# Basic Matrix Analysis and Synthesis

## 1st Edition

### With Applications to Electronic Engineering

**Authors:**G. Zelinger

**Editors:**D. W. Fry L. Costrell K. Kandiah

**eBook ISBN:**9781483224091

**Imprint:**Pergamon

**Published Date:**1st January 1966

**Page Count:**244

## Description

Electronics and Instrumentation, Volume 36: Basic Matrix Analysis and Synthesis presents the application of matrix methods to practical electronics problems. This book focuses on transistor applications.

Organized into three parts, this volume begins with an overview of the fundamental theory of twoports and explains the mechanisms of matrix and determinant operations with applications to the study of twoport networks, both active and passive. This text then explains the concept of impedance transformation and image matching in the different matrix domains. This book presents as well the analysis and synthesis of active networks. The final part deals with the mathematical model concepts of transistors and vacuum tubes that are freely applied to a wide range of problems with an emphasis on practical applications such as conventional amplifiers, single-, and multi-stage transistor feedback amplifiers and oscillators.

This book is a valuable resource for electronics engineers as well as for students with some grounding in mathematics and network theory.

## Table of Contents

Preface

Part I. Basic Matrix Analysis and Synthesis

1. Review of the Basic Mathematical Operations with Matrices and Determinants

(a) Matrices and Determinants; Fundamental Similarities and Differences

(b) Addition and Subtraction

(c) Multiplication

(d) Inversion

2. The Terminated Twoport and Mathematical Models

(a) The Terminated Twoport and the Z Matrix

(b) The Terminated Twoport and the Y Matrix

(c) The Terminated Twoport in Terms of the h Parameter Matrix

(d) The Terminated Twoport in Terms of the g Parameter Matrix

(e) The Terminated Twoport and the Transmission Matrix

Table I: Terminal Properties

3. Interrelations and Conversion of Matrices

(a) Inversion of the Z Matrix Into Y Matrix

(b) Inversion of the g Matrix Into h Matrix

(c) Conversion of the Y Matrix Into ABCD Matrix

(d) Conversion of the h Matrix Into ABCD Matrix

(e) Table of Matrix Conversions, Introductory Comments

Table II: Matrix Interrelations]

4. Elements of Matrix Synthesis and Network Models

(a) The Single Element Twoport

(b) The Two-Element L Network in Terms of Z and Y Parameters

(c) The Three-Element Network in Terms of Z and Y Parameters

(d) The ABCD or Transmission Matrix Applied to the Synthesis of Simple Network Models

(e) Twoport Interconnections and Synthesis of Generalized Mathematical Models

References

Part II. Matrix Methods Applied to Impedance Transformation

1. Impedance Transformation and Image Matching, General

2. Image Impedance Matching of Passive and Active Twoports

(a) Image Impedance Matching in Terms of the ABCD Matrix

(b) Image Impedance Matching in Terms of the Z Parameter Matrix

(c) Image Impedance Matching in Terms of the h Parameter Matrix

(d) Image Impedance Matching in Terms of Arbitrary Matrix Parameters

3. Application of the Z Matrix to Image Matching of a Complex Load and an RF Amplifier

(a) Definition of the Problem

(b) Synthesis of Mathematical Model, Conditions of Image Matching

References

Part III. Matrix Analysis and Synthesis of Vacuum Tube and Transistor Circuits

Introductory Remarks

1. Vacuum Tubes, Linear Models and Matrices

(a) General Definitions

(b) Floating Admittance Matrix of the Triode

(c) Transformation of the Admittance Matrix of the Triode to Arbitrary Matrix Domains

References

Table III: Two Port Matrices of the Triode

2. Single-Stage Vacuum Tube Amplifiers, Z Matrix Applications

(a) Grounded Cathode Amplifier

(b) Negative Feedback Amplifier

References

3. The Single-Stage Transistor Amplifier Design, Applications of the h and ABCD or Transmission Matrix Parameters

(a) Introduction

(b) General Consideration of the Design Target

(c) Interconnecting the Transistor and Terminating Networks, Definition of Parameter Matrices

(d) The Mathematical Model of the Transistor as ABCD Matrix in Terms of Hybrid h Parameters

(e) Input Impedance

(f) Output Impedance

(g) Current Gain

(h) Voltage Gain

(i) Power Gain

References

4. The Single-Stage Composite Feedback Transistor Amplifier Design, Y and ABCD Matrix Applications

(a) Introductory Remarks

(b) Formulation of the Amplifier Design Target

(c) Synthesis of the Composite Feedback Amplifier

(d) Detailed Matrix Analysis

(e) Current Gain

(f) Voltage Gain

(g) Input Impedance

(h) Output Impedance

(i) Concluding Remarks

Table IV: Summary of Terminal Properties

Reference

5. The Transistor Voltage Feedback Pair, h Matrix Applications

(a) Synthesis of the Mathematical Model

(b) Voltage Gain

(c) Current Gain

(d) Input Impedance

(e) Output Impedance

References

Table V: Summary of Terminal Properties

6. The Transistor Current Feedback Pair, g Matrix Applications

(a) Synthesis of the Mathematical Model

(b) Voltage Gain

(c) Current Gain

(d) Input Impedance

(e) Output Impedance

References

Table VI: Summary of Terminal Properties

7. The Feedback Triplet Transistor Amplifier, Applications of the h and Z Matrices

(a) General Considerations

(b) Definitions of the Non-Feedback Single-Stage Amplifier Model

(c) Definitions of the Three-Stage Non-Feedback Model

(d) The Three-Stage Feedback Amplifier and the Z Parameter Matrix

(e) Voltage Gain

(f) Current Gain

(g) Input Impedance

(h) Output Impedance

(i) Concluding Remarks

Table VII: Summary of Terminal Properties

References

8. Oscillatory Circuits, Applications of the Y and h Parameter Matrices

(a) Introductory Remarks

(b) The Oscillatory Circuits, General

(c) The Grounded Plate Colpitts' Oscillator

(d) The Grounded Emitter Colpitts' Oscillator

References

Appendix—Problems

Supplementary References

Index

Other Titles in the Series

## Details

- No. of pages:
- 244

- Language:
- English

- Copyright:
- © Pergamon 1966

- Published:
- 1st January 1966

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483224091