1. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 23 Next Homework Assignment Problem 1 Conventional hard-switched flyback converter Ringing caused by transformer leakage inductance Limit peak transistor voltage using a dissipative snubber circuit Analyze performance via state plane analysis

2. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 2 Lecture 23 Announcements HW #7, Problem #1, Part (b) asks for an expression for power flowing into snubber in terms of F, M s, M, and Q e. The expression for M should be

3. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 3 Lecture 23 The Parallel Resonant Converter Basic state plane analysis The discontinuous conduction mode (DCVM) Summary of converter characteristics Design methodologies

4. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 4 Lecture 23 DC-DC Parallel Resonant Converter During each interval, the tank circuit reduces to

5. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 5 Lecture 23 State plane trajectory

6. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 6 Lecture 23 Averaging and flux linkage arguments

7. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 7 Lecture 23 Averaging and flux linkage arguments

8. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 8 Lecture 23 Steady-state solution

9. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 9 Lecture 23 Steady state solution of state plane 1. Find expr. for radii in subintervals 2 and 3 (Define angles ζ and ξ)

10. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 10 Lecture 23 Steady state solution of state plane 2a. Find expr. for j L at end of subinterval 2 (ω 0 t = γ)

11. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 11 Lecture 23 Steady state solution of state plane 2b. Find expr. for j L at start of subinterval 3 (ω 0 t = γ)

12. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 12 Lecture 23 Steady state solution of state plane 2c. Equate expr. for j L at end of subinterval 2 and (ω 0 t = γ) start of subinterval 3 (ω 0 t = γ)

13. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 13 Lecture 23 Steady state solution of state plane 3a. Find expr. for m c at end of subinterval 2 (ω 0 t = γ)

14. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 14 Lecture 23 Steady state solution of state plane 3b. Find expr. for m c at start of subinterval 3 (ω 0 t = γ)

15. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 15 Lecture 23 Steady state solution of state plane 3c. Equate expr. for m c at end of subinterval 2 and (ω 0t = γ) start of subinterval 3 (ω 0 t = γ)

16. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 16 Lecture 23 Steady state solution of state plane 4. Find expr. for φ using j L and m c boundary matching conditions

17. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 17 Lecture 23 Steady state solution of state plane 5. Solve for J L1 and then M in terms of φ

18. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 18 Lecture 23 Steady state solution of state plane Two possible trajectories for given M and J

19. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 19 Lecture 23 Two possible trajectories for given M and J

20. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 20 Lecture 23 Two possible trajectories for given M and J

21. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 21 Lecture 23 CCM output plane characteristics

22. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 22 Lecture 23 Steady state solution of state plane Solve for initial conditions M c0 and J L0