Permittivity measurements using a frequency-tuned microwave TE01 cavity resonator

Abstract

A measuring system for determining the complex permittivity of low-loss solids using a frequencytuned TE 01 cavity resonator of fixed length is described. Its mechanical construction is simple, and measurements, in particular of the real part e' of the permittivity, can be performed within a relatively short measuring time with high precision (| Ae'/e' | < 7 x 10~4), for a large number of frequencies in a given frequency band. The method is compared with the standard method where a length-tuned resonator is involved. Theoretical error investigations and practical measurements at frequencies of about 10 GHz on polymers and fused silica are carried out showing that the uncertainties have comparable values in both methods. IntroductionFor 40 years the closed cavity resonator operated in the low-attenuation TE 01 mode, which consists of a hollow metallic cylinder of circular cross-section terminated by two short-circuit plates, has been used to measure the real part e' of the complex relative permittivity e = e' -je" and the tangent of the dielectric loss angle ('loss tangent'),of materials in the microwave range [1], in particular of low-loss solids. Reviews of literature on dielectric measuring methods including cavity resonator techniques have been given by Bussey [2], Lynch [3], Chamberlain and Chantry [4] and, more recently, by Birch and Clarke [5]. According to a widely known precision standard method, the lengthtuning method (LTM), e' and e" are obtained, at a fixed frequency /, from the measured changes of the length and of the (?-factor of t n e resonator at resonance which are caused by the disc-shaped dielectric sample which is inserted adjacent to one of the short-circuits [6]. To tune the resonator the short-circuit can be moved in the axial direction to vary the resonator length by a bearing and positioning device, which must be well designed and precisely constructed, to keep the measurement uncertainties small, especially that of e'.With a different principle of measurement already mentioned in Reference 1, the frequency-tuning method (FTM) which involves a very simple mechanical construction, no movable mechanical parts are used. Here the resonator is terminated only by two fixed short-circuits and, at constant resonator length, the frequency is altered to tune it to resonance. The permittivity s' and tan <5 are determined from the measured changes of resonance frequency and Qfactor which are due to the inserted sample. Both quantities and other geometrical parameters of the resonator necessary to calculate the complex permittivity are obtained by means of a frequency counter of good resolution {\Af/f\ ^ 10" 7 ) which, in any case, is required for both methods to determine the Q-factors. In spite of its simplicity the FTM has been used, hitherto, only in special cases for precision measurements [7,8].To test the applicability of the FTM as a precision standard method of measurement a theoretical and experimental error investigation has therefore been carried out the results of which are presented in ...

Relative permittivity and loss tangent measurement using the NIST 60 mm cylindrical cavity

“…(1) and (2) reduce to H(p, 0, z) = [hr(p, 0) + h z (p, 0)] exp(-^z) (3) and E(p, 0, z) = [e T (p, 0) + e 2 (p, 0)] exp(-j^). (4) Since the longitudinal electric field (5) where u is the frequency in radians, po is the permeability of free space, eo is the permittivity of free space, and e a is the relative permittivity of the air inside the waveguide.…”

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Estimation of Q-factors and resonant frequencies

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Dielectric sleeve resonator techniques for microwave complex permittivity evaluation

“…These are requisite for the determination of specimen dielectric loss tangent. From continuity conditions 17) (18where (19) (20) and 21Neglecting the subscript on , the field components for the sample region are In general, is given as , where represents the total electric field energy in the resonant system and represents all power losses in the resonant system. The total electric field energy consists of that stored in the specimen, , that in the sleeve resonator, , and that in the region exterior to the composite dielectric resonator in the cylindrical cavity, .…”