General Formulas for the Average Magnetic Field at a Receiving Circular-Loop Antenna Placed Arbitrarily to a Radiating Loop

For testing the sensitivity of receivers having loop antennas, radiating and receiving loops have been located either coplanar or coaxial to each other. Theoretical analyses of the magnetic fields have been carried out for such alignments of loops. It is often necessary in the actual tests to estimate the effects of deviations from these ideal arrangements of the loops. In this paper, the radiating and receiving circular loops are located arbitrarily in direction, and a formula is derived to obtain the average normal component of the magnetic-field strength incident on the receiving loop using the Eulerian angles. The theory is applied to the design of a generator in which a rotating field is used as the standard field. In this case, the calculated values of the magnetic field are in agreement with the measured ones to within ±0.1 dB.