Roger F. Harrington

Theory of characteristic modes for conducting bodies

A theory of characteristic modes for conducting bodies is developed starting from the operator formulation for the current. The mode currents form a weighted orthogonal set over the conductor surface, and the mode fields form an orthogonal set over the sphere at infinity. It is shown that the modes are the same ones introduced by Garbacz to diagonalize the scattering matrix of the body. Formulas for the use of these modes in antenna and scatterer problems are given. For electrically small and intermediate size bodies, only a few modes are needed to characterize the electromagnetic behavior of the body.

Matrix methods for field problems

A unified treatment of matrix methods useful for field problems is given. The basic mathematical concept is the method of moments, by which the functional equations of field theory are reduced to matrix equations. Several examples of engineering interest are included to illustrate the procedure. The problem of radiation and scattering by wire objects of arbitrary shape is treated in detail, and illustrative computations are given for linear wires. The wire object is represented by an admittance matrix, and excitation of the object by a voltage matrix. The current on the wire object is given by the product of the admittance matrix with the voltage matrix. Computation of a field quantity corresponds to multiplication of the current matrix by a measurement matrix. These concepts can be generalized to apply to objects of arbitrary geometry and arbitrary material.

Multiconductor Transmission Lines In Multilayered Dielectric Media

A method for computing the capacitance matrix and inductance matrix for a multiconductor transmission line in a multilayered dielectric region is presented. The number of conductors and the number of dielectric layers are arbitrary. Some of the conductors may be of finite cross section and others may be infinitesimally thin. The conductors are either above a single ground plane or between two parallel ground planes. The formulation is obtained by rising a free-space Greens function in conjunction with total charge on the conductor-to-dielectric interfaces and polarization charge on the dielectric-to-dielectric interfaces. The solution is effected by the method of moments using pulses for expansion and point matching for testing. Computed results are given for some cases where all conducting lines are of finite cross section and other cases where they are infinitesimally thin.

Time-domain response of multiconductor transmission lines

Evaluation of the time-domain response of multiconductor transmission lines is of great importance in the analysis of the crosstalk in fast digital circuit interconnections, as well as in the analysis of power lines. Several techniques for the computation of the line response, starting from the known circuit-theory parameters, are presented and evaluated. These methods are: time-stepping solution of the telegrapher equations, modal analysis in the time domain, model analysis in the frequency domain, and a convolution technique which uses line Greens functions. The last method can treat the most general case of lossy transmission lines with nonlinear terminal networks. Numerical and experimental results are presented to illustrate these techniques and to give insight into the crosstalk problems in fast digital circuits.

Reactively controlled directive arrays

The radiation characteristics of an N -port antenna system can be controlled by impedance loading the ports and feeding only one or several of the ports. Reactive loads can be used to resonate a real port current to give a radiation pattern of high directivity. The theory of resonance is extended to include complex port currents and impedance loads. The initial design of an array is obtained by resonating a desired port current vector, which is then improved by an optimum seeking univariate search method. The direction of maximum gain can be controlled by varying the load reactances. Several numerical examples are given for a circular array of seven dipole elements.

A generalized network formulation for aperture problems

A general formulation for aperture problems is given in terms of the method of moments. It applies to any two regions isolated except for coupling through the aperture. The aperture characteristics are expressed in terms of two aperture admittance matrices, one for each region. The admittance matrix for one region is independent of the other region, and hence can be used for any problem involving that region and aperture. The solution can be represented by two generalized n -port networks connected in parallel with current sources. The current sources are related to the tangential magnetic field which exists over the aperture region when the aperture is closed by an electric conductor. Formulas for fields (linear functionals) and power (quadratic functionals) are given in terms of the admittance matrices.

Radiation And Scattering From Bodies Of Revolution

The problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered. The mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body. A solution is effected by the method of moments, and the results are expressed in terms of generalized network parameters. The expansion functions chosen for the solution are harmonic in o (azimuth angle) and subsectional in t (contour length variable). Because of rotational symmetry, the solution becomes a Fourier series in o, each term of which is uncoupled to every other term.

Computation of characteristic modes for conducting bodies

A procedure for computing the characteristic modes for conducting bodies of arbitrary shape is developed. The method is applied to conducting bodies of revolution and to wire objects, and general computer programs are discussed. Illustrative examples of the computation of characteristic currents and characteristic fields are given for a cone-sphere, a disk, and a wire arrow. Modal solutions using these modes are computed for representative antenna and scattering problems to illustrate convergence of the solution as the number of modes is increased.

A surface formulation for characteristic modes of material bodies

A theory of characteristic modes for material bodies is developed using equivalent surface currents. This is in contrast to the alternative approach using induced volume currents. The mode currents form a weighted orthogonal set over the material body surface, and the mode fields form an orthogonal set over the sphere at infinity. The characteristic modes of material bodies have most of the properties of those for perfectly conducting bodies. Formulas for the use of these modes in electromagnetic scattering problems are given. A procedure for computing the characteristic modes is developed, and applied to two-dimensional bodies. Illustrative examples of file computation of characteristic currents and scattering cross sections are given for cylinders of different material constants.

Boundary Integral Formulations for Homogeneous Material Bodies

There are many boundary integral formulations for the problem of electromagnetic scattering from and transmission into a homogeneous material body. The only formulations which give a unique solution at all frequencies are those which involve both electric and magnetic equivalent currents, and satisfy boundary conditions on both tangential E and tangential H. Formulations which involve only electric (or magnetic) equivalent currents, and those which involve boundary conditions on only tangential E (or tangential H) are singular at frequencies corresponding to the resonant frequencies of a resonator formed by a perfect conductor covering the surface of the body and filled with the material exterior to the body in the original problem.