Effect of rectifier capacitances on the conversion loss of ring modulators

THE SMALL-signal theory of rectifier modulators is normally developed by assuming that rectifiers switch periodically from their forward to their backward resistance, neglecting the capacitive component of the backward impedance. Such a resistive theory has been quite invaluable to compare the performance of various circuits and especially to study the effect of selective terminations.
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It is well established, however, that capacitive effects are not negligible, and become quite important at high frequencies. For small dissipation, the resistive and capacitive losses clearly add up without interaction, so that it will be sufficient for practical purposes to develop the theory for ideal rectifiers (zero forward and infinite backward impedance) shunted by a parasitic capacitance C. The Cowan modulator of Fig. 1 is then equivalent to a periodic switch shunted by C (Fig. 2). Similarly; a well-known equivalence for lattice networks reduces the ring modulator of Fig. 3, next page (with ideal auto transformers) to an ideal commutator enclosed between two capacitances C (Fig. 4, on the following page). The first step is to develop the theory of the linear variable 4-poles of Figs. 2 and 4 working between purely resistive and frequency independent source and load. The next important case of selective terminations has not yet been attacked.