Spectral, Convolution and Numerical Techniques in Circuit Theory

ISBN-13: 9783319714363 / Angielski / Twarda / 2018 / 976 str.

Fuad Badrieh

Opis

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.

Spis treści

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

O autorze

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.

Blurb

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.