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XIII.Frequency Response XIV.The Laplace Transform XV.. Analysis of Magnetically Coupled Circuits 4.[r]
(1)Electric Circuit Theory
(2)Contents
I. Basic Elements Of Electrical Circuits II. Basic Laws
III Electrical Circuit Analysis IV Circuit Theorems
V Active Circuits
VI Capacitor And Inductor VII First Order Circuits VIII.Second Order Circuits
IX Sinusoidal Steady State Analysis X AC Power Analysis
XI Three-phase Circuits
XII Magnetically Coupled Circuits
XIII.Frequency Response XIV.The Laplace Transform XV Two-port Networks
(3)Magnetically Coupled Circuits
1 Mutual Inductance 2 Dot Convention
3 Analysis of Magnetically Coupled Circuits 4 Energy in a Coupled Circuit
(4)Mutual Inductance (1)
Magnetically Coupled Circuits - sites.google.com/site/ncpdhbkhn
d
v N
dt
Faraday’s law:
+
–
+
–
( )
i t
v
turns
N
d di N
di dt
L di
dt
d
L N
di
(5)Mutual Inductance (2)
1 11 12
1 1 1 d v N dt 12 2 2 d v N dt
1 1
1
d di di
N L
di dt dt
12 1 1
2 21
d di di
N M
di dt dt
1 21 di M dt + – + –
1( )
i t v 12 turns N 11
L L2
+
– v2
2 turns
(6)Mutual Inductance (3)
Magnetically Coupled Circuits - sites.google.com/site/ncpdhbkhn
+
–
+
–
2( )
i t v 21 turns N 22
L L2
+
– v2
2 turns N + – + –
1( )
i t v 12 turns N 11
L L2
(7)Mutual Inductance (4)
+
–
+
–
1( )
i t
1
v
12
1 turns
N 11
1
L L2
+
– v
2 turns
N
1 21
di
v M
dt
1( )
i t
1
v v2
12
11
(8)Mutual Inductance (5)
Magnetically Coupled Circuits - sites.google.com/site/ncpdhbkhn
1( )
i t v 12 11
1( )
i t v 12 11 di v M dt di v M dt
1( )
i t v 12 11 di v M dt
1( )
(9)Magnetically Coupled Circuits
1 Mutual Inductance
2 Dot Convention
3 Analysis of Magnetically Coupled Circuits 4 Energy in a Coupled Circuit
(10)Dot Convention (1)
Magnetically Coupled Circuits - sites.google.com/site/ncpdhbkhn 10
+
–
1( )
i t
1
L
2
L
+
–
2
v M
1 2
di
v M
dt
• If a current enters a dotted
terminal of one coil, it induces a positive voltage at the dotted terminal of the second coil
• If a current leaves a dotted