Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion
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ECEN 5817Housekeeping update
Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion
Chapter 19Resonant Conversion
Introduction
19.1 Sinusoidal analysis of resonant converters
19.2 ExamplesSeries resonant converterParallel resonant converter
19.3 Soft switchingZero current switchingZero voltage switching
19.4 Load-dependent properties of resonant converters
19.5 Exact characteristics of the series and parallel resonant converters
Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion
Equivalent circuit of rectifier
Rectifier input port:
Fundamental components of current and voltage are sinusoids that are in phase
Hence rectifier presents a resistive load to tank network
Effective resistance Re is
With a resistive load R, this becomes
Rectifier equivalent circuit
Loss free resistor
Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion
19.1.4 Solution of convertervoltage conversion ratio M = V/Vg
Eliminate Re:
Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion
Conversion ratio M
So we have shown that the conversion ratio of a resonant converter, having switch and rectifier networks as in previous slides, is equal to the magnitude of the tank network transfer function. This transfer function is evaluated with the tank loaded by the effective rectifier input resistance Re.
Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion
19.2.2 Subharmonic modes of the SRC
Example: excitation of tank by third harmonic of switching frequency
Can now approximate vs(t) by its third harmonic:
Result of analysis:
Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion
Subharmonic modes of SRC
•Not often used - reduced switch utilization and decreased voltage conversion ratio
•Still need to be aware their existence
Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion
19.2 Examples19.2.1 Series resonant converter
iR(t)
vR(t)
+
–
+–
transfer functionH(s)
R
+
v(t)
–
resonant tank network
is(t)
dcsource
vg(t)vs(t)
+
–
switch network
L Cs
NS NT
i(t)
rectifier networkNR NF
low-passfilter
network
dcload
Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion
Model: series resonant converter
Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω
Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω
Buck characteristic
Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion
Construction of Zi
Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion
Construction of H
ee RRQ /0
Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion
Model: series resonant converter
Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion
Construction of Zi – Non-resonant (low Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion
Construction of H – Non-resonant (low Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion
19.2.3 Parallel resonant dc-dc converter
Differs from series resonant converter as follows:
Different tank network
Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filter
Need a new model for rectifier and filter networks
Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion
Model of uncontrolled rectifierwith inductive filter network – input port
Fundamental component of iR(t):
Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion
Model of uncontrolled rectifierwith inductive filter network – output port
Output inductor volt second balance: dc voltage is equal to average rectified tank output voltage
Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion
Effective resistance Re
Again define
In steady state, the dc output voltage V is equal to the average value of | vR |:
For a resistive load, V = IR. The effective resistance Re can then be expressed
Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion
Equivalent circuit model of uncontrolled rectifierwith inductive filter network
Dependent voltage source based on rectified tank voltage. Vs. SRC, dependent current source based on rectified tank current.
Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion
Equivalent circuit modelParallel resonant dc-dc converter
Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion
2 different ways to construct transfer function H
Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
Buck-boost characteristic
Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion
Construction of Zo
Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion
Construction of H
Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion
Dc conversion ratio of the PRC
At resonance, this becomes
• PRC can step up the voltage, provided R > R0
• PRC can produce M approaching infinity, provided output current is limited to value less than Vg / R0
Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics
0.5 0.6 0.7 0.8 0.9 1.00.0
0.2
0.4
0.6
0.8
1.0
exact M, Q=2approx M, Q=2exact M, Q=10approx M, Q=10exact M, Q=0.5approx M, Q=0.5
F
M =
V/V
g
1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0
exact M, Q=0.5approx M, Q=0.5exact M, Q=10approx M, Q=10exact M, Q=2approx M, Q=2
F
M=V
/Vg
Series resonant converter
Below resonance:
0.5 < F < 1
Above resonance:
1 < F
Fundamentals of Power Electronics 30 Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics
Parallel resonant converterExact equation:
solid lines
Sinusoidal approximation: shaded lines