Spectral, Convolution and Numerical Techniques in Circuit Theory

1 Introduction 2 Steady State Solutions to Circuit Problems 3 Differential Equation Solution to Circuit Problems 4 Series Expansion solution for Circuit Problems 5 Numerical Differential Equation Solution to Circuit Problems 6 Fourier Series and Periodic Functions 7 Complex Fourier Series 8 Fourier Transform 9 Properties of the Fourier Transforms 10 Further Examples/Topics on Fourier Transform 11 Fourier Transform of Periodic Signals 12 Approximate and Numerical Techniques in Fourier Transform 13 Bandwidth 14 Laplace Transform 15 Using Complex Integration to Figure Inverse Laplace Transform 16 Properties of Laplace Transform 17 Laplace Transform of Periodic Functions 18 Finding Inverse Laplace Transform via Partial Fractions 19 Convolution 20 Signal Construction in Terms of Convolution Integrals 21 The Delta Function 22 Impulse Response 23 Time Convolution with Impulse Response 24 Time Convolution with the Unit Step Response 25 Sampling and the Sampling Theorem 26 Transfer Functions 27 The Phase 28 Stability and Relation to Poles Placements 29 Impulse Response as Configured from Inverse Transform 30 Unit Step Response as Configured from Inverse Transform 31 Pulse response 32 Causal Cosine and Sine Response 33 Causal, Periodic Pulse Response 34 Slanted Unit Step Response 35 Voltage/Voltage Filters 36 RLC Circuits with Feedback 37 Matrix Solution to MultiBranch Networks 38 MultiSource Networks and Superposition 39 Systems with Initial Conditions 40 Application to Transistor Modeling and Circuits 41 Op-Amp Filters 42 Multi-port Network: Z-, Y-Parameters 43 Scattering (s-) Parameters 44 Application of Spectral Techniques to Solving 2D Electrostatic Problems 45 Application of Spectral Techniques in Solving Diffusion Problems 46 Application of Spectral Techniques in Solving the Wave Equation Appendix References Index

Fuad Badrieh is a Senior Member of Technical Staff Engineer at Micron Technology, in Boise, Idaho. He obtained his BS, MS and PhD in EE at Arizona State University. He brings 17 years of industrial experience in modelling, circuit design, power integrity and automation.