Inverters

Inverters convert DC into AC of controllable voltage and frequency. Learn half- and full-bridge topologies, square-wave and sinusoidal PWM, modulation index, three-phase inverters, dead time, output filters and grid-tied operation.

An inverter switches a DC source across a load in alternating directions to create AC. With pulse-width modulation, the average of the switched voltage follows a sine wave, and a filter or the load's inductance smooths it.

Solar inverters, UPS systems, motor drives, EV traction and grid batteries all rely on inverters — they are the interface between the DC world of batteries and panels and the AC world of the grid and motors.

An analogy

An inverter is like pushing a swing: you push in one direction, then the other, at just the right times. The timing (PWM) decides how smoothly and how high it swings (voltage).

The H-bridge

Four switches form an H around the load. Closing the diagonal pair S1–S4 applies +V_dc; S2–S3 applies −V_dc. Alternating them makes AC. Never close both switches in one leg — that shorts the DC supply (shoot-through).

Output waveforms

Different switching patterns trade cost against waveform quality.

• Square wave: simplest; THD ≈ 48 %, bad for motors and sensitive loads.
• Modified sine (quasi-square): zero steps cut THD to ~30 %; cheap UPSs.
• Sinusoidal PWM: high-frequency switching whose average follows a sine; after an LC filter the output THD can be < 3 %.

Modulation index and frequency

In SPWM, a sine reference is compared with a triangle carrier. The ratio of amplitudes is the modulation index m, which scales output voltage; the reference frequency sets output frequency. Beyond m = 1 (overmodulation) output rises further but low-order harmonics appear.

Three-phase inverters and SVPWM

Six switches in three legs produce three phases. Space-vector PWM treats the eight switch states as voltage vectors and synthesises any reference vector by time-averaging neighbours. It uses the DC bus 15 % better than sine PWM — equivalent to adding third-harmonic injection.

Dead time, filters and grid-tied control

A dead time of ~0.5–2 µs between turning one switch off and the other on prevents shoot-through, but distorts the output voltage. LC or LCL filters remove switching ripple. Grid-tied inverters synchronise with a PLL and control current into the grid; grid codes add anti-islanding, fault ride-through and reactive-power support.

Formulas

• Square-wave full bridge (fundamental peak): V₁ = 4V_dc / π
• SPWM full bridge: V₁,peak = m · V_dc
• SPWM half bridge: V₁,peak = m · V_dc / 2
• Three-phase SPWM (line RMS): V_LL,rms = 0.612 · m · V_dc (0.707 with SVPWM / 3rd-harmonic)

Worked example: Single-phase SPWM inverter output

Given: V_dc = 400 V; Full bridge; m = 0.9

Find: Fundamental peak and RMS.

• V₁,peak = 0.9 × 400 = 360 V
• V₁,rms = 360/√2 = 254.6 V

Answer: ≈ 255 V RMS — enough for 230 V AC

Worked example: Square-wave inverter from 48 V

Given: V_dc = 48 V, full bridge, square wave

Find: Fundamental RMS.

• V₁,peak = 4 × 48/π = 61.1 V
• V₁,rms = 61.1/√2 = 43.2 V

Answer: 43.2 V RMS fundamental (THD ≈ 48 %)

Common mistakes

• Wrong: Switching both transistors of a leg at the same edge. — Right: Insert dead time; simultaneous conduction shorts the DC link (shoot-through).
• Wrong: Running a motor from a cheap square-wave inverter. — Right: Harmonics overheat motors and transformers; use sine PWM.

Applications

• Solar inverters: String and micro-inverters track the panels' maximum power point and inject grid-synchronised current.
• UPS & battery storage: Online UPSs continuously invert from a battery-backed DC bus; home batteries use bidirectional inverters.
• EV traction: A 400/800 V battery feeds a SiC or IGBT three-phase inverter driving the traction motor with field-oriented control.

Key takeaways

• Inverters switch DC into AC; the H-bridge is the building block.
• SPWM: V₁,peak = m·V_dc (full bridge); three-phase V_LL = 0.612 m V_dc.
• SVPWM gives 15 % more voltage from the same DC link.
• Dead time prevents shoot-through; filters clean the output.

Going further

• Multilevel inverters: NPC, flying-capacitor and modular multilevel converters (MMC) synthesise many voltage levels, reducing dv/dt, harmonics and device voltage stress — MMCs are the standard for VSC-HVDC.
• LCL filter resonance: LCL filters attenuate switching ripple strongly but introduce a resonance that must be damped passively (resistor) or actively (control), or the current loop becomes unstable.
• Grid-forming vs grid-following: Grid-following inverters inject current relative to a measured grid voltage; grid-forming inverters set voltage and frequency themselves, enabling islanded operation and stabilising weak grids.