CIRCUITO ORIGINAL
DOMINIO DEL TIEMPO
𝑡 < 0 𝑣𝑐 (0− ) =?
𝑣𝑐 (0− ) = 𝑣2.2𝑘
C.D.V
𝑣𝑐 (0− ) =
(9)(2.2𝑘)
= 6.1875 𝑉
3.2𝑘
𝑡=0
𝑣𝑐 (0) = 𝑣𝑐 (0− ) = 6.1875 𝑣
𝑖0 = −
6.1875
= 0.0281 𝐴
220
𝑡>0
Σ𝑣 = 0
𝑣𝑐 + 𝑣𝑅 = 0
(1000 ∫ 𝑖(𝑡)𝑑𝑡 + 220 𝑖(𝑡) = 0)
1000 𝑖(𝑡)𝑑𝑡 + 220
𝑑
𝑑𝑡
𝑑
=0
𝑑𝑡
𝑖(𝑡)(2200 + 1000) = 0
𝑖(𝑡) = 𝑖𝑒 𝐷𝑡 𝑠𝑜𝑙. 𝑔𝑒𝑛𝑒𝑟𝑎𝑙
𝑖ℎ 𝑦 𝐷 ?
𝐷?
220𝐷 + 1000 = 0
∴ =
−1000
= −4.545
2200
𝑖ℎ =? 𝑡 = 0 𝑖(0) = −0.0281
𝑖(0) = 𝑖ℎ 𝑒 𝐷(0) = −0.0281
DOMINIO DE LA FRECUENCIA
CIRCUITO ORIGINAL
𝑡 < 0 𝑣𝑐 (0− ) =?
𝐶. 𝐼 = lim {𝐹(𝑠)} 𝑡𝑒𝑜𝑟𝑒𝑚𝑎 𝑑𝑒𝑙 𝑣𝑎𝑙𝑜𝑟 𝑓𝑖𝑛𝑎𝑙
𝑠→0
𝑧𝑒𝑞 (𝒮) =
1000
2.2𝑥106
) 1.034𝑥106 ⋅
𝑠
𝑠
=
1000
2.2𝑥106
2670 + 𝑠
2670 +
𝑠
2200 (470 +
1.034𝑥106 + 2.2𝑥106
1.034𝑥106 + 2.2𝑥106
𝑠
𝑧𝑒𝑞 (𝒮) =
=
2670 + 1000
2670 + 1000
𝑠
𝑧𝑒𝑞 (𝒮) =
1000(2670 𝑠 + 1000) + 1.034𝑥106 𝑠 + 2.2𝑥106
2670 𝑠 + 1000
𝑣𝑧𝑒𝑞 (𝒮) =
9
( 𝑠 ) (1.034𝑥106 𝑠 + 2.2𝑥106 )
1000(2670 𝑠 + 1000) + (1.034𝑥106 𝑠 + 2.2𝑥106 )
1000
𝑣𝑧𝑒𝑞 ( 𝑠 )
(6.187)1000
𝑣𝑐 (𝒮) =
=
470𝑠 + 1000 470𝑠 + 1000
𝑣𝑐 (0− ) = lim
𝑠→0
𝑠{𝑣𝑐 (𝑠)} = 6.187 𝑣
𝑡≥0
6.187
6.187
0.028
𝑠
𝐼(𝑠) =
=
=
1000 220𝑠 + 1000 𝑠 + 4.54
220 + 𝑠
𝐼(𝑠) = −0.028 𝑒 −4.54𝑡
C1
𝑡 < 0 𝑣𝑐 (0− ) =?
=
14.8𝑥106
3.2𝑥106
𝐼(0− ) =
9𝑣
= 2.818 𝐴
3.195
𝑡=0
𝑖(0) =
−2.818 𝑣
= −0.0128 𝐴
220
𝑡>0
Σ𝑣 = 0
𝑣𝑙 + 𝑣𝑅 = 0
(0.001 ∫ 𝑖(𝑡)𝑑𝑡 + 220 𝑖(𝑡) = 0)
0.001 𝑖(𝑡)𝑑𝑡 + 220
𝑑𝑖(𝑡)
=0
𝑑𝑡
𝑖(𝑡)(0.011 + 220) = 0
𝑖ℎ 𝑦 𝐷 ?
𝑖(𝑡) = 𝑖𝑒 𝐷𝑡 𝑠𝑜𝑙. 𝑔𝑒𝑛𝑒𝑟𝑎𝑙
220 𝐷 − 0.001 = 0
∴ −
0.001
= −4.554𝑥106
220
𝑖ℎ =? 𝑡 = 0 𝑖(0) = −0.0128
𝑖(0) = 𝑖ℎ 𝑒 𝐷(0) = −0.0128
𝑡 < 0 𝑣𝑐 (0− ) =?
𝑑
𝑑𝑡
𝑍𝑒𝑞 (𝑠) =
1
2420 (470 + 0.001𝑠 )
1
2890 + 0.001𝑠
=
2.42𝑥103
𝑠
2.42𝑥103
2890 +
𝑠
1.1374𝑥106 ⋅
1.1374𝑥106 ⋅ 2.42𝑥106
1.1374𝑥106 + 2.42𝑥103
𝑠
(𝑠)
(
)
𝑍𝑒𝑞
=
=
2890 + 1
1
2890 + 0.001
0.001𝑠
D.D.V
𝑣𝑧𝑒𝑞 (𝑠) =
9 1.1374𝑥106 + 2.42𝑥103
)
(𝑠 ) (
1
2890 + 0.001
1.1374𝑥106 + 2.42𝑥103
)
1000 (
1
2890 +
0.001
𝑣𝑧𝑒𝑞 (𝑠) =
1
(𝑣𝑧𝑒𝑞 ) (0.001)
470𝑠
1
0.001𝑠
=
= 470𝑠
1
470𝑠 +
0.001𝑠