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In this paper we present a lucid, easy, and accurate approach for calculation of the mutual inductance between all inclined circular coils with either rectangular cross section or negligible section. We use Grover's formula for the mutual inductance between two filamentary circular coils with inclined axes that lie in the same plane. Their centers are either displaced along the axis of one coil or displaced along one axis of the first coil and then displaced sideways in addition. We apply the filament method for coil combinations comprising circular coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes), and filamentary circular coils. In this approach we clarify how Grover's formulas have to be used for different coil combinations in the filament treatment. Thus, two well-known methods (Grover's formulas and the filament method) can be easily used to calculate the mutual inductance between all inclined circular coils, even though the problem is purely three-dimensional. Index Terms--Circular coil of rectangular cross section, filament method, filamentary circular coil, mutual inductance, thin disk coil (pancakes), thin wall solenoid.

We present new and fast procedures for calculating magnetic forces between thin coaxial circular coaxial coils in air. The results are expressed in semianalytical form in terms of the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and a term that must be solved numerically. These expressions are accurate and simple to use for several practical applications. We also describe a comparative method based on the filament technique. We discuss the computational cost and the accuracy of two methods and compare them with already published data. Results obtained by our two approaches are in excellent agreement with each other. They can be used in industrial electromagnetic applications such as electrodynamic levitation systems, linear induction launchers, linear actuators, and coil guns. Index Terms--Filamentary circular coil, magnetic force, thin disk coil, thin wall solenoid.

In this paper, we present analytic-numerical expressions for the calculation of the mutual inductance of two axisymetric circular coils with rectangular cross section in air. This original and new method may seem complicated but it is explicit, accurate, and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Heuman's lambda function, and three terms that must be solved numerically. We confirm the validity of this approach by comparing it with other approaches (filament method and previously published data). We also compare the accuracy and the computational cost of this approach and that of the filament method. All results obtained by the various approaches are in excellent agreement. Index Terms--Filament method, Maxwell's coils, mutual inductance, Neumann's formula.

This paper presents an efficient method for computing the mutual inductance between two thin coaxial disk coils in air. The derived principal semi-analytical expressions involve complete elliptic integrals of the first and second kind, Heuman's Lambda function and three terms that have to be computed numerically. The presented method is compared to the filament method where both conductors are approximated by Maxwell's filamentary coils. The mutual inductance values (for a chosen case) computed by both methods are in good agreement. However, the method presented in this work exceeds by far the filament method in its precision and computational efficiency. In another example, the computed mutual inductance is validated by measurement. Index Terms--Mutual inductance, thin disk coils, Biot-Savart law, Maxwelrs coils.

In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at reduced computational cost. In addition, it can be employed to calculate the magnetic field in conductor disk configurations involving complicated geometry as well as to evaluate their self and mutual inductance. Index Terms--Biot-Savart law, magnetic field, radial current-carrying disks.

In this work, theoretical modeling and experimental characterization of composite coaxial-line cells are made for accurate dielectric measurement. The coaxial cells are designed such that highly dispersive materials can be characterized over a wide band of frequencies. In addition, a transmission line matrix (TLM) algorithm with a new type of node is proposed for electromagnetic analysis of the complex composite geometry of the measurement cells. Such a hybrid-mode simulation allows the electrical performance of the proposed cells to be determined for a variety of complex permittivity measurements. The proposed node in the cylindrical coordinate not only accommodates cylindrical coaxial discontinuities in the cell, but also describes the frequency-dependent properties of material. Experiments on a network analyzer were done with a number of APC-7 coaxial cells and various liquid samples to verify the wideband characteristics of the technique. It is found both theoretically and experimentally that the sample volume can be adjusted to ensure a wideband sensibility of the S-parameters. A sensitivity factor is also defined to characterize the frequency response of the coaxial cells. Such an electromagnetic analysis (direct problem) can be used in extracting unknown dielectric characteristics of a material (inverse problem) based on a recently proposed generic approach.

A generic approach is proposed to accurately measure microwave and millimeter-wave properties of dielectric materials. This novel technique first determines the scattering parameters of a discontinuity containing a material having a wide range of complex dielectric permittivity [Epsilon] that is known a priori (the direct problem). The discontinuity is embedded in a rectangular waveguide or a microstrip line. A unified theory, which is essentially based on a combination of the boundary integral equation technique with a modal expansion approach, is presented to tackle the direct problem. A class of generic diagrams are obtained for interrelating the dielectric permittivity [Epsilon] to its S-parameters, and a simple analytical expression is deduced to solve the inverse problem. The proposed analytical formulation is easy to use and much more rapid than its iterative counterparts. It demonstrates a completely new and efficient strategy for accurate complex dielectric measurements.

This paper deals with two efficient approaches for determining the mutual inductance between thin circular coils and disk coils in air. The first approach gives new expressions for calculating the mutual inductance of treated configurations. These results are expressed over the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and one term that must be solved numerically. Another approach is based on the filament method where conductors are approximated by the set of Maxwell's coils. The obtained expressions are expressed over the complete elliptical integrals of the first and second kind and permit also fast calculation of the mutual inductance for mentioned systems. These new expressions are accurate and simple for useful applications. All results obtained by the two approaches are in excellent agreement. Index Terms--Biot-Savart law, circular coils, disk coils, Maxwell's coils, mutual inductance.

This paper presents a mathematical model for calculating 3D linear magnetostatic fields with open boundaries. By using this improved method (based on the integral equations and magnetic surface charge), several field computation problems inside magnetic materials are being avoided. A comprehensive procedure is established for magnetic field computation within the free space and iron, as well as on their boundary--at a reduced computational cost. The proposed method was compared to the analytical solution for a test case. Index Terms--Biot-Savart law, fictitious magnetic charge, integral method, magnetostatic field calculation.