Page 373 - Maxwell House

DISCONTINUITY IN FEED LINES 353

Introduction
There are many ways to define the term “discontinuity” because of a vast variety of them. It
can be the line impedance variations, sudden or smooth change in shape of a line or its direction,
transitions between lines like the ones considered in Chapter 6, some foreign metal, dielectric
or any other material element infringing the line uniformity, etc. Meanwhile, the first and most
important indicator of any discontinuity existence is the alteration of the propagating in line
EM field pattern. If so, we decided to take such occurrence as the discontinuity definition. We
know from Chapter 6 that any deviation from the propagation mode structure means the
appearance in line some extra modes that differ from the propagating one. Such alternation can
be just local and short with respect to wavelength or continuous if any or several of extra modes
are capable of propagating freely in line (multi-mode regime). The latter makes the description
and analysis of discontinuities highly challenging, can be done in general only numerically and
requires a quite sophisticated computer tool.
If so, we decided to pursue in this book only local discontinuities to avoid serious math
complications and have the opportunity to predict the results of computer simulations. It can be
done by simple physical exploration and extensive usage of equivalent circuits. One of the key
theorems for such approach is Poynting’s theorem (see Section 3.1 in Chapter 3) and ability to
use the equivalent transmission line discussed in Chapter 6. Poynting’s theorem gives as the
beneficial and straight criteria how to recognize the presence in line an inductance, capacitance
or resistive element. Recall that if for any reason in some local area belonging to line the
accumulation of E-field energy exceeds H-field energy , i.e. > , this part of line

can be interpreted as a series or shunt lumped capacitor depending on EM field distribution.
The following statement is correct too: if > the equivalent element connected to line is

a lumped inductor. Finally, if = we observe either the resonance energy exchange

→ meaning that the lumped inductor and capacitor are presented and forms
(oscillations)
←
the parallel or series resonance contour, or the lumped resistor mimics the active energy loss,
or all of them together. As well, we can expect that the level of EM field energy accumulation
is frequency dependable since the frequency is the inseparable part of Maxwell’s equations and
sometimes of boundary conditions. If so, the reader will not be surprised later by the
phenomenon that the same discontinuity possesses several equivalent circuit of different
configuration depending on frequency band. Even more, the value of inductor or capacitor
becomes frequency dependable. At that point, the question boils down why we need such
strange equivalent circuits at all. Nevertheless, the equivalent circuits give us so convincing and
rich information about the discontinuities and simplified the complex network analysis so fine
that it would be a sin not to use them.
However, the pronounced approach is slightly controversial since it requires the preliminary
knowledge of EM fields in line with discontinuities. Meanwhile, such information normally is
not well known while some computer simulation is not finished. Therefore, we decided to take
the middle ground. In general, the local discontinuities have a reasonably simple configuration
that allows developing the easily running computer models with any current commercial
computer software like CST, HFSS, Empire, FICO, COSMOL, etc. Doing such, we would get
not only the vivid EM field patterns but a lot of valuable extra data like the input impedance,
reflection coefficient, EM field intensity, 3D field animation, Smith chart presentations, circuit
parameters in term of fields, etc.