1. 1 Lecture #25 EGR 272 – Circuit Theory II Transformers: Our earlier study of mutual inductance introduced the idea that the magnetic field produced by one coil can induce a voltage across another coil. This effect is maximized with transformers, where two coils (or sets of windings) are wound around the same core. This allows for a direct transfer of magnetic flux. Read: Chapter 12 in Electric Circuits, 6 th Edition by Nilsson

2. 2 Lecture #25 EGR 272 – Circuit Theory II Recall that = flux linkage N = number of turns  = magnetic flux (in Webers, Wb) and = N  = Li, where L = inductance in Henries, H Since the same magnetic flux, , flows through the windings it is also true that the rate of change of magnetic flux, d  /dt is the same, so Also So where a = turns ratio

3. 3 Lecture #25 EGR 272 – Circuit Theory II so Key transformer relationships We just saw that Similarly where a = turns ratio

4. 4 Lecture #25 EGR 272 – Circuit Theory II Transformer symbols General TransformerIron-core Transformer

5. 5 Lecture #25 EGR 272 – Circuit Theory II Examples of transformers (reference: www.allelectronics.com) Primary: 120V Secondary: 28V, 1.5A Primary: 120V Secondary: 40VCT, 0.25A Primary: 110V Secondary: 15V, 0.4A Utility pole transformer

6. 6 Lecture #25 EGR 272 – Circuit Theory II Examples of transformers (reference: www.allelectronics.com) PC Mount Transformer Primary: 120V Secondary: 16VCT, 0.8A or 8V, 1.6A Toroidal Transformer Primary: 120V Secondary: 8.5V and 9.4V Up/Down Transformer (110V to 220V) or (220V to 110V) Variac (Variable Transformer) Input: 110V Output: 0 to 130V

7. 7 Lecture #25 EGR 272 – Circuit Theory II Dot Convention The direction of the windings in the secondary with respect to the direction of the windings in the primary determines the polarity of the secondary voltage. However, rather than showing the direction of the windings, dots are often placed at one end of each winding. Then the following convention applies: Dot convention: “A positive voltage at one dotted terminal will produce a positive voltage at the other dotted terminal.” Note that the relationships Imply that: the positive terminals of V 1 and V 2 are at the dotted terminals I 1 enters the dotted terminal and I 2 leaves the dotted terminal These voltage polarities and current directions are indicated to the right. i2i2 V1V1 + _ i1i1 V2V2 + _ N 1 :N 2 a : 1

8. 8 Lecture #25 EGR 272 – Circuit Theory II Four Common Transformer Uses Change voltage levels Change current levels Change impedance levels (impedance matching) Isolation (to isolate the secondary load from the ground in the primary perhaps) Examples: Show simple examples of the four transformer uses listed above.

9. 9 Lecture #25 EGR 272 – Circuit Theory II Example: Determine the V 1 and i 2 in the circuit below. Find these values by: A)Using KVL equations around each loop i2i2 V1V1 + _ 2 20 mH + _ 5 cos(10t) 520 mF 1:2

10. 10 Lecture #25 EGR 272 – Circuit Theory II Example: Determine the V 1 and i 2 in the circuit below. Find these values by: B)Reflecting the impedance of the secondary to the primary. i2i2 V1V1 + _ 2 20 mH + _ 5 cos(10t) 520 mF 1:2

11. 11 Lecture #25 EGR 272 – Circuit Theory II Example: Determine the value of Z ab below.

12. 12 Lecture #25 EGR 272 – Circuit Theory II Example: Recall the example presented in EGR 271 where a transformer was used to insure that maximum power was delivered to a 4 ohm speaker from the output of an amplifier with an output resistance of 100 ohms. Illustrate and discuss.

13. 13 Lecture #25 EGR 272 – Circuit Theory II Example: Determine the inductance, L, and the turns ratio, a, required to achieve maximum power transfer to the secondary load. 320 L + _ 100cos(10 5 t) V 80  62.5 pF a:1

14. 14 Lecture #25 EGR 272 – Circuit Theory II Transformer Models: Transformers considered in this course have been considered to be ideal. Although transformer behavior is often close to ideal, there are cases where non-ideal behavior might be examined. The figures to the left (reference: Electric Power & Machinery by Matsch) show models of a transformer used to approximate non-ideal behavior. The resistances, R 1 and R 2, represent the resistance of the windings and the inductive reactances, X l1 and X l2 represent leakage magnetic flux.