Inverter PWM — sinusoidal PWM, modulation index, SVPWM
How comparing a sine with a triangle generates a clean AC sine at the output; m_a / m_f, over-modulation, and the 3-φ third-harmonic injection that boosts V_LL by 15 %.
Step 1 — The basic inverter: DC bus + switching → AC at the fundamental
Reference notes
Use Next → on the narrator to walk through inverter PWM: from square wave through sinusoidal PWM, modulation index, over-modulation, and three-phase third-harmonic / SVPWM injection.
The basic inverter
An inverter converts DC to AC. Topologies:
- Half-bridge: two switches in series across V_dc, load tied to midpoint. Output swings between +V_dc/2 and −V_dc/2.
- Full-bridge (H-bridge): four switches. Output swings between +V_dc and −V_dc — twice the half-bridge for the same DC bus.
- Three-phase: six switches in three half-bridges; the standard for motor drives.
Switches are IGBTs for ≤ 1700 V, MOSFETs for < 600 V, and IGCTs / SiC MOSFETs for higher voltages or higher switching frequencies.
Square-wave inverter
Switch once per half-cycle of the desired AC fundamental.
Output contains odd harmonics 3rd, 5th, 7th, ... at 1/h amplitudes. THD ≈ 48 %. Used only on the cheapest low-power UPS — modern drives never use square-wave mode.
Sinusoidal PWM (SPWM)
The standard for modern inverters. Two waveforms:
- Modulating signal: a sine at the desired output frequency, peak amplitude V_m,mod.
- Carrier: a triangle at the switching frequency f_carrier, peak amplitude V_m,tri.
Comparator: when sine > triangle, upper switch ON (+V_dc/2). When sine < triangle, lower switch ON (−V_dc/2). Output is a train of variable-width pulses at f_carrier whose average traces the sine.
Modulation index m_a and frequency ratio m_f
In the linear region (0 ≤ m_a ≤ 1):
Harmonics cluster around f_carrier and its multiples — far above the fundamental, so they're easily filtered by the motor's own leakage inductance.
Typical industrial choices:
- f_modulating: 0 to ~120 Hz (motor speed varies)
- f_carrier: 2–10 kHz for industrial IGBT drives; 16+ kHz for small drives (inaudible)
- m_f > 21 for low-distortion synchronous PWM; usually 15–40
Over-modulation
When m_a > 1, the modulating sine's peaks exceed the triangle's peaks. The inverter saturates at those peaks (held at +V_dc or −V_dc), reducing pulse-width modulation effectiveness near the peaks of the sine.
- Gains some additional fundamental output (up to 4·V_dc/π = square-wave limit at m_a ≫ 1).
- Injects low-order harmonics (3rd, 5th, 7th) that are hard to filter.
- Used briefly in field-weakening regions of motor drives where maximum V_LL is needed.
Three-phase PWM + third-harmonic injection / SVPWM
A three-phase inverter has three half-bridges. Each phase compares its own modulating sine (offset by 120°) against the same triangular carrier. Output is three quasi-sinusoidal phases.
The third-harmonic injection trick: add −(1/6) × sin(3·ω·t) to each phase's modulating signal. The third harmonic is in phase across all three phases and CANCELS in the line-to-line voltage. But it lowers the peak of each phase modulating signal — allowing m_a_eff up to ~1.155 in the linear region.
Space-Vector PWM (SVPWM) achieves the same result via a different geometric approach — switching the inverter through 8 discrete voltage vectors. Output line voltages are mathematically identical to third-harmonic SPWM but the implementation is more straightforward in a digital controller. Every modern motor drive uses SVPWM or its equivalent.
Keyboard shortcuts
- → next · ← previous · R replay · M mute · F fullscreen