Studies in Non-Linear Circuits

The series circuit consisting of an inductance L, capacitance C, resistance R, and a source of alternating electromotive force, where the circuit elements are all linear, is regarded as a special case of a more general type of circuit in which L, C, and R may be functions of the current or other variables. The practical importance of these non-linear circuits is noted and some of their properties are reported. In the series circuit with a linear resistance, capacitance, and an iron core inductance it is shown that the abrupt rise in current at a certain critical voltage is characterized by resonance in the sense that L di/dt = - 1/c ∫ i d t. In this non-linear resonance however the above condition is satisfied in but a limited portion of the cycle. During this portion of the cycle the peak current may be calculated from Ohm's law. The series circuit with linear resistance, capacitance, and an iron core reactor with superimposed steady magnetizing force, is shown to exhibit a pulsation oscillation which is explained on the basis of the positive impedance-current characteristic of such reactors. Parallel resonance for the non-linear case of an iron core reactor is reported, and it is shown that in conjunction with series resonance the unique characteristic is obtained wherein the r. m. s. current decreases with increasing applied voltage.