Lossy Thin Loops and Rings with Multiple Impedance Loads

Abstract

Loops and rings, multiply-loaded by impedances have usefulness in a variety of ways, among them beam steering and super-directivity. This chapter derives the effect on the governing equations when the periphery of the loop is loaded with an arbitrary number of lumped impedances and provides some examples of loaded loops; in particular, a loop loaded with one capacitor and with multiple capacitors. The sub-wavelength resonance and its causes are identified in the chapter. This sub-wavelength resonance appears in all rings with gaps, and the capacitance model for that gap is given in a later chapter, but is compared with the capacitance model developed here. The current and the Fourier current coefficients are derived. The effect of multiple impedances on the current distribution and the asymmetry of the current across the modal number n is elaborated. Finally, characteristics of the radiation patterns of mulitply-loaded loops are examined, while the last sections give examples.