Electrical Networks

Preface

Contents

Symbols


1 D.C. Currents and D.C. Voltages


1.1 Current, Potential, Voltage and Resistance


1.2 The Voltage Source and the Current Source


1.3 Energy and Power


1.4 Connection of Resistors


1.5 Voltage and Current Division


1.6 The Solution of Larger Networks


1.7 The Mesh Method


1.8 The Node Method


1.9 The Current Law for a Cut-Set


1.10 Superposition


1.11 Tellegen’s Theorem


1.12 Two-Ports


1.13 Thévenin’s and Norton’s Theorems


1.14 Maximum Power Transfer


1.15 Star-Delta Transformation


1.16 Controlled Sources


1.17 Transactors


1.18 Special Networks


1.19 Thévenin’s Theorem in Networks with Transactors


1.20 The Operational Amplifier


1.21 Problems


2 Varying Currents and Voltages


2.1 Introduction


2.2 Direction and Polarity


2.3 Kirchhoff’s Laws and Ohm’s Law


2.4 Periodical Quantities


2.5 Average Value


2.6 Power


2.7 Effective Value


2.8 Sinusoidal Quantities


2.9 Power for Sinusoidal Voltages and Currents


2.10 The Sum of Two Sinusoidal Quantities


2.11 The Capacitor


2.12 The Inductor


2.13 Energy Stored in Capacitor and Inductor


2.14 The Passive Elements in Sinusoidal Excitation


2.15 A Larger Network in Sinusoidal Excitation


2.16 Complex Numbers


2.17 Operations with Complex Numbers


2.18 Complex Voltages and Currents


2.19 Kirchhoff’s Laws for Complex Quantities


2.20 The Complex → Time Transformation


2.21 Vector Diagrams


2.22 Complex Power


2.23 Maximum Power Transfer for Complex Quantities


2.24 Problems


3 Some Properties of Networks


3.1 Polar Diagrams


3.2 Bode Diagrams


3.3 Duality


3.4 Resonance


3.5 Lossless One-Ports


3.6 Zobel Networks


3.7 Problems


4. Magnetic Coupled Inductors, Transformers


4.1 Introduction


4.2 Mutual Induction


4.3 Current Direction, Voltage Polarity and the Mode of Winding


4.4 The Value of |M|


4.5 Hopkinson’s Formula


4.6 The Transformer


4.7 Impedance Transformation


4.8 Equivalent Circuits for Magnetic Coupled Coils


4.9 The Voltage and the Current Transformer


4.10 Problems


5 Three-Phase Systems


5.1 The Rotating Field


5.2 The Creation of a Rotating Field


5.3 The Principle of the Three-Phase Motor


5.4 The Principle of the Three-Phase Generator


5.5 The Three-Phase Supply


5.6 Complex Three-Phase Voltages


5.7 The Three-Phase Load


5.8 Power in Three-Phase Systems


5.9 Phase Compensation


5.10 Problems


6 Fourier Series


6.1 Introduction


6.2 The Infinity Series of Fourier


6.3 The Frequency Spectrum


6.4 Dirichlet’s Conditions


6.5 Gibb’s Phenomenon


6.6 The Fourier Series in Complex Form


6.7 The Finite Fourier Series


6.8 Reflections on Symmetry


6.9 The Effective Value of a Fourier Series


6.10 Problems


7 The Complex Frequency


7.1 Introduction


7.2 A Capacitor Discharges Over a Resistor


7.3 A Capacitor Discharges Over an Inductor with Series Resistor


7.4 The Complex Frequency Plane


7.5 Extension of the Meaning of Impedance


7.6 Kirchhoff’s Laws if the Frequency is Complex


7.7 Poles and Zeros


7.8 Frequency Characteristics


7.9 The Coincidence of Poles and Zeros


7.10 The Order of a Network


7.11 Natural Oscillations of a One-Port


7.12 The Location of the Poles and Zeros for an Immitance


7.13 The Number of Poles for an Immittance


7.14 Poles and Zeros on the Imaginary Axis


7.15 The Amplitude Surface


7.16 Problems


8 Two-Ports, Filters


8.1 Introduction


8.2 Two-Port Matrices


8.3 Interconnection of Two-Ports


8.4 Reciprocity


8.5 Restoring the Port Condition


8.6 Poles and Zeros of a Transfer Function


8.7 Once More the Operational Amplifier (Opamp)


8.8 The Realisation of Differential Equations


8.9 Filters


9.10 Problems


9 Networks Containing Switches


9.1 Introduction


9.2 Discontinuity


9.3 The Continuity Theorem


9.4 Initial Conditions


9.5 A Second-Order Transient Problem


9.6 Natural Oscillations


9.7 The Impulse Function


9.8 Sine and Cosine Functions with Decreasing Amplitude


9.9 Summarising Example


9.10 Conclusion


9.11 Problems


10 Computer Aided Analysis


10.1 Introduction


10.2 The NA-Matrix


10.3 The Concept ‘Stamp’


10.4 The MNA-Matrix


10.5 Outline of the Stamps


10.6 Earthing a Terminal


10.7 Connecting Two Terminals


10.8 A Terminal Becomes an Internal Node


10.9 Examples


10.10 The Solution of the Matrix Equation


10.11 Numerical Integration


10.12 Equivalent Circuits


10.13 Nonlinear Elements


10.14 Problems

Apendices

Appendix I Linearity and Superposition

Appendix II Tellegen’s Theorem

Appendix III Reciprocity

Appendix IV Thévenin’s and Norton’s Theorems

Appendix V Star-Delta Transformation

Appendix VI Foster’s Theorem

Answers to Problems

Index