chapter 19 resonant conversionecee.colorado.edu/~ecen5817/lectures/l3_ecen5817_notes.pdf19.2.3...
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ECEN5817, ECEE Department, University of Colorado at Boulder
Chapter 19
Resonant Conversion
Introduction
19.1 Sinusoidal analysis of resonant converters
19.2 ExamplesSeries resonant converterParallel resonant converter
19.3 Soft switchingZero current switchingZero voltage switching
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19.4 Load-dependent properties of resonant converters
19.5 Exact characteristics of the series and parallel resonant converters
A class of resonant DC-to-AC inverters
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A resonant DC-DC converter
Transfer functionH(s)
A resonant dc-dc converter:
iR(t)
vR(t)
+
–
+– R
+
v(t)
–
Resonant tank network
is(t)
dcsource
vg(t)vs(t)
+
–
Switch network
L Cs
NS NT
i(t)
Rectifier network
NR NF
Low-passfilter
network
dcload
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network
If tank responds primarily to fundamental component of switch network output voltage waveform, then harmonics can be neglected
Section 19.1: modeling based on sinusoidal approximation
The sinusoidal approximation
Switchoutput
Tank current and output
f
voltagespectrum
Resonanttank
response
ffs 3fs 5fs
f 3f 5f
Tank current and output voltage are essentially sinusoids at the switching frequency fs
Neglect harmonics of switch output voltage waveform, and model only the fundamental
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f
Tankcurrent
spectrum
ffs 3fs 5fs
fs 3fs 5fs component
Remaining ac waveforms can be found via standard phasor analysis
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19.1.1 Controlled switch network model
is(t)NS
1
+–vg vs(t)
+
–
Switch network
1
2
1
2
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Fourier series expansion of square-wave switch network output voltage vs(t):
The fundamental component is
So model switch network output port with voltage source of value vs1(t)
Model of switch network input port
is(t)
+
NS
1
Find dc (average) component of the switch network input current
+–vg vs(t)
–
Switch network
2
1
2
Fundamental component of the
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output current:
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Switch network: equivalent circuit
• Switch network converts dc to ac
• Dc components of input port waveforms are modeled
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• Fundamental ac components of output port waveforms are modeled
• Model is power conservative: predicted average input and output powers are equal
19.1.2 Modeling the rectifier and capacitive filter networks
iR(t)
R
+
(t)
i(t)
+
(t)
| iR(t) |
Rv(t)
–
Rectifier network
NR NF
Low-passfilter
network
dcload
vR(t)
–
Assume large output filter it h i ll i l
If iR(t) is a sinusoid:
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capacitor, having small ripple.
vR(t) is a square wave, having zero crossings in phase with tank output current iR(t).
Then vR(t) has the following Fourier series:
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Sinusoidal approximation: rectifier
Again, since tank responds only to fundamental components of applied waveforms, harmonics in vR(t) can be neglected. vR(t) becomes
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Rectifier dc output port model
iR(t)
R
+
v(t)
i(t)
+
vR(t)
| iR(t) | Output capacitor charge balance: dc load current is equal to average rectified tank output current
Rv(t)
–
Rectifier network
NR NF
Low-passfilter
network
dcload
vR(t)
–
Hence
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Equivalent circuit of rectifier
Rectifier input port:
Fundamental components of current and voltage are i id h i hsinusoids that are in phase
Hence rectifier presents a resistive load to tank network
Effective resistance Re is
Rectifier equivalent circuit
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With a resistive load R, this becomes
Loss free resistor: all power absorbed by Re is transferred to the output port
19.1.3 Resonant tank network
Model of ac waveforms is now reduced to a linear circuit. Tank k i i d b ff i i id l l ( i h k
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network is excited by effective sinusoidal voltage (switch network output port), and is load by effective resistive load (rectifier input port)
Can solve for transfer function via conventional linear circuit analysis
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Solution of tank network waveforms
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19.1.4 Solution of convertervoltage conversion ratio M = V/Vg
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19.2 Examples19.2.1 Series resonant converter
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Model: series resonant converter
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Construction of Zi – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω
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Construction of H = V / Vg – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω
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Model: series resonant converter
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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:
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SRC DC conversion ratio M
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Subharmonic modes
19.2.3 Parallel resonant dc-dc converter
Differs from series resonant converter as follows:
Different tank network
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Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filter
Need a new model for rectifier and filter networks
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Model of uncontrolled rectifierwith inductive filter network – input port
Fundamental component of iR(t):
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Model of uncontrolled rectifierwith inductive filter network – output port
Output inductor volt second balance: dc voltage is equal to average rectified tank output voltage
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Effective resistance Re
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Equivalent circuit model of uncontrolled rectifierwith inductive filter network
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Output port modeled as a dependent voltage source based on rectified tank voltage, in contrast to SRC where output port is modeled as dependent current source based on rectified tank current
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Equivalent circuit modelParallel resonant dc-dc converter
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Ways to construct transfer function H in terms of impedances
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Construction of Zo – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
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Construction of H = V / Vg – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ
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Construction of H
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Dc conversion ratio of the PRC
At resonance, this becomes
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• 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
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Comparison of approximate and exact PRC characteristics
Parallel resonant converterExact equation:
solid linessolid lines
Sinusoidal approximation: shaded lines
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