Minya M. Gavrilovic

New Expression For Calculating Magnetic Fields Due To Current Carrying Solid Conductors

A new closed-form expression based on double integral computation is introduced for 3D magnetostatic fields of current-carrying solid conductors whose vector density satisfies the condition that its curl is zero. Such a reduced expression is derived for a toroidal conductor with radial current flow, solved analytically, and used for 3D field computation. For illustration, by applying the same reduction principle, the 3D magnetic fields are computed for cylindrical and rectangular conductors with longitudinal flowing current.

Calculation improvement of 3D linear magnetostatic field based on fictitious magnetic surface charge

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 avoided. A comprehensive procedure is established for magnetic field computation within 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.

Accuracy control in the optimization of microwave devices by finite-element methods

Automatically optimizing the design of a microwave device can be prohibitively time-consuming when a numerical electromagnetic-field analysis is necessary at each iteration. However, the time taken for the field analysis depends on the accuracy required, and in the early stage of the optimization relatively inaccurate solutions are adequate. This idea is exploited in a scheme that combines a quasi-Newton constrained optimizer with a two-dimensional p-adaptive finite-element method for finding scattering parameters. The scheme has been tested on three H-plane rectangular waveguide devices: a T-junction, a miter bend with a dielectric column, and a two-cavity iris-coupled filter. Time savings of more than an order of magnitude were obtained, compared to the standard approach of requiring equally high accuracy throughout the optimization.

An Error Indicator For The Calculation Of Global Quantities By The P-adaptive Finite Element Method

While general error indicators based on assessment of the quality of the field have been successfully used in adaptive finite element methods, here an error indicator that chooses elements based on their contribution to a specified global quantity is presented. This Targeted Error Indicator (TEI) can be applied to single or multiple solution problems. The inductance of a coil wrapped around a C shaped core and the input impedance to two coupled coils serve as examples of global quantities for single and multiple solution cases. When compared to a general error indicator, the TEI leads to more accurate and more rapidly converging global values.

A port element for p-adaptive S-parameter calculation

A new element is proposed for the treatment of ports in p-adaptive finite-element analysis of microwave devices. The element consists of a number of segments, on each of which the field is represented by high-order, hierarchical polynomials that match those used in the interior. As the p-adaption proceeds, the number of waveguide modes taken into account on the port increases, and so does the accuracy of the port boundary condition. Results for several H-plane problems in rectangular waveguide demonstrate that, with the new element, adaptive convergence to the same scattering parameters can be achieved no matter how closely the ports are placed.

An Error Estimator for Design Sensitivities of Microwave Device Parameters

A new error estimator for design sensitivities is proposed for finite-element analysis of microwave devices. A function of scattering parameters, C, varies with parameter g. By the adjoint method, the sensitivity dC/dg can be found. A new estimate of the error in dC/dg is based on derivatives of C with respect to position for internal nodes in the mesh (not on any parameterized boundaries or interfaces). It is shown that these estimates of the error are close to the actual errors for a variety of test cases. The estimator is tested using a p-adaptive finite-element method.

New closed form expressions for calculating the magnetic field of thin conductors with longitudinal current direction introduction

In this paper, we present relatively simple expressions in the analytical form in order to calculate the magnetic fields of thin cylindrical finite conductors with current in longitudinal direction. The derivation presented here can be employed usefully to calculate the magnetic fields in more complicated geometries. They may also be used for computation of self and mutual inductances for systems with thin conductors [9]. The reduction of the mathematical complexity based on the above expressions makes it desirable for calculation of magnetic fields in various problems. The expressions, obtained in the analytical form, allow easy solving of fields at singular locations. The presented method can be simply applied to derive expressions for the computation of magnetic fields of various thin conductors with the current flow in the longitudinal directions, and whose angular lengths are arbitrary. In this case, all mathematical procedures will be expressed over incomplete elliptic functions of the first, second, and third kinds [8].

New closed-form expressions for calculating the magnetic field of thin conductors with azimuthal current direction

New closed-form expressions are derived and presented to compute the 3D magnetostatic fields of thin finite cylindrical conductors with current flowing in the azimuthal direction. All results are obtained in analytical form and enable one to easily calculate the magnetic field in either regular or singular cases. These closed-form expressions for the thin cylinders are much more convenient for applications than in previous cases.