Samenvatting
The motivation for developing the computational electromagnetic methods presented in this thesis
is to model the radiation of leaky slotted coaxial cables (LCXs), which are used as distributed
antennas in environments that are not readily accessible via conventional antenna substations,
and to model ring cavities that act as circular waveguide ??lters. We employ circuit-based electromagnetic wave theory in the solution of guided-wave scattering problems. Here the term
¿guided wave¿ is actually to be interpreted loosely, since even free space can be viewed as a
waveguide.
Propagation in usual rectilinear waveguides is often phrased in literature in the language of transmission line theory. The theory of equivalent transmission lines has been contrived as a way to
give physical insight into the mathematical method of separation of variables. This opens the
way to the use of unconventional equivalent transmission lines, such as radial or angular ones.
In this thesis we have focused on the concept of radial waveguide, a structure that has the radial
direction as the direction of propagation, and that is possibly bounded by metal plates parallel
to the coordinate surfaces. Unlike the traditional vector mode functions encountered in conventional
waveguides, the radial transmission line concept is introduced in a component basis.
Radial lines are peculiar, because they have an absolute origin and hence is not shift invariant.
Nevertheless, using a suitable vector formalism, the usual circuit theory concepts can be still
applied, including the de??nition of voltages and currents, impedances, propagators, scattering
matrices, etc.
The LCXs are standard coaxial cables from which, on the outer conductor, slots are cut in order
to induce energy exchange between the interior of the cable and the surrounding external domain.
These kinds of antennas are usually employed for indoor communications in places where the
traditional antenna systems fail or their application and installation are problematic, such as in
subways and tunnels. They are also used for security reasons, e.g., in outstations and airports, in
order to con??ne the communications inside speci??c places. In particular, nowadays, there is an
increasing interest in the application of this technology in the GSM and UMTS frequency bands.
LCXs have been studied by several researchers in the past. The analysis techniques employed in
these studies produce solutions, to a varying degree of accuracy, for the particular problem of the
in??nite periodically slotted cable. The problem of junctions between closed and slotted cables
has so far not been addressed. The periodically slotted LCXs considered in the literature suffers
from poor ef??ciency in terms of percentage of incident power used for the radiation. Indeed,
since the decay of the power inside the cable is exponential and the radiated ??eld decays along
the cable length with the same law, the standard periodically slotted LCX requires a compromise
between an almost constant level of power along the slotted cable length and minimum power at
the end of the cable that is not employed for radiation. In the present thesis we have developed
accurate and ef??cient modeling techniques, enabling us to analyze both periodic and aperiodic
LCXs, as well as transitions between open and closed cables.
The second type of devices of interest is a particular category of stop-band ??lters commonly
used in antenna systems to isolate receivers from the signals produced by transmitters, internal
or external to the system, and operating in adjacent frequency bands. The structure that we have
analyzed presents advantages in terms of the radial and longitudinal dimensions, which allows
for the high level of integration that is often essential for space applications. Due to the resonance
behavior of the device, the commercial numerical codes require long computational times before
suf??ciently accurate ??eld solutions are obtained. Our dedicated modeling method is much more
ef??cient in attaining the required results, which has made it possible to produce several design
examples.
Our modeling techniques are based on the magnetic ??eld integral equation. The associated kernel
is the Green's function of the structure, which is been computed in the spectral domain, using radial
transmission line theory. The solution of the corresponding integral equation is obtained, for
both problems, by the method of moments in the Galerkin form, using a suitable set of basis functions.
The computation of the moments requires particular care. We have developed dedicated
numerical techniques by which the numerical convergence is improved and the computation of
the integrals is accelerated considerably.
For LCXs, we have developed a design procedure based on tapering the geometrical dimensions
of the slots in order to obtain an uniform radiation and to maximize the radiated power. Since
a typical LCX consists of thousands of slots, one approaches practical limitations of integral
equation techniques, as the dimension of the linear system resulting from the discretization of
the integral equation increases with the number of slots. For this reason, we have augmented our
approach to analyze LCXs in two alternative directions. One is based on the application of the
Bloch wave approach, the other comprises an extension, for the electromagnetic problem under
consideration, of the so-called eigencurrent approach, that was originally developed for linear
arrays of patches.
First, the Bloch wave approach is not standard in this case since the structure consists of two
different regions, one is closed (the interior of the coaxial cable) the other is open (the unbounded
exterior domain). We have employed a particular mathematical formalism to overcome this
problem, viz., we have solved the junction problem between an closed cable and a slotted one
using the mode matching technique. In the Bloch wave approach a LCX with any number of
slots, all equal and equally spaced, can ef??ciently be analyzed.
Second, the eigencurrent approach is a versatile two-step technique for modelling large compound
structures. The ??rst step is to evaluate the eigenvalues and current eigenfunctions of the
integral operator associated with a single slot. Subsequently, the pertaining eigencurrents act as
global-domain basis functions for the slotted array. In the resulting equivalent linear system, the
interaction between the slots is adequately described in terms of very few of these eigencurrents.
We have applied this method for LCXs with slots of different geometric dimensions, and have
observed a substantial reduction of computation times.
For a LCX with a large but ??nite number of identical slots, it turns out that the dominant Bloch
wave is the same as the one excited in the semi-in??nite case. When this so-called Forward wave
reaches the junction between the slotted and unslotted cable, it gives rise to several re??ected
Bloch waves that, upon scattering at the ??rst junction, couple only with the Forward wave. Further,
we have observed that all the regressive Bloch waves have globally a negligible effect on
the magnetic currents on the slots. Hence the ??eld propagating in the slotted region of the ??nite
slotted cable is essentially a progressive wave.
As regards the radiation properties of an in??nite LCX, a paradox arises. In practical LCX applications
the receiver is always in the near-??eld region of the array, but in the far-??eld region
of the majority of the slots. This is related to the in??nite length of a LCX. Application of the
Poisson sum formula to the expression for the radiated ??eld emanating from a LCX converts
that expression into a linear superposition of spatial harmonics, in line with the Bloch-wave de
scription. As a consequence, cables with different slot spacings are perfectly explained in terms
of the various modes of operation resulting from the Bloch-wave description, i.e., surface-wave,
mono-radiation and multi-radiation operation.
Originele taal-2 | Engels |
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Kwalificatie | Doctor in de Filosofie |
Toekennende instantie |
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Begeleider(s)/adviseur |
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Datum van toekenning | 17 jun. 2008 |
Plaats van publicatie | Eindhoven |
Uitgever | |
Gedrukte ISBN's | 978-90-386-1894-4 |
DOI's | |
Status | Gepubliceerd - 2008 |