Accurate and direct characterization of high-Q microwave resonators using one-port measurement

An accurate and direct characterization of high-Q microwave resonators using one-port vector network measurement technique is presented. In this characterization, the delay due to the connector between the resonator and network analyzer is first deembedded. The elements of the equivalent-circuit of the resonator are then readily extracted from the experimental data in a straightforward manner without any numerical optimization. The extraction method works very accurately for high-Q resonators coupled to external circuits electrically or magnetically, and can deal with universal cases including external lossy couplings and weak under-coupled resonators. Parameters such as coupling coefficient, loaded quality factor, and loaded resonant frequency can also be directly computed. For the loaded resonant frequency, an original expression is derived in this paper. This paper also provides an approximate relation between the loaded resonant frequency and measured frequency at which the minimum magnitude of the reflection coefficient occurs. The high accuracy of the method is demonstrated with two examples: a hollow cavity resonator and a dielectric loaded cavity resonator, which is also supported by the well-established one-port multipoint technique.