Measuring the unloaded, loaded, and external quality factors of one- and two-port resonators using scattering-parameter magnitudes at fractional power levels

A simple and fast technique for measuring resonator quality factors is presented, in which only the magnitudes of the s-parameters are used. For the first time, the equations are presented for all of the basic topologies, including one-port reflection, two-port transmission, and two-port absorption resonators, and for all three quality factors, including the unloaded, loaded and external Q. The method is flexible and suitable to a large number of resonators because the required bandwidth may be measured at almost any level, not only at the classical half-power points. These levels are clearly identified as fractions of the absorbed power at resonance. The technique is then demonstrated by analysing a two-port microstrip ring transmission resonator.