Electromagnetic modes in conical transmission lines withapplication to the linearly tapered slot antenna

A transmission line analysis of the bow-tie antenna and the linearly tapered slot antenna (LTSA) is presented. These structures belong to the class of conical transmission lines defined here in terms of conical coordinates. A complete set of solutions of the Helmholtz equation is obtained exhibiting TE and TM modes. Modal fields are expressed by Lame (1837) and Bessel-Schelkunoff functions. TE and TM eigenmode analysis is particularized to the bow-tie structure. Bow-tie antenna and LTSA are shown to be dual conical transmission lines by the image method and Babinet's principle. The modes of LTSA are calculated on the basis of the results obtained for the bow-tie structure. The radiation pattern of the LTSA is computed as the integral of a closed-form expression of the dyadic Green's function weighted by the modal electric field distribution over the slot aperture. The obtained dominant mode radiation patterns are validated by measurements from the literature. The radiation patterns of the first two-order modes are calculated and compared     

Variational principles compete with numerical iterative methods for analyzing distributed electromagnetic structures

An explicit variational principle (Evp) for the propagation constant of em waves is compared with four numerical tools: the Newton-Raphson algorithm solving a transcendental equation, the spectral domain approach (Sda) applied to the Galerkin method, the 3-D simulatorHfss fromHp, and the finite element method (Fem). Each tool analyses a different planar topology: a lossy dielectric slab supporting surface waves, a planar slotline modelled by transmission line parameters (Tlp), a multilayered high-loss co-planar waveguide, and a shielded microstrip line. For these various structures, the evp is more efficient than previous tools yielding the propagation constant; its explicit form and variational nature yield a drastic reduction of the number of iterations.     

Asymptotic Green's function of a surface magnetic current elementon a perfect electric conductor plane covered by a lossy dielectricsubstrate

Published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical. This paper proposes exact analytical asymptotic expressions of the far-field Green's functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness. From these expressions, the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped-slot antenna structure can be calculated, provided the source distribution across the slot is known. The potentials used in the analysis are defined and their boundary conditions are expressed. The Helmholtz equation is solved in the Laplace domain and the solutions are transformed into the space domain using the inverse Hankel transform and steepest descent method. The influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions. The model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator     

Modeling of ground-penetrating Radar for accurate characterization of subsurface electric properties

The possibility to estimate accurately the subsurface electric properties from ground-penetrating radar (GPR) signals using inverse modeling is obstructed by the appropriateness of the forward model describing the GPR subsurface system. In this paper, we improved the recently developed approach of Lambot et al. whose success relies on a stepped-frequency continuous-wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic horn antenna. This radar configuration enables realistic and efficient forward modeling. We included in the initial model: 1) the multiple reflections occurring between the antenna and the soil surface using a positive feedback loop in the antenna block diagram and 2) the frequency dependence of the electric properties using a local linear approximation of the Debye model. The model was validated in laboratory conditions on a tank filled with a two-layered sand subject to different water contents. Results showed remarkable agreement between the measured and modeled Green's functions. Model inversion for the dielectric permittivity further demonstrated the accuracy of the method. Inversion for the electric conductivity led to less satisfactory results. However, a sensitivity analysis demonstrated the good stability properties of the inverse solution and put forward the necessity to reduce the remaining clutter by a factor 10. This may partly be achieved through a better characterization of the antenna transfer functions and by performing measurements in an environment without close extraneous scatterers.     

Frequency Dependence of the Soil Electromagnetic Properties Derived from Ground-Penetrating Radar Signal Inversion

The accuracy at which the subsurface electromagnetic properties can be identified from full wave inversion of ground penetrating radar (GPR) signals relies on the appropriateness of the model describing their frequency dependence. In this paper, we focus on the characterization of the frequency dependence of the dielectric permittivity and electric conductivity of a sandy soil subject to different water contents from inversion of GPR measurements. Based on previous studies of Lambot et al. the methodology relies on an ultrawide band (UWB) stepped-frequency continuous-wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic (TEM) horn antenna. Forward modeling of the radar signal is based on linear system transfer functions for describing the antenna, and on the exact solution of Maxwells equations for wave propagation in a horizontally multilayered medium representing the subsurface. Model inversion, formulated by the classical least-squares problem, is carried out iteratively using advanced global optimization techniques. The frequency dependence of the electromagnetic properties of the sandy soil is characterized by performing inversions of the radar signal in different and subsequent limited frequency bands, in which the electromagnetic parameters are assumed to be constant. We observed that over the entire frequency band considered in this study (1–3 GHz), the dielectric permittivity of the sand remains constant with frequency, whatever the water content is. In contrast, the electric conductivity increases significantly from 1GHz to 3 GHz, and this effect increases with water content. The frequency dependence of the electric conductivity may be adequately described using a simple linear relationship. This approach is advantageous since it limits the number of parameters to be optimized in the inverse modeling procedure.     

Copolar and cross-polar radiation of Vivaldi antenna on dielectricsubstrate

The copolar and cross-polar radiation patterns of the Vivaldi antenna on a dielectric substrate are calculated and validated by measurements. The method involves a two-step procedure. The electric field distribution across the antenna slot aperture is calculated first. The radiated fields are then calculated, using Green's functions. The continuous exponential tapered shape is approximated by annular linearly tapered sections. The conical transmission-line theory and a variational method yield the electric field in each section. The radiation calculation is based on closed-form expressions for the dyadic Green's function of an elementary electric field source in a conducting half sheet. Both copolar and cross-polar radiation patterns of the Vivaldi antenna are calculated by integrating the Green's functions weighted by the electric field distribution over the antenna aperture. The effect of lateral truncation is taken into account by defining weighting patterns. The method is validated by original measurements and limitations of the model are discussed. Antenna directivity and sensitivity are calculated     

An efficient energetic variational principle for modeling one-portlossy gyrotropic YIG straight-edge resonators

This paper presents a new variational principle for the design of one-port gyrotropic magnetostatic-wave (MSW) resonators. We first prove the stationary character of the magnetic energy in the case of a resonator containing lossy gyrotropic media and supporting microwave MSW's. We then show that the variational expression may be successfully used for calculating the input reflection coefficient of a planar multilayered MSW straight-edge resonator (SER). Results obtained using the variational formulation are validated by experiment carried out at X-band. Hence, the resulting model is an efficient tool for designing low-noise wide-band yttrium-iron-garnet (YIG) tuned oscillators     

Effect of surface wave diffraction on radiation pattern of slotantenna etched in finite ground plane

The effect of ground plane and dielectric truncations on the radiation pattern of a slot antenna etched in a substrate covered conductor plane of finite extent is modelled, measured and validated. The modelling method is based on the evaluation of analytical Green's functions and the numerical computation of single integrals. The importance of taking the surface wave diffraction into account is demonstrated