The effects of parasitic modulation on the accuracy of measurement of the Q-factor of a resonator

When the Q-factor of a resonator is determined by using sinusoidal amplitude modulation and measuring the envelope phase shift, the presence of unwanted frequency or phase modulation may reduce the accuracy of the result. The envelope phase shift now depends on the ratio of the parasitic-modulation index to the amplitude-modulation index, and also on the phase angle between the two modulation components. If measurements are made with the carrier set as close as possible to the resonant frequency of the resonator, increased frequency stability is required. Alternatively, if advantage is taken of an approximation to exact tuning, which is given by setting the carrier so that the envelope phase shift is a maximum, a systematic error is introduced. If the ratio of the modulation indices or the phase relation between the modulation components is known, the systematic error may be determined and a correction can then be applied to the result. If either of two special phase relations can be set up between the modulation components, it appears that the parasitic modulation can be rendered innocuous; under these conditions as high an order of accuracy can be achieved as if pure amplitude modulation were used. This paper is supplementary to a previous paper which described a method for the measurement of very high Q-factors of electromagnetic resonators.