Electromagnetic waves in loaded cylindrical structures : a radial transmission line approach

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.