Representation of Impulses in Time and Frequency Domain

Abstract

Single and continuous signals can be represented by their waveforms in the time domain or by their spectra in the frequency domain. Both forms of representation are equivalent to each other, but which representation will be preferred in an individual case depends on the measurement task and the desired goal. In principle, specifications for the correct measurement of a signal can be derived from the waveform in the time domain as well as from the spectrum in the frequency domain. According to IEC 60060 and IEC 62475, high-voltage and high-current impulses are characterised by parameters of their waveforms in the time domain. In contrast, the measuring instruments used in the low-voltage range, among them analogue oscilloscopes and digital recorders, are often characterised by parameters of their spectra in the frequency domain. Hence, in this chapter, the waveforms and spectra of impulse voltages and currents will be treated as well. Analytical expressions for exponential impulse voltages and currents are derived from the idealised generator circuits using the Laplace transform. Furthermore, the equations for the spectra of these impulses and, in addition, of a wedge-shaped voltage and a short-time current are developed. The calculated spectra of a 1.2/50 lightning impulse voltage, a 250/2500 switching impulse voltage, an 8/20 impulse current and further impulses are shown in a diagram for comparison.