Abstract
AbstractIt is proved that a circuit consisting of non‐linear passive resistances and of any linear invariant passive elements cannot convert power from frequencies ω1 and ω2 into power at frequency mω1 + nω2 with an efficiency better than 1/(|m| + |n|)2. Circuits attaining that efficiency are constructed for all m, n, so that the condition is both necessary and sufficient. For m = μt, n = vt, |μ| + |v| = 2s (all literals are integers), the optimal circuit consists of a finite number of rectifiers and tuned circuits. For values of m, n that are not of the above form an infinite number of tuned circuits is necessary, but an efficiency better than 93 per cent of the optimum is attainable by simple finite circuits in all cases.
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