| Invited Talk

Name of the Speaker: Prof. Ramakrishna Janaswamy
Name of the Organizer: Dr. Uday Khankhoje
Venue: ESB-244 (Seminar Hall)
Date/Time: 25th January 2024 (Thursday), 2:00 PM
Title: Understanding Characteristic Mode Theory for Conducting and Penetrable Bodies Through Simple Examples

Abstract

Abstract: For canonical geometries that fit in one of the eleven separable coordinate systems, it is very effective to expand the potentials, the fields or the induced current densities for time-harmonic excitations in terms of orthogonal functions (or harmonic functions) that are also the eigenfunctions of the original 3D Helmholtz equation. These eigenfunctions are independent of excitation. Familiar examples of eigenfunctions are simple harmonic functions, the Bessel functions, the Legendre functions, etc., which appear as solutions of the separated Helmholtz equation. The advantage of using eigenfunctions as expansion functions is that it will result in a minimal set; for a given accuracy of approximation, the eigenfunctions will result in a smallest possible set to represent the unknown function. Furthermore, the eigenfunctions will give rise to current distributions and far-zone fields that will be mutually orthogonal in some sense, thereby, facilitating easy computation of electromagnetic parameters of interest, such as stored power, impedance, radiated power, antenna gain, radar cross-section, extinction cross-section, etc.

Characteristic modes for an arbitrary object are what the harmonic functions are for canonical objects. For arbitrarily shaped objects or for those canonical shapes with arbitrarily varying constitutive parameters, the starting point is often an operator equation such as an integral equation that captures the relevant boundary conditions. In the numerical solution of these integral equations, one has a lot of freedom in choosing the basis functions in terms of which the unknown function is expanded. The number of basis functions depends on the electrical size, shape and composition of the object. Unlike generic basis functions, characteristic modes form a unique basis set that is intrinsic to the object under consideration and independent of excitation. For both perfectly conducting and homogeneous, penetrable objects, the characteristic mode theory is based on the surface integral equation operators. The characteristic modes are obtained by diagonalizing these operators together with the radiation operator that links the equivalent electric and magnetic currents on the object surface to the power radiated exterior to the object.

Various steps involved in the procedure are demonstrated in this talk by considering electric-field integral equation for a finite length cylindrical dipole and 2D Mu ̈ller type coupled integral equations for penetrable objects. Special example of a circular cylinder sheds new insights on the physical sig- nificance of the eigenvalues in terms of the power dissipated within the object and the power radiated in the exterior volume. Implication of the growth properties of eigenvalues on the solution procedure is also discussed. How the characteristic modes can be used in calculating common parameters of in- terest such as extinction cross-section is demonstrated. The various cases considered in this talk can be readily implemented in MATLAB to generate characteristic modes and the associated eigenvalues and provide insights that are lacking in generic electromagnetic simulation codes.

Bio: Ramakrishna Janaswamy obtained his B. Tech in Electronics & Communications Engineering, NIT-Warangal, M. Tech in Microwave & Radar Engineering from IIT-Kharagpur and PhD in Electrical Engineering from the University of Massachusetts, Amherst. He served as a faculty member at Wilkes University, Pennsylvania (1986-1987), Naval Postgraduate School, California (1987-2001) and the University of Massachusetts, Amherst (2001-Present). He conducts research in electromagnetics with applications to antenna analysis, propagation analysis, computational techniques, and wireless communications.

Professor Janaswamy is the author of the books Engineering Electrodynamics: A Collection of Theorems, Principles and Field Representations, Institute of Physics, Bristol, UK, 2020 and Radiowave Propagation and Smart Antennas for Wireless Communications, Springer, NY, 2000. He is a Fellow of IEEE, Fellow of the Electromagnetics Academy and a recipient of the IEEE Third Millennium Medal, 2000 and of the R. W. P. King Paper Prize Award of the IEEE Transactions on Antennas and Propagation, 1995. He is an elected member of USNC/URSI Commissions B and F. He previously served as an Associate Editor of IEEE Transactions on Antennas & Propagation, IEEE Transactions on Vehicular Technology, IET Electronics Letters, and AGU Radio Science. He is currently serving as Secretary of IEEE Antennas & Propagation Standards Committee and the Vice Chair of Std. P2816: Recommended Practice for Computational Electromagnetics Applied to Modeling and Simulation of Antennas.