** IEC 63185**-2020 Measurement of the complex permittivity for low-loss dielectric substrates balanced-type circular disk resonator method (IEC 63185:2020).

7 Measurement procedure

7.1 Preparation of measurement apparatus

Set up the measurement equipment and apparatus as shown in Figure 3. The cavity resonator and dielectric samples shall be kept in a clean and dry state, as high humidity degrades unloaded Q-factors.

7.2 Adjustment of measurement conditions

Set up the measurement conditions of a vector network analyzer. The interval between discrete frequency points shall preferably be less than one tenth of the half width of the resonant waveform. Intermediate frequency band width (IFBW), like as digital band pass filter condition in vector network analyzer, is determined such that the noise floor is at least 20 dB lower than the peak values.

7.3 Calibration of a vector network analyzer

A vector network analyzer shall be calibrated by using calibration kits.

7.4 Measurement of complex permittivity of test sample

Constitute a balanced-type circular disk resonator by the pair of test samples. Figure 4 shows the frequency dependence of |S 21 |. Resonant frequencies of TM 01 0 to TM 050 modes are indicated by the downward arrows. Measure the resonant frequency and unloaded Q-factor of each mode and calculate the complex permittivity at each resonant frequency of test samples by using Equations (3) and (4).

The alignment between the conductor disk and excitation holes is critical to measurement results, but it is possible to find a misalignment by detecting resonances of unwanted modes between adjacent TM 0m0 modes. In the frequency response of |S 21 |, resonant peaks for unwanted modes shall be at least 1 5 dB lower than those for adjacent TM 0m0 modes.

7.5 Periodic checkup of metal in resonator

Since the conductivity of the conductor plates and circular disk degrades due to oxidation of the metals and scratches on the surfaces, the quality of the metals of the resonator shall be checked periodically. It can be checked by measuring the conductivity by using the two dielectric resonator method [5]. Instead, it can be checked by measuring the same low-loss sample periodically. By checking the reproducibility of the measurement results of loss tangent of the specified verification sample, it is possible to find the surface characteristic change in the metals of the resonator.

The measurement results and associated uncertainties for the complex permittivity of cyclic olefin polymer (COP) sheet sample are obtained as followed. Hereafter, measurement uncertainty of each quantity is expressed by its expanded uncertainty with a coverage factor of k = 2.

a) The parameters such as R, a, and M of the cavity and t of the COP sample used in the measurements are shown in Table A.1 .

b) The resonant frequency f 0 and unloaded Q-factor Q u of the TM 01 0 to TM 080 modes in the cavity with the COP sample are measured and shown in Table A.2. Uncertainty evaluations of the resonant frequency and Q-factor are performed by considering the uncertainty propagation of the uncertainty of S 21 , measurement repeatability, and the effect of frequency resolution determined by the interval between discrete frequency points. Monte-Carlo calculations are performed to evaluate the uncertainties of these resonant properties [7].IEC 63185 pdf download.