![Formulario
DIODOS DE POTENCIA
La corriente del diodo
𝐼 𝐷 = 𝐼𝑆 (𝑒
𝑉 𝐷
𝜂𝑉𝑇⁄
− 1)
𝐼 𝐷 = 𝐶𝑜𝑟𝑟𝑖𝑒𝑛𝑡𝑒 𝑞𝑢𝑒 𝑝𝑎𝑠𝑎 𝑜 𝑎𝑡𝑟𝑎𝑣𝑖𝑒𝑠𝑎 𝑒𝑙 𝑑𝑖𝑜𝑑𝑜
𝑉𝐷 = 𝑉𝑜𝑙𝑡𝑎𝑗𝑒 𝑑𝑒 𝑑𝑖𝑜𝑑𝑜 𝑜 𝑣𝑜𝑙𝑡𝑎𝑗𝑒 𝑢𝑚𝑏𝑟𝑎𝑙
𝐼𝑠 = 𝐶𝑜𝑟𝑟𝑖𝑒𝑛𝑡𝑒 𝑑𝑒 𝑓𝑢𝑔𝑎
𝑉𝑇 = 𝑉𝑜𝑙𝑡𝑎𝑗𝑒 𝑡𝑒𝑟𝑚𝑖𝑐𝑜
𝑉𝑇 =
𝐾𝑇
𝑞
𝑞 = 1,6022𝑥10−19[𝐶]
𝑇 = (273. 15 𝑜]𝑡𝑎𝑛)[𝐾]
𝐾 = 1.3806𝑥10−23 [
𝐽
𝐾
]
𝐼𝑆𝑆 =
𝐼 𝐷
𝑒
𝑉 𝐷
𝜂𝑉𝑇⁄
− 1
Características de recuperación inversa
𝑡 𝑟𝑟 = 𝑡𝑜 + 𝑡𝑏
𝑡𝑎 ≅ 𝑡𝑏
𝐼𝑟𝑟 =
2𝑄 𝑅𝑅
𝑡 𝑟𝑟
𝑡 𝑟𝑟 = √
2𝑄 𝑅𝑅
𝑑𝑖
𝑑𝑡
𝑡𝑎 ≈ 𝑡𝑏
𝑠 𝐹 =
𝑡𝑏
𝑡𝑎
𝐼 𝑅𝑅 = 𝑡𝑎
𝑑𝑖
𝑑𝑡
𝑄 𝑅𝑅 =
1
2
𝑑𝑖
𝑑𝑡
𝑡 𝑟𝑟
2
RECTIFICADOR MONOFASICO NO
CONTROLADO
𝑤 = 2𝜋𝑓
𝑉𝑃
𝑉𝑆
=
𝑛 𝑝
𝑉𝑠
= 𝑁
𝑉 𝑚𝑃
𝑉𝑚𝑠
= 𝑁
𝑉𝑆 = 𝑉𝑅 𝑠𝑒𝑛(𝑤𝑡)
Voltaje puntual
𝑖(𝑤𝑡) =
𝑉𝑅
𝑅
𝑉𝑑𝑐 =
1
𝑇
= ∫ 𝑉𝑆(𝑤𝑡)𝑑(𝑤𝑡)
𝑇
0
Voltaje promedio
Factor de transferencia
𝑉𝑑𝑐 =
𝑉𝑃
𝑉𝑀
𝐹𝑓 =
𝑉𝑝
2
𝑉𝑝
𝜋
𝐹𝑓 =
𝑉𝑝
2
𝜋
2
𝐼0.0 =?
FACTOR DE RISADO
Factor de riso
𝐹𝑟 =
√𝜋2 − 4
2
𝑥100
POTENCIA DC
𝑃 𝐷𝐶 =
𝑉𝑝2
𝜋2 𝑅](https://image.slidesharecdn.com/formulario1-161024013717/85/Formulario-1-1-320.jpg)
![POTENCIA MEDIA O ACTIVA
𝑃 = 𝑉𝑟 𝑚𝑠 ∗ 𝐼𝑟𝑚𝑠 𝑐𝑜𝑠 𝜃
𝐼𝑟𝑚𝑠 =
𝑉𝑟𝑚𝑠
𝑅
POTENCIA APARENTE
𝑆 = 𝑉𝑟 𝑚𝑠 ∗ 𝐼𝑟𝑚𝑠
FACTOR DE POTENCIA
𝑓𝑝 =
𝑃
𝑆
𝑃 = 𝐼𝑟𝑚𝑠
2
∗ 𝑅
𝑃 𝐷𝐶 = 𝑉𝐷𝐶 ∗ 𝐼 𝐷𝐶
𝑉𝐷𝐶 = 𝑉𝑂 = 𝑉𝑅 =
𝑉𝑚
𝜋
𝐼 𝐷𝐶 = 𝐼 𝑂 = 𝐼 𝑅 =
𝑉𝑂
𝑅
Rectificadores de media onda no controlados – RL
𝑉𝑚 = 𝑠𝑒𝑛(𝑤𝑡) = 𝑉𝑅 + 𝑉𝐿
𝑉𝑚 = 𝑠𝑒𝑛(𝑤𝑡) = 𝑅𝑖(𝑤𝑡) + 𝐿
𝑑𝑖
𝑑𝑡
𝑖(𝑤𝑡) = 𝑖𝑓(𝑤𝑡) + 𝑖𝑛(𝑤𝑡)
𝑖𝑓(𝑤𝑡) =
𝑉𝑚
𝑧
𝑠𝑒𝑛(𝑤𝑡 − 𝜃)
𝑧 = √ 𝑅2 + (𝑤𝐿)2
𝜃 = tan−1
(
𝑤𝐿
𝑅
)
𝑖𝑛(𝑤𝑡) = 𝐴𝑒−
𝑤𝑡
𝑤𝜏
𝜏 =
𝐿
𝑅
; 𝐴 =
𝑉𝑚
𝑧
𝑠𝑒𝑛(𝜃)
𝑖(𝑤𝐿) =
𝑉𝑚
𝑧
[𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒−
𝑤𝑡
𝑤𝜏]
𝑖(𝛽) =
𝑉𝑚
𝑧
[𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒−
𝑤𝑡
𝑤𝜏]
𝑖(𝑤𝑡) = {
𝑉𝑚
𝑧
[𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒−
𝑤𝑡
𝑤𝜏] ; 0 ≤ 𝑤𝑡 ≤ 𝛽
0 ; 𝛽 ≤ 𝑤𝑡 ≤ 2𝜋
𝐼 𝑜 =
1
2𝜋
∫ 𝑖(𝑤𝑡)𝑑𝑤𝑡
𝛽
0
𝐼𝑟𝑚𝑠 = √
1
2𝜋
∫ 𝑖(𝑤𝑡)2 𝑑𝑤𝑡
𝛽
0
𝑃 =
1
2𝜋
∫ 𝑣(𝑤𝑡) ∗ 𝑖(𝑤𝑡)𝑑𝑤𝑡
𝑝
0
𝑉𝑜 =
1
2𝜋
∫ 𝑉𝑚𝑑(𝑤𝑡)
𝛽
0
Rectificadores de onda completa y trifásicos
𝑉𝑜(𝑤𝑡) =
1
𝜋
{
𝑉𝑚 𝑝𝑎𝑟𝑎 0 ≤ 𝑤𝑡 ≤ 𝜋
−𝑉𝑚 𝑝𝑎𝑟𝑎 𝜋 ≤ 𝑤𝑡 ≤ 2𝜋
𝑉𝑜 =
1
𝜋
∫ 𝑉𝑚 𝑠𝑒𝑛(𝑤𝑡)𝑑(𝑤𝑡) =
2𝑉𝑚
𝜋
𝜋
0
𝐼 𝑜 =
𝑉𝑜
𝑅
=
2𝑉𝑚
𝜋𝑅
𝐼𝑟𝑚𝑠 =
𝐼 𝑚
√2
𝑉𝑜(𝑤𝑡) = 𝑉𝑜 + ∑ 𝑉𝑛 cos(𝑛𝑤𝑡 + 𝜋)
∞
𝑛=2,4…..
𝑉𝑜 =
2𝑉𝑚
𝜋
𝑉𝑛 =
2𝑉𝑚
𝜋
(
1
𝑛 − 1
−
1
𝑛 + 1
)
𝐼 𝑛 =
𝑉𝑛
𝑍 𝑛
=
𝑉𝑛
|𝑅 + 𝑗𝑛𝑤𝐿|
𝐼𝑟𝑚𝑠 = 𝑉𝑜
2
+ ∑ (
𝐼 𝑛
√2
)
∞
𝑛=2,4,6..
𝑍 𝑛 = |𝑅 + 𝑗𝑛𝑤𝐿|](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Formulario 1
- 1. Formulario DIODOS DE POTENCIA La corriente del diodo 𝐼 𝐷 = 𝐼𝑆 (𝑒 𝑉 𝐷 𝜂𝑉𝑇⁄ − 1) 𝐼 𝐷 = 𝐶𝑜𝑟𝑟𝑖𝑒𝑛𝑡𝑒 𝑞𝑢𝑒 𝑝𝑎𝑠𝑎 𝑜 𝑎𝑡𝑟𝑎𝑣𝑖𝑒𝑠𝑎 𝑒𝑙 𝑑𝑖𝑜𝑑𝑜 𝑉𝐷 = 𝑉𝑜𝑙𝑡𝑎𝑗𝑒 𝑑𝑒 𝑑𝑖𝑜𝑑𝑜 𝑜 𝑣𝑜𝑙𝑡𝑎𝑗𝑒 𝑢𝑚𝑏𝑟𝑎𝑙 𝐼𝑠 = 𝐶𝑜𝑟𝑟𝑖𝑒𝑛𝑡𝑒 𝑑𝑒 𝑓𝑢𝑔𝑎 𝑉𝑇 = 𝑉𝑜𝑙𝑡𝑎𝑗𝑒 𝑡𝑒𝑟𝑚𝑖𝑐𝑜 𝑉𝑇 = 𝐾𝑇 𝑞 𝑞 = 1,6022𝑥10−19[𝐶] 𝑇 = (273. 15 𝑜]𝑡𝑎𝑛)[𝐾] 𝐾 = 1.3806𝑥10−23 [ 𝐽 𝐾 ] 𝐼𝑆𝑆 = 𝐼 𝐷 𝑒 𝑉 𝐷 𝜂𝑉𝑇⁄ − 1 Características de recuperación inversa 𝑡 𝑟𝑟 = 𝑡𝑜 + 𝑡𝑏 𝑡𝑎 ≅ 𝑡𝑏 𝐼𝑟𝑟 = 2𝑄 𝑅𝑅 𝑡 𝑟𝑟 𝑡 𝑟𝑟 = √ 2𝑄 𝑅𝑅 𝑑𝑖 𝑑𝑡 𝑡𝑎 ≈ 𝑡𝑏 𝑠 𝐹 = 𝑡𝑏 𝑡𝑎 𝐼 𝑅𝑅 = 𝑡𝑎 𝑑𝑖 𝑑𝑡 𝑄 𝑅𝑅 = 1 2 𝑑𝑖 𝑑𝑡 𝑡 𝑟𝑟 2 RECTIFICADOR MONOFASICO NO CONTROLADO 𝑤 = 2𝜋𝑓 𝑉𝑃 𝑉𝑆 = 𝑛 𝑝 𝑉𝑠 = 𝑁 𝑉 𝑚𝑃 𝑉𝑚𝑠 = 𝑁 𝑉𝑆 = 𝑉𝑅 𝑠𝑒𝑛(𝑤𝑡) Voltaje puntual 𝑖(𝑤𝑡) = 𝑉𝑅 𝑅 𝑉𝑑𝑐 = 1 𝑇 = ∫ 𝑉𝑆(𝑤𝑡)𝑑(𝑤𝑡) 𝑇 0 Voltaje promedio Factor de transferencia 𝑉𝑑𝑐 = 𝑉𝑃 𝑉𝑀 𝐹𝑓 = 𝑉𝑝 2 𝑉𝑝 𝜋 𝐹𝑓 = 𝑉𝑝 2 𝜋 2 𝐼0.0 =? FACTOR DE RISADO Factor de riso 𝐹𝑟 = √𝜋2 − 4 2 𝑥100 POTENCIA DC 𝑃 𝐷𝐶 = 𝑉𝑝2 𝜋2 𝑅
- 2. POTENCIA MEDIA O ACTIVA 𝑃 = 𝑉𝑟 𝑚𝑠 ∗ 𝐼𝑟𝑚𝑠 𝑐𝑜𝑠 𝜃 𝐼𝑟𝑚𝑠 = 𝑉𝑟𝑚𝑠 𝑅 POTENCIA APARENTE 𝑆 = 𝑉𝑟 𝑚𝑠 ∗ 𝐼𝑟𝑚𝑠 FACTOR DE POTENCIA 𝑓𝑝 = 𝑃 𝑆 𝑃 = 𝐼𝑟𝑚𝑠 2 ∗ 𝑅 𝑃 𝐷𝐶 = 𝑉𝐷𝐶 ∗ 𝐼 𝐷𝐶 𝑉𝐷𝐶 = 𝑉𝑂 = 𝑉𝑅 = 𝑉𝑚 𝜋 𝐼 𝐷𝐶 = 𝐼 𝑂 = 𝐼 𝑅 = 𝑉𝑂 𝑅 Rectificadores de media onda no controlados – RL 𝑉𝑚 = 𝑠𝑒𝑛(𝑤𝑡) = 𝑉𝑅 + 𝑉𝐿 𝑉𝑚 = 𝑠𝑒𝑛(𝑤𝑡) = 𝑅𝑖(𝑤𝑡) + 𝐿 𝑑𝑖 𝑑𝑡 𝑖(𝑤𝑡) = 𝑖𝑓(𝑤𝑡) + 𝑖𝑛(𝑤𝑡) 𝑖𝑓(𝑤𝑡) = 𝑉𝑚 𝑧 𝑠𝑒𝑛(𝑤𝑡 − 𝜃) 𝑧 = √ 𝑅2 + (𝑤𝐿)2 𝜃 = tan−1 ( 𝑤𝐿 𝑅 ) 𝑖𝑛(𝑤𝑡) = 𝐴𝑒− 𝑤𝑡 𝑤𝜏 𝜏 = 𝐿 𝑅 ; 𝐴 = 𝑉𝑚 𝑧 𝑠𝑒𝑛(𝜃) 𝑖(𝑤𝐿) = 𝑉𝑚 𝑧 [𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒− 𝑤𝑡 𝑤𝜏] 𝑖(𝛽) = 𝑉𝑚 𝑧 [𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒− 𝑤𝑡 𝑤𝜏] 𝑖(𝑤𝑡) = { 𝑉𝑚 𝑧 [𝑠𝑒𝑛(𝑤𝑡 − 𝜃) + 𝑠𝑒𝑛(𝜃)𝑒− 𝑤𝑡 𝑤𝜏] ; 0 ≤ 𝑤𝑡 ≤ 𝛽 0 ; 𝛽 ≤ 𝑤𝑡 ≤ 2𝜋 𝐼 𝑜 = 1 2𝜋 ∫ 𝑖(𝑤𝑡)𝑑𝑤𝑡 𝛽 0 𝐼𝑟𝑚𝑠 = √ 1 2𝜋 ∫ 𝑖(𝑤𝑡)2 𝑑𝑤𝑡 𝛽 0 𝑃 = 1 2𝜋 ∫ 𝑣(𝑤𝑡) ∗ 𝑖(𝑤𝑡)𝑑𝑤𝑡 𝑝 0 𝑉𝑜 = 1 2𝜋 ∫ 𝑉𝑚𝑑(𝑤𝑡) 𝛽 0 Rectificadores de onda completa y trifásicos 𝑉𝑜(𝑤𝑡) = 1 𝜋 { 𝑉𝑚 𝑝𝑎𝑟𝑎 0 ≤ 𝑤𝑡 ≤ 𝜋 −𝑉𝑚 𝑝𝑎𝑟𝑎 𝜋 ≤ 𝑤𝑡 ≤ 2𝜋 𝑉𝑜 = 1 𝜋 ∫ 𝑉𝑚 𝑠𝑒𝑛(𝑤𝑡)𝑑(𝑤𝑡) = 2𝑉𝑚 𝜋 𝜋 0 𝐼 𝑜 = 𝑉𝑜 𝑅 = 2𝑉𝑚 𝜋𝑅 𝐼𝑟𝑚𝑠 = 𝐼 𝑚 √2 𝑉𝑜(𝑤𝑡) = 𝑉𝑜 + ∑ 𝑉𝑛 cos(𝑛𝑤𝑡 + 𝜋) ∞ 𝑛=2,4….. 𝑉𝑜 = 2𝑉𝑚 𝜋 𝑉𝑛 = 2𝑉𝑚 𝜋 ( 1 𝑛 − 1 − 1 𝑛 + 1 ) 𝐼 𝑛 = 𝑉𝑛 𝑍 𝑛 = 𝑉𝑛 |𝑅 + 𝑗𝑛𝑤𝐿| 𝐼𝑟𝑚𝑠 = 𝑉𝑜 2 + ∑ ( 𝐼 𝑛 √2 ) ∞ 𝑛=2,4,6.. 𝑍 𝑛 = |𝑅 + 𝑗𝑛𝑤𝐿|