The mutual impedance between two small circular loop antennas

In this work an analytical expression is obtained for the mutual impedance between two small circular loop filamentary antennas having various orientations and a method is outlined to determine the mutual impedance between two circular loop filamentary antennas of any diameter and orientation when the current distribution on each antenna is known. Antenna orientations are divided into three classifications designated as case 1, case 2 and case 3. In each case it is assumed that the first antenna is centered at the origin of a spherical coordinate system and that the second antenna is either completely exterior to or interior to the sphere r = r₀ where r₀ is the radius of the first antenna. Case 1, case 2, and case 3 are defined as follows: Case 1 is the orientation where the antennas are parallel and coaxial. Case 2 is the orientation where the antennas are not parallel but all points of the second antenna lie on a sphere which is concentric with the first antenna. Case 3 is the general orientation case where the second antenna can have any orientation with respect to the first antenna. Laboratory measurements were made for each of the three cases using two identical 2 7/16 inch diameter antennas made of silver solder brazing rod material. Measurements were made at five frequencies ranging from 150 MHz to 250 MHz. In most instances measured values compare favorably with predicted values