Lecture Electric circuit theory: Magnetically coupled circuits - Nguyễn Công Phương

Lecture Electric circuit theory - Magnetically coupled circuits presents the following content: Mutual inductance, Dot convention, analysis of magnetically coupled circuits, energy in a coupled circuit, transformers.

Electric Circuit Theory

Magnetically Coupled Circuits

Nguyễn Công Phương

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

Magnetically Coupled Circuits

1 Mutual Inductance

2 Dot Convention

3 Analysis of Magnetically Coupled Circuits

4 Energy in a Coupled Circuit

5 Transformers

di M

dt di

v L

dt





dt



Magnetically Coupled Circuits

1 Mutual Inductance

2 Dot Convention

3 Analysis of Magnetically Coupled Circuits

4 Energy in a Coupled Circuit

5 Transformers

1 2

di

dt



terminal of one coil, it induces

a positive voltage at the dotted

terminal of the second coil

terminal of one coil, it induces

a negative voltage at the dotted

terminal of the second coil

Dot Convention (2)

terminal of one coil, it induces

a positive voltage at the dotted

terminal of the second coil

terminal of one coil, it induces

a negative voltage at the dotted

terminal of the second coil

1 2

di

dt

 

1 2

di

dt

 

terminal of one coil, it induces

a positive voltage at the dotted

terminal of the second coil

terminal of one coil, it induces

a negative voltage at the dotted

terminal of the second coil

1 2

di

dt



terminal of one coil, it induces

a positive voltage at the dotted

terminal of the second coil

terminal of one coil, it induces

a negative voltage at the dotted

terminal of the second coil

Magnetically Coupled Circuits

1 Mutual Inductance

2 Dot Convention

3 Analysis of Magnetically Coupled Circuits

4 Energy in a Coupled Circuit

5 Transformers

Analysis of Magnetically Coupled Circuits (1)

Analysis of Magnetically Coupled Circuits (2)

R  L  M 

– +

Analysis of Magnetically Coupled Circuits (3)

Analysis of Magnetically Coupled Circuits (4)

1 Write voltages of mutual inductance

2 Assign signs at dotted terminals

(using dot convention)

Analysis of Magnetically Coupled Circuits (5)

Ex 2

Find current?

1 Write voltages of mutual inductance

2 Assign signs at dotted terminals

(using dot convention)

3 Write KVL equations

4 Write the set of equations & solve

for it

– + – +

60

0.4 H 0.2 H

Analysis of Magnetically Coupled Circuits (6)

Ex 3

Find current?

– + – +

60

0.4 H 0.2 H

Analysis of Magnetically Coupled Circuits (7)

+ –

V 2M

V 1M

+ –

1 Write voltages of mutual inductance

2 Assign signs at dotted terminals

(using dot convention)

3 Write KVL equations

4 Write the set of equations & solve

for it

Analysis of Magnetically Coupled Circuits (8)

– +

V 2M

V 1M

– +

Analysis of Magnetically Coupled Circuits (9)

+ –

V 2M

V 3M

+ –

Analysis of Magnetically Coupled Circuits (10)

+ –

V 2M

V 1M

– +

Analysis of Magnetically Coupled Circuits (11)

– +

V 2M

V 1M

+ –

Analysis of Magnetically Coupled Circuits (12)

+ –

V 2M

V 3M

– +

Analysis of Magnetically Coupled Circuits (13)

1 Write voltages of mutual inductance

2 Assign signs at dotted terminals (using dot convention)

3 Write KVL equations (branch current method or mesh

current method)

4 Write the set of equations & solve for it

Analysis of Magnetically Coupled Circuits (14)

Ex 7

Find the Thevenin equivalent subcircuit? I1

– +

Analysis of Magnetically Coupled Circuits (15)

Ex 8

Find the Thevenin equivalent subcircuit? I1

– +

Magnetically Coupled Circuits

1 Mutual Inductance

2 Dot Convention

3 Analysis of Magnetically Coupled Circuits

4 Energy in a Coupled Circuit

5 Transformers

Energy in a Coupled Circuit

Magnetically Coupled Circuits

1 Mutual Inductance

2 Dot Convention

3 Analysis of Magnetically Coupled Circuits

4 Energy in a Coupled Circuit

5 Transformers

Transformers (2)

Ex 1

Given an ideal step-down transformer rated at 22/0.4 kV, 1000 turns

on the primary side Find:

a) The turn ratio?

b) The number of turns on the secondary side?

Transformers (4)

• If v 1 & v 2 are both positive or both negative at the dotted terminals,

use +n

Otherwise, use –n

• If i 1 & i 2 both enter into or both leave the dotted

a b

–

a

b

4 25

in

R n

Z

1 1

Method 2

100 10

 V  V 

o0

10

0 V

22

 I

I

Transformers (15)

• Applications:

– Power supply transformers

– Transformers in power systems

– Isolation applications

– Impedance matching