Novel alternative mathematical description and analysis of synchronized voltage pulse patterns

The mathematical description of synchronized periodic voltage pulse patterns is generally done by using Fourier series expansions based on the switching times of the pulses. An alternative and novel approach for the mathematical description of such voltage pulse patterns is suggested considering pulse widths ∆T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</inf> and delay times T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</inf> of the pulses. The pulse patterns are viewed as a superposition of a main half-wave symmetric pulse pair, describing the fundamental waveform, and additional pulse pairs with half-wave symmetry. These additional half-wave symmetric pulse pairs can be delayed arbitrarily within some limits. Quarter-wave symmetric pulse patterns are developed from the half-wave symmetric pulse patterns. Therefore, they are only a specialization. Half-wave and quarter-wave symmetric pulse patterns with a minimum number of switching actions are analyzed concerning the fundamental voltage harmonic, the total harmonic distortions (THD) of the voltage and current patterns under exemplary conditions of a passive inductive-resistive load. The results show that both the half-wave and the quarter-wave symmetric pulse patterns reveal different dependencies of their characteristics. Generally, there are many different parameter combinations (pulse width, delay), which exhibit the same characteristics of the voltage pulse pattern.