1. “Ideal Transformer” E’ P, E’ S = Voltages induced in the primary, secondary E’ HS, E’ LS = Voltages induced at High-side, Low-Side V HS, V LS = Nameplate voltages of High-side, Low-Side ECE 4411

2. “Ideal Transformer” (continued) Define the turns ratio as “a” –If the primary is the High-Side, ECE 4412

3. Input Impedance, Z’ in Z’ in = Impedance looking into the primary = E’ P / I P Turns ratio a = E’ P / E’ S >>>>> E’ P = aE’ S ECE 4413

4. Input Impedance, Z’ in (continued) For an IDEAL transformer, VA in =VA out E’ P I * P = E’ S I * S I * P = E’ S I * S / E’ P = I * S / a I P = I S / a ECE 4414

5. “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 ECE 4415

6. 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) ECE 4416

7. Equivalent Circuit of a Real Transformer V T = E P + I P R P = E’ P + E lp +I P R P ECE 4417

8. 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) ECE 4418

9. 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 ECE 4419

10. Equivalent Circuit using Leakage Reactance ECE 44110

11. Looking into the primary of the Ideal Transformer Z’ in = a 2 Z LOAD = a 2 (E’ S / I S ) I S = E’ S /(R S +jX ls + Z LOAD ) >>> E’ S / I S = R S + jX ls + Z LOAD Z’ in = a 2 R S + ja 2 X ls + a 2 Z LOAD ECE 44111

12. Equivalent Circuit Parameters Referred to Primary Define Z eqP = The “equivalent impedance” with all parameters referred to the primary Z eqP = R P + a 2 R S +jX lp +ja 2 X ls ECE 44112

13. Equivalent Circuit Parameters Referred to Secondary Z eqS = R S + R P /a 2 +j(X ls + X lp /a 2 ) ECE 44113