1. “Real” Transformer E P = 4.44N P fΦ P E S = 4.44N S fΦ S Φ P = Φ M + Φ lp Φ S = Φ M – Φ ls E P = E’ P + E lp E S = E’ S - E ls

2. KVL @ primaryV T = E P + I P R P = E’ P + E lp +I P R P I P = I fe + I M + I P LOAD “Real” Transformer (continued)

3. Equivalent Circuit of a Real Transformer V T = E P + I P R P = E’ P + E lp +I P R P

4. KVL @ secondaryE S = I S R S + V LOAD = E’ S – E ls E’ S = E ls + I S R S + V LOAD “Real” Transformer (continued)

5. Equivalent Circuit of a Real Transformer V T = E P + I P R P = E’ P + E lp +I P R P E’ S = E ls + I S R S + V LOAD

6. Flux in the “Leakage coils”

7. Voltage generated by flux through the window of a coil

8. Similar expression for the secondary

9. Equivalent Circuit using Leakage Reactance

10. Equivalent Impedance of a Transformer

12. Equivalent Circuit Parameters Referred to the Primary Define Z eqP = The “equivalent impedance” with all parameters referred to the primary

13. Equivalent Circuit Parameters Referred to Secondary

14. Note that the excitation branch has been moved to the left! It’s OK as long as the transformer is operated near rated conditions!

15. Equivalent Circuit for Step-Down Operation Using High-Side Values Use this equivalent circuit to determine the input impedance of the transformer and load.

16. Equivalent Circuit for Step-Down Operation Using Low-Side Values Use this equivalent circuit to determine the no-load voltage and the voltage regulation.

17. Equivalent Circuit for Step-Up Operation Using Low-Side Values Use this equivalent circuit to determine the input impedance of the transformer and load.

18. Equivalent Circuit for Step-Up High-Side Values Use this equivalent circuit to determine the no-load voltage and the voltage regulation.