LSE- and LSM-mode sheet impedances of thin conductors

Abstract

The sheet resistance of very thin conductors is commonly taken as R=1//spl sigma/t. We show that the sheet impedance, defined as the ratio of the tangential electric field at the surface of the conductor to the conduction current per unit length in the conductor, depends on the field distribution. The LSE (TE-to-y) and LSM (TM-to-y) modes used in the spectral domain immittance approach have sheet impedances which are distinct for vanishingly small or large values of the wavenumber /spl gamma/ in the medium surrounding a thin conductor. In the limit /spl gamma//spl rarr/0 and t//spl delta//spl Lt/1, Z/sub sh//sup LSE/ approaches R=1//spl sigma/t while Z/sub sh//sup LSM//spl rarr/2//spl sigma/t. In the limit /spl gamma//spl rarr//spl infin/ and t//spl delta//spl Lt/1, Z/sub sh//sup LSE/ approaches R=2//spl sigma/t and Z/sub sh//sup LSM/ approaches R=1//spl sigma/t. When t//spl delta//spl Gt/1, the sheet impedance approaches the surface impedance Z/sub s/=(1+j)//spl sigma//spl delta/ and is independent of the field distribution.