Inverters: Single-Phase and Three-Phase With easy examples.

An inverter does the opposite of a rectifier: it converts DC into AC. A battery, solar array or DC link feeds a bridge of transistors that switch on and off in a precise sequence, chopping the DC into an alternating waveform that — after filtering — becomes the AC that motors, appliances and the grid itself can use.

Inverters are everywhere clean AC is needed away from the mains: the UPS backing up a computer, the solar inverter feeding a home, the variable-frequency drive spinning an industrial motor, and the traction inverter driving an electric car. The same bridge topology scales from a 100 W camping inverter to a 100 MW grid converter.

Key Concepts

• Half-bridge vs full-bridge: a half-bridge uses two switches and a split supply for ±Vdc/2 output; a full-bridge (H-bridge) uses four switches to apply the full ±Vdc across the load.
• Square-wave output: the simplest switching pattern — full positive, then full negative — rich in harmonics and suitable only for rugged loads.
• Sinusoidal PWM: the switch duty cycle is modulated following a sine reference, pushing harmonics to high frequencies where a small LC filter removes them, yielding near-sine output.
• Three-phase inverter: three half-bridge legs switched 120° apart; operated in 180° or 120° conduction modes for six-step output, or with PWM for sinusoidal output.
• Modulation index: the ratio of the sine reference amplitude to the carrier amplitude in PWM; it sets the output voltage linearly up to overmodulation.
• Dead time: a brief blanking delay between turning off one switch and turning on its complementary partner, preventing a short across the DC bus (shoot-through).

Formulas

• Square-wave full-bridge: Vrms = Vdc (the output swings fully between +Vdc and −Vdc).
• Fundamental of square wave: V1,rms = 4Vdc/(π√2) ≈ 0.900 × Vdc.
• Three-phase 180° mode, line-to-line: Vll,rms = √(2/3) × Vdc ≈ 0.816 × Vdc.
• SPWM linear range: V1,rms (phase) = m × Vdc/(2√2), with modulation index m ≤ 1.

Worked Example

A single-phase full-bridge inverter runs from a 300 V DC bus with plain square-wave switching. The output RMS voltage is simply Vdc = 300 V, but it is a harsh square wave. Its fundamental component is V1,rms = 4 × 300/(π × √2) ≈ 270 V — a 270 V sine buried in harmonics, which an LC filter can extract. The same 300 V bus feeding a three-phase bridge in 180° conduction mode gives a line-to-line RMS of √(2/3) × 300 ≈ 245 V of six-step waveform, close to a 230 V-class motor supply once filtered or PWM-shaped.

Common Misconceptions

• "Inverter output is a sine wave." Only after PWM plus filtering; the raw bridge output is a switched rectangular waveform, and cheap "modified sine" inverters are really stepped squares.
• "A bigger DC bus is always better." Higher bus voltage raises output capability but stresses every switch and the insulation — devices and clearances must be rated for it.
• "Output frequency follows the load." The controller sets the frequency by its switching pattern; the load merely draws whatever current the resulting voltage drives through it.

Real-World Applications

• Solar string inverters convert 600–1500 V DC arrays into grid-synchronized 50 Hz AC with PWM and LCL filters.
• Variable-frequency drives rectify the mains to DC, then invert it back at variable frequency and voltage for precise motor speed control.
• UPS systems invert battery DC instantly when the mains fails, with switchover times under 10 ms.
• Electric-vehicle traction inverters turn 400–800 V battery DC into three-phase AC for the drive motor, and reverse the process for regenerative braking.

An inverter is a rectifier run backwards in spirit: switches, timing and filtering turn steady DC into controlled AC. Start from the square-wave bridge, add sinusoidal PWM to clean the spectrum, extend to three phases for motors and grids — and respect dead time, because one shoot-through event can destroy the whole bridge.