New Results in the Calculation of Modulation Products

HE problem of computing modulation products has long been recognized as being of fundamental importance in communication engineering. Heretofore certain quite fundamental modulation problems have been attacked by methods which are difficult to justify from the standpoint of mathematical rigor and some of the solutions obtained have been in the form of complicated infinite series that are not easy to use in practical computations. In this paper these problems are solved by means of a new method which is mathematically sound and whi£h yields results in a form well suited for purposes of computation. The analysis here given applies specifically to the case of two frequencies applied to a modulator of the " c u t o f f " type; i.e., a modulator which operates by virtue of its being insensitive to input changes throughout a particular range of values. A simple rectifying characteristic forms a convenient basis of approximation for study of such modulators, and hence we consider in detail methods of calculating modulation in rectifiers when two frequencies are applied. Applications to certain other types of modulation problems and to the case of more than two applied frequencies are discussed briefly at the close. H A L F W A V E LINEAR R E C T I F I E R -- T w o A P P L I E D FREQUENCIES We shall define a half wave linear rectifier as a device which delivers no output when the applied voltage is negative and delivers an output wave proportional to the applied voltage when the applied voltage is positive.