非均匀传输线特性重构中的噪声影响分析

利用时域反射技术(Time Domain Reflectometry,TDR),由测量得到的时域反射信号,可以重构出非均匀传输线的一些特征参数。当反射信号中混有噪声时,对非均匀传输线特性参数的重构会产生影响。采用Zakharov-Shabat类型逆散射问题的数值反演算法,以指数型非均匀传输线为例,对时域反射信号中混有高斯白噪声情况下的非均匀传输线特性参数重构问题进行了数值实验。数值计算结果表明,在噪声干扰下,算法本身是稳定的,在较宽的信噪比范围内,能有效地重构出非均匀传输线的特征参数。     

Application of the multilevel single-linkage method toone-dimensional electromagnetic inverse scattering problem

An inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed. The inversion is based on the global minimization of an objective function by the multilevel single-linkage method. The objective function is defined as the mean-square error between the measured data and the data obtained from the solution of the forward problem. An exact formulation for the gradient of the objective function in closed form is derived. The necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed. Reconstruction examples using both experimental and noisy synthetic data are presented     

An efficient algorithm for solving Zakharov-Shabat inversescattering problem

An efficient numerical method for solving Zakharov-Shabat (ZS) inverse scattering problem is presented. In this method, instead of equivalent second-order differential equations to the Gel'fand-Levitan-Marchenko (GLM)-type integral equations, equivalent first-order differential equations are adopted and sufficiently accurate solutions to Zakharov-Shabat inverse problem can be achieved without iterations. Examples for applying it to design nonuniform transmission line (NTL) filters are also provided     

A new numerical method for synthesis of arbitrarily terminatedlossless nonuniform transmission lines

In this paper, the synthesis of a nonuniform transmission line is treated by solving an inverse classical Sturm-Liouville problem, in which the boundary conditions are described by S-parameters. The related inverse problem is readily solvable if the terminated impedances and S-parameters satisfy some required conditions. This method can be used to design transmission-line filters and impedance transducers for almost arbitrarily provided source and load impedances     

Nonuniformly coupled microstrip transversal filters for analog signal processing

The Fourier transform relationship between frequency response and impedance profile for single nonuniform transmission lines is used to derive the time-domain step response of single and coupled nonuniform lines. The expression for the step response of a characteristically terminated nonuniformly coupled transmission line structure is shown to correspond to the characteristic impedance profile. By using this relationship, any arbitrary step response can be realizing by utilizing nonuniformly coupled strip or microstrip lines for possible applications as waveform-shaping networks and chirp filters. A numerical procedure to compute the step response of the nonuniform coupled line four-port is also formulated in terms of frequency-domain parameters of an equivalent cascaded uniform coupled line model with a large number of sections. Sinusoidal and chirp responses are presented as examples that are readily implemented using coupling microstrip structures. The step response of an experimental nonuniformly coupled microstrip structure is presented to validate the theoretical results.<>     

Impedance matching for complex loads through nonuniformtransmission lines

A numerical method for designing nonuniform transmission lines (NTLs) to match complex loads is presented. This method is based on solving an inverse problem derived from the telegrapher's equation. The matched NTLs are expected to have bandpass characteristics covering the sampling frequency points. A numerical algorithm is provided and verified by examples     

Analytical and numerical solution to the two-potentialZakharov-Shabat inverse scattering problem

An analytical and a numerical method are presented in order to solve the inverse scattering problem associated with the two-potential Zakharov-Shabat coupled mode equations. The numerical solution, which uses leapfrogging in space and time, represents a direct numerical solution to the coupled Gel'fand-Levitan-Marchenko (GLM) integral equations as an extension of the authors' previous work on GLM equations of simpler form. The analytical method, which is applied for one-pole reflection coefficients, consists in constructing appropriate differential operators which transform the coupled GLM equations to ordinary linear differential equations. An application of these methods for nonuniform transmission line synthesis is presented     

An efficient method for analysis of arbitrary nonuniformtransmission lines

The analytical solution of an ideal linear varied nonuniform transmission line (LNTL) has been obtained and the exact linear two-port ABCD matrix of LNTL has been given correctly for the first time. By using cascaded LNTL sections to approximate an arbitrary characteristic impedance profile, a new technique has been presented in this paper for analyzing an arbitrary nonuniform transmission line (NTL). The technique is far better than the conventional technique in terms of the computational accuracy and intensity since it uses a piecewise-linear characteristic impedance profile in place of the stepped profile used by the conventional technique. Several numerical examples have been given to demonstrate the method     

Impedance Transformation Equations for Exponential, Cosine-Sqaared, and Parabolic Tapered Transmission Lines

Closed-form equations that give the value of an arbitrary complex impedance transformed through a length of dissipationless, nonuniform transmission line with exponential cosine-squared, and parabolic taper are presented. These equations are obtained by a second order nonlinear differential (Riccati) equation relating impedance, the nonuniform line impedance and the line length. The results presented should be useful in solving impedance matching problems.     

Scattering by a small cavity-backed hole

For plane-wave incidence, an integral equation is obtained for the magnetic current induced on a circular impedance insert in a perfectly conducting plane under the assumption that the radius is electrically small. This integral equation is solved numerically, and an analytical expression for the scattered field is determined. The complementary expression for a small disk is compared with a standard numerical code and conditions for the use of this expression are established. For a cavity-backed hole, the impedance of the insert is identified with the impedance looking into the hole as determined by a simple transmission line model, and results are presented for a few cavity geometries     

Numerical aspects of a dissipative inverse problem

Two numerical aspects of the solution of a one-dimensional electromagnetic inverse problem are considered: the numerical solution of delay integral equations and the sensitivity of the solution of the inverse problem to small changes in the data. In addition a numerical technique is developed for the solution of the direct problem in the time domain. The problem considered is one in which the conductivity and permittivity of the scatterer are continuous functions of depth. The incident field is a transverse electric (TE) plane wave of arbitrary shape, and the inverse problem uses the resulting reflected and transmitted transients to reconstruct the scatterer. For the sake of simplicity, a known scatterer is used to numerically generate the data required for the inverse problem. This is done by using the scattering operators for the problem. The scattering data thus obtained is used to formulate a generalized Gelfand-Levitan integral equation whose solution yields the conductivity and permittivity profiles of the scatterer. The sensitivity of this inversion process is investigated by altering the scattering data.     

Electromagnetic scattering from composite objects using a mixtureof exact and impedance-boundary conditions

Different surface integral equations for characterizing the electromagnetic scattering from a surface impedance object partially coated with dielectric materials are presented. The impedance boundary condition (IBC) is applied on the impedance surface and the exact boundary condition is applied on the dielectric surface. The resulting integral equations are solved for bodies of revolution using the method of moments. The numerical results are compared with the exact solution for a sphere. Other geometries are considered, and their results are verified by comparing results of the numerical solutions which were obtained using different formulations. The internal resonance problem is examined. It is found that the combined field integral equation (CFIE) can be used at any frequency and with any surface impedance     

Electromagnetic analysis of an antenna embedded in a compositeenvironment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern     

Inverse scattering technique applied to remote sensing of layered media

An inverse scattering technique applied to a remote estimation of the dielectric and conductivity profile of an inaccessible layered medium is presented. The inaccessible region is illuminated by plane waves at normal incident, and the data are taken as the reflected power at a fixed remote location for a set of discrete frequencies. The problem of estimating the dielectric and conductivity profile from this set of data is posed as a nonlinear integral equation. This formulation based on reflected power is appealing for practical purpose, in that the phase information of the reflected field is not required. The equation is solved by developing a quasi-Newton iterative scheme in functional space which produces a dielectric and conductivity profile that fits the data. The Backus and Gilbert resolving-power theory is used to assess the reliability of the estimates and the resolving length of the data. Results are given for the numerical reconstruction of various dielectric and conductivity profiles from an artificial data set, together with local averages estimates and resolving kernels.     

Equivalent surface impedance of an infinite periodic array of slot impedance loads based on a semicylinder cavity

A problem of finding the equivalent surface impedance of an infinite periodic array of slot impedance loads based on a semicylinder cavity. The problem is solved by the integral-equation method. As the numerical method for solving the integral equation, the Krylov-Bogoliubov method is used. The results of the numerical experiment are presented in the form of dependences of the impedance on the cavity radius, slot width, conductor width, and angle of electromagnetic-wave incidence. The angular dependences of the impedance are compared to the earlier results obtained for an array of rectangular grooves and a single impedance load based on a semicylinder cavity.     

Arbitrary pulse shape synthesis via nonuniform transmission lines

A discrete inverse scattering technique is used to define the impedance profile for a nonuniform transmission line which reflects an arbitrary waveform. Initially charged nonuniform lines, switched out into a general load, can also be synthesized by this method, and are discussed. The direct or layer peeling algorithm is applied to generate profiles which are subsequently analyzed using the one-dimensional finite difference method and fabricated in stripline. Excitation for the nonuniform line is done by using a charged line connected to a photoconductive Si switch triggered by a mode-locked YLF laser. Several lines were fabricated relevant to amplitude modulation of the master oscillator laser pulse for fusion experiments. Using the layer peeling method, a complex high-voltage pulse shape for use in laser fusion experiments is synthesized to an extraordinary degree of precision. It is possible to generate any arbitrary pulse shape by reflecting a step pulse off a synthesized nonuniform transmission line provided the power spectrum of the reflected pulse does not exceed that of the input pulse at any frequency     

A coaxial probe for the control of parameters of a multilayer dielectric: Direct and inverse problems

Diffraction of an electromagnetic wave by an open end of a coaxial line with an infinite flange adjoining a piecewise-uniform plane-layered lossy medium is considered. The direct problem is solved on the basis of admittance and impedance algorithms taking into account losses in the flange and the medium. For an infinite conductivity of the flange, a stationary functional for the input admittance is used to find an explicit solution in the form of an integral; numerical results are obtained. The inverse problem consisting in determination of the layer parameters (thickness, permittivity, and permeability) from known (experimental) values of the magnitude of the reflection coefficient at specified frequencies via minimization of the corresponding residual of the least-squares method is considered. It is proposed to increase the amount of experimental data through performance of measurements for several positions of the sample relative to the flange and for different impedance conditions behind the sample. In order to solve the inverse problem, a perceptron neural network is constructed. This approach reduces the solution time by several orders of magnitude.     

TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

Time domain direct and inverse problems for a nonuniform LCRG linewith internal sources

In this paper, direct and inverse problems for a nonuniform LCRG line with internal transient voltage and current sources are considered. In the inverse source problem, the compact Green functions approach based on wave splitting is used to reconstruct the transient voltage and current sources from the transient signals that are received at the two endpoints of the nonuniform line. The location of the sources is assumed to be known or possible to estimate from the arrival times of the signals. The compact Green functions are convolution kernels in the map from the received signals (at the two endpoints) to the internal split voltages. The partial differential equations for the compact Green functions are given together with the initial and boundary conditions. The present approach to the inverse source problem is exact and noniterative. To obtain independent synthetic input data for the inverse problem, the direct problem is solved by a finite difference scheme. Numerical results for reconstructions using both clean and noisy data are presented     

A survey of the near-field far-field inverse scattering inverse source integral equation

The Kirchhoff direct integration of the scalar wave equation is reviewed, and some properties of the Kirchhoff surface integral are discussed, from the perspective of the inverse scattering inverse source problem. A modified Kirchhoff surface integral is introduced, leading to a Fredholm integral equation of the first kind for the unknown sources (induced by the incident field) inside a volume in terms of the (scattered) fields on the surface enclosing this volume. The properties and physical meaning of this integral equation are discussed. A generalization of this integral equation for the vector electromagnetic wave equations is presented.