There are different ways to calculate the unloaded bandwidth of a series transmission resonator. For this type of two-port resonators, the availability of both return loss (s11) and insertion loss (s21) over-determines the system; that is, the unloaded 3-dB bandwidth and hence the quality factor of the resonator can be calculated from either s21 or s11. This paper describes different techniques that can be used to determine the unloaded quality factor of a series two-port resonator in order to determine which formulae should be used to most accurately measure the unloaded 3-dB bandwidth of the resonator. Sources of errors are described for both s11 and s21 methods. Then the measurement uncertainty is
analyzed and compared to obtain the most accurate Q0 reading.