Joseph R. Mautz

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.

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.

An E-Field solution for a conducting surface small or comparable to the wavelength

A new E -field solution is presented for the electric current and electric charge induced on a perfectly conducting surface illuminated by an incident electromagnetic field. This solution is a moment solution to the electric field integral equation on the surface. The expansion functions consist of a set of functions suitable for expanding the magnetostatic current and a set of functions whose surface divergences are suitable for expanding the electrostatic charge. The testing functions are similar to the expansion functions. With these expansion and testing functions, the new E -field solution works well with surfaces whose maximum dimension may be as small as 10^{-15} wavelengths or as large as a few wavelengths. Previous E -field solutions begin to deteriorate when the maximum dimension of the surface falls below a few hundredths of a wavelength. The new E -field solution is applied to a conducting circular disk and a conducting sphere.

Quasi-static analysis of a microstrip via through a hole in a ground plane

The equivalent circuit of a via connecting two semi-infinitely long transmission lines through a circular hole in a ground plane is found. The pi -type equivalent circuit consists of two excess capacitances and an excess inductance. These are quasistatic quantities and thus are computed statically by the method of moments from integral equations. The integral equations are established by introducing a sheet of magnetic current in the electrostatic case and a layer of magnetic charge in the magnetostatic case. Parametric plots of the excess capacitances, the excess inductance, and the characteristic admittance of the via are given. >

A combined-source solution for radiation and scattering from a perfectly conducting body

A combined-source solution is developed for electromagnetic radiation and scattering from a perfectly conducting body. In this solution a combination of electric and magnetic currents, called the combined source, is placed on the surface S of the conducting body. The combined-source operator equation is obtained from the E -field boundary-value equation. It is shown that the solution to this operator equation is unique at all frequencies. The combined-field operator equation also has a unique solution, but it is not directly applicable to the aperture radiation problem. The H -field and E -field operator equations fail to give unique solutions at frequencies corresponding to the resonant frequencies of a cavity formed by a hollow conductor of the same shape. The combined-source operator equation is solved by the method of moments. The solution, valid for a three-dimensional closed surface S , is then applied to a surface of revolution. Examples of numerical computations are given for a sphere, a cone-sphere, and a finite circular cylinder.

Computational methods for antenna pattern synthesis

Some general numerical methods for antenna pattern synthesis, with and without constraints, are developed. Particular cases considered are 1) field pattern specified in amplitude and phase, 2) field pattern specified in amplitude only, and 3) these two cases with a constraint on the source norm. Both the source and the field are discretized at the beginning, and the methods of finite dimensional vector spaces are used for the computations. The theory is general, but is applied only to point sources arbitrarily distributed in a plane, and to pattern synthesis in this plane. Some numerical examples are given for ten sources approximately equispaced on one-half of an ellipse, with the desired field pattern chosen to be the csc \phi pattern in the first quadrant.

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.

Radiation and scattering from electrically small conducting bodies of arbitrary shape

A simple moment solution is given for low frequency electromagnetic scattering and radiation problems. The problem is reduced to the corresponding electrostatic and magnetostatic problems. Each static problem is solved using the Method of Moments. The surface of the perfectly conducting scatterer is modeled by a set of planar triangular patches. Pulse expansion functions and point matching testing are used to compute the charge density in the electrostatic problem. For the magnetostatic current a set of charge-free vector expansion functions is used. The problem is formulated assuming the scatterer to be in an unbounded homogeneous region. Scatterers of various shapes, such as the circular disc, the sphere, and the cube are studied. Special attention is paid to a conducting box with a narrow slot. The computed results are the scattered fields, the induced charge and current distributions, and the induced electric and magnetic dipole moments. These are in close agreement with whatever published data are available.

Straight wires with arbitrary excitation and loading

A general analysis of straight wire antennas and scatterers, with arbitrary excitation and loading, is given. The resulting formulas are in matrix notation, in a form suitable for programming on a digital computer. Many numerical results for input admittances, current distributions, radiation patterns, and scattering cross sections of various antennas and scatterers are included.