Introduction -- Steady State Solutions to Circuit Problems -- Differential Equation Solution to Circuit Problems -- Series Expansion solution for Circuit Problems -- Numerical Differential Equation Solution to Circuit Problems -- Fourier Series and Periodic Functions -- Complex Fourier Series -- Fourier Transform -- Properties of the Fourier Transforms -- Further Examples/Topics on Fourier Transform -- Fourier Transform of Periodic Signals -- Approximate and Numerical Techniques in Fourier Transform -- Bandwidth -- Laplace Transform -- Using Complex Integration to Figure Inverse Laplace Transform -- Properties of Laplace Transform -- Laplace Transform of Periodic Functions -- Finding Inverse Laplace Transform via Partial Fractions -- Convolution -- Signal Construction in Terms of Convolution Integrals -- The Delta Function -- Impulse Response -- Time Convolution with Impulse Response -- Time Convolution with the Unit Step Response -- Sampling and the Sampling Theorem -- Transfer Functions -- The Phase -- Stability and Relation to Poles Placements -- Impulse Response as Configured from Inverse Transform -- Unit Step Response as Configured from Inverse Transform -- Pulse response -- Causal Cosine and Sine Response -- Causal, Periodic Pulse Response -- Slanted Unit Step Response -- Voltage/Voltage Filters -- RLC Circuits with Feedback -- Matrix Solution to MultiBranch Networks -- MultiSource Networks and Superposition -- Systems with Initial Conditions -- Application to Transistor Modeling and Circuits -- Op-Amp Filters -- Multi-port Network: Z-, Y-Parameters -- Scattering (s−) Parameters -- Application of Spectral Techniques to Solving 2D Electrostatic Problems -- Application of Spectral Techniques in Solving Diffusion Problems -- Application of Spectral Techniques in Solving the Wave Equation -- Appendix -- References -- Index.

This book describes a set of tools and algorithms then enable the electrical engineer in fields such as circuit design, power delivery, signal integrity, analog design, package and board modeling to arrive at approximate and exact solutions robustly and relatively efficiently, even when typical software packages may fail to do so. By leveraging well established and time tested methods, the author demonstrates how the practitioner will be able to deal with various circuit design problems and signal integrity issues both in the frequency and time domains. The presented tool set is an alternative to “brute force” time discretization and software utilization, offering great insight into the operations of linear systems ranging from RLC networks to device modeling. Integrates the most relevant aspects of signals and systems, circuit theory, mathematical techniques, and graphics into a coherent flow at reasonable depth; Covers a vast range of applications, ranging from RLC circuits, signal integrity, power delivery, feedback, transistor modeling, scattering parameters, multi-port networks, transmission lines, analog circuits, stability,sampling, algorithms, and numerical techniques; Follows a uniform presentation throughout, starting with theory at each stage, presenting multiple methods to solve the given problem, generating a solution and comparing to Spice results; Demonstrates scientific and visual computation both in the time and frequency domain, with special emphasis on computations in the complex plane, spectral analysis, inverse transforms and distributed media; Emphasizes root concepts and particular ins-and-outs of spectral and convolution techniques, which are gradually developed into simpler examples, culminating with real applications, then algorithmically coded, visualized and tested; Utilizes computer simulations, but with the barest lines of code to achieve satisfactory results; Driven by the authors’ industrial experience, but rooted in academic research with ample use of applications, examples, algorithms and verifications.