Impedance of a Non-Linear Circuit Element

Experimental determinations of the impedance of a variable element, such as an iron core coil worked at a high flux density, or a heavily loaded vacuum tube, are found to depend upon the impedance-frequency characteristics of the measuring circuit, as well as upon the complexity of the applied (measuring) potential wave. A physical picture of the action of a non-linear element in producing harmonics is built up, and it is shown that the flow of harmonic currents affects the measured impedance, at the fundamental frequency, of course, in two ways which are designated as the loading and reaction effects. The loading effect is that produced by the superposition of currents without any regard to the production of new frequencies, and the reaction effect, in accordance with energy conservation ideas, is that due to energy storage and dissipation at harmonic frequencies which appear as impedance reactions at the fundamental frequency. The physical picture set up in the above discussion appears to be capable of accounting for the experimental observations mentioned above in a qualitative way at least. In accordance with these ideas, it appears that even when the fundamental current is specified, there is no one definite value which can be assigned as the impedance of a variable element because of its dependence upon the circuit impedance-frequency characteristics. Several measuring methods are reviewed by which the impedance of the variable element may be determined under definite circuit conditions.