Estimation of Current Distribution on Multilayer Printed Circuit Board by Near-Field Measurement

A method of estimating the current distribution on a microstrip transmission line of a multilayer printed circuit board (PCB) by measuring the near-field distribution is proposed. The microstrip transmission line on the PCB is divided into electrically small segments. An electric field integral equation (EFIE) is established to relate the near field to the current on these segments. The current is estimated by measuring the near field, evaluating the mutual impedance between the current segments, and solving the EFIE. The measurement parameters for near-field measurement are optimized by numerical analysis. Experimental results are presented and compared with the numerical results, confirming the validity of this method.     

Transmission line model for field distribution in microstrip linefed H-slots

A method for finding the electric field distribution of microstrip line fed H-slots is described. A transverse resonance technique is first applied to find a second-order approximation of the slot propagation constant, which is then used in the transmission line model for the H-slot. The proposed model for the field distribution can be applied to the transmission line and cavity model analysis of H-slot coupled microstrip antennas     

基于Matlab微带线静电场分析

推导出二维Laplace方程的有限差分公式,用Matlab语言编写程序,实例分析并绘制了屏蔽单微带线、屏蔽耦合微带线的等位线和电场强度分布图。实例计算结果表明:Matlab在解决实际的工程和数学问题中,具有使用更为简便、语句功能更强的特点,能直观地演示屏蔽微带线的电势分布图和场强立体分布图。     

Variational Method for the Analysis of Microstrip-Like Transmission Lines

A theoretical method is presented by which microstrip-like transmission lines can be analyzed. These transmission lines are characterized by conducting strips, large ground planes, multi-dielectric-layer insulation, and planar geometry. The method is essentially based on a variational calculation of the line capacitance in the Fourier-transformed domain and on the charge density distribution as a trial function. A shielded double-layer microstrip line is analyzed by this method. Derived formulas for this structure are also applicable to simpler structures: a double-layer microstrip line, a shielded microstrip line, and a microstrip line. The calculated values of the line capacitance and the guide wavelength are compared with the measured values where possible. Oxide-layer effects on a silicon microstrip line and shielding effects on a sapphire microstrip line are also discussed based on this theory. The limitations and possible applications of this method are described.     

Dynamic analysis of a microstrip line over a perforated groundplane

A full wave analysis is presented to compute the characteristic impedance and propagation constant of a microstrip line over a perforated ground plane. The perforations in the ground plane are modeled by equivalent magnetic currents. The method of moments is applied to solve the coupled integral equations for the unknown electric current on the microstrip line and the unknown magnetic currents in the apertures. The fields are formulated using the space domain Sommerfeld type Green's functions. The matrix pencil technique is used to obtain the amplitude and the propagation constant of the fundamental modes for both current and the voltage on the microstrip line. Typical numerical results are given     

A full-wave model for EMI prediction in planar microstrip circuitsexcited in the near-field of a short electric dipole

A full-wave model to evaluate the interference induced in planar microstrip lines of arbitrary shape exposed to the near-field of an elementary electric dipole is presented. The analysis of the line response, consisting in the evaluation of the surface current excited along the microstrip line, is based on the electric dyadic Green's function method. The surface current induced on the metal strip which, for the sake of generality, is considered as embedded in the dielectric substrate, is obtained solving by means of the spectral-domain approach (SDA) the electric integral equation, which enforces the boundary condition of zero tangential electric field on the surface of the strip. The induced current is computed for different line geometries and loads, and for various positions (inside or outside the dielectric substrate) and orientations of the dipolar source. Indications towards reducing the level of the signal induced on the loads of the line are inferred     

The Effect of Neighboring Conductors on the Currents and Fields in Plane Parallel Transmission Lines

In this paper the current distribution is calculated for a microstrip line in the presence of a neighboring strip. The electric field is calculated and the characteristic impedance of the slotted microstrip line is determined. A graph of characteristic impedance is given for odd and even excitations. The calculations are carried out by setting up a singular integral equation which is solved using a finite integral transform. This method has the advantage that the calculations can be generalized in a straightforward manner for the multislotted line.     

Closed-form expressions for the current distributions on openmicrostrip lines

The authors systematically clarify the characteristics of current distributions for various cases of substrate relative permittivity, shape ratio, and normalized frequency. These characteristics are clarified, and closed-form expressions are proposed. An open microstrip line with isotropic dielectric substrate is numerically analyzed by the spectral-domain method to clarify current distributions on a strip conductor. The current distributions obtained are illustrated in figures for typical cases. A full view of current distributions on a strip conductor in any microstrip line is provided by showing those close-form expressions. These expressions for the current distribution have been compared with the theoretical results, and good agreement has been obtained     

Finite element analysis of MMIC structures and electronic packagesusing absorbing boundary conditions

In this paper, a three-dimensional finite element method (FEM) is employed in conjunction with first and second-order absorbing boundary conditions (ABC's) to analyze waveguide discontinuities and to derive their scattering parameters. While the application of FEM for the analysis of MMIC structures is not new, to the best of the knowledge of the authors the technique for mesh truncation for microstrip lines using the first and higher-order ABC's, described in this paper, has not been reported elsewhere. The scattering parameters of a microstrip discontinuity are computed in two steps. As a first step, the field distribution of the fundamental mode in a uniform microstrip is obtained by exciting the uniform line with the quasi-static transverse electric field, letting it propagate, and then extracting the dominant mode pattern after the higher order modes have decayed. In step two, the discontinuity problem is solved by exciting the structure by using the fundamental mode obtained in step one. The scattering parameters based on the voltage definition are calculated by using the line integral of electric fields underneath the strip. Numerical solutions for several waveguide discontinuities and electronic packages are obtained and compared with the published data     

Theoretical and measured electric field distributions within anannular phased array: Consideration of source antennas

A detailed calculation of sources and electric fields associated with a prototype annular phased array for clinical hyperthermia is presented. Two antenna current distributions are used as field sources. One is based on a linear dipole model. The second models the thin strip antenna elements in detail, and the current is derived using the theory of a microstrip transmission line. These currents are then used to calculate the magnetic vector potential and the electric field. To verify the theoretical simulations, the magnitude of the electric field is measured under the same conditions as those used in the theoretical simulations. The comparison between measured and calculated fields demonstrates better convergence of theory and experiment when the antenna sources are modeled in detail. Thus, the use of these results for an improved incident-scatter model that will allow more general calculations of E fields in inhomogeneous media with irregular geometries is anticipated     

Etude statique de structures planaires complexes: application à la modélisation de l’excitation de lignes analysées par l’algorithme des différences finies transitoires

In this paper, a static electromagnetic study of planar structures is effected. The determination of electric and magnetic field distribution in a line cross-section is discussed. This electric and magnetic field distribution is used to deduce the characteristic impedance of this line. The second application concerns the simulation of the line feed when a transient analysis using the finite difference time domain method is used to analyse the line behaviour. In the case of a microstrip line, this new excitation method is compared to two excitations which are generally used.     

Analysis of a thin slot discontinuity in the reference plane of amicrostrip structure

This paper presents a perturbational approach based upon the spectral domain technique for the analysis of the discontinuity effects introduced by a thin slot in the ground plane of a microstrip line. The discontinuity problem is formulated in terms of the unknown slot field by using the notion of equivalent half-space problems, using a new rigorous procedure for deriving the TE-TM decomposition of the fields and equivalent transmission line models. The perturbation current on the infinite microstrip is computed once the electric field in the slot has been derived, and an equivalent circuit for the discontinuity is obtained from this perturbation current for the low-frequency regime. Computed results are presented and compared to the measured data     

Analysis of a slot microstrip antenna

The slot microstrip antenna is used as a folded slot dipole symmetrically fed across a gap by means of a strip line. A theoretical model equivalent to several lossy transmission lines had been described previously to explain the bandwidth and the radiation admittance. The theory is improved when coupling between the two equivalent radiating lines of every slot is taken into account, and explains a fourth resonance near the third one, which had been measured on several models. Theoretical results and experiments are in good agreement. They are radiation admittance in a wide frequency band, current distribution along each slot and radiation patterns.     

Corner Function Analysis of Microstrip Transmission Lines

A new method of analysis of microstrip transmission lines using corner functions (eigenfunctions) is presented. Assuming the TEM mode propagation for the shielded microstrip line structure, solutions are set up in a series of corner functions, which isolates the singularity at the edge of the strip. The boundary conditions are satisfied by using a method of successive integration of boundary errors. Numerical results are obtained for the charge distribution from which the microstrip line characteristic impedance is determined. Excellent agreement with published theoretical results and experimental data is obtained. The numerical results clearly bring out the power of the method.     

Analysis of a microstrip line terminated with a shorting pin

A full-wave moment method solution to the problem of a semi-infinite microstrip line terminated with a shorting pin is presented. The electric current on the line is expanded in terms of longitudinal piecewise sinusoidal modes near the open end, with entire domain traveling-wave modes to represent incident and reflected waves away from the open end. Also, the electric current near the shorting pin is simulated by an attachment mode which insures continuity of the current between the pin and the line and models the rapidly varying current on the line near the feed connection point. Results are given for the magnitude of the reflection coefficient and are compared with experimental data     

INPUT IMPEDANCE OF MICROSTRIP ANTENNA WITH THICK MULTILAYER SUBSTRATE

A method has been devised to analyze multilayer electrically thick circular mi-crostrip antenna excited by a probe.The current on the probe is taken to be uniform.Thismethod was verified by analysis and experiment of an electrically thick circular microstrip an-tenna with an air gap.Based on the free space electric dyadic Green's function,the field expressionof an horizontal electric dipole(HED),which is located at any point of the multilayer media andpoints in any direction,has been derived.By using this field expression and the Richmond re-action equation,an integral equation in terms of electric current on the patch is formulated.Byproperly choosing current expansion modes,this method can be used for an electrically thick mi-crostrip antenna.The theoretical results agree very well with experimental data for an electricallythick circular microstrip antenna with an air gap.     

Generalized Partial-Element Equivalent-Circuit Analysis for Planar Circuits With Slotted Ground

A generalized partial-element equivalent-circuit (PEEC) method is proposed for modeling a planar circuit with a thin narrow slot on the ground. The approach is based on the coupled mixed potential integral equations for a problem with mixed electric and magnetic currents. The coupled integral equations are converted into a lumped-element circuit network using Kirchhoff's voltage law and Kirchhoff's current law of the circuit theory. The full-wave Green's functions for a grounded dielectric substrate problem are used. The interactions between electric current on a microstrip line and magnetic current on a slot are taken into account by introducing two kinds of controlled sources. This generalized PEEC model will be very useful in signal-integrity analysis for multilayered circuits. To validate the generalized model, three numerical examples consisting of microstrip lines and slots on the ground are presented. The results obtained by the proposed generalized PEEC model are compared with those obtained by commercial electromagnetic simulation software and published experimental results. Good agreement is obtained.      

多层电厚微带天线的阻抗特性

本文提出了一种多层介质电厚微带天线的一种分析方法。从无界空间中的电并矢格林函数出发,导出了分层介质中任意一点具有任意取向的水平电偶极子场的表达式。以此为基础,利用Richmond反作用积分方程,建立了关于贴片上电流分布的积分方程。通过适当选取电流基函数,使本方法适用于电厚介质微带天线。应用Galerkin方法建立矩阵方程。借助于计算机求解该矩阵方程,可得到天线的各项特性。文中用实例进行了验证。     

Analysis and design of a leaky-wave EMC dipole array

An analysis of an electromagnetically coupled (EMC) dipole array is presented, in which a microstrip line is coupled to an infinite periodic linear array of microstrip dipoles, arranged perpendicular to the line. The spectral-domain immittance method is used to obtain the periodic Green's function for the two-layered structure, and the method of moments with a Galerkin testing procedure is then used to enforce the electric field integral equation (EFIE) on the line and the dipole within a unit cell of the structure to obtain the determinantal equation for the unknown leaky-wave propagation constant. One of the interesting features of this analysis is the path of integration in the complex plane used to compute the moment method reactions, which must be partly on the improper sheet for the m=-1 space harmonic when it radiates in the forward direction. Measured radiation patterns for a 10-element EMC dipole array are presented and compared with the corresponding theoretical ones     

Estimation of spurious radiation from microstrip etches usingclosed-form Green's functions

The problem of spurious radiation from electronic packages is considered by investigating the power radiated from microstrip etches that are excited by arbitrarily located current sources and terminated by complex loads at both ends. The first step in the procedure is to compute the current distribution on the microstrip line by using the method of moments (MoM). Two contributions of this paper are: (i) employing the recently derived closed-form Green's functions in the spatial domain, which permits an efficient computation of the elements of the MoM matrix; and (ii) incorporating complex load terminations in a convenient manner with virtually no increase in the computation time. The computed current distribution is used to calculate the spurious radiated power, and the result is compared with that derived by using an approximate, transmission line analysis