Magnetic field outside perfect rectangular conductors
Parametric solutions for magnetic field due to surface currents flowing outside rectangular conductor
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Parametric solutions for magnetic field due to surface currents flowing outside rectangular conductor
The resistance of the electric machine’s windings is an important parameter when analyzing the machine’s performance, as conduction losses in the winding are often the largest loss component. However, this resistance changes with frequency due to the skin and proximity effects, making it challenging to accurately estimate these losses. In this article, a computationally efficient, general method of calculating the ac resistance of an electric machine winding with rectangular conductors is presented. The method uses a 1-D magnetoquasi-static model of the stator slot region to develop boundary transfer relations between individual turns. These relations are then used to create an impedance matrix from which the ac resistance can be calculated. This technique is more flexible than previous solutions since it can accommodate different winding configurations such as fractional-pitch windings. It is shown that a fractional-pitch winding has a lower ac resistance than a full-pitch winding. Finally, finite-element analysis simulations and experimental results are used to validate the proposed method.
An iteration method is introduced to obtain the asymptotic form of the impedance per unit length of a rectangular conductor when the half side lengths are large compared to the skin depth. The first terms of the asymptotic expansion are extracted in closed form. The manner in which the corner corrections fit into the expansion are illustrated. The asymptotic results are compared to a numerical solution in the square limit. The odd corner correction for a right angle edge is also discussed.
Rectangular electric conductors for conductor cables to withstand spacecraft vibration and controlled atmosphere
Attention is called to the grid array as a possible useful antenna design for UHF clear air radars. This type of antenna integrates radiating elements and the feed network into a single structure so that a fairly large array can be driven from a single feed point. Figures are given which demonstrate the basic principle of the grid array, which are adapted from Conti et al. (1981). Conductors are arranged above a ground plane in a repeating, staggered array of connected rectangles. Each rectangular element is approximately one by one-half wavelength in size. The currents on the conductors at resonance is indicated. The grid array illustrated can be expanded in both vertical and horizontal directions about the feed point by adding additional rectangular conductors. The design eliminates the feed network and would provide a thin, panel-like antenna that could be easily built and transported.
A proof-of-feasibility demonstration showed that high temperature superconductor (HTS) coils can be used in a high-load, active magnetic bearing in liquid nitrogen. A homopolar radial bearing with commercially wound HTS (Bi 2223) bias and control coils produced over 200 lb (890 N) radial load capacity (measured non-rotating) and supported a shaft to 14000 rpm. The goal was to show that HTS coils can operate stably with ferromagnetic cores in a feedback controlled system at a current density similar to that in Cu in liquid nitrogen. Design compromises permitted use of circular coils with rectangular cross section. Conductor improvements will eventually permit coil shape optimization, higher current density and higher bearing load capacity. The bias coil, wound with non-twisted, multifilament HTS conductor, required negligible power to carry its direct current. The control coils were wound with monofilament HTS sheathed in Ag. These dissipated negligible power for direct current (i.e. for steady radial load components). When an alternating current (AC) was added, the AC component dissipated power which increased rapidly with frequency and quadratically with AC amplitude. In fact at frequencies above about 2 hz, the effective resistance of the control coil conductor actually exceeds that of the silver which is in electrical parallel with the oxide superconductor. This is at least qualitatively understandable in the context of a Bean-type model of flux and current penetration into a Type II superconductor. Fortunately the dynamic currents required for bearing stability are of small amplitude. These results show that while twisted multifilament conductor is not needed for stable levitation, twisted multifilaments will be required to reduce control power for sizable dynamic loads, such as those due to unbalance.
A quantization procedure for the electromagnetic field in a rectangular cavity with perfect conductor walls is presented, where a decomposition formula of the field plays an essential role. All vector mode functions are obtained by using the decomposition. After expanding the field in terms of the vector mode functions, we get the quantized electromagnetic Hamiltonian.
Intelligent electronic circuit is used to monitor other circuits within module and to warn of imminent failure of module under surveillance. Monitor is housed in rectangular connector and plugs into mating jack originally designed to terminate flat conductor cables. Device can be made from existing premolded rectangular connectors.
Analytical expressions are derived for the cutoff wavenumbers and the corresponding modes in annular-cross-section waveguides having inner conductors of small radius. Waveguides with circular and rectangular outer boundary are considered. In the case of the circular eccentric annular waveguide, comparison is made between the values of cutoff wavenumbers computed from the expressions derived in this paper and data obtained by a more rigorous numerical technique.
Superconducting cable for a cryogenic electromagnet with improved mechanical and thermal properties consists of a rectangular cross-sectioned combination of superconductor and normal conductor. The conductor cable has superconductors embedded in a metallic coating with high electrical and mechanical conductivity at liquid helium temperatures.
Dielectric material between resistive thin film and pure conductor considered as n-port distributed RC network
Abstract For designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest for computing stress and strain, and due to superconducting quench limits. For these force, inductance, energy, and internal field calculations, the coils cannot be naively approximated as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables the internal magnetic field vector, self-force, and self-inductance to be computed rapidly and accurately within a 1D filament model. The method is applicable to coils for which the curve center-line can have general noncircular shape, as long as the conductor width is small compared to the radius of curvature. This paper extends a previous calculation for circular-cross-section conductors (Hurwitz et al 2024 IEEE Trans. Magn. ) to consider the case of rectangular cross-section. The reduced model is derived by rigorous analysis of the singularity, regularizing the filament integrals such that they match the true high-dimensional integrals at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce full finite-cross-section calculations for a non-planar coil of a stellarator magnetic fusion device. Due to the efficiency of the model here, it is well suited for use inside design optimization.
Treatment of conductor surfaces and effects of surface roughness and surface structure on attenuation of waveguides in millimeter waves
Two slot-coupled feeding techniques for exciting a patch antenna with a coplanar waveguide (CPW) were experimentally investigated. In the first technique, a CPW with two notches on both sides of the slot lines is used to couple power to the antenna through a narrow rectangular slot. In the second technique, a grounded CPW with a series gap in the center strip conductor is used to couple power to the antenna through a 'dumbbell' slot. Results indicated that both techniques are feasible and yield high coupling efficiency.
A low inductance, low characteristic impedance transmission line was designed for a 20 kHz power distribution system. Several different conductor configurations were considered: strip lines, interdigitated metal ribbons, and standard insulated wires in multiwire configurations (circular and rectangular cylindrical arrangements). The final design was a rectangular arrangement of multiple wires of the same gauge with alternating polarities from wire to wire. This offered the lowest inductance per unit length (on the order of several nanohenries/meter) and the lowest characteristic impedance (on the order of one Ohm). Standard multipin connectors with gold-plated elements were recommended with this transmission line, the junction boxes to be internally connected with flat metal ribbons for low inductance, and the line to be constructed in sections of suitable length. Computer programs for the calculation of inductance of multiwire lines and of capacitances of strip lines were developed.
A method of moments (MOM) model for the analysis of the Linearly Tapered Slot Antenna (LTSA) is developed and implemented. The model employs an unequal size rectangular sectioning for conducting parts of the antenna. Piecewise sinusoidal basis functions are used for the expansion of conductor current. The effect of the dielectric is incorporated in the model by using equivalent volume polarization current density and solving the equivalent problem in free-space. The feed section of the antenna including the microstripline is handled rigorously in the MOM model by including slotline short circuit and microstripline currents among the unknowns. Comparison with measurements is made to demonstrate the validity of the model for both the air case and the dielectric case. Validity of the model is also verified by extending the model to handle the analysis of the skew-plate antenna and comparing the results to those of a skew-segmentation modeling results of the same structure and to available data in the literature. Variation of the radiation pattern for the air LTSA with length, height, and taper angle is investigated, and the results are tabulated. Numerical results for the effect of the dielectric thickness and permittivity are presented.
An interconnect, having some length, that reliably connects two conductors separated by the length of the interconnect when the connection is made but in which one length if unstressed would change relative to the other in operation. The interconnect comprises a base element an intermediate element and a top element. Each element is rectangular and formed of a conducting material and has opposed ends. The elements are arranged in a generally Z-shape with the base element having one end adapted to be connected to one conductor. The top element has one end adapted to be connected to another conductor and the intermediate element has its ends disposed against the other end of the base and the top element. Brazes mechanically and electrically interconnect the intermediate element to the base and the top elements proximate the corresponding ends of the elements. When the respective ends of the base and the top elements are connected to the conductors, an electrical connection is formed therebetween, and when the conductors are relatively moved or the interconnect elements change length the elements accommodate the changes and the associated compression and tension forces in such a way that the interconnect does not mechanically fatigue.
Program results are described in which the use of a/high permittivity rectangular dielectric image waveguide has been investigated for use in microwave and millimeter wavelength circuits. Launchers from rectangular metal waveguide to image waveguide are described. Theoretical and experimental evaluations of the radiation from curved image waveguides are given. Measurements of attenuation due to conductor and dielectric losses, adhesives, and gaps between the dielectric waveguide and the image plane are included. Various passive components are described and evaluations given. Investigations of various techniques for fabrication of image waveguide circuits using ceramic waveguides are also presented. Program results support the evaluation of the image line approach as an advantageous method for realizing low loss integrated electronic circuits for X-band and above.