Although the three sets of results were determined by different methods, they appear satisfactory and in good agreement with each other. The analytical (MATLAB) and numerical (ADS) model responses and the experimental responses (VNA measurements) compared closely. The analytical and numerical cases yielded approximately the same values, with some differences compared to the experimental results. This is best explained by the fact that the theoretical models do not fully account for the complex characteristics of the components used in the fabrication of the transformers, which were modeled as more or less "ideal" components.
These model equations represent a simplified equivalent-circuit model for a coil transformer. Recent studies have shown the need to use a more elaborate model that includes resistive and reactive effects as a function of increasing frequency and number of turns.12
These advanced models also include the effects of inter-winding capacitance, which decreases the self-resonant frequency of the inductor. Still, these simplified design equations can provide reasonable results, replacing the more involved empirical processes usually involved in the design of a 1:4 impedance transformer. As these simplified equations show, they can be used to design transformers over a wide frequency range (three octaves) with low insertion loss and at low cost.
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