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

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

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

3 Lecture 19

Tank Capacitor Charge Variation

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

4 Lecture 19

Relating the tank capacitor ac voltageto the dc load current

q = C (VCP – (–VCP)) = 2CVCP

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

5 Lecture 19

Tank inductor flux linkage variation

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

6 Lecture 19

Relating the tank inductor ac currentto the dc load voltage

= L (ILP – (–ILP)) = 2LILP

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

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

8 Lecture 19

Integral KCL: Example

By KCL, we know that i1 = iC + i2. Hence,

where

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

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

10 Lecture 19

Integral KVL: Example

By KVL, we know that v2 = v1 – vL. Hence,

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

11 Lecture 19

Normalization and Notation

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

12 Lecture 19

Normalization and Notation

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

13 Lecture 19

Normalization and Notation: Time and Frequency

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

14 Lecture 19

State plane trajectory of a series tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

15 Lecture 19

State plane trajectory of a series tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

16 Lecture 19

State plane trajectory of a parallel-loaded tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

17 Lecture 19

State plane trajectory of a parallel-loaded tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

18 Lecture 19

Analysis of series resonant converterCh. 4 Notes

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

19 Lecture 19

Q1 subinterval

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

20 Lecture 19

+

D1 subinterval

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

21 Lecture 19

Q2 subinterval

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

22 Lecture 19

Q1 subinterval

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

23 Lecture 19

Complete state trajectory

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

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics

25 Lecture 19

State plane trajectory: Series resonant converter, below resonance, CCM