Pole Voltage Waveform With Sinusoidal Modulating Signal
Pole Voltage Waveform with Sinusoidal Modulating Signal:
- A slowly varying sinusoidal voltage, with the following constraints, be considered as the modulating signal:
- The peak magnitude of the sinusoidal signal is less than or equal to the peak magnitude of the carrier signal. This ensures that the instantaneous magnitude of the modulating signal never exceeds the peak magnitude of the carrier signal.
- The frequency of the modulating signal is several orders lower than the frequency of the carrier signal. A typical figure will be 50 Hz for the modulating signal and 20 Kilohertz for the carrier signal. Under such high frequency ratios, the magnitude of modulating signal will be virtually constant over any particular carrier-signal time period.
- Because of the above assumptions some results of the previous section, where a pure dc modulating signal was considered, may be used. Since the slowly varying modulating signal is virtually constant over a high frequency carrier time period, the mean magnitude of the inverter pole voltage averaged over a carrier time period will be proportional to the mean magnitude of the modulating signal.
- Thus the discretely averaged magnitude of pole voltage (averaged over successive high frequency carrier time period) is similar to the modulating signal. The pole voltage waveform thus has a low frequency component whose instantaneous magnitude is proportional to the modulating signal (also implying that they will have same frequency and will be in-phase).
- Apart from this low frequency component the pole voltage will also have high frequency harmonic voltages. However, unlike in the case of pure dc modulating signal the harmonic frequencies are now not simply integral multiples of carrier frequency.
- This is so because here the widths of the high frequency pole-voltage pulses do not remain constant throughout. The pulse widths get modulated due to slowly varying modulating signal. As a result the harmonics in the pole voltage waveform are of frequencies that are shifted from the carrier (and multiples of carrier frequency) by the integral multiples of modulating wave frequency.
- In fact one gets a band of harmonic frequencies centered around the carrier and integral multiples of carrier frequency. The individual frequencies that form the band are displaced from these central frequencies by integral multiples of modulating wave frequency. However, the modulating wave frequency being negligible compared to the carrier frequency, the dominant harmonics are still in the vicinity of carrier frequency and multiples of carrier frequency.
- A more detailed harmonic analysis of the sine-modulated pole voltage waveforms is beyond the scope of this course. The low frequency (modulating frequency) component of the pole output voltage is often referred as fundamental frequency component.
- The ratio of carrier and modulating frequencies may not be very high but the pole voltage still has a fundamental frequency component proportional to and in-phase with the modulating signal. The essential advantage of having very high carrier frequency, in comparison to the modulating wave frequency, is that the useful fundamental frequency component of pole voltage and the unwanted harmonics (having frequencies close to the carrier and multiples of carrier frequency) are far apart on the frequency spectrum and one can virtually filter away the harmonic voltages without attenuating the magnitude of the fundamental frequency component by putting a suitable low pass filter.
- The filter size requirement remains small if the harmonics are of high frequencies. In some applications, like ac motor drive application, the inherent low pass filtering characteristics of the motor-load itself is enough to satisfactorily block the flow of harmonic currents to the load. In such cases the need for external filter may not arise.
- High carrier frequency calls for high switching frequency of the inverter switches. In fact the switches turn-on and turn-off once during each carrier cycle. Generally the switches used in high power applications (say, more than few hundred kW) can be switched only at sub kilohertz frequency and hence the carrier frequency cannot be arbitrarily high. The switching frequency related loses are also to be considered before deciding the carrier frequency of the sine-PWM inverter.