A modification of the small loop approximation for fractal and bent wire loop antennas

The small loop approximation has been previously applied to the fractal loop and it was concluded that fractal loop antennas do not obey the generalizations of the small loop approximation because of their fractal geometry. In this work, the small loop approximation and its applicability to fractal and other bent wire loop antennas is re-evaluated. It is demonstrated that the small loop approximation for the radiation resistance of a small loop is valid for loops with fractal or bent wire geometries, when these loops meet all of the small loop criteria. In applying the small loop approximation criteria to these loop antennas, a modification of the small loop area limit is presented that allows an approximate determination of the frequency at which fractal and other bent wire loop antennas can be considered electrically small.