Measuring quality factors of the radio-frequency system components using equivalent circuits

In this paper, we discuss the influence of equivalent circuit components on the frequency dependence for the quality factor of a varactor. The authors have obtained complete equations for determining the complex resistance of the varactor and its quality factor. Also, equations have been obtained to determine by parameters of the equivalent circuit a frequency range, where the varactor quality factor is maximal or exceeds a certain value (more than 10 were considered in the paper). A method has been proposed for evaluating the maximum frequency of an operating frequency range of the varactor by parameters of its equivalent circuit, provided that a reactance of the varactor is more than 10 times higher than an inductive resistance of its outputs. Considering results of an analysis, equations have been obtained for estimating the maximum value of the varactor quality factor and a frequency corresponding to its maximal quality factor. Theoretical results have been verified experimentally on varactors manufactured by Skyworks Solutions, type SMV20xx. Equivalent parameters of active and capacitive components of the serial and parallel varactor equivalent circuits have been determined and their frequency dependencies have been analyzed. For four types of varactors, frequency ranges have been determined, where an equivalent capacitance of the equivalent circuit differed from a barrier capacitance by less than 1%, and an equivalent resistance of the equivalent circuit differed from a loss resistance in emitter and base regions by less than 5%. It has been substantiated that in the frequency range, where the varactor quality factor was greater than 10, equivalent capacitances of the serial and parallel equivalent circuits can be regarded as independent of frequency and equal to a capacitance of the varactor junction with an error of up to 1%.