A simple formula exists for calculation of radiation resistance of a small transmitting loop in free space. The derivation is in most good antenna text books.

The expression depends on an assumption that current around the loop is uniform, so the question is what is the acceptable limit for loop size.

NEC might provide some guidance. A series of NEC-4 models of a octagonal loop of thin lossless wire in free space was constructed with varying perimeter. Perimeter shown is that of a circle of the same area.

Above is a comparison of the two methods of estimation of Rr. To the extent that we trust NEC-4, the graph indicates that error in the simple formula grows quickly for loop perimeter greater than 0.1λ. (The results using NEC-2 are visually identical.)

Many authors set the criteria for a small loop to perimeter<0.3λ, but it is clear that current is not sufficiently uniform for perimeter>0.1λ for estimation of Rr as 31149*(A/λ^2)^2 to 0.1pu error or better.

Last update: 14th August, 2015, 9:28 AM