1. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 19 Time-Domain Analysis of Resonant and Soft-Switching Converters Principles of state-plane analysis and averaging In a large number of cases, the circuit waveforms are not approximately sinusoidal The mechanisms of soft-switching PWM converters cannot be understood using the sinusoidal approximation The mechanisms of switching loss in hard-switched PWM converters cannot be understood using the sinusoidal approximation “Exact” time-domain analysis of these converters initially appears to be very complex, but is considerably simplified when certain analysis principles are employed (there are 4-5 logical leaps to be learned) Goals of this part of the course: learn the basic analysis principles learn to analyze the basic soft-switching circuits and resonant converters learn the physical properties of the most well-known soft-switching converters

2. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 2 Lecture 19 Key Concepts Averaging current (charge) and voltage (flux-linkages) over one switching period Relating average current to change in tank capacitor charge, and relating average voltage to change in tank inductor flux linkages Kirchhoff’s Laws in integral form Steady-state tank capacitor charge balance and inductor volt-second (flux linkage) balance for resonant circuit waveforms Normalization of voltage, current, time, and other quantities The state plane trajectory of resonant tank waveforms Examples: series and parallel resonant dc-dc converters Examples: quasi-resonant, zero-voltage transition, and active-clamp converters Examples: modeling switching loss in hard-switched converters having ringing waveforms

3. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 3 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

4. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 4 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

5. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 5 Lecture 19 Tank Capacitor Charge Variation where

6. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 6 Lecture 19 Relating the tank capacitor ac voltage to the dc load current q = C (V CP – (–V CP )) = 2CV CP

7. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 7 Lecture 19 Tank inductor flux linkage variation where

8. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 8 Lecture 19 Relating the tank inductor ac current to the dc load voltage = L (I LP – (–I LP )) = 2LI LP

9. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 9 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

10. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 10 Lecture 19 Integral KCL: Example By KCL, we know that i 1 = i C + i 2. Hence, where

11. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 11 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

12. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 12 Lecture 19 Integral KVL: Example By KVL, we know that v 2 = v 1 – v L. Hence, where

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

14. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 14 Lecture 19 Normalization and Notation

15. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 15 Lecture 19 Normalization and Notation: Time and Frequency

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

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

18. ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 18 Lecture 19 State plane trajectory of a parallel-loaded tank circuit

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