Gridley / Hammond Principles of Electrical Transmission Lines in Power and Communication

The Commonwealth and International Library: Applied Electricity and Electronics Division
1. Auflage 2014
ISBN: 978-1-4831-8603-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 360 Seiten

Principles of Electrical Transmission Lines in Power and Communication is a preliminary study in the transmission of electricity, which particularly discusses principles common to all electrical transmission links, whether their functions be communication or bulk power transfer. This book explains the propagation on loss-free lines I and II and introduces the finite loss-free lines. The sinusoidal excitation of dissipative lines I and II is then examined, and the occurrence of standing waves and quarter-wave is then discussed. This text also looks into topics on frequencies. This book will be invaluable to students and experts in the field of electronics and related disciplines.

Autoren/Hrsg.

Gridley, J. H.

Hammond, P.

Inhaltsverzeichnis

1;Front Cover;1
2;Principles of Electrical Transmission Lines in Power and Communication;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;Synopsis;10
7;Acknowledgements;11
8;CHAPTER 1.
Propagation on Loss-free Lines I (The Infinite Loss-free Line);12
8.1;1.1. The General Transmission-line Problem;12
8.2;1.2. The Infinite Loss-free Line: Solution of Intrinsic Equations;15
8.3;1.3. Travelling Waves;18
8.4;1.4. The Wave Equation — Validity of Solution;21
8.5;1.5. Surge Impedance;22
8.6;1.6. Summary;25
8.7;1.7. A Simplified Approach;26
8.8;1.8. Energy in Travelling Waves;29
8.9;Worked Example;30
9;CHAPTER 2.
Propagation on Loss-free Lines II (Effect of Terminations and Junctions);33
9.1;2.1. Reflection;33
9.2;2.2. Reflection and Transmission Coefficient;34
9.3;2.3. Practical Implications;41
9.4;Worked Examples;43
9.5;Exercises;59
9.6;Further Reading;60
10;CHAPTER 3. Finite Loss-free Lines: An Introduction;61
10.1;3.1. The Generalized Problem;61
10.2;3.2. Constant Applied p.d.;61
10.3;3.3. Harmonic Excitation;64
11;CHAPTER 4. Sinusoidal Excitation of Dissipative Lines I (Steady-state Solution of General Equations);71
11.1;4.1. The General Line Equations: Steady-state Solution;71
11.2;4.2. Correlation with Infinite Line Theory;74
11.3;4.3. Finite Dissipative Lines;76
11.4;4.4. Further Interpretation of the Finite Line
Equations;80
12;CHAPTER 5. Sinusoidal Excitation of Dissipative Lines II (Characteristic Impedance, Attenuation, Distortion);82
12.1;5.1. Input Impedance. Characteristic Impedance;82
12.2;5.2. Attenuation;85
12.3;5.3. Distortion;86
12.4;Worked Examples;91
12.5;Exercises;102
13;CHAPTER 6. Potential and Current Distribution:
Standing Waves;104
13.1;6.1. Standing Waves;104
13.2;6.2. Quarter-wave Lines;106
13.3;Worked Example;110
13.4;Exercise;112
14;CHAPTER 7. Lumped-circuit Equivalents;113
14.1;7.1. Two-port Networks;113
14.2;7.2. The Equivalent .;116
14.3;7.3. The Equivalent p and the T-p Transformation;118
14.4;7.4. Open-circuit and Sliort-circuit Impedances;121
14.5;7.5. Linear Network Parameters;125
14.6;7.6. Applicability of Equivalent Circuits;131
14.7;Worked Examples;133
14.8;Exercises;143
15;CHAPTER 8. Low-frequency Transmission Lines I (Steady-state Operation of Power Transmission Lines);144
15.1;8.1. The Meaning of ''Low Frequency";144
15.2;8.2. Three-phase Working;145
15.3;8.3. Transmission in the Steady State: Nominal Equivalents;151
15.4;8.4. Power Transfer in Terms of Terminal p.d.s: Short Lines;154
15.5;8.5. Power Lines of Medium Lengtli;160
15.6;8.6. Line Charts;161
15.7;Worked Examples;166
15.8;Exercises;175
16;CHAPTER 9.
Low-frequency Transmission Lines II (Stability of Transmission Systems);177
16.1;9.1. Interconnected Systems;177
16.2;Exercises;178
17;CHAPTER 10. Audio-frequency Lines;179
17.1;10.1. The Function and Nature of Audio-frequency Lines;179
17.2;10.2. Distortion;180
17.3;10.3. Loading Coils and Loaded Lines;181
17.4;10.4. Equalization;191
17.5;Worked Example;192
17.6;Further Reading;192
18;CHAPTER 11. The Transmission Line at Radio Frequencies I (Introductory);193
18.1;11.1. Radio-frequency Working;193
18.2;11.2. Radio-frequency Lines;194
18.3;11.3. Microwaye Strip Lines;200
18.4;Worked Examples;202
19;CHAPTER 12. The Transmission Line at Radio Frequencies II (Propagation Characteristics);211
19.1;12.1. Imperfection of Radio-frequency Lines;211
19.2;12.2. Resistance in Radio-frequency Lines. Skin Eflfect;211
19.3;Worked Example;214
19.4;12.3. Conductance in Radio-frequency Lines: Dielectric Loss;217
19.5;12.4. Lines of Minimum Attenuation;221
19.6;12.5. Velocity of Propagation on Loss -free Radio-frequency Lines;225
19.7;12.6. Lines of Deliberately High Dissipation;226
19.8;12.7. Power Limitations of Radio-frequency Lines;227
19.9;Exercise;229
20;CHAPTER 13. The Terminated Radio-frequency Line;230
20.1;13.1. Radio-frequency Line Impedance;230
20.2;13.2. Radio-frequency Lines as Circuit Elements;232
20.3;13.3. Impedance Transformation by Radio-frequency Lines;240
20.4;13.4. Mismatched Radio-frequency Lines;242
20.5;13.5. Standing-wave Ratio;254
20.6;13.6. Loci of Constant Standing-wave Ratio;256
20.7;13.7. Current and Power Standing-wave Ratio;259
20.8;Worked Examples;260
20.9;Suggestions for Further Reading;268
21;CHAPTER 14.
Measurement of Standing-wave Ratio;269
21.1;14.1. Methods of Measurement;269
21.2;14.2. Slotted Lines;269
21.3;14.3. The Directional Coupler;272
21.4;14.4. Application to Impedance Measurement;276
22;CHAPTER 15. Travelling Waves on Electrical Power Lines;279
22.1;15.1. Surge Phenomena on Power Lines;279
22.2;15.2. The Generation of Surges on Power Lines;279
22.3;15.3. Surge Attenuation and Distortion;282
22.4;15.4. Protective Measures;283
22.5;15.5. Methods of Minimizing Interruption to Supply;288
22.6;Further Reading;291
23;CHAPTER 16.
Transmission-line Parameters;292
23.1;16.1. Inductance and Capacitance: General;292
23.2;16.2. Capacitance of Single-phase
Overhead Lines;293
23.3;16.3. Capacitance of a Concentric Cable;297
23.4;16.4. Inductance of Single-phase Lines;298
23.5;16.5. Energy and Inductance;303
23.6;16.6. Earth Proximity Effects;311
23.7;16.7. Inductance and Capacitance Calculations for Multi-conductor Systems;318
23.8;Worked Example;328
23.9;Further Reading;330
24;APPENDIX I: The Growth of Current in an Inductive Termination;331
25;APPENDIX II: Solution of a Wave Equation by the Method of Laplace Transforms;337
26;APPENDIX III: Useful Expressions: Hyperbolic Functions;340
27;Answers to Exercises;341
28;Index;342

Leseproben

CHAPTER 1 Propagation on Loss-free Lines I (The Infinite Loss-free Line)
Publisher Summary
The use of electricity in communication or power requires that as much as possible of the electrical energy generated in a source is transferred to a load. The physical appearances of systems to affect this transfer differ according to the nature of the undertaking; there is a little in common between the high-voltage lines of a major power system and the coaxial cable between aerial and television set. Certain principles underlie the operation of both systems and such principles are to be established. The connection of a source to a load forms a complete circuit. This circuit affects the desired energy transference, but might also dissipate an appreciable amount of energy as heat and store energy in magnetic and electric fields. The circuit must be regarded as having resistance, inductance, and capacitance. It might be that by far the greater part of the energy dissipation or storage is localized, in which case the appropriate parameter can be regarded as concentrated and the familiar concept of a network of “lumped” parameters follows. This chapter discusses the problems that arise when a finite number of lumped elements no longer suffice to describe a process of electrical energy transference. 1.1 The General Transmission-line Problem
The use of electricity in communication or power requires that as much as possible of the electrical energy generated in a source be transferred to a load. The physical appearances of systems to effect this transfer differ greatly according to the nature of the undertaking; there is at first sight little in common between the high-voltage lines of a major power system and the coaxial cable between aerial and television set. But certain principles underlie the operation of both systems and, in what follows, such principles are to be established. The connection of a source to a load forms a complete circuit. This circuit effects the desired energy transference, but may also dissipate an appreciable amount of energy as heat and store energy in magnetic and electric fields. The circuit must then be regarded as having resistance, inductance and capacitance. It may be that by far the greater part of the energy dissipation or storage is localized, in which case the appropriate parameter can be regarded as concentrated and the familiar concept of a network of “lumped” parameters follows. The elementary principles on which the analysis of such networks is based will be assumed; we shall be concerned with problems which arise when a finite number of lumped elements no longer suffices to describe a process of electrical energy transference, and now consider how such a situation can arise. Suppose a source and load are connected by conducting wires between appropriate terminals. Whatever degree of accuracy is required in analysis it will always be possible to find a distance between source and load such that for this and shorter distances the effect of the connecting wires on the current flow can be neglected. The precise distance will depend on the degree of accuracy demanded, the nature of the source e.m.f.—e.g. whether constant or alternating—the physical nature and disposition of the conductors and the quality of the insulation. Now suppose the distance between source and load to be increased beyond this length. In many practical instances the first noticeable effects are those due to the insertion between source and load of the resistance of the connecting wires, and to the increase in circuit inductance by the increased magnetic flux within the loop formed by source, connecting wires and load. So far as a calculation of the electrical conditions at source and load is concerned the increased resistance and inductance can be assumed concentrated at a point in the connecting wires, and the desired accuracy regained. But as the distance between source and load is increased still further, a more complicated situation arises. The source and load currents will differ by reason of current flow through the conductance and capacitance between conducting wires. Again, the length at which this effect becomes important will depend on the nature of the wires and their disposition, the insulation and the rate at which the source p.d. changes with time. Clearly, we will at some stage be forced to consider a system in which both potential and current at any instant vary appreciably with distance along the connections between source and load. It is at this stage that the connections form a transmission line in the sense that we shall use the term. A generalized theory of transmission should result in the construction of expressions describing the distribution of potential and current over a transmission line and its terminals, the expressions being applicable whatever the characteristics of the line and the nature of its excitation. Such expressions would, however, by their generality, be so complex as to frustrate any desire to gain understanding which inspired their derivation. Having posed the general problem we shall simplify it as much as possible at first, and consider later the further complications which are important in practice. Firstly, we shall throughout the study restrict consideration to uniform lines, i.e. lines for which any section is identical with any other section of equal length. If a uniform distribution of potential difference were applied between conductors of such a transmission line, open-circuited at both ends, the capacitance so measurable would tend to increase directly with line length. This is because as the line becomes longer the electrostatic field tends towards axial uniformity, the effect of the ends of the line becoming progressively less important. The line may be regarded as having a certain capacitance per unit length and, by an extension of the same argument, a certain inductance per unit length. For our first discussion we shall also assume the line to be free from power loss, i.e. to have zero resistance along the conductors and zero conductance between them. This far we have simplified the problem by idealizing the line. Now we shall simplify the system as a whole. Clearly, the electrical conditions on the line depend both on the characteristics of the line and the constraints imposed by source and load. Now if it be accepted that energy transference cannot be instantaneous it follows that changes in load impedance, for instance, cannot affect the source current or p.d. until a finite time has elapsed. In fact, if the load be assumed infinitely distant, its characteristics need not be considered at all in any analysis of the electrical conditions at finite times from the instant of source application. It is natural to consider next what simplification can be made in the source characteristics. To minimize assumptions we shall characterize the source only by the p.d. which it applies between line conductors, that is, regard the source as of zero impedance. To crystallize the discussion then, we imagine a source of p.d. to be applied at one end of an infinite loss-free line, and it is our purpose to discover what response the line has to the application of this p.d., that is what potential and current distributions exist along the line and what relationship there may be between the distributions. 1.2 The Infinite Loss-free Line: Solution of Intrinsic Equations
Suppose that at some instant potential and current are distributed along a loss-free line of infinite extent, of inductance per unit length L and capacitance per unit length C. The distributions will be functions both of distance and time since, in general, both current and p.d. will vary with time at any point and with distance from the source at any instant. Using x as distance from the point at which the driving p.d. is applied, and t the time elapsed since the beginning of the application, we may write for the p.d. and current distributions ?=V(x,t)andi=I(x,t). Now consider two points on the line at distances x and x + ?x. The currents at these points will differ by the capacitance current flowing between conductors over the section ?x. Over any incremental section of length dx the capacitance current is Cdx)??/?t, the partial differentiation signifying that it is the variation of p.d. with time at any point that specifies the capacitance current at that point. Then the total capacitance current over the section ?x is (x,t)-I(x+?x,t)=?xx+4xC???tdx. Now if ?x is made to tend to zero, we have in the limit ?x?0?xx+?xC???tdx=?x·C???t, and therefore ?x?0I(x,t)-I(x+?x,t)?x=C???t or i?x=-C???t. (1.1) (1.1) Similarly, the excess of p.d. between conductors at x over that between them at x + ?x is given by the inductive drop over the section ?x, i.e. (x,t)-V(x+?x,t)=?xx+?xL?i?tdt, and by an argument parallel with that...