B. Stockbroeckx

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 Greens 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.

Estimating soil electric properties from monostatic ground‐penetrating radar signal inversion in the frequency domain

[1] A new integrated approach for identifying the shallow subsurface electric properties from ground-penetrating radar (GPR) signal is proposed. It is based on an ultrawide band (UWB) stepped frequency continuous wave (SFCW) radar combined with a dielectric filled transverse electric and magnetic (TEM) horn antenna to be used off the ground in monostatic mode; that is, a single antenna is used as emitter and receiver. This radar configuration is appropriate for subsurface mapping and allows for an efficient and more realistic modeling of the radar-antenna-subsurface system. Forward modeling is based on linear system response functions and on the exact solution of the three-dimensional Maxwell equations for wave propagation in a horizontally multilayered medium representing the subsurface. Subsurface electric properties, i.e., dielectric permittivity and electric conductivity, are estimated by model inversion using the global multilevel coordinate search optimization algorithm combined sequentially with the local Nelder-Mead simplex algorithm (GMCS-NMS). Inversion of synthetic data and analysis of the corresponding response surfaces proved the uniqueness of the inverse solution. Laboratory experiments on a tank filled with a homogeneous sand subject to different water content levels further demonstrated the stability and accuracy of the solution toward measurement and modeling errors, particularly those associated with the dielectric permittivity. Inversion for the electric conductivity led to less satisfactory results. This was mainly attributed to the characterization of the frequency response of the antenna and to the high frequency dependence of the electric conductivity.

Electromagnetic modes in conical transmission lines with application 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 Babinets 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 Greens 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.

GPR design and modeling for identifying the shallow subsurface dielectric properties

A ground penetrating radar (GPR) system for identifying the shallow subsurface dielectric properties is proposed. It consists in a stepped frequency continuous wave (SFCW) radar operating in the 0.8-4 GHz ultrawide band combined with a dielectric filled TEM horn antenna to be used off ground in monostatic mode. This radar configuration is of practical interest since it responds to subsurface mapping requirements and allows for an efficient and realistic modeling of the radar-antenna-subsurface system. Forward modeling of the system is based on linear system response functions and on the exact solution of the three-dimensional Maxwell equations for damped wave propagation in a horizontally multilayered medium representing the shallow subsurface. The model is validated under controlled laboratory conditions. This model is destined to be inverted to reconstruct the depth dependent shallow subsurface dielectric properties from field observations.

An efficient energetic variational principle for modeling one-port lossy 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 MSWs. 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.

Asymptotic Green's function of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate

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 Greens 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.

Planar Gyrotropic Devices Analyzed by using a Variational Principle

This paper presents results obtained with a new explicit variational principle developed by the authors for planar multilayered gyrotropic structures. It is applied here to planar YIG films coupled to planar lines, used as resonators in Yig Tuned Oscillators. Under- and overcoupled topologies are modelled. The calculation of YIG Magnetostatic Wave resonators as equivalent resonant transmission lines agree very well with measurements carried out up to 20 GHz.

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.RésuméUn principe variationnel explicite (pve) pour I’exposant de propagation d’ondes électromagnétiques est comparé à quatre out numériques: I’algorithme de Newton-Raphson résolvant une équation transcendentale, la méthode de Galerkin appliquée dans le domaine spectral, le simulateur 3-DHfss deHp, et la methode des éléments finis. Chaque outil analyse une structure planaire différente: une plaque dielectrique supportant des ondes de surface, une structure à fente caractérisée par ses parametrés de ligne de transmission, une structure coplanaire multicouches à penes dielectriques élevees et une ligne microruban en boîtier. Pour ces structures, lePve s’avére plus performant que les outils numériques, car sa nature variationnelle explicite permet d’atteindre une même précision tout en réduisant drastiquement le nombre d’itérations.

Variational principles are efficient CAD tools for planar tunable MICs involving lossy gyrotropic layers

The paper presents an efficient design method for frequency-tunable planar devices using gyrotropic ferrite YIG films. The behaviour of the tunable YIG film is modelled by an equivalent lossy transmission line. Its parameters are the function of the permeability tensor components, which depend on the frequency and magnitude of the DC biasing magnetic field. We propose two analytical variational models for computing these transmission line one- or two-port parameters, depending on their coupling to the planar MIC accesses. Compared with most numerical methods, the two resulting models offer the advantage to be fully analytical and remain valid when losses of the anisotropic material are taken into account. These two models are able to predict the expected and also the unwanted effects, such as non-reciprocity and losses, with a very limited numerical complexity. The efficiency of the proposed approach is illustrated by comparing theoretical designs using these variational models with measurements carried out on the various topologies of the tunable one- and two-port planar resonators in the microstrip and slotline technology. Copyright (C) 1999 John Wiley & Sons, Ltd.