# Laplace Transforms for Electronic Engineers

## 2nd Edition

### International Series of Monographs on Electronics and Instrumentation

**Editors:**D. W. Fry W. A. Higinbotham

**Authors:**James G. Holbrook

**eBook ISBN:**9781483185651

**Imprint:**Pergamon

**Published Date:**1st January 1966

**Page Count:**364

## Description

Laplace Transforms for Electronic Engineers, Second (Revised) Edition details the theoretical concepts and practical application of Laplace transformation in the context of electrical engineering. The title is comprised of 10 chapters that cover the whole spectrum of Laplace transform theory that includes advancement, concepts, methods, logic, and application. The book first covers the functions of a complex variable, and then proceeds to tackling the Fourier series and integral, the Laplace transformation, and the inverse Laplace transformation. The next chapter details the Laplace transform theorems. The subsequent chapters talk about the various applications of the Laplace transform theories, such as network analysis, transforms of special waveshapes and pulses, electronic filters, and other specialized applications. The text will be of great interest to electrical engineers and technicians.

## Table of Contents

Chapter I. Functions of a Complex Variable

1.1. Introduction

1.2. Complex Numbers

1.3. Complex Planes

1.4. Relations Between the z- and s-Planes

1.5. Additional Transformations Between the z- and s-Planes

1.6. Simplification of Problems by Transforming into the Complex s-Plane

1.7. Functions in the Complex Plane

1.8. Poles of Complex Functions

1.9. Zeros of Complex Functions

1.10. The Pole-Zero Diagram'

1.11. Integration along a Curve in the s-Plane

1.12. Integration around a Pole

1.13. Integration around a Path Not Containing a Pole

1.14. Residues

1.15. Integration around Two or More Poles in the s-Plane

1.16. Summary of Chapter I

Chapter II. The Fourier Series and Integral

2.1. The Fourier Series

2.2. Exponential Form of the Fourier Series

2.3. The Fourier Integral

2.4. The Unit Step Function

2.5. The Fourier Transform of the Unit Step Function

2.6. Convergence Factors

2.7. The Complex Fourier Integral Transform

2.8. The Laplace Transform

Chapter III. The Laplace Transformation

3.1. Introduction

3.2. Transforms of Constants

3.3. The Laplace Transform of Exponentials

3.4. The Laplace Transform of Imaginary Exponents

3.5. The Laplace Transform of Trigonometric Terms

3.6. The Laplace Transform of Hyperbolic Functions

3.7. The Laplace Transform of Complex Exponentials

3.8. Transforms of More Complicated Functions

3.9. Additional Practice with Sine Waves

3.10. The Laplace Transform of a Derivative

3.11. The Laplace Transform of an Integral

Chapter IV. The Inverse Laplace Transformation

4.1. Introduction

4.2. Functions of s from Electronic Networks

4.3. Functions of s Involving Simple Poles

4.4. Functions of s Involving Both Simple Poles and Zeros

4.5. Functions of s Having Higher Order Poles

Chapter V. Laplace Transform Theorems

5.1. Introduction

5.2. Linear s-Plane Translation

5.3. Final Value Theorem

5.4. Initial Value Theorem

5.5. Real Translation

5.6. Complex Differentiation

5.7. Complex Integration

5.8. Sectioning a Function of Time

5.9. The Convolution Theorem

5.10. Scale Change Theorem

5.11. Summary of Chapter V

Chapter VI. Network Analysts by Means of the Laplace Transformation

6.1. Introduction

6.2. Writing Network Equations for Multiple Loop Circuits

6.3. Relay Damping Problems

6.4. The Wien-Bridge Oscillator

6.5. A Phase-Shift Oscillator

6.6. Harmonic Discrimination in a Three-Section Phase Shift Oscillator

6.7. The R-C Cathode Follower Oscillator

6.8. Odd and Even Functions of s

6.9. R-C Voltage Step-up Networks

6.10. R-C Oscillator, Single Section Variable Capacity

6.11. Active Integrating and Differentiating Networks

6.12. Operational Amplifiers

6.13. Charge Amplifiers

6.14. Analysis of the Charge Amplifier

6.15. Reactive Feedback Voltage Amplifiers

6.16. Analysis of Three-Stage Reactive Feedback Amplifier

6.17. Single Section Low-Pass R-C Filter

6.18. Two-Section Non-Tapered R-C Low-Pass Filter

6.19. Three-Section Non-Tapered R-C Low-Pass Filter

6.20. Iterative Networks

6.21. Initial Conditions in Network Parameters

6.22. Initial Charge or Voltage on Condenser

6.23. Initial Current in an Inductance

6.24. Mutual Inductance

Chapter VII. Transforms of Special Waveshapes and Pulses

7.1. Introduction

7.2. Laplace Transform of a Displaced Step Function

7.3. Transform of the Dirac Delta Function

7.4. Derivatives of Infinite Slopes Expressed as Delta Functions

7.5. Sampling Another Function with a Delta Function

7.6. Fourier Coefficients Ascertained by Means of Delta Functions

7.7. The Laplace Transform of a Series of Pulses

7.8. The Laplace Transform of a General Periodic Wave

7.9. The Laplace Transform of a Single Sawtooth Pulse

7.10. Pulsed Periodic Functions

7.11. Transform of a Displaced Ramp Function

Chapter VIII. Electronic Filters

8.1. Introduction

8.2. Normalization of Transfer Functions

8.3. Low-Pass Filters

8.4. Maximally Flat Functions

8.5. Pole Location for Butterworth Functions

8.6. Synthesis of the Third-Order Maximally Flat Function

8.7. High-Pass Maximally Flat Functions

8.8. Maximally Flat Band-Pass Filters

8.9. Design of a Band-Pass Filter

8.10. The Band-Rejection Filter

8.11. Matched Low-Pass Filters

8.12. Magnitude and Phase Functions of s

8.13. Maximally Flat Time-Delay Filters

8.14. The Linear-Phase Approximation

8.15. Bessel Polynomials, or Linear-Phase Filter Design Made Easy

8.16. Finding the Transfer Function from a Given Magnitude

8.17. Tchebycheff and Legendre Polynomial Filters

8.18. Active nth Order Low-Pass Filters

8.19. Optimum n-Section R-C Filters for High Voltage Power Supplies

Chapter IX. Specialized Applications of the Laplace Transform

9.1. Functions of √s

9.2. Application of the Impedance 1/√s In Oscillator Design

9.3. Iterative Networks

9.4. Transfer Functions by Tabular Methods

9.5. Simplifications with the Tabular Method

9.6. Iterative Networks, Pascal Triangle Method

9.7. Formulas for Iterative Network Coefficients

9.8. Alternate Approach to the Laplace Integral

9.9. The Laplace Integral Used to Sum Infinite Series into Closed Form

Chapter X. Synthesis of Transfer Functions By Models

10.1. Introduction

10.2. Lossless Network Models

10.3. Odd and Even Parts of the Transfer Function

10.4. Synthesis of Transfer Impedances

10.5. Alternate Method of Transfer Function Synthesis

10.6. Conclusion

Appendix I

(a) Driving Point Transforms

(b) Transfer Functions

(c) Active Transfer Functions

Appendix II. Operational Laplace Transform Pairs

Appendix III. Table of Laplace Transform Pairs

Index

Other Titles in the Series

## Details

- No. of pages:
- 364

- Language:
- English

- Copyright:
- © Pergamon 1966

- Published:
- 1st January 1966

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483185651