XIII.Frequency Response XIV.The Laplace Transform XV.. Analysis of Magnetically Coupled Circuits 4.[r]
Trang 1Electric Circuit Theory
Magnetically Coupled Circuits
Trang 2I 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
Trang 3Magnetically Coupled Circuits
1 Mutual Inductance
2 Dot Convention
3 Analysis of Magnetically Coupled Circuits
4 Energy in a Coupled Circuit
5 Transformers
Trang 4Mutual Inductance (1)
d
dt
Faraday’s law:
–
–
( )
i t
turns
N
d di N
di dt
dt
d
di
Trang 5Mutual Inductance (2)
1 11 12
1
d
dt
d
dt
1 1 1
1
di dt dt
1 21
di M
dt
–
–
i t
1
v
12
1 turns
N
11
1
L L2
– v2
2 turns
N
Trang 6Mutual Inductance (3)
–
–
i t
1
v
21
1 turns
N
22
1
L L2
2 turns
N
–
–
i t
1
v
12
1 turns
N
11
1
L L2
– 2
v
2 turns
N
1 1
1
di
v L
dt di
v M
dt
2
2 2
di
v M
dt di
v L
dt
Trang 7Mutual Inductance (4)
–
–
i t
1
v
12
1 turns
N
11
1
L L2
– 2
v
2 turns
N
1
di
v M
dt
1( )
i t
1
12
11
Trang 8Mutual Inductance (5)
1( )
i t
1
v
12
11
1( )
i t
1
v
12
11
1 2
di
v M
dt
2
di
v M
dt
1( )
i t
1
v
12
11
1 2
di
v M
dt
1( )
i t
1
v
12
11
1 2
di
v M
dt
Trang 9Magnetically Coupled Circuits
1 Mutual Inductance
2 Dot Convention
3 Analysis of Magnetically Coupled Circuits
4 Energy in a Coupled Circuit
5 Transformers
Trang 10Dot Convention (1)
–
i t
1
L
2
L
–
2
v M
1 2
di
dt
• If a current enters a dotted
terminal of one coil, it induces
terminal of the second coil
• If a current leaves a dotted
terminal of one coil, it induces
a negative voltage at the dotted
terminal of the second coil