The effects of eddy currents in transformer windings are considered, and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings. The method consists in dividing the winding into portions, calculating the d.c. resistances and d.c. leakage inductances of each of these portions, and then multiplying the d.c. values by appropriate factors to obtain the corresponding a.c. values. These a.c. values are then referred to, say, the primary winding and summed to give the total winding resistance and leakage inductance of the transformer. Formulas are derived and quoted for calculating the d.c. resistances and leakage inductances of the winding portions. Theoretical expressions are derived for the variation with frequency etc. of the factors by which the d.c. values must be multiplied to obtain the corresponding a.c. values. These expressions are presented in the form of graphs, permitting the factors to be read as required.

Effects of eddy currents in transformer windings

A form of circuit which is of considerable interest for the transmission of high frequency currents is one consisting of a cylindrical conducting tube within which a smaller conductor is coaxially placed. Such tubes have found application in radio stations to connect transmitting and receiving apparatus to antennae. As a part of the development work on such coaxial systems, it has been necessary to formulate the theory of transmission over a coaxial circuit and of the shielding against inductive effects which is afforded by the outer conductor. This paper deals generally with the transmission theory of coaxial circuits and extends the theory beyond the range of present application both as regards structure and frequency.

The electromagnetic theory of coaxial transmission lines and cylindrical shields

Inductive power transfer (IPT) systems for transmitting tens to hundreds of watts have been reported for almost a decade. Most of the work has concentrated on the optimization of the link efficiency and has not taken into account the efficiency of the driver. Class-E amplifiers have been identified as ideal drivers for IPT applications, but their power handling capability at tens of megahertz has been a crucial limiting factor, since the load and inductor characteristics are set by the requirements of the resonant inductive system. The frequency limitation of the driver restricts the unloaded Q-factor of the coils and thus the link efficiency. With a suitable driver, copper coil unloaded Q factors of over 1000 can be achieved in the low megahertz region, enabling a cost-effective high Q coil assembly. The system presented in this paper alleviates the use of heavy and expensive field-shaping techniques by presenting an efficient IPT system capable of transmitting energy with a dc-to-load efficiency above 77% at 6 MHz across a distance of 30 cm. To the authors knowledge, this is the highest dc-to-load efficiency achieved for an IPT system without introducing restrictive coupling factor enhancement techniques.

/pdf/maximizing-dc-to-load-efficiency-for-inductive-power-59f4ma5xmj.pdf

Maximizing DC-to-Load Efficiency for Inductive Power Transfer

The addition of an auxiliary quartz crystal to the usual composite piezoelectric resonator provides a convenient strain gauge, which simplifies the measurement procedure and permits the evaluation of amplitude dependent decrements over a wide range of strain amplitudes. A unique feature of the new procedure is that virtually instantaneous values of the decrement are obtained, thus bringing transient internal friction phenomena under observation. Mechanical resonance frequencies may be precisely determined for high as well as low decrement specimens. The numerical evaluation of terms is carried out for a recommended driver‐gauge construction of 18.5° X‐cut quartz bars.

Use of the Piezoelectric Gauge for Internal Friction Measurements

Alkali-metal magnetometers use the coherent precession of polarized atomic spins to detect and measure magnetic fields. Recent advances have enabled magnetometers to become competitive with SQUIDs as the most sensitive magnetic field detectors, and they now find use in a variety of areas ranging from medicine and NMR to explosives detection and fundamental physics research. In this thesis we discuss several developments in alkali-metal atomic magnetometry for both practical and fundamental applications. We present a new method of polarizing the alkali atoms by modulating the optical pumping rate at both the linear and quadratic Zeeman resonance frequencies. We demonstrate experimentally that this method enhances the sensitivity of a potassium magnetometer operating in the Earth’s field by a factor of 4, and we calculate that it can reduce the orientation-dependent heading error to less than 0.1 nT. We discuss a radio-frequency magnetometer for detection of oscillating magnetic fields with sensitivity better than 0.2 fT/ √ Hz, which we apply to the observation of nuclear magnetic resonance (NMR) signals from polarized water, as well as nuclear quadrupole resonance (NQR) signals from ammonium nitrate. We demonstrate that a spin-exchange relaxation-free (SERF) magnetometer can measure all three vector components of the magnetic field in an unshielded environment with comparable sensitivity to other devices. We find that octadecyltrichlorosilane (OTS) acts as an anti-relaxation coating for alkali atoms at temperatures below 170◦C, allowing them to collide with a glass surface up to 2,000 times before depolarizing, and we present the first demonstration of high-temperature magnetometry with a coated cell. We also describe a reusable alkali vapor cell intended for the study of interactions between alkali atoms and surface coatings. Finally, we explore the use of a cesium-xenon SERF comagnetometer for a proposed measurement of the permanent electric dipole moments (EDMs) of the electron and the 129Xe atom, with projected sensitivity of δde=9×10−30 e-cm and δdXe=4×10−31 e-cm after 100 days of integration; both bounds are more than two orders of magnitude better than the existing experimental limits on the EDMs of the electron and of any diamagnetic atom.

Developments in alkali -metal atomic magnetometry

https://iopscience.iop.org/article/10.1088/1478-7814/27/1/330/pdf

On Electrically-maintained Vibrations

It is well-known that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance. It is therefore important to have reliable formulae for the eddy-current resistance of such coils in order to determine the conditions which will reduce the eddy-current losses to a minimum. The simplest case, that of a long straight cylindrical wire under the action of its own current, has been treated by Kelvin, Rayleigh, Heaviside, and others. The general effect is known as the “skin effect,” because the current tends to concentrate more and more upon the skin of the conductor as the frequency increases.

Eddy-Current Losses in Cylindrical Conductors, with Special Applications to the Alternating Current Resistances of Short Coils

In a paper published some time ago by the present writer a formula was given for computing the alternating current resistance of single-layer coils in which the spacing of the wires is not too close. Recently Mr. C. N. Hickman has made a comparison between the measured and computed values of the resistance of solenoidal coils and has used the above formula. Owing mainly to a misconception in regard to the scope of the formula, he came to the conclusion that the formula could be in error by as much as 300 per cent. It has been pointed out, however, that when the formula is legitimately applied the discrepancy is reduced to 30 per cent. In order to account for the outstanding difference it is necessary to extend the theory so as to include closely wound coils. This extension has been made in the present paper, with the result that the difference between theory.

On the Alternating Current Resistance of Solenoidal Coils

The Joule effect in magnetostriction is defined by the relation S = λB, where S is the stress produced by a small increment of induction B of an existing induction B0; and the converse effect by the relation H = κξ, where H is the magnetic field produced by a small strain ξ. Conservation of energy requires that κ = 4πλ. These equations are used in investigating the motion of a magnetostriction oscillator consisting of a closed circular ring inside a toroid, eddy currents and hysteresis being taken into account. It is shown that the oscillator can be represented by an equivalent electrical circuit comprising a pair of parallel impedances Zc, Zm, in series with an impedance Zl, where Zl represents leakage impedance and Zc impedance due to core flux in the absence of motion, while Zm is a resonant shunt to Zc and represents the effect of the motion. Expressions for the elements of the circuit in terms of the fundamental constants of the material are given. The circle-diagram of impedances is deduced, and the modifying effects of eddy currents and hysteresis are investigated. Some simple geometrical relations between the vectors in the diagram are derived. It is shown that the size of the circle diagram for solid material having a large value of λ depends mainly upon permeability and resistivity and only slightly upon λ, and that a high degree of resonance may be associated with poor magnetostriction quality; the circle-diagram may, in fact, lead to erroneous conclusions unless interpreted in the light of an adequate theory. An experimental investigation of the resonant radial vibrations of solid and laminated nickel rings verifies the theoretical deductions and leads to numerical values of λ and κ in agreement with values deduced from the work of Masumoto and Nara and of McKeehan and Cioffi. For nickel in the annealed state, λ=1.76×104 and κ = 22.1 × 104 at a point on the curve corresponding to H0 = 14.5 gauss.

https://iopscience.iop.org/article/10.1088/0959-5309/43/2/307/pdf

The equivalent circuit of the magnetostriction oscillator

The methods usually employed in the determination of the constants of a vibration galvanometer involve the measurement of a deflection under three different conditions. Two of these deflections can only be obtained very approximately. By extending the theory of the vibration galvanometer it is shown how the constants may be determined by methods which involve only the measurement of one deflection. The remaining measurements are carried out on an alternating-current bridge, and the results obtained are practically independent of the wave-form of the source. The principle of the method depends on the fact that a vibration galvanometer behaves as a parallel combination of a conductance, a capacity and an inductance, in series with a resistance. It is shown how to balance such a combination, and the method is illustrated experimentally. The constants of various galvanometers are quoted in order to show the applicability of the method. Other uses of the bridge are suggested.

/pdf/on-a-null-method-of-testing-vibration-galvanometers-11ftb625n1.pdf

S Butterworth

Papers

On Electrically-maintained Vibrations

Eddy-Current Losses in Cylindrical Conductors, with Special Applications to the Alternating Current Resistances of Short Coils

On the Alternating Current Resistance of Solenoidal Coils

The equivalent circuit of the magnetostriction oscillator

On a Null Method of Testing Vibration Galvanometers