In this case, unlike that of the pole voltage, the largest harmonic component becomes the order of 2 m f ± 1. 7.33 depicts the harmonic spectrum for the line-to-line voltage in the case of m f = 21 and MI=0.8. In that case, the harmonic of order 2 m f ± 1 becomes the largest component for the range of MI<0.9, while m f ± 2 around MI=1. Furthermore, among these values, only the odd values can eliminate the even harmonics for the symmetry of three-phase PWM patterns. For this reason, the value of m f is usually selected as multiples of three. Hence, if we select the value of m f as multiples of three, then the total harmonics will be reduced in the line-to-line voltage due to the elimination of the harmonics at multiples of three. As mentioned earlier, this is because the harmonics at multiples of three included in the pole voltages will have no phase difference with each other. Since the line-to-line voltage is the difference between the two pole voltages, they do not have any harmonic at multiples of three, which exist in the pole voltages. Next we will examine the harmonic components for the line-to-line and phase voltages. On the other hand, different pole voltage reference can be used according to the PWM techniques. Typical SPWM technique uses a phase voltage reference as the pole voltage reference. Thus the voltage reference that is compared with the triangular carrier wave is considered as the pole voltage reference. Difference Between Pole Voltage and Phase Voltage ReferencesĪn inverter output determined by comparing a voltage reference with the triangular carrier wave is the pole voltage. Typical SPWM technique uses the sinusoidal modulating waveform. On the other hand, different forms of modulating wave can be used according to the PWM technique. The triangular waveform is the most commonly used carrier in the PWM technique for modulating AC voltage. The carrier wave usually has a much higher frequency than the modulating wave. In addition, a wave which is modulated with the modulating wave is referred to as carrier wave or carrier. The frequency of oscillation can be determined as f o = 1/T, where T represents the time required for one oscillation.In the carrier-based PWM techniques, the desired voltage reference waveform is referred to as modulating wave. Therefore, total time required for one oscillation is given as The time taken by capacitor to charge from V UT to V LT is same as time required for charging capacitor from V LT to V UT. At t = T 1, voltage across capacitor reaches V UT and therefore equation (3) becomes Let us consider the charging of capacitor from V LT to V UT, where V LT is the initial voltage, V UT is the instantaneous voltage and +V sat is the maximum voltage. V max is the voltage toward which the capacitor is charging. V C(t) is the instantaneous voltage across the capacitor. The voltage across the capacitor as a function of time is given as
BIPOLAR SQUARE WAVE EQUATION GENERATOR
The frequency of oscillation of Square Wave Generator Using Op amp is determined by the time it takes the capacitor to charge from V UT to V LT and vice versa. Once the, initial cycle is completed, the waveform become periodic, as shown in the Fig. The capacitor will discharge from V LT to 0V and then recharge to V UT, and the process is repeating. 2.84(a) is reestablished except that capacitor now has a initial charge equal to V LT. When V C becomes slightly more negative than the feedback voltage V LT, output voltage V o switches back to +V sat. The current I – discharges capacitor to 0 V and recharges capacitor to V LT. As V o switches to -V sat, capacitor starts discharging via R f, as shown in the Fig. This switches the output voltage from +V sat to -V sat and we have V p = V LT, which is negative with respect to ground. As long as the capacitor voltage V C is less than V UT, the output voltage remains at +V sat.Īs soon as V C charges to a value slightly greater than V UT, the (-) input goes positive with respect to the (+) input. With V o = +V sat we have – V p = V UT and capacitor starts charging towards +V sat through the feedback path provided by the resistor R f to the inverting (-) input. When power is turn ON, V o automatically swings either to +V sat or to -V sat since these are the only stable states allowed by the schmitt trigger.