Arbitrary Conductor Research Articles

Characterization of picosecond pulse crosstalk between coupled microstrip lines with arbitrary conductor width

The propagation and crosstalk properties of picosecond electrical pulses along coupled microstrip lines with arbitrary strip widths are investigated. The current distributions and propagation constants of the dominant c- and pi -modes in these asymmetric coupled striplines are calculated using the spectral domain approach; and the full-wave analysis results obtained are incorporated into a fast Fourier transform (FFT) algorithm to simulate pulse distortion and crosstalk in the coupled transmission lines. Several samples of asymmetric coupled microstrip lines are fabricated and their characteristics are measured. The results of experiments are found to be in good agreement with those of computer simulations. For the first time, rigorous results of picosecond pulse distortion and crosstalk in asymmetric coupled transmission lines are provided. >

The induced charge on a grounded conductor near a point charge

The induced charge on a grounded arbitrary conductor, excited by a nearby point charge, is shown to be approximated by that on an equivalent conducting sphere near the same point charge. The proof is modified from that for capacitance by Payne and Weinberger [J. Math. Phys. 33, 291 (1955)]. A number of examples for different grounded blocks and plate are given. The potential field distributions from the induced charge are also given.

Gaussian periods and units in certain cyclic fields

We analyze the property of period-unit integer translation (there exists a Gaussian period η \eta and rational integer c c such that η + c \eta + c is a unit) in simplest quadratic, cubic, and quartic fields of arbitrary conductor. This is an extension of work of E. Lehmer, R. Schoof, and L. C. Washington for prime conductor. We also determine the Gaussian period polynomial for arbitrary conductor.

General approach for finding the characteristics of chiral layered media

In this paper, a systematic approach is presented for finding the resonant frequency, damping factor and EM field distribution of a layered planar structure consisting of chiral media and having arbitrary conductor sheets at the interfaces. The analysis is based on the spectral dyadic Green's function followed by a Ritz-Galerkin's process, using matrix analysis in the Fourier transform spectral domain. The great value of our formulation lies in that it provides methodology for the solutions to chiral layered media problems.

Integrated imaging of neuromagnetic reconstructions and morphological magnetic resonance data

New neuromagnetic imaging methods provide spatial information about the functional electrical properties of complex current distributions in the human brain. For practical use in medical diagnosis a combination of the abstract neuromagnetic imaging results with magnetic resonance (MR) or computed tomography (CT) images of the morphology is required. The biomagnetic images can be overlayed onto three-dimensional morphological images with spatially arbitrary selectable slices, calculated from conventional 2D data. For the current reconstruction the 3D images furthermore provide a priori information about the conductor geometry. A combination of current source density calculations and linear estimation methods for handling the inverse magnetic problem allows quick imaging of impressed current source density in arbitrary volume conductors.

Evaluation of characteristic impedances of two conductor transmission lines with arbitrary dielectrics by moment methods under tem approximation

In this paper the characteristic impedances for TEM or quasi-TEM transmission lines with arbitrary conductor cross-sections and dielectrics are calculated by moment methods. Formulation is based on the analysis for two dimensional electrostatic felds under the TEM approximation. Pulse functions are used for the expansion of the charge distribution and the point matching for testing. Numerical samples are given. Some are compared with those obtained by other methods. Results show that they are in good agreement.

On Currents Induced in Power Transmission Systems During Geomagnetic Variations

Theoretical estimation of the electric field occurring at the earth's surface during a time variation in the geomagnetic field is discussed. Numerical computations, which have been made assuming an idealized behaviour for the magnetic field or using measured magnetic values, indicate the existence of horizontal electric fields in the order of 1 V/km in connection with geomagnetic disturbances. Calculation of quasi-direct currents produced in an arbitrary conductor network (e. g. a power transmission system) by a geomagnetically-induced electric field is discussed. Numerical results concerning the Finnish 400 kV grid are given. It is seen that currents in the order of 100 A can be expected to flow through transformers during geomagnetic disturbances. The largest current measured in the Finnish recordings so far has been 165 A. These recordings carried out since 1977 are also described in this paper.

On Currents Induced in Power Transmission Systems During Geomagnetic Variations

Theoretical estimation of the electric field occurring at the earth's surface during a time variation in the geomagnetic field is discussed. Numerical computations, which have been made assuming an idealized behaviour for the magnetic field or using measured magnetic values, indicate the existence of horizontal electric fields in the order of 1 V/km in connection with geomagnetic disturbances. Calculation of quasi-direct currents produced in an arbitrary conductor network (e. g. a power transmission system) by a geomagnetically-induced electric field is discussed. Numerical results concerning the Finnish 400 kV grid are given. It is seen that currents in the order of 100 A can be expected to flow through transformers during geomagnetic disturbances. The largest current measured in the Finnish recordings so far has been 165 A. These recordings carried out since 1977 are also described in this paper.

The capacitances of two arbitrary conductors

The capacitances of two arbitrary conductors

Electromagnetic waves near perfect conductors. II. Casimir effect

The Casimir free energy of the electromagnetic field in regions bounded by thin perfect conductors with arbitrary smooth shapes is studied. This free energy is expressed as a convergent multiple scattering expansion, in which the wave is damped between scatterings taking place on conductors. The result depends neither on the large box needed to render the spectrum discrete, nor on the shape of the high frequency cut-off corresponding to slightly imperfect conductivity; this establishes the universal character of quantum electro-magnetic forces on perfectly conducting thin objects. General expansions are derived for the Casimir free energy in the low and high temperature limits. They exhibit a dependence on the topology of the conducting surfaces. At low temperature, the Casimir entropy vanishes as T 3 for simply connected conductors, and as T for multiply connected ones. At high temperature, the free energy has the semiclassical behavior − C T log( T h ̵ cQ ) . The constant C = (128φ) −1ʃdθ( 3 R 1 2 + 3 R 2 2 + 3 R 1 R 2 )−n may be interpreted as the number of additional modes of finite frequency created by introducing the conducting surface. It depends on the topology of the surface through its genus n, and on its local curvature radii R 1, R 2. The average wave number Q depends on the shape of the surface and its size. The symmetry between low and high temperatures is recovered for parallel plates. While a plane foil is stable against Casimir stresses at zero temperature, such stresses would tend at finite temperature to create wrinkles of dimensions larger thn 2.9 h ̵ c T . The same wrinkling effect exists for an arbitrary conductor at high enough temperature. The presence of a curved conducting surface transfers the free energy of radiation from the concave to the convex side at zero temperature, and does the converse at high enough temperatures. Wedges may be considered for slightly imperfect conductors; the electro-magnetic energy is lowered at finite temperature by creation of wedges, and also at zero temperature by creation of multiple wedges as in a honeycomb structure. The formalism is also applied to evaluate Van der Waals forces and torques at arbitrary temperature between remote conductors, and to show that the Casimir energy of a cylinder at zero temperature vanishes to lowest order in the multiple scattering expansion. Finally, the sphere is used as a test for studying convergence of the multiple scattering expansions. Using radial and transverse combinations of vector spherical harmonics yields a simple expression for the electromagnetic Green functions. This expression is recovered by summation of the multiple scattering expansion; the convergence domain, in the plane kR = x + iy, of the expansion includes a neighborhood of the origin, as well as the whole region y >0.0348 |x| 1 3 . The numerical convergence of the Casimir free energy is rapid, the lowest order term already yields a result with less than 7% error.

Advances in Finite Element Techniques for Calculating Cable Resistances and Inductances

In theory, finite element procedures can be applied to arbitrary conductor configurations in order to determine their frequency dependent resistances and inductances to an arbitrarily high degree of accuracy. In practice, limitations are imposed by the shapes of the finite elements used and by the accuracy of the formulae invoked to estimate their inductances. This paper reviews the concepts underlying extant finite element procedures, proposes a more efficient set of element shapes than are used in extant procedures and develops the inductance formulae necessary to implement these shapes. This results in a considerably more capable algorithm.

A charged particle moving near a perfectly conducting sphere

The problem of a charged particle moving in an arbitrary prescribed trajectory near a perfectly conducting sphere is formulated in terms of the magnetic-field integral equation on the sphere. The integral equation is solved with the aid of the solutions of the associated eigenvalue problem. A detailed study of the canonical problem, where the charged particle moves around a sphere in a circular orbit, reveals that a sufficiently accurate solution can be obtained by solving two independent quasi-static problems. Validity criteria are established for the quasi-static solutions in terms of the particle's speed and distance from the sphere. These quasi-static problems can be easily generalized and solved for particles of arbitrary motion and conductors of arbitrary shape. Induced surface currents and charges on the sphere as well as the rate of energy loss of the charged particles are calculated.

Application of complex ray tracing to scattering problems

Representations and geometric constructions associated with complex points, complex lines, and complex rays are introduced. They are applied to the problem of scattering of an evanescent plane wave by a conducting circular cylinder. This problem has an exact solution, which provides a check of the validity of complex ray tracing and suggests more general applications. An important role is played by the transformation that maps the point of reflection, on the complex extension of the scattering surface, onto the trace in real space of the complex reflected ray. For the particular problem considered, the phase and amplitude of the reflected field are computed and the "phase paths" and "phase fronts" are constructed. The reflected field and phase paths obtained in this manner are not to be taken in their entirety because some reflection points are not "illuminated" by the incident wave, and because the reflector may be only part of the cylinder. Tentative selection and truncation rules are used which yield good agreement with the exact solution over some regions. The disagreement, where it occurs, comes-as it does for real rays-from neglecting the diffracted field such as the creeping waves around smooth surfaces and, in the case of truncation, the edge waves from the discontinuity. Some consideration is given to scattering by an arbitrary smooth conductor. Some problems peculiar to the use of complex rays are stated.

Comments on "Diffraction by arbitrary cross-sectional semi-infinite conductor"

The far scattered fields by a semi-infinite conductor are composed of the geometic-optics and the diffraction field. By applying the technique of complex number integral, the separation of these two fields in the neighborhood and other region of the geometrical shadow and reflection boundaries is clarified. This was ambiguous in the above paper.

Diffraction by arbitrary cross-sectional semi-infinite conductor

This paper investigates the problem of diffraction of an electromagnetic wave by a semi-infinite conductor by means of the computer method based on an integral equation formulation. The cross section of the conductor can have an arbitrary shape, provided the face shined by the incident wave is a uniform plane in the region far from the edge. In that plane region, the problem is simply that of reflection from a conductor wall for which a solution is known. This known part of the solution is analytically excluded to derive an integral equation describing the edge effect over a limited region. The limited region is unknown at first and must be determined from the results of some numerical computations. As a numerical example, a thick half-plane conductor is treated in which the electric field polarization is parallel to the conductor, i.e., the case of an incident E wave.

Evaluation of Current-Produced Two-Dimensional Magnetic Fields

Formulas are developed for the two-dimensional magnetic field (and its derivatives of all orders) produced by a long straight conductor of uniform current density. These formulas are independent of whether the field point lies inside or outside the conductor and avoid ambiguities due to multiple values of the complex logarithm. Evaluation of the formulas can be done numerically, with the arbitrary conductor boundary approximated by a polygon, or graphically, or mechanically.