Inverters

DC-DC converters reshape DC voltage levels. But solar panels, batteries, and fuel cells all produce DC — and the grid, motors, and most appliances need AC.

An inverter bridges that gap by switching DC polarity rapidly to synthesize an AC waveform.

Half-Bridge Inverter

The simplest inverter topology uses two switches and a split DC supply. When S1 is on, the load sees $+V_{dc}/2$ ; when S2 is on, it sees $-V_{dc}/2$ .

Figure 1. Half-bridge inverter — two switches, split DC supply, and load

V_{1,rms} = \frac{2V_{dc}}{\pi\sqrt{2}}

Output is a square wave swinging between $+V_{dc}/2$ and $-V_{dc}/2$ .
Only two switches — simple and low cost, but limited output amplitude.

Full-Bridge (H-Bridge) Inverter

Four switches arranged in an H configuration deliver the full DC bus voltage to the load. S1+S4 fire together for the positive half-cycle; S2+S3 fire for the negative half-cycle.

Figure 2. Full-bridge inverter — four switches in an H configuration with load across the mid-points

V_{1,rms} = \frac{4V_{dc}}{\pi\sqrt{2}}

Output swings the full $\pm V_{dc}$ — double the half-bridge amplitude.
No split supply needed, making it the standard topology for kW-class inverters.

PWM Control

A square wave carries heavy harmonics. Sinusoidal PWM compares a high-frequency triangle carrier against a sine reference to generate variable-width pulses whose fundamental tracks the reference.

Figure 3. PWM control — triangle carrier vs sine reference, switching pattern, and filtered output

m_a = \frac{V_{control}}{V_{tri}}

V_1 = m_a \times V_{dc}

Modulation index $m_a$ sets the fundamental amplitude — 0 to 1 in the linear range.
Higher switching frequency pushes harmonics further from the fundamental, making the LC filter smaller and cheaper.

Total Harmonic Distortion

THD measures how much of the output energy sits in harmonics rather than the fundamental. Lower THD means a cleaner waveform closer to a pure sine.

THD = \frac{\sqrt{V_{rms}^2 - V_1^2}}{V_1}

A square wave has THD ≈ 48.3% — nearly half its energy is harmonic content.
Sinusoidal PWM with an LC filter brings THD below 5%, suitable for sensitive loads.

Waveform	THD	Cost	Typical use
Square wave	≈ 48%	Low	Resistive heaters, simple tools
Modified sine	≈ 25%	Medium	Budget UPS, camping inverters
Pure sine (PWM)	< 5%	Higher	Grid-tie solar, motor drives, medical