Multi-pole Debye Models Research Articles

A Method to Determine Dielectric Model Parameters for Broadband Permittivity Characterization of Thin Film Substrates

This article introduces an efficient method to determine the dielectric model parameters of a thin film substrate from microstrip line measurements and electromagnetic analysis. The proposed method avoids using optimization algorithms which normally require extensive computation time. The complex permittivity is extracted through only one full-wave simulation. The multipole Debye model was employed to fit the extracted complex permittivity. The parameters of the best-fitting model obtained through this procedure are considered as the final results, which also ensure physically consistent characteristics. Polyimide was selected to validate the methodology. The best-fitting model generated by the proposed method has shown excellent agreement to the polyimide data sheet values at 1 MHz. Moreover, simulations using the parameters of the best-fitting model exhibit good agreement with the experimental propagation constant data of microstrip lines up to 60 GHz.

Dielectric Properties of Common Building Materials for Ultrawideband Propagation Studies [Measurements Corner

Signal propagation is affected by the characteristics of the materials in the medium. Therefore, information about material properties is of paramount importance when radio propagation is investigated. In this article, the measured complex relative permittivity of 20 common materials in indoor environments (including plastics, wood and woodbased materials, glass, gypsum plaster and plasterboard, brick, and concrete) across the frequency band of 0.2-67 GHz is shown. The dielectric properties are measured by using two open-ended coaxial probes. The single-pole Cole-Cole model is employed for fitting the measured data since most of the materials follow it. Moreover, fitting parameters for the multipole Debye model, which can be used instead of the Cole-Cole [it is more appropriate for finite-distance, timedomain (FDTD) applications], are given. Thus, an easy way for obtaining the data is provided, which can be helpful when wideband propagation is considered.

Simulation of ground penetrating radar on dispersive media by a finite element time domain algorithm

This paper presents a two-dimensional finite element time domain (FETD) algorithm for simulation of ground penetrating radar (GPR) on dispersive and lossy media. The medium of linear dispersion is modeled by a multi-pole Debye model, which is incorporated into the FETD scheme through the Fourier transform. We apply the finite element Galerkin method to discretize the computation domain using triangular elements. A perfectly matched layer is extended to match the dispersive media and is used as an absorbing boundary condition to truncate the computation domain. The proposed FETD algorithm is proven to have comparable accuracy with the finite difference time domain (FDTD) method by comparing the simulated electromagnetic waves propagating in a homogeneous dispersive medium with the corresponding analytical solution. At an expense of computational costs, the FETD approach can yield more accurate results when simulating a complex geometry than the FDTD approach, which suffers from the staircase error. Moreover, we analyze the influence of material dispersion on GPR data acquired by different survey geometries. The results demonstrate that material dispersion will bring a great challenge for quantitative interpretation of GPR data. Numerical simulation of GPR data with dispersion does help in accurate interpretation of GPR data.

Closed-Form Multipole Debye Model for Time-Domain Modeling of Lossy Dielectrics

Lossy dielectrics in printed circuit boards and integrated circuit packages can be represented by using a Debye model. This allows accurate signal and power integrity analysis, which depends on the accuracy of material properties of the board or package. Such a Debye model needs multiple poles for accurate representation of the loss tangent over a broad frequency range. Electromagnetic and circuit simulations can then include the impact of frequency-dependent dielectric constant and loss. In this letter, we present an efficient and closed-form multipole Debye model, automating the modeling of lossy dielectrics for inclusion in time-domain electromagnetic or circuit simulators.

Dielectric Properties of Human Hand Tissue for Handheld Devices Testing

The operation of antennas deployed in mobile terminals is affected by the presence of human tissue in their near-field region. Therefore, testing the antenna performance, when the radiator is located in close vicinity to the user, is of paramount importance for any handset. In order to conduct such a study, knowledge about the dielectric properties of relevant human tissues is needed. In this paper, the results for in vivo measured complex relative permittivity of the dry and wet human hand palm and fingertip of thumb are presented. For the sake of having a broader set of data, the palms of 22 individuals and thumbs of 16 individuals are tested at multiple points. The measurements are conducted over the frequency band of 5-67 GHz by using an open-ended coaxial probe. The single-pole Cole-Cole model is used for fitting the measured results. Furthermore, the fitting parameters for the multi-pole Debye model are extracted by using the Cole-Cole ones. The effect of the difference in the dielectric properties between dry and wet palm on the performance of a dual-element PIFA antenna array (operating in the band of 5.8-7.7 GHz) is numerically studied. Useful finding for antenna designers is that the S-parameters and radiation efficiency of the antennas are insensitive to the change in the complex permittivity of the hand.

Hybrid sub-gridded ADE-FDTD method for modeling ground-penetrating radar on dispersive soils

Based on the sub-gridding scheme, a hybrid method with explicit finite-difference time-domain (FDTD) and implicit Crank–Nicolson (CN) FDTD is presented for ground-penetrating radar (GPR) simulations on dispersive and conductive soils in this paper. The time step of CN-FDTD can be set to a large value so that the whole region can be run with a common time step determined by the coarse grid in a stable fashion. The missing information in the sub-gridded border region is obtained with an interpolation in space. The dispersion of the soil is modeled by a multi-pole Debye model and is solved with auxiliary differential equations (ADEs) for both FDTD and CN-FDTD. Additionally, examples of the GPR scenario are calculated to verify the accuracy and efficiency of the hybrid sub-gridded ADE-FDTD method.

Frequency-Dependent Fundamental LOD-FDTD Formulation for a Multipole Debye Model

A simplified algorithm for frequency-dependent calculations of a multipole Debye model is developed on the basis of the locally 1-D finite-difference time-domain method (LOD-FDTD) with a fundamental scheme. For absorbing outgoing waves, the convolutional perfectly matched layer is incorporated into the frequency-dependent algorithm. High efficiency of the developed algorithm is demonstrated through the analysis of THz wave radiation to a healthy skin and a basal cell carcinoma. The computation time is reduced in comparison with the traditional explicit FDTD while maintaining the comparable numerical accuracy.

DEVELOPMENT OF ACCURATE MULTI-POLE DEBYE FUNCTIONS FOR ELECTROMAGNETIC TISSUE MODELLING USING A GENETIC ALGORITHM

The development of anatomically and dielectrically representative tissue models is key to the design and reflnement of electromagnetic based diagnostic and therapeutic technologies. An important component of any such model are accurate and e-cient Debye models which allow for the incorporation of the frequency dependent properties of biological tissues. The establishment of multi-pole Debye models is often a compromise between accuracy and computational cost. Furthermore, some flnite difierence time domain schemes impose constraints on the minimum Debye pole time- constant. In this study, the authors have developed an optimised genetic algorithm to establish Debye coe-cients with minimal yet su-cient Debye poles for several difierent biological tissues. These Debye coe-cients are fltted to existing Cole-Cole models and their accuracy is compared to previously fltted Debye models.

Enhancement of intra-body propagation and communication under the Brillouin precursor perspective

The emergence of the Brillouin precursor is presented as a plausible form to understand classical phenomena observed in intra-body propagation and through-tissue imaging technologies that can be associated with the features of these precursors formation, such as the non-exponentially level decay and the broadening of pulse duration. The authors describe the evolution of different pulses through skin, muscle as well as normal and malignant breast tissues by using both a time-domain and a frequency-domain analysis technique and multi-pole Debye models to characterise the dielectric properties of the considered tissues, in a frequency band designated by the Federal Communication Commission (FCC) for ultra wideband medical applications, 0.5–20 GHz. The Cole–Cole model is also tested for the same frequency range and tissues in order to determine the influence of the dielectric model. The authors tested the influence of one of the main parameters considered critical for precursor emergence: the input pulse configuration. The results reveal that the precursor is a phenomenon to take into account for application in areas where larger signal-to-noise ratios can be of interest.

A genetic algorithm for optimizing multi-pole Debye models of tissue dielectric properties

Models of tissue dielectric properties (permittivity and conductivity) enable the interactions of tissues and electromagnetic fields to be simulated, which has many useful applications in microwave imaging, radio propagation, and non-ionizing radiation dosimetry. Parametric formulae are available, based on a multi-pole model of tissue dispersions, but although they give the dielectric properties over a wide frequency range, they do not convert easily to the time domain. An alternative is the multi-pole Debye model which works well in both time and frequency domains. Genetic algorithms are an evolutionary approach to optimization, and we found that this technique was effective at finding the best values of the multi-Debye parameters. Our genetic algorithm optimized these parameters to fit to either a Cole–Cole model or to measured data, and worked well over wide or narrow frequency ranges. Over 10 Hz–10 GHz the best fits for muscle, fat or bone were each found for ten dispersions or poles in the multi-Debye model. The genetic algorithm is a fast and effective method of developing tissue models that compares favourably with alternatives such as the rational polynomial fit.

Maximum Frequency Range Limit of Multi-Pole Debye Models of Human Body Tissues

The maximum frequency range limit is investigated for the dielectric property of human body tissues to be fitted with the Debye dispersion of up to three poles. The dielectric properties of the human body tissues compiled by Gabriel in the form of the 4-pole Cole-Cole models are reformulated into the Debye models by means of a weighted least squares method (W-LSM). It has been found that three-pole Debye function can model permittivity over the broad frequency range of five orders of magnitude, e.g., from 1 MHz to 100 GHz or from 100 kHz to 10 GHz within the root mean square error of several %.

FD2TD ANALYSIS OF ELECTROMAGNETIC FIELD PROPAGATION IN MULTIPOLE DEBYE MEDIA WITH AND WITHOUT CONVOLUTION

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD2TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD2TD method. A comparative analysis of several FD2TD methods in terms of stability, dispersion, computational time and memory is carried out.

A modular implementation of dispersive materials for time-domain simulations with application to gold nanospheres at optical frequencies

The development of photonic nano-structures can strongly benefit from full-field electromagnetic (EM) simulations. To this end, geometrical flexibility and accurate material modelling are crucial requirements set on the simulation method. This paper introduces a modular implementation of dispersive materials for time-domain EM simulations with focus on the Finite-Volume Time-Domain (FVTD) method. The proposed treatment can handle electric and magnetic dispersive materials exhibiting multi-pole Debye, Lorentz and Drude models, which can be mixed and combined without restrictions. The presented technique is verified in several illustrative examples, where the backscattering from dispersive spheres is calculated. The amount of flexibility and freedom gained from the proposed implementation will be demonstrated in the challenging simulation of the plasmonic resonance behavior of two gold nanospheres coupled in close proximity, where the dispersive characteristic of gold is approximated by realistic values in the optical frequency range.