Theory of the Detection of Two Modulated Waves by a Linear Rectifier

In this paper there is developed a mathematical analysis of the detection, by a linear rectifier, or two modulated waves. Solutions are obtained which are manageable over wide ranges of values of carrier ratio and degrees of modulation. These solutions are of greater applicability and are more convenient than those previously obtained, and give a full treatment of the action of an ideal linear rectifier under the action of two modulated waves. The development is first made in terms of the derivatives of zonal harmonics of an angle which is directly related to the phase difference between the carriers. As these derivatives are tabulated functions the solution is convenient. The solutions are limited by the condition that K <(1-M)/(1+m), K being the carrier ratio, M the degree of modulation of the stronger carrier, and m that of the weaker. Two methods of attack are developed one of which is applicable when K is small and M and m large, and the other when M and m are small and K large. The cases of identical and of different programs are both considered and a number of curves are given showing the magnitudes of various output frequency components under typical operating conditions. In the latter part of the paper the phase angle between the carriers is set equal to μt so that a beat note exists.