1. Terminology and Relationship
Current:
(A)
Magnetic Flux:
(Wb)
Current Density :
(A/m2)
Magnetic Flux Density :
(Wb/m2)
Conductivity:
(1/Ω·m)
Permeability:
(Wb/A·m)
Electrical Field Intensity:
(V/m)
Magnetic Field Intensity:
(A·t/m)
Votage:
(V)
Magnetomotive Force:
(A·t)
Resistance:
(Ω)
Reluctance:
(A·t/Wb)
for constant and A is perpendicular to B

2. Terminology and Relationship
For a wire carrying a current i, the magnetic field intensity H surrounding the wire is
For a coil around a magnetic core, the magnetic field intensity H inside the core is
where l is the core mean length

3. Inductance According to Faraday’s Law:
where N is the turns in the coil
The total flux is proportional to the current in the coil:
Here L is the inductance, and therefore we obtain:

4. Inductance
define reluctance
(Final)

5. B versus H behavior

6. Limitation of Input Voltage and Frequency

7. Coupled Inductors
where k is coupling coefficient and 0≤ k ≤1

8. Coupled Inductors
Apply KVL:

9. Coupled Inductors

10. Ideal Transformer
For k=1,
where n is called turns ratio n=N2/N1

11. Ideal Transformer
For an ideal transformer, it does not dissipate power, therefore the input
power should equal the output power:
Therefore, the input impedance for the transformer:

12. Non-Ideal Transformer
For a non-ideal transformer, we don’t know whether V1 and I1 in phase or not:

13. Non-Ideal Transformer
When ?

14. Non-Ideal Transformer
When
we have