Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering

We introduce a new version of the combined field integral equation (CFIE) for the solution of electromagnetic scattering problems in three dimensions. Unlike the conventional CFIE, the new CFIE is well-conditioned, meaning that it is a second kind integral equation that does not suffer from spurious resonances and does not become ill conditioned for fine discretizations (the so-called "low-frequency problem"). The new CFIE combines the standard magnetic field integral operator with an analytically preconditioned electric field integral operator. We also report numerical results showing that the new formulation stabilizes the number of iterations needed to solve the CFIE on closed surfaces. This is in contrast to the conventional CFIE, where the number of iterations grows as the discretization is refined.     

Applications of differential forms to boundary integral equations

In this paper we discuss the application of differential forms to integral equations arising in the study of electromagnetic wave propagation. The usual Stratton-Chu integral equations are derived in terms of differential forms and corresponding Galerkin formulations are constructed. All numerical schemes require the specification of basis functions and the use of differential forms provides a very general method for the construction of arbitrary order basis functions on curvilinear geometries. It is noted that the lowest order approximations on flat geometries reduce to forms essential equivalent to the standard Rao-Wilton-Glisson functions. The effect on accuracy is investigated for electric field integral equation and magnetic field integral equation formulations for a range of bases. Hierarchical classes of functions are also developed, as are transition elements useful in p-adaptive schemes where variable orders of approximation are sought.     

CAD techniques for microwave circuits

In little more than 10 years computer-aided design (CAD) of microwave circuits has moved from dumb terminals on mainframe computers to PCs, and now to powerful RISC workstations. Commercial CAD software now integrates the various stages of microwave circuit design: schematic capture, simulation and layout. This paper reviews the different CAD packages that are available for microwave circuit design. The basic principles employed in the modelling of microstrip circuits are introduced and the reasons for the extensive use of frequency-domain simulations are explored. The developments in nonlinear, electromagnetic and system-level simulation methods are described     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.     

Improved quadrature formulas for boundary integral equations with conducting or dielectric edge singularities

In this paper we derive new two-dimensional (2-D) quadrature formulas for the discretization of boundary integral equations in the presence of conducting or dielectric edges. The proposed formulas allow us to exactly integrate polynomials of degree less than or equal to five, multiplied by an algebraic singular factor that diverges along one side of the triangular integration domain. This is the kind of singularity that occurs when physical edges are present in both conducting and dielectric bodies. Numerical tests are performed on the presented formulas, in order to validate the achieved improvement in accuracy, and examples are given of their application to the determination of radar cross-section of 3-D metallic objects.     

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.     

Thick-film fabrication techniques for millimetre-wave dielectric waveguide integrated circuits

The letter presents the results of an initial study performed in the development of millimetre-wave dielectric waveguide integrated circuits using novel thick-film printing techniques. The measurements of the propagation characteristics of sample lines at 60 GHz demonstrate the feasibility of such an approach and examples of printed components indicate its potential in low-cost high-volume applications.     

Integral equations and discretizations for waveguide apertures

We present integral equations and their discretizations for calculating the fields radiated from arbitrarily shaped antennas fed by cylindrical waveguides of arbitrary cross sections. We give results for scalar fields in two dimensions with Dirichlet and Neumann boundary conditions and for (vector) electric and magnetic fields in three dimensions. The discretized forms of the equations are cast in identical format for all four cases. Feed modes can be TM, TE, or transverse electromagnetic (TEM). A method for numerically computing the modes of an arbitrarily shaped, cylindrical waveguide aperture is also given     

Regularized integral equations and curvilinear boundary elementsfor electromagnetic wave scattering in three dimensions

The boundary integral equations (BIEs), in their original forms, which govern the electromagnetic (EM) wave scattering in three-dimensional space contain at least a hypersingularity (1/R³ ) or a Cauchy-singularity (1/R²), usually both. Thus, obtaining reliable numerical solutions using such equations requires considerable care, especially when developing systematic numerical integration procedures for realistic problems. Regularized BIEs for the numerical computation of time-harmonic EM scattering fields due to arbitrarily-shaped scatterers are introduced. Two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration. Both approaches differ from all existing approaches to EM scattering problems. Both work for integral equations initially containing either hypersingularities or Cauchy-singularities, without the need to introduce surface divergences or other derivatives of the EM fields on the boundary. Also, neither approach is limited to flat surfaces nor flat-element models of curved surfaces. The Muller linear combination of the electric- and magnetic-field integral equations (EFIE) and (MFIE) is used to avoid the resonance difficulty that is usually associated with integral equation-based formulations. Some preliminary numerical results for EM scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions     

Line integral representation of the modal radiation for anopen-ended waveguide

A line integral representation of the Kirchhoff-type aperture integration is derived for an open-ended waveguide with arbitrary cross section, excited by an arbitrary mode. The problem is formulated by taking advantage of the equivalence between the radiation of the aperture and the radiation of the modal currents along the semi-infinite waveguide walls     

High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.     

Volume integral equations for analysis of dielectric branchingwaveguides

Novel forms of volume integral equations are developed for the exact treatment of wave propagation in two-dimensional dielectric branching waveguides. The integral equations can be obtained by considering the condition at a point far away from the junction section. An approximate solution by the Born approximation and a numerical solution by the moment method establish the validity of the new volume integral equations. The numerical results are discussed from the viewpoint of energy conservation and reciprocity. The solution is exact if sufficiently large computer memory and computational time are used. The method can be extended to problems of a more general nature (i.e. the incident TM mode), and complex configurations of branching waveguides. The basic idea is also applicable to techniques using boundary (surface) integral equations which are applicable to three-dimensional problems     

A new absorbing boundary condition structure for waveguide analysis

The existence of evanescent waves and waves near cutoff frequencies limits the accuracy of the fields computed in waveguides using the finite-difference time-domain method, and prompted several researchers to design complicated boundary conditions, including combinations of perfectly matched layers and Higdon's higher order absorbing boundary conditions (ABCs). Instead, we employ a terminating structure in which the lateral walls are made absorbing in addition to the longitudinal walls. The undesirable lateral waves at the normal boundary interface are slowed down and effectively attenuated in the lateral walls, while the propagating waves are absorbed in the longitudinal walls. Numerical calculations for pulse excitation of a rectangular waveguide, using the simple Mur's first-order ABC, demonstrate the usefulness of the method     

Design of layered ridge dielectric waveguide for millimeter and sub-millimeter wave circuits

Design rules for Layered Ridge Dielectric Waveguide (LRDW) are presented for the first time through simple figures and closed form equations. The Effective Dielectric Constant (EDC) method is used to develop the design rules that account for typical circuit specifications such as higher order mode suppression, dispersion, attenuation, and coupling between adjacent transmission lines. Comparisons between the design of LRDW, image guide, and millimeter-wave dielectric ridge guide are made.     

Simple method for obtaining the equations of switched-capacitor circuits

A systematic method for writing the time-domain equations of switched-capacitor circuits is presented. By following four well-defined steps, as many linearly independent equations are obtained as there are capacitors in the circuit. The method is especially well suited for hand analysis, and relies on the intuitively appealing concept of identifying physical regions where charge is trapped.     

Polarization sensitivity of a silica waveguide thermooptic phaseshifter for planar lightwave circuits

A thermooptic (TO) phase shifter, which consists of a thin-film heater loaded on a silica-based single-mode waveguide on a Si substrate, was found to exhibit a sli1h,t polarization dependence of about 3.1% between the TE and TM modes. This dependence, which is caused by anisotropic stress concentration due to local heating, was successfully reduced by forming stress-releasing grooves on either side of the heater     

Accurate parametric modeling of folded waveguide circuits for millimeter-wave traveling wave tubes

In this paper, results of different models are compared for calculating effective, cold-circuit (beam-free) phase velocities and interaction impedances of folded waveguide (FW) slow wave circuits for use in millimeter-wave traveling wave tubes (TWT). These parameters are needed for one-dimensional (1-D) parametric model simulations of FW traveling wave tubes (FWTWTs). The models investigated include approximate analytic expressions, equivalent circuit, three-dimensional (3-D) finite difference, and 3-D finite element. The phase velocity predictions are compared with experimental measurements of a representative FW circuit. The various model results are incorporated into the CHRISTINE1D code to obtain predictions of small signal gain in a 40-55 GHz FWTWT. Comparing simulated and measured frequency-dependent gain provides a sensitive, confirming assessment of the accuracy of the simulation tools. It is determined that the use of parametric 1-D TWT models for accurate, full band predictions of small signal gain in FWTWTs requires knowledge of phase velocity and impedance functions that are accurate to <0.5% and <10%, respectively. Saturated gain predictions, being approximately half as sensitive to these parameters, appear to require correct specification of phase velocity and interaction impedance to within /spl sim/1% and 20%, respectively. Although all models generate sufficiently accurate predictions of the interaction impedance, not all generate sufficiently accurate predictions of the effective axial phase velocity.     

CAD techniques for the electromagnetic design of monolithic millimetre-wave integrated circuits

It is well known that mm-waves have an important role to play in the rapid expansion of mobile and personal communications, mmic technology is an important factor since it can provide a means of mass producing the user terminal rf subsystems. Millimetre-wave integrated circuits do not yet however offer the high packing density and functionality which is now possible for lower frequency applications where lumped elements are used. This problem is influenced most of all by the extreme modelling difficulties encountered at frequencies above 30 GHz. This paper reviews the current state-of-the-art for cad techniques used in mmic design. It describes some limitations of the standard Smarttm library approach and looks at the application of commercial electromagnetic simulators in the design of both microstrip and cpw circuits.