Measurement Error of Temperature Coefficient of Resonant Frequency for Microwave Dielectric Materials by $\mathrm{TE}_{\mathrm {01\delta }}$ -Mode Resonant Cavity Method

The temperature coefficient of resonant frequency of a microwave dielectric material (τ
_f,s
) is defined as the τf of an ideal resonant system that is homogeneously filled with this material, while it is usually measured as the τ
_f
of a nonideal resonant system (τ
_f,r
) such as a cavity dielectric resonator. In the present work, finite element analysis is used to investigate the measurement error of τ
_f,s
by TE
_01δ
-mode resonant cavity method, for which the sample is placed on a support and far from the cavity walls. Several error sources contribute to the total measurement error, which is usually several ppm/°C and decreases with the dielectric constant of the sample (ε
_r,s
). Besides, the measurement error is strongly dependent on the cavity size. In comparison, the measurement error is much lower and usually within 1 ppm/°C for TE
₀₁₁
-mode parallel plate method, where the sample is clamped between two metal plates. It is suggested to measure τf,s by TE
₀₁₁
-mode parallel plate method but not by TE
_01δ
-mode resonant cavity method if τ
_f,s
is treated as τf,r, especially whenεr,s is low and high measurement accuracy is needed. If TE
_01δ
-mode resonant cavity method is used to measure τf,s, the result must be corrected with the aid of numerical calculation to improve the measurement accuracy.