Equivalent Electric Surface Research Articles

Two‐dimensional transverse magnetic scattering using an exact surface admittance operator

This paper presents a new approach to solve two‐dimensional transverse magnetic (TM) scattering problems involving homogeneous penetrable scatterers. The scatterers can be replaced by equivalent electric surface currents provided a proper surface admittance operator is introduced relating those currents to the electric fields on the scatterer's surface. The surface operator for a scatterer with rectangular cross section can be determined analytically. The paper emphasizes that the proposed technique remains valid in a complex scattering environment and in the presence of both conducting and nonconducting scatterers. The new method allows for a considerable gain in CPU time and memory requirements and remains very accurate even in the presence of very good conductors and this from the DC regime to the high‐frequency skin effect regime. Scattering of a plane wave by a periodic arrangement of rectangles or crosses embedded in a dielectric slab is used to illustrate the use of the surface admittance operator in conjunction with an integral equation method.

On the Validity of Physical Optics for Narrow-band Beam Scattering and Diffraction from the Open Cylindrical Surface

The exact formulas for the induced electric surface current (in the scattering phenomenon) and the equivalent electric surface current (in the diffraction phenomenon) on the open cylindrical surface due to an arbitrary narrow-band beam have been shown in their closed-form expressions within the context of the cylindrical harmonics, which gives information about the validity of the Physical Optics (PO) approximation. Both the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE) are used to find the induced (equivalent) electric surface currents in the context of the cylindrical harmonics. The numerical example of the scattering and diffraction of the Hermite Gaussian beam from the open cylindrical surface is shown. The result is useful for the evaluation of the validity of the PO approximation in the cylinder-like surface.

Skin effect modeling based on a differential surface admittance operator

An important issue in high-frequency signal integrity prediction is the modeling of the skin effect of thick conductors. A new differential surface admittance concept is put forward allowing to replace the conductor by equivalent electric surface currents and to replace the material of the conductor by the material of the background medium the conductor is embedded in. This new concept is studied in detail for the two-dimensional TM case starting from the Dirichlet eigenfunctions of the cross section. Detailed expressions are derived for the important practical case of a rectangular cross section. Next, the differential surface admittance operator is exploited to determine the resistance and inductance matrices of a set of multiconductor lines. A first set of numerical results provides the reader with some insight into the behavior of the surface admittance matrix. A second set of results demonstrates the correctness and versatility of the new approach to determine inductance and resistance matrices.

Application of modal expansion and method of moments to study electromagnetic scattering from a rectangular cavity recessed in a three‐dimensional conducting surface

The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three‐dimensional (3‐D) conducting body is analyzed using the modal expansion inside and the integral equation method outside the cavity. Assuming (1) an equivalent electric surface current density flowing on the 3‐D conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture, only the scattered fields outside the cavity are determined . The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting 3‐D surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the method of moments (MoM). The numerical results on scattering from rectangular cavities embedded in various 3‐D objects are compared with the results obtained by other numerical techniques.

Surface integral formulation for calculating conductor and dielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents. >

On the surface impedance used to model the conductor losses of microstrip structures

In the numerical analysis of microstrip structures their finite conductivity is often modelled by using an equivalent surface impedance to relate the nonzero tangential electric field on the conductor surface to an equivalent electric surface current. The fields on top and below the patch are not necessarily the same and to account for this discontinuous tangential electric field a strict equivalence formulation should include magnetic surface currents. However, it is common practice to neglect them, presumably because they considerably complicate the surface integral equation and its numerical solution. Here it is shown that this practice leads to the use of an incorrect, although conservative, surface impedance. A basic assumption is that δ≪Δ≪λ, with δ the skin depth, Δ the conductor thickness, and λ the free space wavelength.