Inverters

Problem

A full-bridge inverter with $V_{dc} = 200\,\text{V}$ drives a resistive 50 Ω load using a square wave. Find the RMS output voltage, fundamental RMS voltage, and THD.

Step 1 — RMS Output Voltage

A full-bridge square wave swings between $+V_{dc}$ and $-V_{dc}$ . Both halves have equal magnitude, so the RMS equals the DC bus voltage.

V_{rms} = V_{dc} = 200\,\text{V}

Step 2 — Fundamental RMS

V_{1,rms} = \frac{4 V_{dc}}{\pi\sqrt{2}} = \frac{4 \times 200}{\pi \times 1.414} = 180.0\,\text{V}

Step 3 — THD

THD = \frac{\sqrt{V_{rms}^2 - V_1^2}}{V_1} = \frac{\sqrt{200^2 - 180^2}}{180} = \frac{87.2}{180} = 48.4\%

Figure 1. Square wave output (green, ±200 V) with fundamental sine (blue, 180 V RMS)

Nearly half the energy in a square wave sits in harmonics. PWM + filtering reduces THD to under 5%, making the output safe for sensitive loads.