Pl. Overfelt, NEAR FIELDS OF THE CONSTANT-CURRENT THIN CIRCULAR LOOP ANTENNA OF ARBITRARY RADIUS, IEEE transactions on antennas and propagation, 44(2), 1996, pp. 166-171
Assuming a known (constant) current distribution on the thin circular
loop antenna of arbitrary radius in free space, an exact integration o
f the vector potential is performed without recourse to approximations
. The only restrictions on the solution variables are that the observa
tion point distance must be greater than the loop radius and that the
polar angle must run between 0 and pi. The resulting vector potential
infinite series solution possesses a real part composed of linear comb
inations of complete elliptic integrals of the first and second kind a
nd an imaginary part composed of elementary functions. Thus, it is pos
sible to obtain an exact solution which is valid everywhere that r > a
and 0 less than or equal to theta less than or equal to pi. The elect
romagnetic field components of the constant current circular loop ante
nna are then determined by direct series differentiation. These soluti
ons are valid in the near and induction fields, converging rapidly the
re, and are also valid in the far field, although many terms of the se
ries are needed for convergence.