^{1,a)}, E. Martínez

^{2}and W. T. Norris

^{3}

### Abstract

Pickup coils are widely used for measurements of magnetic susceptibility and hysteretic losses in magnetic and superconducting materials. A general formulation for the calibration of such pickup coils with different geometries is presented. Although the procedure described here is general and can be applied to any coil and sample, special emphasis has been placed on the calibration of saddlelike coils usually used to measureac losses of long superconductors under ac fields perpendicular to their long dimension. Numerical simulations and experimental measurements have been carried out in order to determine the geometrical limitations of the pickup coil/sample configurations. This is especially important when simple coils of small dimensions and number of turns are used and/or samples of high demagnetization factor are measured.Superconductors of different geometry, in particular, wires and tapes under parallel and perpendicular fields, have been analyzed.

I. INTRODUCTION

II. METHODS

III. CALIBRATION OF PICKUP COILS FOR ac LOSS MEASUREMENT

A. Analytical relation for proportionality constant of pickup coils

B. Application to ac loss measurement on tapes

IV. VERIFICATION AND ERROR ESTIMATION WITH SIMULATED CONDUCTORS

A. Tapes under perpendicular fields

B. Tapes under parallel fields

V. EXPERIMENTAL TRIALS

A. Perpendicular fields

B. Parallel fields

VI. CONCLUSION

### Key Topics

- Alternating current power transmission
- 18.0
- Calibration
- 12.0
- Electric measurements
- 10.0
- Magnetic susceptibility measurements
- 10.0
- Superconductors
- 7.0

## Figures

Scheme of single-turn (a), (b) and multipleturn (c) saddlelike pickup coils used to measure ac losses in long superconductors.

Scheme of single-turn (a), (b) and multipleturn (c) saddlelike pickup coils used to measure ac losses in long superconductors.

Schematics of theoretical and practical configurations for the measurement of ac losses and magnetization, where (a) shows an external sinusoid field of amplitude generated by a source solenoid coil with a sinusoidal current of amplitude from a current source at a voltage . (b) indicates a change in the voltage by at the current source when a magnetic sample is introduced in ac field . It is noted that is generally many orders of magnitude greater than . (c) replaces the source coil with a simple coil; an ac current is now required to produce the same field from the current source at a voltage . In (d) the voltage change due to a magnetic sample is comparable to . It is noted, however, that the current required to generate an useful applied field with such a simple coil is often too high to be practical. (e) shows the practical solution of maintaining the source solenoid coil for field generation and using the simple coil as the pickup to measure the magnetic signal from the sample against a background inductive pickup of similar magnitude.

Schematics of theoretical and practical configurations for the measurement of ac losses and magnetization, where (a) shows an external sinusoid field of amplitude generated by a source solenoid coil with a sinusoidal current of amplitude from a current source at a voltage . (b) indicates a change in the voltage by at the current source when a magnetic sample is introduced in ac field . It is noted that is generally many orders of magnitude greater than . (c) replaces the source coil with a simple coil; an ac current is now required to produce the same field from the current source at a voltage . In (d) the voltage change due to a magnetic sample is comparable to . It is noted, however, that the current required to generate an useful applied field with such a simple coil is often too high to be practical. (e) shows the practical solution of maintaining the source solenoid coil for field generation and using the simple coil as the pickup to measure the magnetic signal from the sample against a background inductive pickup of similar magnitude.

Numerically calculated errors, , of estimating ac losses of tapes under perpendicular fields with Eq. (6) for single-turn coils of different width, . Different tape side ratios, (squares) and (circles), have been considered. The results correspond to saturation field (full symbols) and (open symbols).

Numerically calculated errors, , of estimating ac losses of tapes under perpendicular fields with Eq. (6) for single-turn coils of different width, . Different tape side ratios, (squares) and (circles), have been considered. The results correspond to saturation field (full symbols) and (open symbols).

(a) Errors calculated for a tape of under perpendicular ac fields using coils of different dimensions and with (a) infinite number of turns , Eq. (9). The lines are the errors for a single-turn coil and the shaded areas in the basal plane are the configurations that give errors higher than . (b) Finite number of turns, , Eq. (8). Light gray and dark gray surfaces correspond to and , respectively. A reference plane at is plotted.

(a) Errors calculated for a tape of under perpendicular ac fields using coils of different dimensions and with (a) infinite number of turns , Eq. (9). The lines are the errors for a single-turn coil and the shaded areas in the basal plane are the configurations that give errors higher than . (b) Finite number of turns, , Eq. (8). Light gray and dark gray surfaces correspond to and , respectively. A reference plane at is plotted.

Calculated errors estimated using Eq. (6) to obtain losses of tapes under parallel fields using single-turn pickup coils of different dimensions, . Different tape side ratios, (□) and (▵), have been considered. The results correspond to the saturation field (full symbols) and (open symbols).

Calculated errors estimated using Eq. (6) to obtain losses of tapes under parallel fields using single-turn pickup coils of different dimensions, . Different tape side ratios, (□) and (▵), have been considered. The results correspond to the saturation field (full symbols) and (open symbols).

Calculated errors of the losses estimated using Eq. (11) for tapes under parallel fields using single-turn pickup coils of different dimensions, . The same symbols as in Fig. 4 have been used.

Calculated errors of the losses estimated using Eq. (11) for tapes under parallel fields using single-turn pickup coils of different dimensions, . The same symbols as in Fig. 4 have been used.

(a) Calculated errors of the losses estimated using Eq. (9) for a tape of under parallel fields using pickup coils of infinite number of turns and different dimensions. The solid and dashed lines correspond to errors of 5% and , respectively. (b) Errors of using Eq. (8) for narrow coils as a function of . Different values of the applied parallel fields (full symbols) and (open symbols); and tape aspect ratios 30 (circles) and 10 (squares) have been considered.

(a) Calculated errors of the losses estimated using Eq. (9) for a tape of under parallel fields using pickup coils of infinite number of turns and different dimensions. The solid and dashed lines correspond to errors of 5% and , respectively. (b) Errors of using Eq. (8) for narrow coils as a function of . Different values of the applied parallel fields (full symbols) and (open symbols); and tape aspect ratios 30 (circles) and 10 (squares) have been considered.

(a) Experimentally measured losses of the tape under perpendicular ac fields using a narrow planar coil (circles), a wide planar coil (triangles), and a solenoid coil of eight turns (line). The ratio between the losses measured with the one-turn coils and the eight-turn coil are plotted in (b).

(a) Experimentally measured losses of the tape under perpendicular ac fields using a narrow planar coil (circles), a wide planar coil (triangles), and a solenoid coil of eight turns (line). The ratio between the losses measured with the one-turn coils and the eight-turn coil are plotted in (b).

(a) Experimentally measured losses of the tape under parallel ac fields using a narrow planar coil (circles), a wide planar coil (triangles), and a solenoid coil of eight turns (line). The ratio between the losses measured with the one-turn coils and the eight-turn coil are plotted in (b).

(a) Experimentally measured losses of the tape under parallel ac fields using a narrow planar coil (circles), a wide planar coil (triangles), and a solenoid coil of eight turns (line). The ratio between the losses measured with the one-turn coils and the eight-turn coil are plotted in (b).

## Tables

Recommended pickup coil configurations for ac loss measurements.

Recommended pickup coil configurations for ac loss measurements.

Characteristics of conductor used in experimental trials

Characteristics of conductor used in experimental trials

Experimental details for the tested pickup coils. in , in ; in .

Experimental details for the tested pickup coils. in , in ; in .

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