1. Lecture 17: Analysis with Sinusoidal Sources, Transformers Nilsson 9.7-9.12 ENG17 : Circuits I Spring 2015 1 May 26, 2015

2. Impedance and Reactance 2

3. Review 3 Find v o (t)

4. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 4

5. Impedances in Series 5

6. Impedances in Parallel 6

7. Delta-to-Wye 7

8. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 8

9. Source Transformations 9 Same as before, but now with impedances

10. Thevenin-Norton Equivalents 10

11. Example 11 Find using source transformation

12. Example 12 Find Thevenin Equivalent

13. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 13

14. Node-Voltage Example 14 Find I a, I b, I c

15. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 15

16. Mesh-Current Example 16 Find V a, V b, V c

17. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 17

18. Phasor Diagrams 18

19. Example 19 Use phasor diagram to find R that will cause resistor current (i R ) to lag the source current (i S ) by 45° when ω = 5 krad / s.

20. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 20

21. Transformer Circuit 21

22. Frequency Domain Circuit 22

23. Overview Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 23

24. Ideal Transformer 24

25. Sign Convention 25

26. Impedance Matching 26

27. Example 27

28. Recap Series / Parallel Simplifications Source Transformations Node-Voltage Mesh-Current Phasor Diagrams Transformers Ideal Case 28