Accurate characterization of low-Q microwave resonator using critical-points method

The critical-points method for direct characterization of high-Q microwave resonators is adapted to low-Q resonators. Based on a new approximation, the crossover points are removed and the critical points are used in the computation of the equivalent-circuit elements for the low-Q resonator. Due to the large separation of the crossover frequencies from the resonant frequency, the modification is necessary in order to have a good estimate of the element values in the equivalent circuit. The high accuracy of this one-port measurement method is verified using a microstrip patch antenna.