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6 Introduction
the selectivity effects that result. Also, the resonator slope-equivalence technique
is described to extend the method to adapted elements other than the
ideal lumped elements usually considered. The full range of response shapesfrom
overcoupled (equal ripple), through maximum flatness, to undercoupled
-is described; the important minimum-loss case is covered too. Tuning
methods and sensitivity relationships are explained in terms of laboratory
methods and the loaded-Q parameter.
The last chapter deals with other direct filter design methods, especially
those that depend on recursive formulas for element values or means other
than synthesis. This potpourri was chosen because the methods are useful,
frequently applicable, and demonstrate worthwhile principles. Chapter Nine
begins with Taub's equal-stub microwave filter design method. Then, a new
elliptic filter design method is introduced by a general discussion of filter types
and performance parameters. The entire family of related selectivity functions
is reviewed, and a standard nomograph and program provide performance
estimates. Next, the basis of two new and powerful programs for doubly
terminated filter design by Amstutz is explained, and program operation is
illustrated. Useful tables of lumped-element equivalence transformations are
included.
Chapter Nine also contains theory and design tools to estimate load effects
on passive networks, and maximum possible efficiency is shown to be the
controlling parameter. This topic is important because filters designed to
operate properly between carefully defined load resistances are likely to be
operated between quite different terminations. The last topic in Chapter Nine
extends the load effects concept to invulnerable (intrinsic) filters that absorb
rather than reflect energy. These may be regarded as selective attenuators;
they are quite valuable in mixer and low-frequency applications where circulators
are not feasible. Equations and a design chart.for a lowpass, invulnerable
network are derived.
Another way to view the contents of this book is according to the mathematical
subjects treated, even though the material was organized according to
design applications. Matrix algebra topics include multiplication, exponentiation,
inner products and norms, quadratic forms and conics, and partitioning.
Polynomial algebra of real and complex variables touches on power series and
product forms, as well as rational-polynomial continued fractions, partial
fractions, and Chebyshev expansions. Calculus tools include multivariate
Taylor series, partial derivatives and gradient vectors, the Cauchy-Riemann
principle, numerical differentiation and integration, and infinite summations
and products. Complex variables appear throughout, and special attention is
given to bilinear transformations and the generalized Smith chart. Hilbert,
Fourier, and Laplace transforms and the convolution integral are employed.
The material that follows has been tested in industry and can become an
important part of your set of engineering tools.