Transcript Ch 19 - University of Colorado Boulder

ECEN 5817
Housekeeping update
•
•
•
For both on-campus and CAETE students: A DVD of recorded lectures
from Professor Erickson’s Spring ’06 class will be mailed to you
sometime next week. These will not be available on the CAETE
website CUAnywhere.colorado.edu
For on-campus students: You will not have access to this semesters
recorded lectures on the CAETE website
For CAETE students: By popular request, scanned and e-mailed
homework will be accepted provided the submissions meet the
following requirements:
• Black and white (no color, no grayscale)
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Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Chapter 19
Resonant Conversion
Introduction
19.1
Sinusoidal analysis of resonant converters
19.2
Examples
Series resonant converter
Parallel resonant converter
19.3
Soft switching
Zero current switching
Zero 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
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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
Rectifier equivalent circuit
With a resistive load R, this becomes
Loss free resistor
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
19.1.4 Solution of converter
voltage conversion ratio M = V/Vg
Eliminate Re:
Fundamentals of Power Electronics
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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
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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
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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
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Chapter 19: Resonant Conversion
19.2 Examples
19.2.1 Series resonant converter
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Model: series resonant converter
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 10 Ω
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 10 Ω
Buck characteristic
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of Zi
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of H
Qe  R0 / Re
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Model: series resonant converter
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of Zi – Non-resonant (low Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of H – Non-resonant (low Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics
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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
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Chapter 19: Resonant Conversion
Model of uncontrolled rectifier
with inductive filter network – input port
Fundamental component of iR(t):
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Model of uncontrolled rectifier
with inductive filter network – output port
Output inductor volt second balance:
dc voltage is equal to average
rectified tank output voltage
Fundamentals of Power Electronics
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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
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Chapter 19: Resonant Conversion
Equivalent circuit model of uncontrolled rectifier
with 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
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Chapter 19: Resonant Conversion
Equivalent circuit model
Parallel resonant dc-dc converter
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
2 different ways to construct transfer function H
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ
Buck-boost characteristic
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of Zo
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion
Construction of H
Fundamentals of Power Electronics
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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
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Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics
1.0
Below resonance:
0.8
M = V/Vg
Series resonant
converter
0.5 < F < 1
exact M, Q=2
approx M, Q=2
exact M, Q=10
approx M, Q=10
exact M, Q=0.5
approx M, Q=0.5
0.6
0.4
0.2
0.0
0.5
0.6
0.7
0.8
0.9
1.0
F
1.0
Above resonance:
0.8
M=V/Vg
1<F
exact M, Q=0.5
approx M, Q=0.5
exact M, Q=10
approx M, Q=10
exact M, Q=2
approx M, Q=2
0.6
0.4
0.2
0.0
1
Fundamentals of Power Electronics
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2
3
F
4
5
Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics
Exact equation:
Parallel resonant converter
solid lines
Sinusoidal approximation:
shaded lines
Fundamentals of Power Electronics
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Chapter 19: Resonant Conversion