Subject : Power Electronics
Unit : DC to AC Converters
Analysis Of The Pole Voltage Waveform With A Dc Modulating Signal
Analysis of the Pole Voltage Waveform with a Dc Modulating Signal:
Fig: Inverter pole voltage for a pure dc modulating waveform
- Before analyzing the sine-modulated pole voltage waveform, it would be revealing to consider a pure dc signal (of constant magnitude) as the modulating wave.
- The magnitude of the dc modulating signal is constrained to remain between the minimum and maximum magnitudes of the triangular carrier signal.
- The figure illustrates one such case where the triangular carrier signal varies between -1.0 and 1.0 units of voltage and the magnitude of the modulating wave is kept at 0.4 unit of voltage. Now, the high frequency triangular carrier waveform is compared with the dc modulating signal and the comparator output is used to control the high and low level switches (S_{U }and S_{L }respectively) of the inverter pole shown in the figure.
- The figure also shows the comparator output (Q) and the pole voltage (V_{AO}) waveforms for this case. As can be seen, with pure dc modulating signal the pole voltage consists of pulses of identical shapes repeating at carrier frequency.
- The Fourier series decomposition of pole voltage waveform results into a mean (dc) voltage and harmonic voltages whose frequencies are integral multiples of carrier frequency.
- By using simple mathematics the high-duration of the pulses (t), during which the pole voltage magnitude is 0.5Eh_{dc}, can be found to be where T_{C} is the time period of the triangular carrier waveform, is the magnitude of the modulating signal and V_{c} is the peak (positive) magnitude of the carrier signal. The low-duration (t_{l} ) of pulses during which the pole voltage magnitude is -0.5E_{dc}, is found as
- The dc component of the pole voltage (V_{0}) can be found to be
- The dc modulating signal could acquire any magnitude between V_{c} and - V_{c}and accordingly the mean magnitude of pole voltage can vary within 0.5E_{dc }and -0.5E_{dc}.
- When the modulating signal magnitude (V_{m}) is zero, the high and low durations of the pole output pulses will be identical and the mean pole voltage magnitude will be zero. Apart from the dc component, the pole voltage consists of harmonics of integral multiples of carrier frequency. The lowest order harmonic-frequency is same as the carrier frequency.