Note on Circular Loop Antennas with Non-Uniform Current Distribution

Abstract

In this paper are presented the approximate formulas for the components of radiation vectors of a short-circuited circular loop with non-uniform current distribution. The formulas are valid for the ratio of loop perimeter to wavelength of the order of 0.5 or less, and assume the current distribution of the hyperbolic cosine form. These formulas lead to the radiation intensity formula from which the expressions for the horizontal and vertical field patterns are derived. The latter formulas are further simplified assuming that the attenuation constant is much smaller than the phase constant. From the expression for horizontal field pattern, it follows that the pattern is symmetrical about the loop axis of symmetry. Moreover, this horizontal pattern exhibits a directional effect with maximum field in the direction of the feeder end of the loop. This directional effect is a function of loop dimensions. The theoretical horizontal pattern agrees very closely with the experimental one. From the expression for vertical field pattern, it follows that the non-uniform current distribution produces a pattern intermediate between that for horizontal dipole and horizontal small loop with uniform current distribution. The field intensity in the zenithal direction is again a function of loop dimensions. Using the expression for radiation intensity, formulas for a radius of equivalent circular horizontal field pattern, power gain, average power gain, and radiation resistance are derived. It is shown that the average power gain is essentially a function of loop radius and decreases with the increase of the latter. Finally, the approximate expression for the attenuation constant of the transmission line equivalent to the loop is derived.

A General Solution of the Thin Circular Loop Radiation

“…The radiation problem of a circular loop is among those classic electromagnetic problems treated in papers published some five decades ago (Foster, 1944;Sherman, 1944;Glivinski, 1947) and also in numerous textbooks (Schelkunoff, 1952;King & Smith, 1981;Blanis, 1982;Collin, 1985). Nevertheless, this problem is still of interest for many researchers.…”

Analyzing multi-circular loop scatterers by Maxwellian circuits

“…Foster [5] and Sherman [6] gave the current formula if circular loops have an integral number of wavelengths in the circumference. Glinski [7] assumed that the current of the hyperbolic cosine function is effective when the ratio of loop circumference to wavelength is 0.5 or less. There are still some other methods [8][9][10] , but most of them are complex and difficult to implement.…”

The near-zone magnetic field of a small circular-loop antenna

“…If the radius of the wire with which the loop is wound is small compared to the loop radius, r" it can be assumed that the current distribution around the loop is, to a first approximation, of the hype rbolic·cosin e form [19] The loop will be considered sufficiently loss free that a can be assumed negligible compared to 13. This is a reasonable assumption for the type of loop used, so that eq (28) can be written I == 10 cosh (jf3/) == 10 cos 131.…”

“…Ro (19) The infinite series in eq (19) The integral in eq (20) can be e valuated from the following relations [13]:…”