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The procedure for a complete mathematical analysis of the AM-rejecting properties of the ratio detector is presented. The operation with 100-per cent efficient diodes is first treated, and it is shown that in this case compensating resistors which reduce the effective efficiency of the diodes must be used to obtain optimum AM rejection. The operation with practical diodes is then treated and design charts for optimum AM rejection are presented. From the theory, the effect of variations in ratio-detector transformer parameters upon the AM-rejection properties is predicted. Unbalanced effects and the manner in which they can be made to cancel each other mutually are briefly described. It is pointed out that the degree of apparent limiting action within the ratio-detector circuit is incidental and unrelated to its AM-rejection properties, and thus represents an inadequate design basis for the ratio detector.