1. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 19 Averaging: Charge Arguments Averaging a terminal current of a (resonant) converter to find the dc or low-frequency component: where We will relate this charge to the change in charge on a tank capacitor within the converter

2. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 2 Lecture 19 Averaging: Volt-Second, or Flux-Linkage, Arguments Averaging a terminal voltage of a (resonant) converter to find the dc or low-frequency component: where We will relate these volt-seconds to the change in flux-linkages in a tank inductor within the converter

3. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 3 Lecture 19 Tank Capacitor Charge Variation where

4. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 4 Lecture 19 Relating the tank capacitor ac voltage to the dc load current q = C (V CP – (–V CP )) = 2CV CP

5. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 5 Lecture 19 Tank inductor flux linkage variation where

6. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 6 Lecture 19 Relating the tank inductor ac current to the dc load voltage = L (I LP – (–I LP )) = 2LI LP

7. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 7 Lecture 19 Kirchhoff’s Laws in Integral Form: KCL KCL: sum of currents into a node = 0 Integrate over a time interval: net charge entering the node = 0 where

8. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 8 Lecture 19 Integral KCL: Example By KCL, we know that i 1 = i C + i 2. Hence, where

9. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 9 Lecture 19 Kirchhoff’s Laws in Integral Form: KVL KVL: sum of voltages around a loop = 0 Integrate over a time interval: net volt-seconds around the loop = 0 where

10. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 10 Lecture 19 Integral KVL: Example By KVL, we know that v 2 = v 1 – v L. Hence, where

11. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 11 Lecture 19 Normalization and Notation

12. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 12 Lecture 19 Normalization and Notation

13. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 13 Lecture 19 Normalization and Notation: Time and Frequency

14. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 14 Lecture 19 State plane trajectory of a series tank circuit

15. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 15 Lecture 19 State plane trajectory of a series tank circuit

16. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 16 Lecture 19 State plane trajectory of a parallel-loaded tank circuit

17. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 17 Lecture 19 State plane trajectory of a parallel-loaded tank circuit

18. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 18 Lecture 19 Analysis of series resonant converter Ch. 4 Notes

19. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 19 Lecture 19 Q1 subinterval

20. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 20 Lecture 19 + D1 subinterval

21. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 21 Lecture 19 Q2 subinterval

22. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 22 Lecture 19 Q1 subinterval

23. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 23 Lecture 19 Complete state trajectory

24. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 24 Lecture 19 Tank capacitor charge arguments: Relating the peak tank capacitor voltage to average load current

25. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 25 Lecture 19 State plane trajectory: Series resonant converter, below resonance, CCM