Karl F. Warnick

Numerical simulation methods for rough surface scattering

Abstract Numerical methods are of great importance in the study of electromagnetic scattering from random rough surfaces. This review provides an overview of rough surface scattering and application areas of current interest, and surveys research in numerical simulation methods for both one- and two-dimensional surfaces. Approaches considered include numerical methods based on analytical scattering approximations, differential equation methods and surface integral equation methods. Emphasis is placed on recent advances such as rapidly converging iterative solvers for rough surface problems and fast methods for increasing the computational efficiency of integral equation solvers.

Minimizing the Noise Penalty Due to Mutual Coupling for a Receiving Array

For phased array receivers, mutual coupling leads to beam-dependent active impedances which must be taken into account when matching the array ports to front end amplifiers for optimal noise performance. We study the noise penalty for several noise matching conditions and develop a matching condition that minimizes the average beam equivalent receiver noise temperature over multiple beams. For non-beamforming applications such as multiple input multiple output communications, we show that noise performance for coupled arrays can be quantified using the spectrum of an equivalent receiver noise temperature correlation matrix.

Signal Processing for Phased Array Feeds in Radio Astronomical Telescopes

Relative to traditional waveguide feeds, phased array feeds (PAFs) for radio telescopes can increase the instrument field of view and sky survey speed. Unique challenges associated with PAF observations, including extremely low signal levels, long-term system gain stability requirements, spatially correlated noise due to mutual coupling, and tight beamshape tolerances, require the development of new array signal processing techniques for this application. We propose a calibration and beamforming strategy for PAFs including interference mitigation with power spectral density (PSD) estimation bias correction. Key efficiency metrics for single-feed instruments are extended to the array case and used to verify performance of the algorithms. These techniques are validated using numerical simulations and experimental data from a 19-element PAF on the Green Bank 20-m telescope.

Optimal Noise Matching for Mutually Coupled Arrays

From classical two-port noise theory, the noise figure of an amplifier is minimized when a source is matched to a particular optimal reflection coefficient at the amplifier input. In this paper, we show that this result extends in a natural way to the multiport case, with a coupled N-port source network such as an array antenna connected by a multiport matching network to the inputs of N low-noise amplifiers. For optimal noise performance, the matching network must decouple the array and present isolated, individually noise-matched ports to the amplifier inputs.

Error analysis of the moment method

Because of the widespread use of the Method of Moments for simulation of radiation and scattering problems, analysis and control of solution error is a significant concern in computational electromagnetics. The physical problem to be solved, its mesh representation, and the numerical method all impact accuracy. Although empirical approaches such as benchmarking are used almost exclusively in practice for code validation and accuracy assessment, a number of significant theoretical results have been obtained in recent years, including proofs of convergence and solution-error estimates. This work reviews fundamental concepts such as types of error measures, properties of the problem and numerical method that affect error, the optimality principle, and basic approximation error estimates. Analyses are given for surface-current and scattering-amplitude errors for several scatterers, including the effects of edge and corner singularities and quadrature error. We also review results on ill-conditioning due to resonance effects and the convergence rates of iterative linear-system solutions.

Teaching electromagnetic field theory using differential forms

The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. Second, Amperes and Faradays laws obtain graphical representations that are as intuitive as the representation of Gausss law. Third, the vector Stokes theorem and the divergence theorem become special cases of a single relationship that is easier for the student to remember, apply, and visualize than their vector formulations. Fourth, computational simplifications result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of vector identities are replaced by algebraic rules. In this paper, EM theory and the calculus of differential forms are developed in parallel, from an elementary, conceptually oriented point of view using simple examples and intuitive motivations. We conclude that because of the power of the calculus of differential forms in conveying the fundamental concepts of EM theory, it provides an attractive and viable alternative to the use of vector analysis in teaching electromagnetic field theory.

Accuracy of the method of moments for scattering by a cylinder

We study the accuracy and convergence of the method of moments for numerical scattering computations for an important benchmark geometry: the finite circular cylinder. From the spectral decomposition of the electric-field integral equation for this scatterer, we determine the condition number of the moment matrix and the dependence of solution error on the choice of basis functions, discretization density, polarization of the incident field, and the numerical quadrature rule used to evaluate moment-matrix elements. The analysis is carried out for both the TM polarization (weakly singular kernel) and TE polarization (hypersingular kernel). These results provide insights into empirical observations of the convergence behavior of numerical methods in computational electromagnetics.

Effects of mutual coupling on interference mitigation with a focal plane array

A focal plane array feed of electrically small elements has been proposed as a means for achieving high sensitivity for radio astronomy applications in the presence of radio frequency interference (RFI). For a broadband system, mutual coupling effects become significant as the array element spacing becomes small relative to the electromagnetic wavelength. We present a theoretical framework for modeling the effects of mutual coupling and for determining the optimal multiport matching network between array elements and front-end transistor low-noise amplifiers for maximum signal-to-noise ratio (SNR). Numerical results are given for a model scenario including spillover and amplifier thermal noise and point signal and interference sources. A suboptimal self-impedance matching network yields performance close to that of a full network match.

Electromagnetic Green functions using differential forms

In this paper we redevelop the scalar and dyadic Green functions of electromagnetic theory using differential forms. The Green dyadic becomes a double form, which is a differential form in one space with coefficients that are forms in another space, or a differential form-valued form. The results presented here correspond closely with the usual dyadic treatment, but are clearer and more intuitive. Many of the usual expressions using green functions in vector notation require a surface normal; with the Green forms the surface normal is unnecessary. We illustrate the formalism by computing scattering from a randomly rough conducting surface and deriving the Green form for a dielectric half-space. We also define the interior derivative, which is equivalent to the coderivative but for a constant metric has a computational rule dual to that of the exterior derivative and simplifies calculation in coordinates. This work makes available some of the tools that have not yet been presented in the language of differ...

Voltage-controlled separation of proteins by electromobility focusing in a dialysis hollow fiber

Electromobility focusing (EMF) is a relatively new protein separation technique that utilizes an electric field gradient and a hydrodynamic flow. Proteins are focused in order of electrophoretic mobility at points where their electrophoretic migration velocities balance the hydrodynamic flow velocity. Steady state bands are formed along the separation channel when equilibrium is reached. Further separation and detection can be easily achieved by changing the electric field profile. In this paper. we describe an EMF system with on-line UV absorption detection in which the electric field gradient was formed using a dialysis hollow fiber. Protein focusing and preconcentration were performed with this system. Voltage-controlled separation was demonstrated using bovine serum albumin and myoglobin as model proteins. The limitations of the current method are discussed, and possible solutions are proposed.