# Theory of Linear and nonlinear circuits - Engberg J.

ISBN 0-47-94825

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9.6.2 Example 2....................................................247

9.6.3 Example 3....................................................2 49

9.6.4 Example 4....................................................253

9.7 Conclusion ...........................................................254

9.8 References............................................................255

A Mathematical concepts 257

A.l Stochastic processes .................................................'257

A.2 Fourier series representation.........................................259

A.3 Signal energy and average power.......................................263

A.4 References............................................................264

В Expressions for reflection coefficients and exchangeable po-wers 265

B.l Derivation of reflection coefficients.................................26-5

B.2 Incident power wave expressed by exchangeable power...................266

B.3 Reference.............................................................268

С Extended noise factor as a hyperboloid of two sheets 269

D Some useful FORTRAN subroutines 271

E Determination of Volterra transfer functions using Map/e 275

E.l Program listing for listgen source code...............- ...........27o

E.2 Program listing for vtf source code............................280

E.3 Program listing for example 1..........................................235

E.4 Program listing for example 2.........................................2S6

ii.5 Program listing for example 3..........................................288

F.o Program iistiiig lor example 4........................................290

Preface

This book consists of a linear part written by .J. Engberg and a nonlinear part written by T. Larsen. Noise is anything unwanted by the hearer. Electrical noise in this work is the result of quantification of processes and electronic movements thus leaving out hum, intermodulacioii phenomena and regular harmonic oscillations, distortions etc. The book begins with a short historical review 011 the main developments in noise theory.

Chapter 2 concerns noise in one-ports. From Nyquist’s expression for thermal noise, where the frequency dependency is mentioned, the expressions for noise resistance, noise conductance and noise temperature are developed and extended to active as well as passive one-ports. The noise expressions are defined for thermal as well as for other noise sources. The last section of the chapter is devoted to calculation rules for noise quantities of networks consisting of two-ports in various combinations.

Chapter 3 is devoted to the definition of noise quantities for multiports. Here all types of noise quantities - the noise factor, the effective noise temperature and the operating noise temperature - are extended to active as well as passive networks and terminations. The definitions are for passive networks and terminations in accordance with the IRE definitions except for the operating noise temperature, where a minor correction is included. The noise quantities are defined in two ways: spot frequency and average values. Also the equivalent noise bandwidth is discussed. In a discussion of the noise quantities an operating load noise temperature is introduced.

In Chapter 4 the noise parameters of a two-port are developed from the equivalent noise two-port of Rot he and. Dahlke. Similarly noise parameters are developed on the basis of noise power waves. The chapter finally presents transformation formulae between the many types of noise parameters.

In Chapter 5 the extended noise measure is introduced. The chanter is devoted to graphic representations ol the noise measure. In order to do this the exchangeable power gain, which takes part in the definition of the noise measure, is illustrated. The graphic representation is shown in both the source admittance plane and in the source reflection plane. Both representations lead to a third-degree equation from which the extreme values of the noise measure can be caicuiateu.

Chapter 6 concerns embedded circuits. In the first section a three-pole embedded in lumped one-ports is discussed. This makes it possible to calculate the noise

Preface

quantities of a transistor with bias and feedback elements included. Then a two-port with a lossy transmission line in front is considered, and from that the noise parameters of a transmission line are deduced. Then interconnection of two-ports is considered in various ways, and a method by Pucel et al. making it possible to compute the noise parameters at one high frequency from data at a lower frequency is presented. This method makes extensive use of embedding theory as '.veil as matrix formulation. Two special circuits are considered next. One is a transistor with mixed transformer feedback and the other is a circuit with input at both base and emitter. Finally formulae for noise parameter transformations from common emitter to common base and common collector are presented.

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