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In sinusoidal PWM, a low-frequency sine reference is compared against a high-frequency triangular carrier. Whenever the sine is above the carrier the top switch is on, so the duty cycle of each switching pulse follows the sine wave. Around zero-crossing the duty is 50%; at the sine peak it reaches its maximum; at the trough its minimum. The instantaneous duty is d(θ) = 0.5×(1 + ma·sinθ).
| Quantity | Formula |
|---|---|
| Instantaneous duty | d(θ) = 0.5(1 + ma·sinθ) |
| Maximum duty (θ=90°) | dmax = 0.5(1 + ma) |
| Minimum duty (θ=270°) | dmin = 0.5(1 − ma) |
| Pulse on-time | ton = d(θ) / fsw |
The duty swings symmetrically around 0.5. With ma = 1 it spans the full 0–100% range; with smaller ma it stays closer to 50%, producing a smaller output voltage. This averaged duty, filtered by the load inductance, reconstructs the sine wave at the inverter output.
The instantaneous duty is d(θ)=0.5×(1+ma·sinθ), where ma is the amplitude modulation ratio and θ is the electrical angle of the sine reference.
At the sine zero-crossing the reference equals the carrier centre, so the pulse is symmetric — on for half the period and off for half. This produces zero average output at that instant.
They occur at the sine peak and trough: dmax=0.5(1+ma) at 90° and dmin=0.5(1−ma) at 270°. With ma=1 they reach 100% and 0%.
ma sets how far the duty swings away from 50%. A larger ma gives a wider swing and larger output voltage; a smaller ma keeps the duty near 50% with a smaller output.
Multiply the duty by the switching period: ton=d(θ)/fsw=d(θ)×Tsw. For example, 90% duty at 10 kHz (100 µs period) gives a 90 µs on-time.
Bipolar SPWM switches the full bridge between +Vdc and −Vdc; unipolar switching adds a third level (0 V), halving the effective harmonic content and doubling the apparent switching frequency at the output. The per-leg duty formula is the same.
Not physically. If ma>1 the ideal formula would exceed 0–100%, but the hardware clamps the duty at the rails — this clamping is what causes overmodulation distortion.
Each of the three legs uses the same formula but with references 120° apart: da=0.5(1+masinθ), db at θ−120°, dc at θ−240°. The line-to-line voltages then form a balanced three-phase set.
mf=fcarrier/foutput is the number of carrier cycles per output cycle. A high mf gives more PWM pulses per sine cycle, pushing harmonics to high frequencies that the load inductance easily filters.
Yes. A small dead-time is inserted between the top and bottom switch turn-on to prevent shoot-through, which slightly reduces the effective on-time and distorts the output near zero-crossings, especially at low ma.
One duty value per switching pulse, i.e. mf points per output cycle. A higher carrier frequency needs a larger table but produces a smoother sine and lower audible noise.
No. SPWM compares each phase to a carrier independently. Space-vector PWM (SVPWM) treats the three phases together and adds a common-mode component, using the DC bus about 15% more effectively while producing a similar per-leg duty pattern.
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