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Power Electronics

Inverters and SPWM

An inverter produces AC from DC — this is the road from a solar panel to the grid, or from an electric car’s battery to its motor. In a half-bridge, two switches connect the output alternately to the + and − rail; when the resulting fast square pulses pass through an LC filter, a smooth sine wave remains.

The way to "draw" the sine is SPWM: the duty is varied continuously along with the desired sine — d(t) = ½(1 + m·sin(2πf₀t)). At the sine’s crest the pulses widen; in its trough they narrow. m (the modulation depth) is the volume knob for the output amplitude.

A deadly trap: if the two switches in the same leg conduct together for even an instant, they short-circuit the supply (shoot-through). The cure is a microsecond-scale dead time during every transition in which both stay off. Drive three half-bridges 120° apart in phase and you get three-phase power.

Formulas

d(t) = ½(1 + m·sin(2πf₀t))
V₁(fundamental) = m · VDC/2
fLC = 1/(2π√(LC)) « f_carrier

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Test Yourself

Why is dead-time necessary?
Answer: To prevent the switches in the same leg from overlapping and shorting the supply — Overlap (shoot-through) short-circuits the rail current through the switches.
In a 3-phase inverter, what is the angle between phases?
Answer: 120° — Three phases are generated at 360°/3 = 120° intervals.