Some General Properties of Nonlinear Elements-Part I. General Energy Relations

Two independent equations relating the average powers at the different frequencies in nonlinear inductors and capacitors are derived. These equations are a consequence only of the assumption of a single-valued characteristic for the nonlinear element. They are independent of the particular shape of this characteristic, of the power levels at the various frequencies, and of the external circuit in which the nonlinear reactor is connected. These general energy relations give information regarding the gain and stability of nonlinear reactor modulators and demodulators, and consequently of magnetic and dielectric amplifiers, without requirng detailed information about these devices. The utility of these equations is illustrated by discussing the gain and stability of the simplest types of nonlinear reactor modulators and demodulators and harmonic generators. This analysis for nonlinear inductors and capacitors is extended to include the effects of hysteresis in the nonlinear characteristic in the special case where the operating hysteresis loop is no more than double-valued. A similar analysis applied to nonlinear resistors yields two equations relating the reactive powers at the different frequencies, rather than the real powers as above. The interpretation of reactive power under these conditions is not clear.