# Linear Network Theory

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Linear Network Theory presents the problems of linear network analysis and synthesis. This book discusses the theory of linear electrical circuits, which is important for developing the scientific outlook of specialists in radio and electrical engineering. Organized into 13 chapters, this book begins with an overview of circuit theory that operates with electrical quantities, including voltage, charge, and current. This text then examines sinusoidal function as the predominant form of a periodic process in electrical circuits. Other chapters consider the reduction of a series–parallel network to single equivalent impedance, which is one of the main forms of converting circuit diagrams often used in practice. The final chapter deals with the Laplace transformation or operational calculus, which is a combination of methods of mathematical analysis. This book is intended to be suitable for students in the specialized branches of electrical and radio engineering, post-graduates, and engineers extending their theoretical knowledge.

## Table of Contents

Foreword

Notation

Chapter I. Basic Definitions and Concepts

1. Circuit Theory and its Relation to Field Theory

2. Elements of an Electrical Circuit

3. Voltage Source and Current Source

4. Circuit Diagrams of Networks

5. Linear Electrical Circuits

6. Basic Laws of Electrical Circuits

7. Energy and Power

8. Periodic and Nonperiodic Processes in Linear Electrical Circuits

9. Effective Value and Average Value for a Periodic Function

Chapter II. Basic Relationships in Sinusoidal-Current Circuits

1. Representation of Sinusoidal Functions by Rotating Vectors

2. Current-Voltage Relations in Basic Circuit Elements

3. Series Connexion of r, L and C

4. Parallel Connexion of r, L and C

5. Applications of Complex Quantities

6. Ohm's and Kirchhoff's Laws in Complex Notation

7. Power in Sinusoidal-current Circuits

8. Maximum Power Transfer

9. Balance of Power

Chapter III. Network Reduction and Transformation

1. Simplification of Series-Parallel Networks

2. Series-to-Parallel Transformation

3. Star-to-Mesh Transformation

4. Mesh-to-Star Transformation

5. Equivalent Voltage and Current Sources

6. Conversion of Circuits with Two Nodes

7. Mobility of Sources

Chapter IV. Methods of Solving Networks

1. Direct Application of Kirchhoff's Laws (Branch-Current Method)

2. Loop-Current Method

3. Node-Voltage Method

4. Superposition Method

5. Input and Transfer Impedances and Admittances. Current and Voltage Ratios

6. Reciprocity Theorem

7. Compensation Theorem

8. Alteration Theorem

9. Equivalent Source Theorem

10. Circuits with Magnetic Coupling

11. Coefficient of Coupling. Leakage Inductance

12. Equations and Equivalent Circuits of an Air-Core Transformer

13. Input Impedance of Coupled Circuits

14. Duality

Chapter V. Loci Method

1. Loci in a Complex Plane

2. Transformation of Y = 1/Z

3. Transformation of W = (A + B . k)/(C + D . k)

4. Locus Diagrams for Impedances and Admittances of the Simplest Circuits

5. Locus Diagrams for Voltage Ratios in the Simplest Circuits

Chapter VI. Two-Terminal Networks

1. Definition and Classification of Two-Terminal Networks

2. Single-Element Reactive Two-terminal Networks

3. Twin-Element Reactive Two-Terminal Networks

4. Multi-Element Reactive Two-Terminal Networks

5. General Expression for the Impedance of a Passive Dissipationless Multi-Element Two-Terminal Network

6. Canonic Forms of Dissipationless Two-Terminal Networks

7. Sign of the Frequency Derivative of the Reactance or Susceptance Functions of a Dissipationless Two-Terminal Network

8. Dissipationless Ladder Networks

9. Potentially Equivalent Two-Terminal Networks and the Conditions for their Equivalence

10. Potentially Inverse (or Dual) Two-Terminal Networks and the Conditions for their Duality

11. Multi-Element Dissipative Two-Terminal Networks Containing Two Types of Element

12. Real or Imaginary Parts of Input Impedance or Admittance. Sign of Resistance and Conductance

13. Complex Frequency

14. Immittance of a Two-terminal Network as a Positive-real Function

15. Properties of Positive Real Functions

16. Construction of a Two-terminal Network from a given Positive-real Function

17. Effect of Pole-Zero Locations on the Frequency Properties of Two-Terminal Networks

18. Relationship Between Resistance and Reactance (Conductance and Susceptance)

Chapter VII. Four-Terminal Networks

1. Basic Definitions and Classification of Four-Terminal Networks

2. Sets of Equations

3. Open-Circuit and Short-Circuit Parameters

4. Image Parameters

5. Amplitude-Phase Characteristic or Transfer Function

6. Input Impedance of a Four-terminal Network with Arbitrary Load Conditions

7. Effective Attenuation and Insertion Loss of a Four-Terminal Network

8. Cascade of Unsymmetrical Networks on the Image-Impedance Basis

9. Equations of Composite Four-Terminal Networks in Matrix Form

10. Regular Interconnexions of Four-Terminal Networks

11. Single-Element Four-Terminal Networks

12. L-Network

13. T-Network

14. Pi-Network

15. Lattice (Bridge) Network

16. Bridged T-Network

17. Ideal Transformer as a Four-terminal Network

18. Lattice Equivalent of a General Symmetrical Four-Terminal Network

19. Conversion of an Ideal Transformer with a Series or Parallel Arm into an Equivalent Four-Terminal Network

20. Poles and Zeros of Transfer Functions

21. The Relation Between the Amplitude Characteristic and the Phase Characteristic of a Four-Terminal Network

22. Construction of Four-Terminal Networks with Prescribed Frequency Characteristics

Chapter VIII. Resonant Circuits. Filters

1. Resonant Circuits and their Characteristics

2. General Information about Electrical Filters

3. Conditions for T- and Pi-Networks as Filters

4. Constant-k Filters

5. m-derived Filters

6. Coupled Circuits as Selective Networks

7. Lattice Filters. Piezoelectric Resonators

8. Filters Based on the Chebyshev Approximation

Chapter IX. Circuits with Distributed Parameters

1. Primary Parameters of a Uniform Line

2. Differential Equations of a Uniform Line

3. Steady-State Solution

4. Secondary (Image) Parameters of a Uniform Line

5. Distortionless Line

6. Dissipationless Line

7. Standing Waves

8. Input Impedance of a Line

9. Power in a Dissipationless Line

10. Line as a Matching Transformer

11. Single-Stub Impedance Matching on a Line

12. Circle Diagrams for a Dissipationless Line

13. Line as a Resonant Circuit Element

14. Artificial Line

Chapter X. Nonsinusoidal Periodic Waves (Fourier Series)

1. Trigonometric Fourier Series

2. Cases of Symmetry

3. Shift of Origin

4. Exponential Fourier Series

5. Spectra of Periodic Functions

6. Parseval's Relation

7. Effective Value and Average Value of a Nonsinusoidal Periodic Wave

8. Active (Average) Power with Nonsinusoidal Current and Voltage

9. Factors Characterizing Nonsinusoidal Periodic Waves

10. Use of Fourier Series in Circuit Analysis

Chapter XI. Trancent Analysis (Classic Method)

1. Transients in Linear Systems

2. Commutation Laws and Initial Conditions

3. Forced and Natural (Free) Responses

4. Transient Response of an rL Circuit

5. Transient Response of an rC Circuit

6. Transient Response of an rLC Circuit

7. Transient Analysis of Multi-Loop Networks

Chapter XII. The Fourier Integral

1. The Fourier Integral in Complex Form

2. Frequency Spectrum of Nonperiodic Function

3. Relation Between the Spectrum and the Envelope of the Factors of a Fourier Series

4. Cases of Symmetry of a Nonperiodic Function

5. Basic Properties of Fourier Transforms

6. Generalized Form of the Fourier Integral

7. Transient Response of a Two-Terminal Network

8. Transient Response of a Four-Terminal Network

Chapter XIII. The Laplace Transformation

1. General Information

2. Direct and Inverse Transform Integrals

3. Laplace Transforms

4. Laplace Transforms of Unit Step Functions and Exponential Functions

5. Basic Properties of the Laplace Transformation

6. Calculation of Inverse Transforms

7. Expansion Theorem

8. Transform Tables

9. Solution of Differential Equations for Electrical Circuits by the Laplace Transformation

10. Solutions in Real and Complex Form

11. Calculation by the Equivalent Source Method Taking Initial Conditions into Account

12. Switching-In Formulae

13. Transient Analysis Based on the Superposition Principle (Duhamel's Integral)

14. Initial Conditions Replaced by Pulse Functions

15. Laplace Transforms of Jump Functions and Sections of Periodic Functions

16. Transients in Transmission Lines

7. Spectrum Concepts and Laplace Transforms

18. Transfer Function

Appendixes

I. Elements of Complex Variable Theory

II. Basic Properties of the Fourier Transformation

III. Basic Properties of the Laplace Transformation

IV. Laplace Transforms

References

Index

## Product details

- No. of pages: 644
- Language: English
- Copyright: © Pergamon 1965
- Published: January 1, 1965
- Imprint: Pergamon
- eBook ISBN: 9781483181295