POWER ELECTRONICS – PAGE 10
Numerical Problems – Half Wave Controlled Rectifier
Problem 1
A Half Wave Controlled Rectifier is supplied with Vm = 200V. Firing angle α = 60°. Find average output voltage.
Solution
Formula:
Vavg = (Vm / 2π) (1 + cos α)
Convert α into radians: 60° = π/3
cos 60° = 0.5
Vavg = (200 / 2π)(1 + 0.5)
= (200 / 6.283) × 1.5 = 31.83 × 1.5 = 47.75 V
Problem 2
Input RMS voltage = 230V. Find Vavg when α = 90°.
Solution
First convert RMS to peak:
Vm = √2 × 230 = 325V
cos 90° = 0
Vavg = (325 / 2π)(1 + 0)
= 325 / 6.283 = 51.74 V
Problem 3
For what firing angle will output voltage become zero?
Solution
From formula:
(1 + cos α) = 0
cos α = −1
α = 180°
GATE Focus Points
- Always convert RMS to Peak
- Always convert degrees carefully
- Check if α given in radians or degrees
- Maximum output at α = 0°
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