Use of whispering-gallery modes for complex permittivity determinations ofultra-low-loss dielectric materials

Whispering-gallery modes are used for very accurate permittivity, dielectri c loss, and temperature coefficient of permittivity measurements for both i sotropic and uniaxially anisotropic dielectric materials. The relationship between resonant frequencies, dimensions of the resonant structure, and per mittivity of the sample under test is calculated with a radial mode-matchin g technique. The relative accuracy of these computations is better then 10( -4). The influence of conductor losses' on dielectric loss tangent determin ation is treated for both whispering-gallery-mode and TE01 delta-mode diele ctric-resonator techniques. Two permittivity tensor components of sapphire and their temperature dependence were measured from 4.2 to 300 K, The total uncertainty in permittivity when use is made of whispering-gallery modes w as estimated to be less than 0.05%, The uncertainty was limited principally by uncertainty in sample dimensions, Experimental and calculated resonant frequencies of several whispering-gallery modes differed by no more than 0. 01%. The dielectric loss tangent of sapphire parallel and perpendicular to its anisotropy axis was calculated to be less than 10(-9) at 4.2 K, The per mittivity and dielectric loss tangent of a commercially available low-loss high-permittivity ceramic material has also been measured at S- and C-band frequencies using a large number of whispering-gallery modes.