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In the conventional partial element equivalent circuit (PEEC) method, all partial inductances are connected at both ends to other circuit elements of a PEEC or modified nodal approach (MNA), simulation program with integrated circuit emphasis (SPICE) type circuit. This article shows that if at least one end of a partial inductance remains without a connected element, it is called an open loop, which is also physical and is theoretically closed by displacement current. It is shown in this article that the open loop is only consistent if the partial inductance is evaluated using the Coulomb gauge; else, the magnetic energy computation of open loop is inconsistent. This article focuses on the difference and presents an analytical method for the calculation of partial inductance with Coulomb gauge in quasi-static field to figure it out. This difference is proven to be related to the calculation of vector potential A , whereas existing calculation is based on Lorentz gauge. Then, analytical results of conductor segments are derived for comparison of the two different gauges, and show the difference. Also, numerical experiments of the self- and mutual-partial inductances of conductor segments in open-loop problems are given for further comparison. The results illustrate that the proposed method is consistent with magnetic energy, and could be directly be applied to closed-loop problems without affecting the validity of the PEEC method. This method is believed to be an effective supplement in physical sense of partial inductance.

Magnetic field energy could be calculated by means of inductance, magnetic field intensity, or vector potential A, respectively. However, the former two methods may not reach an agreement in open loop problems. Partial inductance is calculated through A , whereas magnetic field intensity is also related to A . This letter analytically derives the difference between the former two methods. It is necessary that displacement current have to be carefully considered in open loop problems. A numerical example is given out for validation.

A soft-magnetic-metal-based shield structure was designed to reduce magnetic flux leakage in magnetic-induction wireless power transfer systems. Soft magnetic metals have the advantages of high permeability and low magnetic loss, but have the disadvantage of high power loss owing to eddy current that is induced on the surface as a result of low-insulating characteristics. In order to solve this problem, a patterned soft magnetic metal was used to cut the route of the induced current. This decreases the power loss and reduces the leakage of magnetic field. A soft-magnetic-metal-based structure that has various patterns was designed to find the optimal structure for reducing the leaking magnetic field. By applying this structure to Wireless Power Consortium commercial A10 coil, the inductance, transfer efficiency, and magnetic flux leakage of the coil according to the material and the structure of the soft-magnetic-metal-based structure were observed. Fabrication and measurement tests were performed to verify the proposed structure, and it was found that the test results corresponded to the simulation results. It was confirmed that the proposed structure had a 84% thinner thickness compared with that of a conventional ferrite shield, an equivalent transfer efficiency of 74.5%, and a reduction in magnetic flux leakage of 20.9%.

The Van Veen loop is intrinsically well adapted to time-domain measurements of net magnetic dipole moment. That is, the system comes very close to preserving the shape of the time-domain waveform of the net or residual magnetic dipole moment produced by the device under test. This property makes the Van Veen Loop very useful in the characterization of magnetic field wireless power transfer systems in which short-time-scale features such as ringing in inverter and rectifier circuits are present in the extraneous magnetic field. We present a unified derivation of the frequency response of the internal coaxial structure of the Van Veen loop showing explicitly why the system intrinsically provides nearly flat frequency response and hence distortionless time response. Additionally, we present two simple modifications to the internal circuitry, which further improve the time- and frequency-domain performance of the system to the extent that it approaches having a distortionless transfer function. A physical explanation for the mechanism by which the time-domain performance is improved is provided. This argument is based on the source termination in a time-domain transmission line analysis. Finally, an alternative frequency-domain analysis based on the high-pass Kuroda transform is given, which provides significant insight into the operation of the distortionless system.

In this paper, an efficient mesh-free method (MFM) is introduced to evaluate the shielding effectiveness of a metallic enclosure with aperture. To this end, equivalent magnetic current densities and their relative electrical vector potentials are assumed on both sides of the aperture. Magnetic current of each side is related to its vector potential, using an integrating operator including proper Green's functions. Then, the electromagnetic field at each side is obtained by a differential operation on its respective electrical vector potential. Enforcing the continuity of the tangential magnetic and electric fields on the aperture leads to two decoupled differential and integral equations that are solved together by using proper shaping functions for the assumed magnetic currents and electrical vector potentials at the defined nodes. The proposed method is validated by the commercial software FEKO and measurements. In addition, it is shown that the proposed MFM is very efficient compared to two similarly formulated efficient method-of-moments-based methods.

A numerical method for computation of the resultant quasi-static magnetic field in the vicinity of parallel wires and metal shields is presented. The primary magnetic field source is time-harmonic currents in wires. This field is modified by conducting magnetic and/or nonmagnetic shields. The material is assumed to be linear under the applied source field. The shielding effectiveness can be estimated by a comparison between the primary and the resultant field. The reaction magnetic field is expressed by a sum of fields caused by equivalent single- and double-layer sources distributed on the shield surface. Integral equations for unknown distributions of these equivalent sources are derived from the Green's second identity implemented inside and outside the shields. These equations are coupled integral equations, and are solved by the moment method. Numerical results of the resultant (shielded) magnetic field obtained with the proposed method are compared with the results of: 1) analytically solvable problems; 2) measurements; and 3) two different numerical methods.

A previously proposed simple method to characterize magnetic fields near electric appliances was extended to intermediate frequencies of up to 100 kHz. The method consists of identification of the magnetic dipole moment that is equivalent to a magnetic field source of an electric appliance and simple estimation of the magnetic field distribution around the appliance. In addition, frequency characteristics of the magnetic field were taken into account by considering the harmonic components in the magnetic-field waveform for both power frequency and intermediate frequency ranges. For the application of the method, a wide-frequency range (from power frequency to 100 kHz) magnetic-field measuring instrument was developed and applied to appliances that generate intermediate frequency magnetic fields, i.e., an induction heating cooker, a TV set, and a metal detector. The results revealed that the method is adequate to quantify the magnetic field near the electric appliances at frequencies of up to 100 kHz.

A simple method of quantifying the ELF (extremely low frequency) magnetic field distribution around electric appliances, which takes the harmonics into account, is newly proposed. The proposed method involves: (1) a simple estimation of the position of an equivalent magnetic dipole moment inside an appliance, using two magnetic field meters; (2) identification of the amplitude of the dipole moment magnetic-field measurements at certain points; and (3) calculation of the magnetic field distribution around the appliance using the estimated dipole moment. In this method, the dipole moment vector is assumed to be a similar value by allowing an uncertainty of 6 dB in the estimated magnetic field, which enables easy estimation of the dipole moment. In addition, the frequency characteristics of the magnetic field are taken into account by considering the harmonic components in the magnetic field waveform. The proposed method was applied to 13 types of appliances, and their equivalent magnetic dipole moments and harmonic components were determined. The results revealed that the proposed method is applicable to many electric appliances. The conditions required for the adoption of the method were also clarified.

During geomagnetic disturbances voltages are induced in electrically conducting networks such as power systems, pipelines, and phone cables. The voltage produced in a horizontal loop at the Earth's surface can be calculated by considering the changing vertical magnetic field through the loop or by calculating the electric field around the loop from the horizontal magnetic field variations. The two approaches are equivalent, both being a consequence of Maxwell's equations, however, this equivalence is difficult to visualize. By considering the nondivergent nature of the magnetic field, it is shown how the vertical magnetic field through a horizontal loop is related to the horizontal magnetic field at the periphery of the loop. The case of a magnetic disturbance due to a line current above the earth's surface is used to illustrate the equivalence of the two approaches for calculating the voltage induced in a conducting network.

Discusses signal solutions to Maxwell's equations for charge carriers with non-negligible mass. In order to find solutions the authors add information to Maxwell's equations by means of a physical assumption to obtain a defined solution. The authors' assumption is that magnetic dipoles and magnetic dipole currents should be represented by a magnetic (dipole) current density term just as electric dipoles and electric dipole currents-or electric polarization currents-have always been represented by an electric current density term. It is perfectly possible that other physical assumptions can be made that yield defined solutions and that will withstand public scrutiny. >

The author comments on issues brought up by P. Hillion and M.F. Harmuth (see ibid., vol.33, no.2, p.144-5, 1991) regarding the need to have a magnetic conductivity term in the formulation for pulse transmission. The initial boundary problem and the question of deriving the magnetic field from the electric field for pulse transmission in homogeneous lossy media are discussed. >

For pt.II see ibid., vol.30, no.1, p.37-40 (1988). The representation of a function with a general time variation by a series expansion of time-shifted transients is discussed. On the basis of this representation, numerical solutions of Maxwell's equations are presented for the electric and magnetic field strengths in a lossy medium due to electric and magnetic excitation functions consisting of a finite number of sinusoidal cycles. The solutions are derived by means of a time-series expansion of the available solutions for the electric and magnetic exponential ramp function excitations. >

For pt.I see ibid., vol.30, no.1, p.29-36 (1988). Solutions for the electric and magnetic field strengths in a lossy medium due to a magnetic exponential ramp function excitation are presented. The solutions are in integral form and are evaluated by numerical integration methods using a digital computer. Computer plots for the electric and magnetic field strengths at different locations in the propagation medium are given. The plots obtained for the transients can be used to represent solutions in lossy media for signals that can be represented in terms of a time-series expansion of the transients. >

Additional comments on an ongoing controversy on Maxwell's equations are presented. Harmuth (see ibid., vol.EMC-30, no.1, p.90, 1988) claims that three scientists searching through Stratton's (1941) book could not find equations for the magnetic field strength associated with an electric excitation force or the electric field strength associated with a magnetic excitation force. >