Weakly Nonlinear Systems : : With Applications in Communications Systems.

• Superior document: Understanding Complex Systems Series
• Author: Beffa, Federico.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2023.; Ã2024.
• Year of Publication: 2023
• Edition: 1st ed.
• Language: English
• Series: Understanding Complex Systems Series
• Physical Description: 1 online resource (376 pages)

Table of Contents

Intro -- Foreword -- Preface -- Contents -- 1 Introduction -- 1.1 Nonlinear Phenomena -- 1.1.1 Multiple Equilibrium Points -- 1.1.2 Limit Cycles -- 1.1.3 Bifurcations -- 1.1.4 Chaos -- 1.2 Weakly-Nonlinear Systems -- 1.3 Distributions -- 1.4 Numerical Simulations -- 1.5 Historical Notes -- Part I Signals -- 2 Distributions -- 2.1 Test Functions -- 2.2 Distributions -- 2.3 Basic Properties -- 2.4 Differentiation of Distributions -- 2.5 Distributions with Compact Support -- 2.5.1 Single-Point Support -- 3 Convolution of Distributions -- 3.1 Tensor Product -- 3.2 Convolution of Distributions -- 3.3 Approximation of Distributions -- 3.4 Convolution of Periodic Distributions -- 4 Fourier Transform of Distributions -- 4.1 Test Functions of Fast Descent -- 4.2 Fourier Transform of Tempered Distributions -- 4.3 Distributions with Bounded Support -- 4.4 Fourier Transform and Convolution -- 4.5 Periodic Distributions -- 4.6 Extension to Several Variables -- 5 Laplace Transform of Distributions -- 5.1 Definition -- 5.2 Properties -- 5.3 Inverse Laplace Transform -- 5.4 Extension to Several Variables -- 6 Summable Distributions -- 6.1 Definition and Canonical Extension -- 6.2 Convolution of Summable Distributions -- 6.3 Fourier Transform of Summable Distributions -- Part II Systems -- 7 Convolution Equations -- 7.1 Convolution Algebra -- 7.2 Convolution Equations -- 7.3 Initial Value Problems -- 7.4 Integro-Differential Equations -- 7.5 Periodic Solutions -- 7.6 General Convolution Equations -- 7.6.1 General Solutions -- 7.6.2 Tempered Solutions -- 7.7 Systems of Convolution Equations -- 8 Linear Time Invariant Systems -- 8.1 Basic Definitions -- 8.2 Causality -- 8.3 Stability -- 8.4 Transfer Function -- 8.4.1 Stable Systems -- 8.4.2 Causal Systems -- 8.5 Rational Transfer Functions -- 8.6 System State -- 8.6.1 Controllability -- 8.6.2 Observability.

8.6.3 Jordan Normal form -- 9 Weakly Nonlinear Time Invariant Systems -- 9.1 Introduction -- 9.2 Graded Algebra of Test Functions -- 9.3 Direct Product of Distributions -- 9.4 Symmetric Distributions -- 9.5 Weakly Nonlinear Systems -- 9.6 Nonlinear Transfer Functions -- 9.7 Periodic Input Signals -- 9.8 Multi-tone Input Signals -- 9.8.1 General Case -- 9.8.2 Real Case -- 10 Composition of Weakly Nonlinear Time Invariant Systems -- 10.1 Cascade of Noninteracting Systems -- 10.2 Feedback -- 10.3 Linearisation -- 10.4 System Manipulations -- 10.5 Structure -- 11 Weakly Nonlinear Time Invariant Circuits -- 11.1 Metrics for Nonlinear Effects -- 11.1.1 Gain Compression and Expansion -- 11.1.2 Intermodulation -- 11.1.3 Desensitisation -- 11.2 Nonlinear Two-Terminal Elements -- 11.2.1 Nonlinear Resistors -- 11.2.2 Nonlinear Capacitors -- 11.2.3 Nonlinear Inductors -- 11.3 Nonlinear Multi-port Elements -- 11.4 Low-Pass Filter with Nonlinear Capacitor -- 11.4.1 Nonlinear Transfer Functions -- 11.4.2 Second Order Intermodulation -- 11.4.3 Third Order Intermodulation -- 11.4.4 Large Signal Effects -- 11.5 Class-AC Common-Source Stage -- 11.6 Common-Gate Stage -- 11.6.1 Nonlinear Transfer Functions -- 11.6.2 Cascode -- 11.7 Degenerated Common-Source Stage -- 11.7.1 Nonlinear Transfer Functions -- 11.7.2 Resistive Degeneration -- 11.7.3 Inductive Degeneration -- 11.8 Pseudo-Differential Circuits -- 12 Linear Time-Varying Systems -- 12.1 Linear Time-Varying Systems -- 12.2 Linear Ordinary Differential Equations -- 12.2.1 Fundamental Solution -- 12.2.2 Formal Solution -- 12.2.3 Perturbation Theory -- 12.2.4 Non-smooth Coefficients -- 12.3 Impulse Response Generalisation -- 12.4 Time-Varying Frequency Response -- 12.4.1 Definition -- 12.4.2 Differential Equation -- 12.5 Linear Periodically Time-Varying Systems -- 12.5.1 Floquet Theory.

12.5.2 Time-Varying Frequency Response -- 13 Weakly Nonlinear Time-Varying Systems -- 13.1 Weakly Nonlinear Time-Varying Systems -- 13.1.1 Definition -- 13.1.2 Time-Varying Nonlinear Impulse Responses -- 13.1.3 Time-Varying Nonlinear Frequency Responses -- 13.2 Weakly Nonlinear Periodically Time-Varying Systems -- 13.2.1 Discrete Convolution -- 13.2.2 Product of Fourier Series -- 13.2.3 Response to Multi-tones -- 14 Periodically Switched Circuits -- 14.1 Switched Circuits -- 14.2 Voltage-Mode Quadrature Modulator -- 14.2.1 Single Input Response -- 14.2.2 Input Current and Switched Resistor -- 14.2.3 Full Response -- 14.2.4 Carrier Leakage -- 14.2.5 Image-Rejection -- 14.2.6 Effect of Mismatch -- 14.2.7 Second-Order Distortion -- 14.2.8 Third-Order Distortion -- 14.3 Sampling Mixer -- 14.3.1 Time-Varying Impulse Response -- 14.3.2 Time-Varying Transfer Function -- 14.3.3 Selectivity -- 14.3.4 Even Harmonic Response Suppression -- 14.4 N-Path Filters -- 14.4.1 Time-Varying Frequency Response -- 14.4.2 Selectivity -- Appendix A Signal-Flow Graphs -- A.1 Linear Signal-Flow Graphs -- A.1.1 Construction Rules -- A.1.2 Reduction Rules -- A.1.3 Mason's Rule -- A.2 Nonlinear Systems -- A.3 Weakly-Nonlinear Systems -- Appendix References -- -- Index.