ES2C6 – Power Electronics 7 - Rectifiers
Rectifiers
Half Wave Rectifier
A half wave rectifier acts by blocking the negative part of the AC sine wave.
As only the first half of each wave is output, the voltage can be calculated by integration:
𝑇
1 2
𝑉𝐷𝐶 = ∫ 𝑉𝑃 sin 𝜔𝑡 𝑑𝑡
𝑇 0
𝑇
𝑉𝑃 cos 𝜔𝑡 2
= [− ]
𝑇 𝜔 0
𝑉𝑃
= (22)
𝜋
A capacitor is used to smooth the voltage in an attempt to make it steadier:
𝑉𝑖𝑛 = 𝐼𝑅 + 𝑉𝐶
𝑑𝑉𝐶
𝐼=𝐶
𝑑𝑡
𝑑𝑉𝐶
𝑉𝑖𝑛 = 𝑅𝐶 + 𝑉𝐶
𝑑𝑡
𝑡
𝑉𝐶 = 𝑉𝑖𝑛 (1 − 𝑒 −𝑅𝐶 ) (23)
During the negative half of the cycle the capacitor will discharge into the load, resulting in a
smoother voltage supply.
30
Rectifiers
Half Wave Rectifier
A half wave rectifier acts by blocking the negative part of the AC sine wave.
As only the first half of each wave is output, the voltage can be calculated by integration:
𝑇
1 2
𝑉𝐷𝐶 = ∫ 𝑉𝑃 sin 𝜔𝑡 𝑑𝑡
𝑇 0
𝑇
𝑉𝑃 cos 𝜔𝑡 2
= [− ]
𝑇 𝜔 0
𝑉𝑃
= (22)
𝜋
A capacitor is used to smooth the voltage in an attempt to make it steadier:
𝑉𝑖𝑛 = 𝐼𝑅 + 𝑉𝐶
𝑑𝑉𝐶
𝐼=𝐶
𝑑𝑡
𝑑𝑉𝐶
𝑉𝑖𝑛 = 𝑅𝐶 + 𝑉𝐶
𝑑𝑡
𝑡
𝑉𝐶 = 𝑉𝑖𝑛 (1 − 𝑒 −𝑅𝐶 ) (23)
During the negative half of the cycle the capacitor will discharge into the load, resulting in a
smoother voltage supply.
30
