Calculation Of Mutual Inductance Research Articles

VALIDITY CHECK OF MUTUAL INDUCTANCE FORMULAS FOR CIRCULAR FILAMENTS WITH LATERAL AND ANGULAR MISALIGNMENTS

In this paper we derived the formula for calculating the mutual inductance between circular fllaments with lateral and angular misalignment by using the approach of the magnetic vector potential. The results obtained correspond to those of F. W. Grover, although the latter used the general formula given by the Neumann integral instead of a vector potential approach. However, the major purpose of this paper is to clarify some confusion introduced in previous works regarding the mutual inductance calculation between thin fllamentary circular coils with parallel axes in air. This problem has been solved by Kim etal. (8) using the magnetic vector potential, but unfortunately it leads to erroneous results, even for slight misalignments of the coils' center axes. This is why we chose to use the approach of the magnetic vector potential to show that, when properly derived, the results must indeed reduce to the well known F. W. Grover's formulas.

Quantitative Magnetic Immunoassays With a SQUID by Means of Mutual Inductance Calculations

We recently developed a SQUID system for magnetic immunoassays which allows fast measurements of the remanent magnetization of samples containing magnetic particles used as markers in biomedical applications. In this paper, we propose to quantify the immunoassays by estimating the specific magnetization of the samples, after magnetic flux measurements and remanent magnetic moment calculations. Since the SQUID and the sample have about the same size, we need to take into account their geometries in order to calculate properly their magnetic moments. This is accomplished by means of mutual inductance calculations. The values for the mass of particles obtained from the specific magnetization are compared with those estimated by using sample dilution factors.

CAD formula for inductance calculation of double‐level square spiral inductors

AbstractThis article derives simple CAD inductance formula of double‐level spiral inductors by analytical moment method, synthetic asymptote, and the duality of inductance and capacitance LC = μ0ε0 of the transmission line theory. The main contribution of this article is the mutual inductance calculation of the upper and lower spirals. Compared with IE3D, commercial software by Zeland, the average error of inductance is generally less than 2% with maximum error of 5%. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2648–2651, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22807

A comparison of single-layer coaxial coil mutual inductance calculations using finite-element and tabulated methods

Quick and accurate methods to calculate the mutual inductance of coaxial single layer coils remains important to this day in a large variety of engineering and physical disciplines. While modern finite-element electromagnetic field codes can do this accurately, the engineer often requires only a first- or second-order estimate before proceeding to the numerical analysis stage. Grover's tabular data, developed in the first half of the 20th century, remains the standard for manually calculating mutual inductance for a wide variety of coil and wire forms. This investigation reports the accuracy of mutual inductance calculations for single-layer coaxial coils based on Grover's tables when compared to estimates obtained with a finite-element electromagnetic field code (FEEFC). Since it is impractical to construct and characterize the numerous coils needed for this type of investigation, the FEEFC results are treated as actual inductance measurements. Grover reported his tabular data to be accurate within five significant digits excluding the cases when the coils are loosely coupled and when the coils are short. This investigation found Grover's tabular method to be inaccurate for loosely coupled and short coils, but also found that significant error for closely coupled coils as well. The maximum error between Grover's tabular method and the FEEFC results is 9.8%. Knowing the error associated with Grover's method and the coil geometry for which the error occurs is an important aid for the engineer and scientist.

New Mutual Inductance Calculation of the Magnetically Coupled Coils: Thin Disk Coil-Thin Wall Solenoid

This paper deals with new expressions for calculating the mutual inductance between thin wall solenoids and thin disk coils in air. This original method which appears in this mathematical form for the first time may seem complicated but it is exact and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Neumann's Lambda function and one member that has to be solved numerically. Results of the presented approach are compared to results obtained by the well-known filament method regarding the accuracy and computational cost. Also results of this approach are compared to previously published data These new expressions are accurate and simple for useful applications and they considerably reduce computational time.

Four coplanar superconducting strips: flux-focusing effects and inductance

We present analytic solutions for the Meissner-state magnetic-field and current-densitydistributions for four long parallel coplanar superconducting strips carrying subcriticalcurrents in a perpendicular magnetic field when there is no net magnetic flux throughthe two slots between the outermost strips. We make use of these solutions toinvestigate the flux-focusing effect; i.e., we calculate how much magnetic flux per unit length is focused into the central slot when the strips are in a perpendicular magnetic fieldHa = Ba/μ0 and the outermost pairs of strips carry no net current. We also calculate the inductance perunit length of the system when the net current flowing in the two right strips is equal inmagnitude and but opposite in direction to the net current flowing in the two left strips.We show that for narrow superconducting strips mutual-inductance calculations based onexact results for two strips provide good approximations to our exact results for four strips.

Induced voltage and alternating current loss in superconducting magnet system for SSTF

The induced voltage in the Samsung Superconducting Test Facility (SSTF) is analyzed according to the calculation of self-inductance and mutual inductance. The voltage induced by blip and compensating coils in the main coils is about 6.4 V. In order to charge the main coils, the power supply must provide the minimum voltage of 1.1 kV. The compensating coils have an influence on the field distribution. The compensating coils result in the decreasing center field about 2.67%. AC losses that include the coupling, hysteresis and eddy losses are calculated in the main, blip and compensating coils. It leads to the temperature rise of about 8 K in main coils.

Calculation of self and mutual inductances and 3-D magnetic fields of chokes with air gaps in core

This work deals with the analysis of 3-D magnetic field in electric choke (reactor) with two windings. The analysis is related to the solutions of Laplace's and Poisson's equation by the Finite Element Method. The package OPERA-3d has been used. The self and mutual inductances of windings, which are connected in series aiding as well as in series opposing, have been determined. The calculation results of magnetic flux density components and the inductances are compared with the measured values.

Improvement in calculation of the self- and mutual inductance of thin-wall solenoids and disk coils

The self-inductance expressions given by Yu and Han (1987) for air-core circular coils with rectangular cross sections, thin solenoids, and disk coils can be solved only by the numerical integration methods. We propose as an alternative a combined analytic and numeric approach. The approach brings some improvement in the calculations of self-inductance of thin-wall solenoids and disk coils that can be encountered in superconducting magnetic energy storage (SMES) problems. We also give a method for the calculation of mutual inductance of disk coils and of thin-wall solenoids. The results are obtained in an analytical form over the complete elliptic integrals of the first and second kind and Heuman's Lambda function. It is important to mention that the kernels of these integrals are always continuous functions on intervals of integration, so singularities are avoided. The results enable one to calculate the self-inductance and the mutual inductance of any thin air-core coil precisely and fast. For practical applications, the results are so simple to use that we recommend them to avoid the problems of solving the singular cases.

Analysis of Multi-Pin Modular Daughterboard-to-Backplane Connectors at High Bit Rate Signals

A theoretical model for the electrical characterization of multi-pin modular daughterboard-to-backplane connectors at high bit rate signals is developed. The fundamental field equations are transformed into a linear system of equations for the currents and voltages at the edges of the pins of the connector.Efficient formulaes for the calculation of self and mutual inductances and capacitances between the pins which are involved in the linear system of equations are obtained. Using the previous developed theoretical model the connector's performance can be examined in both the frequency and the time domain.Numerical calculations are performed for three types of existing connectors. Furthermore, they are compared to each other for bit-rates in the range of 100 Mbits/sec up to 500 Mbits/sec.

Calculation of mutual inductances by means of the toroidal multipole expansion method

A method is proposed for the calculation of mutual inductances in axisymmetric iron-free current systems. It is based on a toroidal multipole expansion of the magnetic flux function. The mutual inductance is expressed by means of a series of toroidal multipole moments of the two currents. Each term of the series is the product of the internal moment of one of the two currents and the corresponding external moment of the other one. The method can be applied to any axisymmetric current system independently of the current distribution. An example application is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Explaining reversal in half a population of magnetic dipoles

At a critical magnetic field certain dipole arrays surprisingly switch from full to half-alignment. The result is explicable by mutual inductance calculations for expanding current-loopdipoles. A known triangular lattice configuration becomes energetically unfavourable as its loops expand and nearly touch. Mutual inductance plunges negatively as opposed current-elements near the touching point.

Inductive interaction between polarizable conductors: An explanation of a negative coincident‐loop transient electromagnetic response

Theoretically, the coincident‐loop transient electromagnetic (TEM) voltage responses of an earth with frequency‐invariant conductivities and permeabilities cannot change sign. In Australia, where prospecting is often done with the SIROTEM system operating in coincident‐loop mode, the response occasionally changes sign at late times from the normal positive transient to negative values. Because it has been shown that the observed negatives cannot be explained by poor instrument design, normal displacement currents, dispersive permeabilities, or geometric effects, the mechanism causing the negatives is now inferred to be a frequency dependence (dispersion) of the conductivity. To obtain negative values, the conductivity must increase with frequency over the spectral range covered by the TEM survey (∼10–1000 Hz). Slightly dispersive conductivities are observed by induced‐polarization (IP) surveys and are geologically common; however, field experience suggests that whereas some negatives are associated with IP anomalies, others are not. We present an interpretation of SIROTEM field data in which a negative response is observed between the positive responses of two steeply dipping conductors. Although no IP survey has been performed in this area, field experience in similar areas suggests that a significant IP anomaly is not likely to be directly associated with the negative anomaly. The negatives in the field data can be explained (i) if at least one of the two conductors is moderately dispersive in the frequency range 10–1000 Hz and (ii) if the inductive coupling between the conductors is taken into account. The magnitude of the dispersion is such that no significant IP anomaly would be measured in the region where the TEM negative transient is observed. The least complicated model that can fit the field data comprises two circular, polarizable wire‐filament circuits, which are inductively coupled to each other. The geometry of the field situation has been accounted for quantitatively by mutual inductance calculations, but the conductivity and polarizability of the bodies are modeled only in terms of simple circuit analogies.

Numerical calculation of self and mutual inductances

The magnetic field due to a circular current‐carrying coil placed in air is determined numerically by the method of finite differences. The magnetic field due to an air‐core solenoid is determined by superposition. The self or mutual inductance is calculated by considering the flux linking the solenoid concerned. Computed results are compared with results obtained by conventional methods and experiments.

Calibration of ac susceptometer for cylindrical specimens

The absolute magnetic susceptibility of cylindrical specimens is obtained with an ac susceptometer whose calibration is based on a calculation of mutual inductance. An axially magnetized cylinder is modeled as a solenoid of the same size. The mutual inductance between such a solenoid and a pickup coil of arbitrary dimensions is computed. The susceptibility is then a function of the mutual inductance, the cylinder length, the magnitude and frequency of the ac magnetizing field, and the voltage induced on the pickup coil. Demagnetization factor and eddy-current effects are considered, an example is given, and pickup coil compensation is discussed. Other calibration methods are also presented.

New Tables for the Mutual Inductance of Coaxial Cylindrical Coils

Tables for the calculation of mutual inductance be· tween coaxial cylindrical coils are presented. 'They are based on electromagnetic theory formulas, which, while available for quite time, have not hitherto been tabulated. The use of these tables is explained by examples and definitions of the tabulated functions are given.

Calculation of Fields, Forces, and Mutual Inductances of Current Systems by Elliptic Integrals

A minimum-ordered set of elliptic integral equations is given for magnetic vector potential, axial and radial fields, the mixed gradient ∂Bρ/∂z for axially symmetric iron-free current systems, and for mutual inductance and force between coaxial units. The units may be circular loops, cylindrical or plane annular current sheets, or coils of thick section. With full use of correlations, six basic equations suffice for all properties of loops, solenoids, or combinations. The axial solenoid field is calculated by a superior new method. Thick coils are analyzed with the solenoid rather than the loop as element. Magnetic properties are then integrated in radial depth by Gaussian numerical quadrature of variable order. This method can deal with coils whose sections are not rectangular, and whose current densities are a function of the cylindrical radius. No tables are used, and the procedure is simpler and faster than previous methods, for computer use or for solving smaller problems by hand. It has been coded as a unified set of programs for the IBM 7090. These will be described elsewhere; they can compute fields, and trace lines of force even within the windings, or force and mutual inductance between coils in contact, also self-inductance of ideal solenoids or of thick cylindrical coils. Errors are normally less than one part per million, in extreme cases less than one per thousand.

Mathematical Analysis of Inductor Alternators

A mathematical analysis has been put forward to analyze a 3-phase inductor alternator. Although one particular type of inductor alternator within the frequency range of 400-800 cps (cycles per second) has been analyzed in this paper,1 with suitable modifications, this analysis can be extended to other type of inductor alternators. This analysis is based on the calculation of self and mutual inductances of the coils, and so is quite suitable to analyze the machine under transient conditions.

Inductance Calculations

PROF. F. W. GROVER, makes an authoritative selection among the numerous formulæ which have been suggested for the calculation of mutual and self inductances. He does not attempt proofs of the formulæ, but gives adequate references to the original papers. He gives sufficient explanation of general principles to allow the adaptation of the formulæ to particular cases which are not directly covered (an improbable contingency, however). As the majority of exact formulæ are cumbersome to use, he usually offers numerical tables giving an accuracy of 1 in 1,000 or better, with some indication of the accuracy. Where interpolation between tabulated values would be inaccurate, he gives either alternative formulæ or tables using a different argument. Every likely shape and relative disposition of circuit element is included. There are formulæ for deeply wound coils, and for coils of spaced turns of round wire or of flat tape. The discussion of inductance at high frequencies is less precise than the rest of the book—excusably so, in view of the uncertain effects of self-capacitance. (Here is a field for some useful new work.) The mechanical forces between inductors are also calculated. Inductance Calculations Working Formulas and Tables. By Prof. Frederick W. Grover. Second printing. Pp. xii + 286. (New York : D. Van Nestrand Co., Ltd., 1947.) 31s. 6d. net.

The computation of the integrals required in mutual-inductance calculations

A method, based on the reduction of classical formulae, whereby the numerical computation of complete elliptic integrals of the third kind can be considerably simplified in certain cases is suggested. A particular case considered in detail is that which arises in the calculation of the mutual inductance of a helix and a coaxial circle. A considerably simplified formula, well adapted for numerical working, is deduced, together with an extremely simple result for the case when the helix and circle have the same radius.