An Accurate Low-Cost Method for Q-Factor and Resonance Frequency Measurements of RF and Microwave Resonators

A new technique for measurement of the resonant frequency and Q-factor of resonators is presented. In this technique, the derivative of the insertion phase with respect to frequency of resonators are measured and used for the calculation of their resonance frequency and Q-factor. A slow-rate chirp signal is passed through a resonator, and the output signal is amplified and equally divided into two signals which are delayed by different amounts. The two delayed signals are fed to a phase detector measuring their phase difference. The derivative of the insertion phase with respect to frequency of the resonator can be simply found from the phase difference between the two delayed signals. The proposed measurement technique is realized using low-cost components and utilized for measuring the resonant frequency and Q-factor of several L-band resonators. Compared with the resonators' performance measured by a vector network analyzer, the introduced approach measures the resonant frequency and Q factor by less than 0.6% and 4% error, respectively.