Holbrook / Fry / Higinbotham Laplace Transforms for Electronic Engineers

International Series of Monographs on Electronics and Instrumentation
2. Auflage 2014
ISBN: 978-1-4831-8565-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 364 Seiten, Web PDF

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.

Autoren/Hrsg.

Holbrook, James G.

Fry, D. W.

Higinbotham, W. A.

Inhaltsverzeichnis

2;Laplace Transforms for Electronic Engineers;4
3;Copyright Page;5
4;Table of Contents;6
5;CHAPTER 1. FUNCTIONS OF A COMPLEX VARIABLE;16
5.1;1.1. Introduction;16
5.2;1.2. Complex numbers;16
5.3;1.3. Complex planes;20
5.4;1.4. Relations between the z- and s-planes;23
5.5;1.5. Additional transformations between the z- and s-planes;24
5.6;1.6. Simplification of problems by transforming into the complex s-plane;27
5.7;1.7. Functions in the complex plane;30
5.8;1.8. Poles of complex functions;31
5.9;1.9. Zeros of complex functions;33
5.10;1.10. The pole-zero diagram;34
5.11;1.11. Integration along a curve in the s-plane;35
5.12;1.12. Integration around a pole;38
5.13;1.13. Integration around a path not containing a pole;40
5.14;1.14. Residues;42
5.15;1.15. Integration around two or more poles in the s-plane;47
5.16;1.16. Summary of Chapter I;50
6;CHAPTER 2. THE FOURIER SERIES AND INTEGRAL;52
6.1;2.1. The Fourier series;52
6.2;2.2. Exponential form of the Fourier series;55
6.3;2.3. The Fourier integral;61
6.4;2.4. The unit step function;65
6.5;2.5. The Fourier transform of the unit step function;66
6.6;2.6. Convergence factors;67
6.7;2.7. The complex Fourier integral transform;69
6.8;2.8. The Laplace transform;70
7;CHAPTER 3. THE LAPLACE TRANSFORMATION;72
7.1;3.1. Introduction;72
7.2;3.2. Transforms of constants;73
7.3;3.3. The Laplace transform of exponentials;74
7.4;3.4. The Laplace transform of imaginary exponents;75
7.5;3.5. The Laplace transform of trigonometric terms;75
7.6;3.6. The Laplace transform of hyperbolic functions;77
7.7;3.7. The Laplace transform of complex exponentials;79
7.8;3.8. Transforms of more complicated functions;79
7.9;3.9. Additional practice with sine waves;80
7.10;3.10. The Laplace transform of a derivative;81
7.11;3.11. The Laplace transform of an integral;83
8;CHAPTER 4. THE INVERSE LAPLACE TRANSFORMATION;87
8.1;4.1. Introduction;87
8.2;4.2. Functions of s from electronic networks;91
8.3;4.3. Functions of s involving simple poles;94
8.4;4.4. Functions of s involving both simple poles and zeros;98
8.5;4.5. Functions of s having higher order poles;101
9;CHAPTER 5. LAPLACE TRANSFORM THEOREMS;105
9.1;5.1. Introduction;105
9.2;5.2. Linear s-plane translation;105
9.3;5.3. Final value theorem;108
9.4;5.4. Initial value theorem;111
9.5;5.5. Real translation;113
9.6;5.6. Complex differentiation;116
9.7;5.7. Complex integration;118
9.8;5.8. Sectioning a function of time;120
9.9;5.9. The convolution theorem;123
9.10;5.10. Scale change theorem;127
9.11;5.11. Summary of Chapter V;129
10;CHAPTER 6. NETWORK ANALYSTS BY MEANS OF THE LAPLACE TRANSFORMATION;131
10.1;6.1. Introduction;131
10.2;6.2. Writing network equations for multiple loop circuits;132
10.3;6.3. Relay damping problems;134
10.4;6.4. The Wien-bridge oscillator;137
10.5;6.5. A phase-shift oscillator;141
10.6;6.6. Harmonic discrimination in a three-section phase shift oscillator;144
10.7;6.7. The R–C cathode follower oscillator;146
10.8;6.8. Odd and even functions of s;148
10.9;6.9. R–C voltage step-up networks;151
10.10;6.10. R–C oscillator, single section variable capacity;154
10.11;6.11. Active integrating and differentiating networks;157
10.12;6.12. Operational amplifiers;160
10.13;6.13. Charge amplifiers;162
10.14;6.14. Analysis of the charge amplifier;164
10.15;6.15. Reactive feedback voltage amplifiers;167
10.16;6.16. Analysis of 3-stage reactive feedback amplifier;171
10.17;6.17. Single section low-pass R–C filter;174
10.18;6.18. Two-section non-tapered R–C low-pass filter;175
10.19;6.19. Three-section non-tapered R–C low-pass filter;177
10.20;6.20. Iterative networks;179
10.21;6.21. Initial conditions in network parameters;182
10.22;6.22. Initial charge or voltage on condenser;182
10.23;6.23. Initial current in an inductance;184
10.24;6.24. Mutual inductance;188
11;CHAPTER 7. TRANSFORMS OF SPECIAL WAVESHAPES AND PULSES;194
11.1;7.1. Introduction;194
11.2;7.2. Laplace transform of a displaced step function;194
11.3;7.3. Transform of the dirac delta function;198
11.4;7.4. Derivatives of infinité slopes expressed as delta functions;199
11.5;7.5. Sampling another function with a delta function;200
11.6;7.6. Fourier coefficients ascertained by means of delta functions;201
11.7;7.7. The Laplace transform of a series of pulses;204
11.8;7.8. The Laplace transform of a general periodic wave;206
11.9;7.9. The Laplace transform of a single sawtooth pulse;209
11.10;7.10. Pulsed periodic functions;210
11.11;7.11. Transform of a displaced ramp function;213
12;CHAPTER 8. ELECTRONIC FILTERS;214
12.1;8.1. Introduction;214
12.2;8.2. Normalization of transfer functions;214
12.3;8.3. Low-pass filters;218
12.4;8.4. Maximally flat functions;220
12.5;8.5. Pole location for Butterworth functions;223
12.6;8.6. Synthesis of the third-order maximally flat function;226
12.7;8.7. High-pass maximally flat functions;228
12.8;8.8. Maximally flat band-pass filters;229
12.9;8.9. Design of a band-pass filter;230
12.10;8.10. The band-rejection filter;233
12.11;8.11. Matched low-pass filters;234
12.12;8.12. Magnitude and phase functions of "s";236
12.13;8.13. Maximally flat time-delay filters;240
12.14;8.14. The linear-phase approximation;243
12.15;8.15. Bessel polynomials, or linear-phase filter design made easy;249
12.16;8.16. Finding the transfer function from a given magnitude;252
12.17;8.17. Tchebycheff and Legendre polynomial filters;254
12.18;8.18. Active nth order low-pass filters;257
12.19;8.19. Optimum n-section R–C filters for high voltage power supplies;260
13;CHAPTER 9. SPECIALIZED APPLICATIONS OF THE LAPLACE TRANSFORM;264
13.1;9.1. Functions of vs;264
13.2;9.2. Application of the impedance 1vs in oscillator design;267
13.3;9.3. Iterative networks;270
13.4;9.4. Transfer functions by tabular methods;273
13.5;9.5. Simplifications with the tabular method;276
13.6;9.6. Iterative networks, Pascal triangle method;280
13.7;9.7. Formulas for iterative network coefficients;286
13.8;9.8. Alternate approach to the Laplace integral;287
13.9;9.9. The Laplace integral used to sum infinite series into closed form;289
14;CHAPTER 10. SYNTHESIS OF TRANSFER FUNCTIONS BY MODELS;299
14.1;10.1. Introduction;299
14.2;10.2. Lossless network models;299
14.3;10.3. Odd and even parts of the transfer function;303
14.4;10.4. Synthesis of transfer impedances;304
14.5;10.5. Alternate method of transfer function synthesis;305
14.6;10.6. Conclusion;310
15;APPENDIX I;312
15.1;(a) Driving point transforms;312
15.2;(b) Transfer functions;314
15.3;(c) Active transfer functions;324
16;APPENDIX II: OPERATIONAL LAPLACE TRANSFORM PAIRS;328
17;APPENDIX III: TABLE OF LAPLACE TRANSFORM PAIRS;329
18;INDEX;360
19;OTHER TITLES IN THE SERIES;364