Inverter Modulation Index Calculator

The amplitude modulation ratio m_a is the ratio of the peak of the sinusoidal reference to the peak of the triangular carrier in SPWM. It directly scales the fundamental output voltage in the linear region (m_a ≤ 1).

In the linear region the fundamental output is proportional to m_a. For a single-phase full bridge V_1(rms)=m_a·V_dc/√2, so doubling m_a doubles the output (up to m_a=1).

It is 0 ≤ m_a ≤ 1. Within this range the output rises linearly with m_a and the harmonics stay near the switching frequency, making them easy to filter.

When m_a > 1 the reference exceeds the carrier for part of the cycle, so the output stops rising linearly and low-order harmonics appear. It boosts the fundamental beyond the linear limit at the cost of distortion.

The absolute maximum is the six-step (square-wave) mode: for a single-phase full bridge (4/π)·V_dc/√2 ≈ 0.90·V_dc RMS, and for a three-phase inverter 0.78·V_dc line-to-line RMS.

For SPWM the phase peak is m_a·V_dc/2. The line-to-line value is √3 times the phase, and RMS divides the peak by √2, giving √3/(2√2)=0.612 times m_a·V_dc.

A full bridge applies the whole DC bus across the load and gives twice the output of a half bridge, which only swings between +V_dc/2 and −V_dc/2. Hence the full-bridge fundamental is m_a·V_dc/√2 versus m_a·V_dc/(2√2).

m_f = f_carrier/f_output is the ratio of the switching (carrier) frequency to the output frequency. A high, odd, integer m_f pushes harmonics to high frequencies and keeps the waveform symmetric.

Rearrange the formula. For a three-phase inverter, V_dc = V_LL(rms)/(0.612·m_a). Designers usually pick m_a around 0.85–0.95 to leave margin, which sets the required bus voltage.

Yes. Space-vector modulation (SVPWM) uses the bus about 15% more effectively than basic SPWM, reaching a line-to-line RMS of roughly 0.707·V_dc at the edge of the linear region versus 0.612·V_dc for SPWM.

A VFD keeps a constant volts-per-hertz ratio, so as it raises the output frequency it raises m_a to raise the voltage, until m_a reaches its limit at base speed. Above that, the motor runs in the field-weakening (constant-power) region.

Zero fundamental output. With no reference signal the inverter produces equal positive and negative pulses that average to zero, so no net AC voltage appears at the output.