Abstract . i Résumé . 11 Table of Contents . iv List of Figures vil List of Tables . x 1 Introduction 1 1 -1 Background and Motivation . 1 1.2 Nonlinear Signal Processing in Log-Domain . 2 1.2.1 Translinear.Principle. . . . . 3 1 .2.2 Translinear Circuit Examples 6 1.2.3 LOG and EXP Operators . 8 1.2.4 Linearization of Log-Domain System . 9 1.2.5 Log-domain Integrators . 12 2 Synthesisof Log-DomainFilters . 17 2.1 Exponential State-Space Synthesis .1 7 2.2 LC Ladder(SFG) Synthesis 20 2.2.1 Log-Domain Lowpass Biquadratic Filter 21 2.2.2 Log-Domain Bandpass Biquadratic Filter . 23 2.2.3 High-Order Log-Domain Lowpass Filter 23 2.2.4 High-Order Log-Domain Bandpass Filter . 27 2.3 High-Order Filter Sensitivity- Comparative Studies 30 2.4 Surnmaries 31 3 Nonideality Analysis of Biquadratic Log-Domain Filters 33 Parasitic Emitter Resistances (RE) . 34 Finite Beta . 39 . Parasitic Base Resistances (RB) 43 Early Voltages . -45 Area Mismatches 46 Area Mismatches- Statistical Analysis . d Combined Effects . . . 52 Extension to Bandpass Biquad Filters 52 Summary . . . 54 4 Extending the Nonideality Analysis toHigh-Order Ladder Filters 55 . 4.1 Relationships to Classical Filter Theones 55 4.2 Study of Nonideal High-Order Log-domain Filters . 58 4.2.1 Classical Theories of Nonideal LC Ladder 59 4.2.2 Applications to Log-Domain Filters 61 4.3 Compensation of High-Order Log-Domain Filters 66 4.3.1 Parasitic Emitter Resistances (RE) 67 4.3.2 Finite Beta 68 4.3.3 Early Voltages 72 4.3.4 Extension to High-Order Bandpass Log-Domain Ladder Filters 73 4.4 IrnplementationConsiderations Under Finite Beta 74 4.5 Summary . 80 5 Conclusion 82 5.1 SummaryofResults 82 5.2 Topics of Future Research . -83 Appendix . ,., . . -84 1 Synthesis of High-Oder Log-Domain Filter by Cascade of Biquads .84 2 Deviation of Equation (3.15). Compensation of RE .87 3 Goodness of Fit Test . .88 References . 90
