Abstract
This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time; dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.
Highlights
IntroductionIt is known that periodical non-harmonic discontinuous function is possible to portray in compact closed form using Fourier infinite series [1] [2]
This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering
The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms
Summary
It is known that periodical non-harmonic discontinuous function is possible to portray in compact closed form using Fourier infinite series [1] [2]. 22 increasing saw-tooth function with angular frequency ω can be expressed in closed form fsaw +. Classical solution leads to results in Fourier series form, otherwise the Heaviside calculus is to be used [2], [6]. Based on zero order hold function and unipolar modulation [8]-[10], the switch-off impulses will be substituted by zero points, and result waveforms can be presented as follow from, Figure 2.
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