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Introduction 3
level of sophistication once the possibilities are clear. To that end, extensive
references are provided for further inquiry. Many references are quite recent,
which is not to overlook some of the older classics-for example, an early
direct-coupled-filter article by Dishal (1949). There are some derivations that
are crucial to important issues; these have been included in an appendix or
outlined in the problem set.
There are several indispensable numerical analysis tools that will be required
throughout this book and that are applicable in almost all phases of
electrical engineering. Chapter Two begins with the most elemental of these
(especially in steady-state sinusoidal network analysis): the complex addition,
subtraction, multiplication, and division functions. A hand-held computer
program is given for convenient usage, and the reader will need to have ready
access to this capability on many occasions. The Gauss-Jordan method for
solving real equations in real unknowns is discussed in connection with a
BASIC language program; this is used later in Chapter Two for fitting rational
polynomials to discrete complex data sets and in Chapter Three in the
Gewertz synthesis method. A very convenient extension of this method to
solve systems of complex equations is also described; this technique is convenient
for solving nodal analysis equations and similar systems.
Chapter Two also describes the trapezoidal rule and its application in the
Romberg method of numerical integration; this is used in the broadband
impedance-matching methods in Chapter Six. Also, Simpson's rule is derived
for later use in time-domain analysis in Chapter Four. Chapter Two concludes
with methods for fitting polynomials to data. First, real polynomials are
generated to provide a minimax fit to piecewise linear functions using Chebyshev
polynomials. Second, complex data are fit by a rational function of a
complex variable, especially the frequency-axis variable in the Laplace s
plane. This will be applied to broadband matching, and is useful in other
ways, such as representing measured antenna impedance data.
Many of the computer aids developed in this book are not only efficient
tools, but are based on important principles worth the attention of any
network designer. Moore's root finder in chapter three is a good example,
because it depends on the Cauchy-Riemann conditions and a powerful but
little-known method for evaluating a complex-variable polynomial and its
derivatives.
Engineers interested in network synthesis, automatic control, and sampled
data systems need many other mathematical aids. Polynomial addition and
subtraction of parts, multiplication, long division, and partial and continued
fraction expansions of rational polynomials are described in Chapter Three.
Their application to network synthesis is used to develop the characteristic
and transducer functions in terms of the ABCD (chain) matrix of rational
polynomials. These are then realized as doubly terminated ladder networks.
Gewertz's singly terminated network synthesis method concludes Chapter
Three; this method accomplishes input impedance synthesis, given the network
function's real part.