ÿþ2
P a r a m e t r y p r z e b i e g u s i n u s o i d a l n e g o
i ( t ) = I m s i n ( Ét + Õ)
P o d s t a w y e l e k t r o t e c h n i k i
W a r t o [ c h w i l o w a
f a z a
p r d u
A m p l i t u d a p r d u
Õ f a z a p o c z t k o w a
( w a r t o [ m a k s y m a l n a )
É p u l s a c j a
T
É = 2 Àf c z s t o t l i w o [
f
i
1
f =
T o k r e s
I m
T
t
Ét
Õ
3 4
W a r t o [ s k u t e c z n a W a r t o [ s k u t e c z n a
R R
W a r t o [ s k u t e c z n a p r d u o k r e s o w e g o j e s t t o w a r t o [
z a s t p c z e g o p r d u s t a Be g o , k t ó r y w c i g u c z a s u T w y w o Ba
t a k i s a m s k u t e k c i e p l n y .
i ( t ) - f u n k c j a o k r e s o w a
I = c o n s t .
D l a p r d u s i n u s o i d a l n e g o
T o k r e s f u n k c j i
E = R I 2 T
T T T T T
1 1 1 - c o s ( 2 Ét ) d t = I m
2 2
2 2 2
E = d t = R d t R I 2 T = R d t I s k =
m m
+"R i +"i +"i +"[ I s i n ( Ét ) ] d t = +"I
T T 2
2
0 0 0 0 0
D l a n a p i c i a s i n u s o i d a l n e g o
u ( t ) = U m s i n ( Ét )
T W a r t o [ s k u t e c z n a
1
2
U m
I =
+"i d t p r d u o k r e s o w e g o U s k =
T
0
2
5 6
W a r t o [ [r e d n i a W a r t o [ [r e d n i a
R
T
R
1
M o c c h w i l o w a p ( t ) = u ( t ) Å"i ( t )
I [r =
+"i ( t ) d t
T
0
T
E n e r g i a p o b r a n a w c i g u o k r e s u
1
i ( t ) = I m s i n ( Ét ) I [r = s i n ( Ét ) d t = 0
m
+"I
T T
T
0
W = Å"i d t = d t
+"u +"p
0 0
W a r t o [ [r e d n i a p ó Bo k r e s o w a
W a r t o [ [r e d n i a e n e r g i i z a o k r e s
T 2
2 I m 1 2 I m
2
T 2
I [r =
T
0
m
+"I s i n ( Ét ) d t = [ - c o s ( Ét ) ] =
W 1
T É À
T
0
P = = d t
M o c c z y n n a p r d u o k r e s o w e g o
+"p
T T
2 À 0
É =
M o c c z y n n a P j e s t w a r t o [c i [r e d n i m o c y c h w i l o w e j p ( t )
T
7 8
R e z y s t o r w o b w o d z i e p r d u s i n u s o i d a l n e g o C e w k a w o b w o d z i e p r d u s i n u s o i d a l n e g o
u ( Ét ) L
R
i ( Ét )
t
Ét
i ( t ) = I m s i n ( Ét )
À/ 2
i ( t ) = I m s i n ( Ét ) U m
U m
N a p i c i e n a i n d u k c y j n o [c i
d i
u ( t ) = R Å"i ( t ) = R I m s i n ( Ét )
u ( t ) = L = L ÉI m c o s ( Ét )
w y p r z e d z a p r d o k t À/ 2 ( 9 0 º )
d t
u ( t ) = U m s i n ( Ét )
À
u ( t ) = U m c o s ( Ét ) = U m s i n ( Ét + )
2
1
U m = R I m
1
X L r e a k t a n c j a i n d u k c y j n a
2 U m = ÉL I m = X L I m
2
U = R I - d l a w a r t o [c i s k u t e c z n y c h
- d l a w a r t o [c i s k u t e c z n y c h
U = X L I
9 1 0
K o n d e n s a t o r w o b w o d z i e p r d u
M e t o d a a m p l i t u d z e s p o l o n y c h
s i n u s o i d a l n e g o
j ( Ét + È)
Z e s p o l o n y s y g n a B w y k Ba d n i c z y j = - 1
u ( t ) = U m e
C
u
I m
i ( t ) = I m s i n ( Ét )
t
U m
À/ 2
N a p i c i e n a p o j e m n o [c i
1 1
u ( t ) =
o p ó zn i a s i z a p r d e m o
+"i d t = I m [ - c o s ( Ét ) ]
R e
C C É
k t À/ 2 ( 9 0 º )
À
u ( t ) = - U m c o s ( Ét ) = U m s i n ( Ét - )
2
1
1
j ( Ét + È)
U m = I m = X C I m
u ( t ) = U m s i n ( Ét + È)
U m e = U m c o s ( Ét + È) + j U m s i n ( Ét + È)
X C r e a k t a n c j a p o j e m n o [c i o w a
ÉC 2
I m { u ( t ) } = u ( t )
U = X C I - d l a w a r t o [c i s k u t e c z n y c h
u ( t ) a" u ( t )
1 1 1 2
M e t o d a a m p l i t u d z e s p o l o n y c h M e t o d a a m p l i t u d z e s p o l o n y c h
u
R
j Ét
i U m e j ( Ét + È) = U m e j Èe j Ét
d ( I m e ) + +"I e d t = E m e
1
j Ét j Ét j Ét
R I m e + L
R m
d t C
e ( t ) L
u
L
U m - a m p l i t u d a z e s p o l o n a
C
1 1
j Ét j Ét j Ét j Ét
R I m e + L j ÉI m e + I m e = E m e
j Ét
u R + u L + u C = e C j É
e
u
C
ÉL = X L
1
e ( t ) = E m s i n ( Ét ) d i 1
= X C
R i + L + = e
+"i d t ÉC
d t C
R I m + j X L I m - j X C I m = E m 1
j Ét j Ét j 0
e ( t ) = E m e i ( t ) = I m e E m = E m e = E m
P o d s t a w i a m y :
2
R I + j X L I - j X C I = E
r ó w n a n i e d l a w a r t o [c i
d i ( t ) 1
s k u t e c z n y c h z e s p o l o n y c h
R i ( t ) + L +
+"i ( t ) d t = e ( t )
d t C
j Õ j È
I = I e E = E e
Z e s p o l o n e w a r t o [c i s k u t e c z n e :
1 3 1 4
M e t o d a a m p l i t u d z e s p o l o n y c h O p o r n o [ z e s p o l o n a
I [ R + j ( X L - X C ) ] = E
E
i m p e d a n c j a z e s p o l o n a
= R + j ( X L - X C ) = Z
( o p o r n o [ p o z o r n a )
E
j Õ
I
= I e
I =
R + j ( X L - X C )
R e a k t a n c j a
X
( o p o r n o [ b i e r n a )
E
X L - X C
öø
I =
Õ = a r c t g ëø-
ìø ÷ø
2
R
íø øø
R 2 + ( X L - X C ) Z = ( R + j X ) = Z e j ´ = Z ( c o s ´ + j s i n ´)
j Õ
P o s t a
I m = 2 I e P o s t a P o s t a
t r y g o n o m e t r y c z n a
a l g e b r a i c z n a w y k Ba d n i c z a
j Ét j ( Ét + Õ)
= 2 I e
i ( t ) = 2 I e j Õe
X
Z = R 2 + X 2 ´ = a r c t g R
i ( t ) = I m { i ( t ) } = 2 I s i n ( Ét + Õ) = I m s i n ( Ét + Õ)
R = Z c o s ´ X = Z s i n ´
1 5 1 6
P r z e w o d n o [ z e s p o l o n a
W y k r e s f a z o r o w y ( w s k a z o w y )
E
f a z o r n a p i c i a f a z o r p r d u
U
R j 0
I =
E = E e
I
Z
1
R
j Õ
Y = = ( G + j B )
Z = R + j ( X L - X C )
= Z e
X
E
L U
Z L
X
C
X L - X C
s u s c e p t a n c j a
Z = R 2 + ( X L - X C ) 2 Õ = a r c t g R
( p r z e w o d n o [ b i e r n a )
U
C
E E Õ < 0 d l a X L < X C
k o n d u k t a n c j a I = = e - j Õ
j Õ
Õ > 0 d l a X L > X C
Z
Z e
( p r z e w o d n o [ c z y n n a )
P r z e w o d n o [ z e s p o l o n a ( p o z o r n a )
a d m i t a n c j a
À
j ( - Õ- )
U L U R 2 2
U C = I ( - j X C ) = I X C e - j À = I X C e
E
À
j À
U C - Õ j ( - Õ+ )
2 2
U L = I ( j X L ) = I X L e = I X L e
I
U R = I R
= I R e - j Õ E
I =
Z
1 7 1 8
I m p e d a n c j a r e p r e z e n t a c j a g r a f i c z n a I m p e d a n c j a r e p r e z e n t a c j a g r a f i c z n a
Z = ( R + j X ) = Z e j ´ = Z ( c o s ´ + j s i n ´) Z = ( R + j X ) = Z e j ´ = Z ( c o s ´ + j s i n ´)
I m
I m ( Z ) = X
j X
´ ´
R
R e
R e ( Z ) = R
T r ó j k t i m p e d a n c j i
1 9 2 0
I m p e d a n c j a I m p e d a n c j a s c h e m a t d l a É= c o n s t .
C
R L Z
I I I I U
Z =
I
U
U U
U
s c h e m a t s z e r e g o w y
U U
U U U 1
Z R = = R Z L = = j ÉL = j X L Z C = =
R X R X
Z = R + j X
I I
I I I j ÉC
1 1
1 j À
2
Y R = Z - 1 = = G Z L = j X L = X L e Z C = = - j = - j X C
R
Z d l a X < 0
R j ÉC ÉC
Z d l a X > 0
1
s c h e m a t r ó w n o l e g By
Y L = Z - 1 = 2
U U
Z C = - j X C = X C e - j À
L
j ÉL
G G
Y = Z - 1 = G + j B
1 1
I I
-
Y L = = - j = - j B L
Y C = Z C 1 = j ÉC = j B C
j ÉL ÉL
B
B
j À
2
2
Y L = - j B L = B L e - j À Y C = j B C = B C e
Y d l a B < 0 Y d l a B > 0
Z
Z
2 1 2 2
I m p e d a n c j a s c h e m a t d l a É= c o n s t . P r a w o O h m a
U
R
I I Z R + I Z L + I Z C = E
I
Y = Z - 1
I
Z
R
R
Y = G - j B ( Z R + Z L + Z C ) I = E
Z
E
L U
L
Z
1 R - j X
C
G B U
a"
U
Z - 1 = =
Z = Z R + Z L + Z C
R + j X ( R + j X ) ( R - j X )
X R - j X R X U
C
Z I = E
= = - j
R 2 + X 2 R 2 + X 2 R 2 + X 2
I
R X
G = B =
R 2 + X 2 R 2 + X 2
I
E Z E = Z I
P r a w o O h m a
w p o s t a c i z e s p o l o n e j
1 R 2 + X 2 1 R 2 + X 2
R 0 X 0 U
R 0 = = X 0 = =
G R B X
2 3 2 4
P r a w a K i r c h h o f f a w p o s t a c i z e s p o l o n e j P r a w a K i r c h h o f f a w p o s t a c i z e s p o l o n e j
i 1 + i 2 + i 4 = i 3 + i 5
I I I
u 1 - u 2 - u 3 + u 4 = 0
i 1 + i 2 + i 4 = i 3 + i 5
u 1 - u 2 - u 3 + u 4 = 0
1
j Ét j Ét j Ét j Ét j Ét
I 1 m e + I 2 m e + I 4 m e = I 3 m e + I 5 m e
j Ét
2 e
I 1 + I 2 + I 4 = I 3 + I 5
1
j Ét j Ét j Ét j Ét
U 1 m e - U 2 m e - U 3 m e + U 4 m e = 0
j Ét
I 1 + I 2 - I 3 + I 4 - I 5 = 0
2 e
U 1 - U 2 - U 3 + U 4 = 0
N
= 0 N
"I k
k = 1
= 0
"U k
k = 1
2 5 2 6
M o c w o b w o d z i e p r d u s i n u s o i d a l n e g o
I m p e d a n c j a z a s t p c z a
Z Z Z
u ( t ) = U m s i n ( Ét + Õu )
N 2 1 N
Z =
"Z
k
i ( t ) = I m s i n ( Ét + Õi )
k = 1
M o c c h w i l o w a
p ( t ) = u ( t ) Å"i ( t ) = U m I m s i n ( Ét + Õu ) s i n ( Ét + Õi )
N
T
1
1
Y = 1
Z Z Z Z =
N 2 1 "Y
k
M o c c z y n n a
P = d t
Y
+"p = U m I m c o s ( Õu - Õi )
k = 1
2
T
0
1
1 U m I m = U I
Y k =
Õu - Õi = Õ U m I m =
Z k
2
2 2
Z 1 Z 2
Z =
Z Z
K t p r z e s u n i c i a
2 1
Z 1 + Z 2
f a z o w e g o m i d z y
P = U I c o s Õ
n a p i c i e m i p r d e m
2 7 2 8
M o c w o b w o d z i e p r d u s i n u s o i d a l n e g o
T r ó j k t m o c y
u ( t ) = U m s i n ( Ét + Õu )
i ( t ) = I m s i n ( Ét + Õi )
j Q
Z
Õ
U m I m
u u i i
U = e j Õ = U e j Õ I = e j Õ = I e j Õ
P
2 2
S = P 2 + Q 2
S = U I * I * = I e - j Õi
M o c p o z o r n a z e s p o l o n a
P
Õ Q = S s i n Õ Q = P t g Õ
u
S = U I e j ( Õ - Õi ) = U I ( c o s Õ+ j s i n Õ)
= U I c o s Õ+ j U I s i n Õ
P = S c o s Õ
S - m o c p o z o r n a
c o s Õ - w s p ó Bc z y n n i k m o c y
- m o c b i e r n a
Q
S = P + j Q
S
2 9 3 0
T w i e r d z e n i e T h e v e n i n a
M e t o d a p o t e n c j a Bó w w z Bo w y c h
Z L 1 l i n i o w y u k Ba d a k t y w n y
Z L = j ÉL 2 Z R C = R 3 - j
ÉC 1
Z R L = R 1 + j ÉL 1
I 1
O k r e [l a n i e p a r a m e t r ó w U T , Z T
I 2
I 1 - I 2 - I 3 - I 4 = 0
d w ó j n i k a k t y w n y
V 1 I 3
Z R C V 2 U Z - V 1 + V 2
V 1 - V 2
I 1 = I 2 =
I 4
Z L Z R C
U T
V 1 - V 2
I 3 = I Z
I 4 =
Z R L s c h e m a t z a s t p c z y
Z R L
d w ó j n i k p a s y w n y
U Z - V 1 + V 2 V 1 - V 2 V 1 - V 2
Z T
- - I Z - = 0
Z L Z R C Z R L
Z T
U Z
U T
I Z -
Z L I Z - U Z Y L
z a B. : V 1 = 0 V 2 = =
1 1 1
Y L + Y R C + Y R L
+ +
Z L Z R C Z R L
3 1 3 2
D o p a s o w a n i e m o c o w e D o p a s o w a n i e m o c o w e
I I
U 2
z
Z o = ? Ò! P o = P m a x
P o = R o
P o P o
( R z + R o ) 2 + ( X z + X o ) 2
Z z Z z
Z z = R z + j X z Z o = R o + j X o
0
Z o Z o
U z
U z
U z U z "P o
( R z + R o ) 2 + ( X z + X 0 ) 2 - 2 R o ( R z + R o )
I = =
= U 2
Z z + Z o
R z + R o + j ( X z + X o )
2
"R o z
[ ( R z + R o ) 2 + ( X z + X o ) 2 ]
U z
P o = I 2 R o
I =
0
2
R 2 - R o = 0 Ô! R 2 - R o = 0
2
( R z + R o ) 2 + ( X z + X o ) 2
= U 2 z
z
z
U 2 ( R z + R o ) 4
z
P o = R o
R o = R z R o = - R z
( R z + R o ) 2 + ( X z + X o ) 2
Z o = R z - j X z z
= Z *
"P o 2 ( X z + X o )
Ô! X z + X o = 0
= U 2 R o = 0
2
"X o z
[ ( R z + R o ) 2 + ( X z + X o ) 2 ]
U 2 U 2 U 2
z z z
P o = R z = R z =
X o = - X z
( R z + R z ) 2 + ( X z - X z ) 2 ( 2 R z ) 2 4 R z
3 3
D o p a s o w a n i e m o c o w e
I
P o m o c zr ó d Ba S z = U z I *
Z z
U z U z
I = =
Z o
R z + R z + j ( X z - X z ) 2 R z
U z
U *
z
I * =
2 R z
Z z = R z + j X z
Z o = R z - j X z
U z U * z
U 2 2 P o = P z
z
=
S z = =
2 R z 2 R z
P o
s p r a w n o [ · = 1 0 0 % = 5 0 %
P z
Wyszukiwarka
Podobne podstrony:
Analog 12 72 Vinge, Vernor Original Sin v1 0sinKorzybski Obwody elektryczne 3Teoria Obwodyobwody reaktancyjneLovecraft, H P Ciudad sin nombre, LaSin And VengeanceGeneratory funkcji Exp i Sinarm sin cos q31?obwody szkic tech gniazdaOBWODY ELEKTRYCZNE i MAGNETYCZNE w5dolina el salón de baile sin baĄos o el rapto de los orinantesarm sin cos ?2?TAB SINfunction sinwięcej podobnych podstron