# Basic Matrix Algebra and Transistor Circuits

## 1st Edition

**Authors:**G. Zelinger

**eBook ISBN:**9781483151243

**Imprint:**Pergamon

**Published Date:**1st January 1963

**Page Count:**132

## Description

Basic Matrix Algebra and Transistor Circuits deals with mastering the techniques of matrix algebra for application in transistors. This book attempts to unify fundamental subjects, such as matrix algebra, four-terminal network theory, transistor equivalent circuits, and pertinent design matters.

Part I of this book focuses on basic matrix algebra of four-terminal networks, with descriptions of the different systems of matrices. This part also discusses both simple and complex network configurations and their associated transmission. This discussion is followed by the alternative methods of deriving the transmission matrix using Kirchhoff's law. Part II introduces matrix analysis of transistor circuits, and then shows in detail the three transistor configurations: common-base, common-emitter, and common collector. A step-by-step method of transmission matrices derivation for each transistor configuration is then explained. This book notes the significance of matrix algebra in dealing with amplifier problems in a variety of output network configurations. Part III focuses on several aspects of single-stage transistor ampler design. This part explains how matrix algebra can be used to derive the exact input, output impedances, and the reverse transfer properties of transistor amplifiers with full load and generator terminations. Through mathematical analysis, the book shows the accuracy of matrix analysis in transistor amplifier design.

This book is suitable for design engineers, electrical engineers, and students and practitioners of applied mathematics.

## Table of Contents

Preface

I. Basic Matrix Algebra of Four-terminal Networks

1. Why Matrix Algebra

2. Matrices and Determinants: Fundamental Similarities and Differences

3. Matrix Representation of Networks

(a) The Transmission Matrix and General Parameters

(b) The Z Matrix

(c) The Y Matrix

(d) The h Matrix

4. Basic Operations with Matrices

(a) Addition and Subtraction

(b) Multiplication

(c) Inversion

5. Simple Network Elements and their Associated Transmission Matrices

(a) Series Impedance Element

(b) Parallel Admittance Element

6. More Complex Network Configurations and Associated Transmission Matrices

(a) L Network with Series Input Element

(b) L Network with Shunt Input Element

(c) T Network

(d) π Network

(e) Series Connection of Impedances

(f) Parallel Connection of Admittances

7. Alternative Methods of Deriving the Transmission Matrix by Kirchhoff's Law

(a) The T Network

(b) The π Network

8. Networks Containing Mutual Inductance

(a) Inductively Coupled Circuits, General

(b) Ideal Transformer

(c) Series Tuned Inductively Coupled Circuits

(d) Parallel Tuned Inductively Coupled Circuits

9. Reciprocal and non-reciprocal Networks, Characterized by the Determinant of Matrix

(a) Passive or Reciprocal Networks

(b) Active or non-reciprocal Networks

10. Transformation of Matrices

(a) Inversion of the Transmission Matrix in Terms of General Parameters

(b) Transformation of the Z Matrix into Y matrix in Terms of Z Parameters

(c) Tables of Transformations

List of References

II. Introduction to Matrix Analysis of Transistor Circuits

Summary

Introduction

1. The Common-base Connection

Derivation of Transmission Matrix

Determinant of Transmission Matrix

Short-circuit Current Gain

Open-circuit Voltage Gain

Simplified Resistive Parameters

Modification of Resistive Model for High Frequencies

Amplifier with Generalized Load Impedance

Amplifier with Tuned LC Load

2. The Common-emitter Connection

Derivation of Transmission Matrix

Determinant of Transmission Matrix

Short-circuit Current Gain

Open-circuit Voltage Gain

Simplified Resistive Parameters

Amplifier with Generalized Load Impedance

Amplifier with Tuned LG Load

3. The Common-collector Connection

Derivation of Transmission Matrix

Determinant of Transmission Matrix

Simplified Resistive Parameters

Short-circuit Current Gain

Open-circuit Voltage Gain

Conclusion

List of References

III. Application of Matrix Algebra to Design Topics of Single-stage Transistor Amplifiers

Introduction

1. Impedance and Admittance

(a) Input Impedance, General Definition

(b) Output Impedance, General Definition

(c) Reverse Transfer Admittance, General Definition

2. The Common-base Amplifier

(a) Input Impedance

(b) Output Impedance

(c) Reverse Transfer Admittance

3. The Common-emitter Amplifier

(a) Input Impedance

(b) Output Impedance

(c) Reverse Transfer Admittance

4. The Common-collector Amplifier

(a) Input Impedance

(b) Output Impedance

(c) Reverse Transfer Admittance

Conclusion

List of Rreferences

Supplementary References

Index

## Details

- No. of pages:
- 132

- Language:
- English

- Copyright:
- © Pergamon 1963

- Published:
- 1st January 1963

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483151243