A general analytical theory of frequency conversion

Three theorems are announced as the groundwork of a new methodology for rigorous analysis of frequency conversion. One of several advantages of this methodology is that it obviates numerical integrations for Fourier coefficients. Casting the Taylor series in the formalism of differential operators leads to the introduction of a new entity called Mixer Functional which is composed of modified Bessel functions. Harmonic generation, frequency mixing, frequency modulation, and heterodyne detection are consolidated under one common approach. The Mixer Functional of first order yields Fourier coefficients of nonlinear functions of cos ωt (Theorem 1). The second- and higher order functionals give amplitudes of mixed harmonics of two or more primary frequencies (Theorem 2). A definition of the basic passive nonlinear elements is proposed and used, and then the methodology is illustrated by application to typical semiconductor devices. Nonlinear perturbation theory is developed for analyzing feedback when a linear load is in series with a nonlinear device and a voltage source. Theorem 3 addresses augmented conversion when the linear load is a resistor. This theorem also yields an analytical solution for the quiescent operating point in electronic circuits, thus complementing the traditional graphical load line approach