Modulation Index & Over-Modulation
- Modulation index is the ratio of peak magnitudes of the modulating waveform and the carrier waveform. It relates the inverter’s dc-link voltage and the magnitude of pole voltage (fundamental component) output by the inverter. Now let be the modulating signal and let the magnitude of triangular carrier signal vary between the peak magnitudes of .The ratio of the peak magnitudes of modulating wave and the carrier wave is defined as modulation-index (m). In other words:
- Normally the magnitude of modulation index is limited below one (i.e., 0<m<1). From the discussion in the previous section it can be concluded that for 0<m<1, the instantaneous magnitude of fundamental pole voltage (V AO,1) will be given by:
VAO,1 = 0.5Edc(msinωt)
where ‘ω’ is the angular frequency of the modulating waveform.
- For = 1 the pole output voltage (fundamental component) will have a rms magnitude .This magnitude is only 78.5% of the fundamental pole voltage magnitude output by a square wave inverter operating from the same dc link voltage.
- When the peak magnitude of modulating signal exceeds the peak magnitude of carrier signal (resulting in m >1), the PWM inverter operates under over-modulation.
- During over-modulation the fundamental component of the pole voltage increases slightly with increase in modulation index but the linear relation between them no longer continues.
- Also, lower frequency harmonics crop up in the pole-output waveform. It may easily be seen that for ‘m’ very high (say m = infinity), the pole voltage shape will be identical to the square wave shape.
- Over modulation is generally not preferred because of the introduction of lower frequency harmonics in the output waveform and subsequent distortion of the load current.