William A. Johnson

Electrophysics of micromechanical comb actuators

A simple approximate theory is developed for the electrostatic forces operating in a micromechanical comb actuator. The comb drive is considered both without (for simplicity) and with an underlying ground plane. The forces are partitioned into local forces (electric fields confined to the cross-sections of the individual comb fingers) and global force corrections (electric fields resulting from effective equipotential sheets representing the engaged and unengaged comb finger regions). The local forces are obtained by applying the principle of virtual work (both engaged and unengaged regions are involved when a ground plane is present beneath the comb fingers). The global forces are obtained from the force between magnetic current filaments introduced to model the electric-potential discontinuities in the effective equipotential sheets of the engaged and unengaged finger regions. Conformal mapping, in addition to a static mode decay approximation, is used to obtain simple and accurate formulas for the local charge per unit length (local forces) and, when a ground plane is present, for the effective sheet potentials (magnetic currents and global forces). The forces in the separated case (which are also global in nature) are also obtained by the principle of virtual work. The results of the paper show that the attractive local forces are independent of engagement distance and the smaller repulsive global forces are inversely proportional to engagement distance. The attractive separated forces are inversely proportional to the separation distance without the ground plane and inversely proportional to the square of the separation distance with the ground plane. >

Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method

The Ewald method is applied to accelerate the evaluation of the Greens function of an infinite periodic phased array of line sources. The Ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave, and a systematic general procedure is applied to extend previous results. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. Singularities and convergence rates are analyzed, and a recipe for selecting the Ewald splitting parameter /spl epsiv/ is given to handle both low and high frequency ranges. Indeed, it is shown analytically that the choice of the standard optimal splitting parameter /spl epsiv//sub 0/ will cause overflow errors at high frequencies. Numerical examples illustrate the results and the sensitivity of the Ewald representation to the splitting parameter /spl epsiv/.

Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method

The Ewald method is applied to accelerate the evaluation of the Green’s function (GF) of an infinite equispaced linear array of point sources with linear phasing. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. It is shown analytically that the choice of the standard ‘‘optimal’’ Ewald splitting parameter E0 causes overflow errors at high frequencies (period large compared to the wavelength), and convergence rates are analyzed. A recipe for selecting the Ewald splitting parameter is provided.

Modeling Scattering From and Radiation by Arbitrary Shaped Objects with the Electric Field Integral Equation Triangular Surface Patch Code

ABSTRACT PATCH is a frequency domain electromagnetic scattering code based on a method-of-moments solution to the Electric Field Integral Equation (EFIE). The numerical methods are based on an earlier version of the code. The present code has the following capabilities: computation of scattering from multiple bodies, treatment of multiple intersecting surfaces, use of symmetry planes to reduce the number of unknowns, treatment of surfaces with lumped and distributed impedance loads, and the capability for plane wave or voltage source excitation. A primitive mesh generator has been included to ease the problem of input data generation. The outputs of the code are the currents on the body, radiated fields, far fields, radar cross section, and Thevenin equivalent circuits. Furthermore, thin wires attached to conducting surfaces may be modeled by use of an equivalent thin strip.

Statistical properties of linear antenna impedance in an electrically large cavity

The paper presents models and measurements of linear antenna input impedance in resonant cavities at high frequencies. Results are presented for both the case where the cavity is undermoded (modes with separate and discrete spectra) as well as the overmoded case (modes with overlapping spectra). A modal series is constructed and analyzed to determine the impedance statistical distribution. Both electrically small as well as electrically longer resonant and wall mounted antennas are analyzed. Measurements in a large mode stirred chamber cavity are compared with calculations. Finally, a method based on power arguments is given, yielding simple formulas for the impedance distribution.

Electromagnetic scattering of an arbitrary plane wave from a spherical shell with a circular aperture

The problem of the scattering of an electromagnetic plane wave with arbitrary polarization and angle of incidence from a perfectly conducting spherical shell with a circular aperture is solved with a generalized dual series approach. This canonical problem encompasses coupling to an open spherical cavity and scattering from a spherical reflector. In contrast to the closed sphere problem, the electromagnetic boundary conditions couple the TE and TM modes. A pseudodecoupling of the resultant dual series equations system into dual series problems for the TE and TM modal coefficients is accomplished by introducing terms that are proportional to the associated Legendre functions P−m0. The solutions of the TE and TM dual series problems require the further introduction of terms proportional to P−mn, where 0≤n<m. These functions effectively complete the standard spherical harmonic basis set when an aperture is present and guarantee the satisfaction of Meixner’s edge conditions. Having generated the modal coeffic...

EIGER: Electromagnetic Interactions GEneRalized

EIGER (Electromagnetic Interactions GEneRalized), a single integrated software tool set, brings together a variety of spectral domain analysis methods. These include moment method solutions of integral equation formulations and finite elements solutions of partial differential equations. New software engineering methods, specifically, object oriented design, are being used to implement abstractions of key components of spectral analysis methods so that the tools can be easily modified and extended to treat new classes of problems. The key components of the numerical analysis tool, and their roles, are: elements-to describe the geometry, basis functions-to interpolate the unknowns (e.g., fields) locally, and operators-to express the underlying physics formulations used to propagate the energy or enforce fundamental principals. The development of EMPACK by Yesantharao (1989) provided the fundamental impetus for these abstractions which are discussed.

EIGER ™ : An open-source frequency-domain electromagnetics code

EIGERtrade is a general-purpose, 3D frequency-domain electromagnetics code suite consisting of a pre-processor (Jungfrau), the physics code (EIGER), and post processor (Moench). In order to better enable collaborative development, EIGERtrade version 2.0 has been approved for release as open source software under a GNU Public License. EIGERtrade is primarily an integral-equation code for both frequency-domain electromagnetics and electrostatics. This version includes the following Greens functions: 2D and 3D free space, symmetry-planes, periodic and layered media. There is a thin-wire algorithm as well as junction basis functions for attachment of a wire to a conducting surface, and also thin-slot models for coupling into cavities. The code is written in Fortran 90 using object-oriented design and has the capability to run both in parallel and serial.

Advanced Numerical Schemes for the Accurate Evaluation of 4-D Reaction Integrals in the Method of Moments

In this paper, we present a simple and efficient fully numerical technique for the evaluation of 4-D reaction integrals arising in the method of moments. In the proposed approach, the accuracy of the source integration, which uses a singularity cancellation scheme, is retained in the final 4-D reaction integral through the application of an appropriate variable transformation and numerical quadrature scheme to the test integral. Several numerical results compared to the usual Gauss-Legendre test quadrature demonstrate the accuracy of the method for both planar and curvilinear discretizations. Moreover, the proposed scheme is independent of test basis functions; hence, it can be used for higher order basis functions as well as curl-conforming or Buffa- Christiansen test basis functions.

Perturbation Theory in the Design of Degenerate Rectangular Dielectric Resonators

The design of resonators with degenerate magnetic and electric modes usually requires the ability to perturb one or both types of modes in order to induce alignment of magnetic and electric properties. In this paper perturbation theory is used to identify difierent types of inclusions that can be used to realize fundamental- mode degeneracy in a rectangular dielectric resonator and thus, can ultimately be used in the design of negative-index metamaterials. For reasons associated with fabrication in the infrared-frequency regime, rectangular resonator designs are of particular interest.