A Low-Complexity Time-Domain Method for a Fast and Accurate Measurement of Q-Factor and Resonant Frequency of RF and Microwave Resonators

A new time-domain technique for an accurate and fast measurement of the resonant frequency and $Q$ -factor of resonators is presented. In this technique, the phase slope with respect to frequency of a resonator is characterized and used to specify its $Q$ -factor and resonant frequency. To measure the phase slope, a slow-rate linear chirp signal is generated and passed through the resonator under test. The output signal is amplified and subsequently divided into two equal parts which are delayed by different amounts. Due to the linear time-frequency relationship of the chirp signal, the instantaneous frequencies of the two delayed signals are slightly different at any given time, and their phase difference can determine the resonator’s phase slope. Detailed analysis of the proposed approach is presented and its accuracy is verified through simulations and measurements. Based on the measured results, the proposed approach characterizes the resonant frequency and $Q$ -factor by less than 0.6% and 4% error, respectively.