Analysis of oscillating and non-oscillating impulse waveform for high-voltage impulse test using the roots of biquadratic equation

This paper describes the waveform analysis of impulse voltage or impulse current. The analysis is accomplished by solving the biquadratic equation for the lightning impulse test circuit. Three discriminants classify the solutions into nine categories. Some calculations using the roots of biquadratic equation demonstrate the effectiveness of the analysis. For example, the overshoot or oscillating impulse superposed on standard lightning impulse voltage is calculated as the magnitude of relative overshoot. The polarity reversal waveform together with the double frequency oscillation or without oscillation is analyzed, which is not expressed by the third-order differential equation. The analyses also clarify the relationship between the waveform and the circuit parameters. This means that the definition of relative overshoot magnitude based on the base curve for oscillating impulse or overshoot is supported by the theory.