rd-Order Chebyshev Filter. 2127.5.1 The Test Set-Up... 2137.5.2 Frequency Performance....... 2137.5.3 Linearity and Noise Measurements. 2147.6 Test Chip #6: Third-Order State-Space Filter...... 2157.6.1 The Test Set-Up... 2167.6.2 Demonstration of Filter Programmability.. 2167.7 Test Chip #7: Fifth-Order State-Space Filter ....... 2177.7.1 Measured Elliptical Behavior. 2197.8 Summary.... 221Appendix. ASeevinck’s Companding Current-Mode Integrator....... 223Appendix. BMultitone Testing Using SPICE.. 229B.1 Review of the Discrete Fourier Transform. 230B.2 The SPICE File..... 231B.2.1 The Signal Sources... 231B.2.1.1 Frequency. 231B.2.1.2 Phase. 235B.2.1.3 Amplitude. 235B.2.1.4 A Complete SPICE Current Source. 235B.2.2 Analysis Requests..... 235B.3 An Example using the Log-Domain Biquad........ 236Appendix. CSynthesis of High-Order Log-Domain Filters by aCascade of Biquads..239x Design and Analysis of Integrator-Based Log-Domain Filter CircuitsAppendix. DDerivation of Equation (5.16) - Compensation of EmitterResistance, RE.. 243Appendix. EGoodness of Fit Test 245References.. 247Index 253
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