3. ﻣﻘﺪﻣﻪ :
ﺑﺮﺍﻱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﺗﻮﺍﻥ ﻳﻚ ﺑﺎﺭ ﻣﻘﺎﻭﻣﺘﻲ ﺩﺭﻳﻚ ﺷﺒﻜﺔ DCﻣﻲ ﺗﻮﺍﻧﻴﻢ
ﻭﻟﺘﺎﮊ ﻭ ﺟﺮﻳﺎﻥ ﺭﺍ ﺍﻧﺪﺍﺯﻩ ﺑﮕﻴﺮﻳﻢ . ﺑﺮﺍﻱ ﺍﻳﻦ ﻣﻨﻈﻮﺭ ﺩﻭ ﺭﻭﺵ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ
Ic
ﺑﮑﺎﺭ ﺑﺮﺩ .
Ic
IR
+ _
A
Ip
+ V
c
VR
+
V
_
2
Vp
_
+ IR
R
_
V
Ip
+
V
A
Vp
_
1
2
VR
= PP
RV
3
2 PC = R A I R
Pm = I C V P = ( I R + I P ) V R = PR + PP where
)1
Pm = I C V P = ( V R + V C ) I R = PR + PC where
)2
8. ﺣﺎﻝ ﺍﮔﺮ ، I p = VR / R p ، I c = I Rﺑﺎﺷﺪ ﺩﺍﺭﻳﻢ:
θ
RP
=θ
=⇒P
K
′K
ﻭﻟﻲ ﺩﺭ ﻭﺍﻗﻊ ،
1 dM VR
P
=θ
IR
=K
S dθ R P
RP
VR
I R VR
θ = KI C I P = KI C
≈K
= K′P
RP
RP
ﻳﻌﻨﻲ θ ≈ K ′Pﺩﺭ ﺣﺎﻟﻲ ﮐﻪ ) θ = K ′Pﻳﻌﻨﻲ ﻭﺍﺗﻤﺘﺮ ﺑﺮ ﺍﺳﺎﺱ ﺍﻳﻦ ﺿﺮﻳﺐ
ﻣﺪﺭﺝ ﻣﻲ ﺷﻮﺩ.(
m
8
9. ﺍﮔﺮ ﺟﺮﻳﺎﻧﻬﺎ acﺑﺎﺷﻨﺪ ﻧﻴﺰ
ﻭ ﺍﮔﺮ i = i Cﻭ i P = vﺑﺎﺷﺪ ﺩﺍﺭﻳﻢ :
i
RP
ic
+
V
_
Z
ip
1T
θ = k ∫ i Ci P dt
0T
T
1 k
k
=θ
P = k′P
= ∫ ivdt
0 RP T
RP
R
p
1T
ﻫﻤﺎﻥ ﺗﻌﺮﻳﻒ ﺗﻮﺍﻥ ﺍﮐﺘﻴﻮ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﻣﻮﺭﺩ ﺳﻴﻨﻮﺳﻲ )VICos(ϕ
ﮐﻪ ∫ ivdt
0T
9
ﻣﻲ ﺷﻮﺩ .
10. : ﻭ ﻳﺎ
RP
RP T
Pm =
θ=
∫ i Ci P dt
k
T 0
: ﺍﻟﺒﺘﻪ ﺧﻄﺎﻳﻲ ﮐﻪ ﻗﺒﻼ ﺍﺷﺎﺭﻩ ﮐﺮﺩﻳﻢ ﻭﺟﻮﺩ ﺩﺍﺭﺩ ﻭ ﺩﺭ ﻭﺍﻗﻊ
k 1T
k 1T
kT
θ = ∫ i Ci P dt ≈
∫ i C vdt ≈
∫ ivdt = k ′P
RP T 0
RP T 0
T0
P≈
Rp
k
θ ﻭﻟﻲPm =
Rp
k
θ ﺩﺭ ﺍﻳﻨﺠﺎ ﻧﻴﺰ
10
14. ﺁﻧﺎﻟﻴﺰ ﻭﺍﺗﻤﺘﺮ ﺩﺭ ﺣﺎﻟﺖ ﺩﺍﺋﻤﻲ ﺳﻴﻨﻮﺳﻲ
~
iC = I C Cos (ωt + ϕC ) I C = I C e jϕ
~
iP = I P Cos (ωt + ϕ P ) I P = I P e jϕ
~
v(t ) = VCos (ωt )
V =V < 0
C
P
~
iC = Re{I C e jωt }
~
iP = Re{I P e jωt }
~
IC
R
p
~
I
LP
~
IP
~
Z
14
15. RP T
1T
ﺍﻣﺎPm = ∫ iC iP dt ﻭθ = k ∫ i Ci P dt ﺩﻳﺪﻳﻢ ﮐﻪ
T 0
T0
1T
1
~~
(ϕc − ϕ P ) = 1 Re I C I *P
∫ iC iP dt = I C I PCos
2
2
T0
{
{
RP
~~
Pm =
Re I C I * P
2
}
}
: ﻳﻌﻨﻲ
15
16. :ﺣﺎﻝ ﺑﺮﺍﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﺧﻄﺎﻱ ﻭﺍﺗﻤﺘﺮ
~ = ze jϕ
z
~ = R + j ωL = z e j β
zp
p
p
p
ﻳﺎ
~
~ ~ ~ ~ v V − jϕ
I C = I + I P I = ~ = e = Ie − jϕ
z z
~ V − jβ
v
~
Ip = ~ = e
zp zp
16
17. [
]
(
1
1
~ ~ ~* 1
~~
2
Pm = R p Re (I + I p )I p = RP I P + RP Re I I p*
2
2
2
⎛ − jϕ V + jβ ⎞
1
= PP + RP Re⎜ Ie
e ⎟
⎜
⎟
2
zp
⎝
⎠
1 RP
= PP + VI
cos(ϕ − β )
2 zP
1
= PP + VI cos(β ) cos(ϕ − β )
2
ωLP
ﻭRP = cos(β)
= sin(β )
zP
zP
)
: ﺯﻳﺮﺍ
17