ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 19 Averaging: Charge...
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Transcript of ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 19 Averaging: Charge...
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