Finite-Difference Analysis of Dispersive Transmission Lines Within a Circuit Simulator

Discusses a computational procedure, based on the finite difference time domain (FDTD) algorithm, for extremely low-frequency (1 Hz) modeling of electromagnetic scattering by buried objects in lossy sedimentary layers under sea water. The FDTD algorithm is found to be accurate for modeling such objects tens of meters away from a constant current dipole source of 1 A in sea water. For validation of the extremely low-frequency and lossy FDTD modeling, the computed FDTD results are compared with those calculated by using integral equation techniques.

In this paper we discuss a low-frequency computational procedure based on the Finite Difference Time Domain (FDTD) algorithm, for numerical modeling of electromagnetic scattering by buried objects in sediment layers under sea water. The FDTD algorithm is found to be accurate for modeling buried objects in sediment layers tens of meters away from a constant current dipole source of 1A in sea water. For validation of the low-frequency FDTD modeling, the computed FDTD results are compared with those calculated by using analytic expressions and integral,equation techniques. In this paper we also present a technique for detecting conductivity anomalies in sediments, e.g., a buried object in sedimentary layers under sea water, by using the neural network approach. The electric field values are used as the inputs to the neural network and the associated conductivities are used as the targets. The neural network is then trained to associate these conductivities and field values. It is shown in this paper...

In order to study the parameters of cable coupling characteristics, we calculated the voltage and current distribution at each point of the transmission line numerically. An iterative solution method based on Theory of Multiconductor Transmission Line (MTL) and finite difference time domain (FDTD) is used. Firstly, the appropriate FDTD parameters are selected, and in each iteration step, the voltage and current along the line are calculated using the Finite Difference Time Domain (FDTD) algorithm, and the voltage and current distribution is updated accordingly. When the convergence condition is satisfied, the solution of the transmission line equation is obtained. The main advantage of this method is that the inherent parallel algorithm can reduce the computation time and obtain more detailed numerical values within the line.

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.

Ground penetrating radar (GPR) forward is one of the geophysical research directions.Through the forward of geological model,the database of radar model can be enriched and the characteristics of typical geological radar echo images can be understood,which in turn can guide the data interpretation of GPR measured profile,thereby improving the GPR data interpretation level.In this article,the interpolating wavelet scale function by using iterative interpolation method is presented,and the derivative of scale function is used in spatial differentiation of discrete Maxwell equations. The forward modeling formula of GPR based on the interpolation wavelet scale method is derived by using fourth-order Runge-Kutta method (RK4) for calculating the higher time derivative.Compared with the conventional finite difference time domain (FDTD) algorithm based on the central difference method,the interpolation wavelet scale algorithm improves the accuracy of GPR wave equation in both space and time discretization.Firstly,the FDTD algorithm and the interpolation wavelet scale method are applied to the forward modeling of a layered model with analytic solution. Single channel radar data and analytical solution fitting indicate that the interpolation wavelet scale method has higher accuracy than FDTD,with the same mesh generation used.Therefore,auxiliary differential equation perfectly matching layer (ADE-PML) boundary condition is used on an interpolation wavelet scale,and the comparisons between reflection errors obtained using CPML (FDTD),RK4ADE-PML (FDTD),and RK4ADE-PML (interpolating wavelet scales) in a homogeneous medium model show that the absorption effect of RK4ADE-PML (interpolating wavelet scales) is better than the other two absorbing boundaries.Finally,interpolation wavelet scale method,with both UPML,FDTD and RK4ADE-PML loaded,is used for two-dimensional GPR forward modeling,showing good absorption effect for evanescent wave.From all the experimental results,the following conclusions are obtained.1) Using the derivative of the interpolating wavelet scale function instead of central difference schemes for the spatial derivative discretization of Maxwell equations and time derivative calculated using the fourth-order Runge Kutta algorithm,the interpolating wavelet scale algorithm has higher accuracy than regular FDTD algorithm due to the improvement in the spatial and time accuracy of GPR wave equation.2) The best absorption layer parameters of interpolating wavelet scale RK4ADE-PML are selected, when the maximum value of the reflection error is the minimum.The maximum reflection error can reach-93 dB,which increases 20 dB compared with that of UMPL boundary in FDTD algorithm.And the higher simulation accuracy of interpolating wavelet scale algorithm than FDTD algorithm is confirmed after calculating single channel radar data.3) Comparing wave field snapshots of GPR forward modeling,radar pictures from wide-angle method and section method indicates that interpolating wavelet scale RK4ADE-PML reduces reflection error of absorption boundary,improves both spatial and time accuracy,is more effective than UPML boundary in eliminating false reflection of large angle incidence, and has better absorption effect for evanescent wave and low-frequency wave.

The nonuniform transmission line is traditionally modeled and analyzed in the frequency domain. However, it is difficult to characterize and simulate nonuniform lossy transmission lines accurately in the time domain. A highly accurate and general approach for time domain analysis of lossy inhomogeneous transmission lines is described. The propagator method presented is an exact solution to the lossy telegrapher's equations based on the modal matrix technique. Simpson's rule is applied to produce a remarkably accurate numerically compatible result. An exponentially tapered transmission line example shows that this method is not only simple and efficient, but also an accurate technique for analyzing lossy nonuniform transmission lines with minimal numerical dispersion. Multiple sectioned transmission lines can be handled by a straightforward application of the presented equations.

Recently, there has been a growing interest in the use of cylindrical transmission lines in a variety of applications. In this paper, the finite difference time domain (FDTD) method is used to calculate the propagation characteristics of cylindrical transmission lines. An efficient two-dimensional (2D) FDTD algorithm is developed by projecting the three-dimensional FDTD cell in the cylindrical coordinates on to the r−φ plane. An effective absorbing boundary condition is employed to truncate the mesh at its outer radial boundary. In addition to a detailed description of the developed 2D-FDTD algorithm, extensive numerical results are derived for different cylindrical transmission lines and compared with data available in the literature. Specifically, the newly proposed cylindrical coplanar waveguide is studied both theoretically and experimentally.

A proper dielectric coating can reduce the electromagnetic scattering of the conducting object significantly so that it cannot be detected by the radar. However, when the object contains a thin coating, fine grid size is needed to discretize the thin coating in the conventional finite-difference time-domain (FDTD) algorithm, which increases the amount of memory and computational time significantly. To overcome this dilemma, we present a transformation optics-based FDTD (TO-FDTD) algorithm to accelerate the solution of electromagnetic scattering from objects with thin dielectric coatings. Two kinds of novel TO-FDTD models are proposed in this paper for a coated cylinder and a coated arbitrary polygonal cylinder, respectively. Through coordinate transformation, the size of the object remains unchanged while its thin coating is enlarged to a thicker one, meaning that it can be simulated by the FDTD algorithm with uniform coarse grids instead of fine grids. The transformed material parameters become inhomogeneous and anisotropic in the transformed region, which can be obtained by solving a Jacobian transformation matrix. We then develop a stable FDTD algorithm for solving anisotropic Maxwell’s equations. Bistatic scatterings of coated cylinders and a coated polygonal cylinder are solved by the TO-FDTD algorithm proposed in this paper, respectively. The result of the TO-FDTD algorithm matches well with the exact value and the result of the commercial software Comsol. The computational efficiency and accuracy of the proposed TO-FDTD algorithm are validated by numerical experiments. Numerical results show that the TO-FDTD algorithm has higher computational accuracy than the conventional FDTD algorithm that fails to simulate the absorbing property of the coating, when the same coarse grid size is used in the simulation. Under the same level of accuracy, the proposed TO-FDTD method can improve the computational efficiency by 62-63 times than the conventional FDTD method with fine grids in the simulations in the paper.

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

As with the number of cancer increases year by year, so it is important to be found and treated earlier. With biological cells and tissues are sensitive to infrared and visible light, cell morphology and physical structure of the optical properties can easily obtain, we can provide theoretical basis for the early diagnosis of cancer by observing the difference of optical properties between normal and cancerous cells. Compared with Mie scattering theory, finite difference time domain (FDTD) algorithm can analyze any complex structure model. In this paper we use mathematical modeling method to establish the single cell mathematical model and with finite difference time domain algorithm to simulate the propagation and scattering of light in the biological cells, you can calculate the scattering of electromagnetic field distribution at anytime and anywhere. With radar cross section (RCS) to measure the results of the scattering characteristics. Due to the difference between normal cells and cancerous cells are embodied in cell shape, size and the refractive index, through the simulation we can get different cell parameters of light scattering information, Find out the cell parameters change the changing rule of the influence on the scattering characteristics and find out change regularity of scattering characteristics. These data can judge very accurate of the cells is normal or cancerous cells.

Based on the reciprocity theorem, a simple method for the analysis of the radiated electromagnetic fields from a arbitrary nonuniform lossless transmission line with a linear termination is presented. The radiation problem is solved using the known solution of the coupling problem. The method of the solution for the coupling problem in nonuniform transmission lines is based on the steplines approximation of the nonuniform transmission line and quasi-TEM assumptions. An example of nonuniform transmission line is then solved to show the capabilities of the present method.

In this paper a new compact type of nanosecond high voltage pulse generator, developed for innovative medical treatments, which combines microstrip line technology and microchip laser triggered photoconductive semiconductor switches (PCSS), has been numerically characterized. Two different modeling methodologies have been considered. The first is based on a full wave finite difference time domain (FDTD) analysis. The second approach proposes a circuit model of the generator solved through SPICE simulations. Further, considering the FDTD analysis an appropriate model for the PCSS has been developed. The presented results show a good agreement between the two modeling methodologies and first experimental measurements performed on a generator prototype. Therefore, these outcomes suggest the presented approaches as suitable modeling tools for the development of such kind of innovative devices.

In order to reduce computer memory and computational time required by three dimensional Finite-Difference Time-Domain (FDTD) microwave passive component analysis, two strategies are developed in this paper. First, the recently reported dispersive boundary condition (DEC) is modified thereby enabling the absorbing boundary to be located near to the main field area; second, an exact source plane field distribution itself produced by the FDTD algorithm is adopted to improve numerical accuracy. This leads to a reduction in computer memory requirements. As an example, a full-wave 3D FDTD analysis of a slotline is performed on a 33 MHz PC486. The dispersion characteristic of the slotline is presented up to 1000 GHz this agrees well with that of closed form formula. When compared with previous slotline solutions, frequency range results are extended by an octave and less than 9 percent of the computer memory previously required is demanded. The unique and highly efficient combination of the two strategies presented here could be applied to other microwave waveguide component analyses.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents a rigorous analysis of the numerical error of the reflection coefficient of the finite-difference time-domain (FDTD) algorithm at planar material boundaries. The derived expressions show that the numerical reflection depends on a large number of parameters, such as the grid resolution and the time step, the frequency, the angle, and the polarization of the incident wave. In conclusion, the FDTD algorithm does not accurately fulfil the boundary conditions for the continuity of the fields. The theoretical findings enable the detailed characterization of the field behavior in the grid at material interfaces. The numerical total reflection and the Brewster angle are studied as well as the discretization influences on the specific absorption rate (SAR).

In this study, two finite-difference time-domain algorithms are proposed for time domain analysis of the lossy non-uniform composite right/left-handed transmission line (CRLH TL). The results of the proposed algorithm are confirmed with those of the ADS commercial software. The numerical stability of the proposed algorithms is studied and a closed form formula for maximum temporal step size that guarantees algorithm stability is extracted. Finally, a new algorithm for time-domain analysis of the non-linear CRLH TLs using finite-difference time-domain is proposed. This algorithm does not impose any limitation on type of non-linearity. The results of the proposed algorithm have a good agreement with the results of the ADS commercial software.