Question

A single-phase inverter has a square wave output voltage. The percentage of the fifth harmonic component in relation to the fundamental component is:

• A. 10
• B. 20
• C. 30
• D. 40

Hint:

For a square wave, the harmonic components follow an inverse relationship with their order: \( V_n = \frac{4V_m}{n\pi} \). The fifth harmonic is always 20% of the fundamental.

Answer 1

The Correct Option is B

Step 1: The Fourier series representation of a square wave contains only odd harmonics, represented as: \[ V_n = \frac{4V_m}{n\pi}, \quad n = 1, 3, 5, 7, \dots \] where:
- \( V_n \) is the \( n \)-th harmonic component.
- \( V_m \) is the peak value of the square wave.
- \( n \) is the harmonic order. 
Step 2: The fundamental component (\( n = 1 \)) is: \[ V_1 = \frac{4V_m}{\pi} \] 
Step 3: The fifth harmonic component (\( n = 5 \)) is: \[ V_5 = \frac{4V_m}{5\pi} \] 
Step 4: The percentage of the fifth harmonic relative to the fundamental is calculated as: \[ \frac{V_5}{V_1} \times 100 = \frac{\frac{4V_m}{5\pi}}{\frac{4V_m}{\pi}} \times 100 \] \[ = \frac{1}{5} \times 100 = 20% \] 
Step 5: Therefore, the fifth harmonic component represents 20% of the fundamental.