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Resonant Conversion
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Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion
Chapter 19
Resonant Conversion
Introduction
19.1 Sinusoidal analysis of resonant converters
19.2 Examples
Series resonant converterParallel resonant converter
19.3 Exact characteristics of the series and parallel resonantconverters
19.4 Soft switching
Zero current switchingZero voltage switching
The zero voltage transition converter
19.5 Load-dependent properties of resonant converters
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Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion
Introduction to Resonant Conversion
Resonant power converters contain resonant L-C networks whosevoltage and current waveforms vary sinusoidally during one or moresubintervals of each switching period. These sinusoidal variations arelarge in magnitude, and the small ripple approximation does not apply.
Some types of resonant converters:
Dc-to-high-frequency-ac inverters
Resonant dc-dc converters
Resonant inverters or rectifiers producing line-frequency ac
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Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion
A basic class of resonant inverters
Resonanttanknetwork
v
+
csourcevg
t vs
Switchnetwork
p
Seriestank
t
Basic circuit
Several resonant tank networks
Paralleltan
t
LC
tank
t
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Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion
Tank network responds only to fundamentalcomponent of switched waveforms
ResonanttankresponseTankcurrentspectrum
s3
ss
sssfs3fs
sTank current and outputvoltage are essentiallysinusoids at the switching
frequencyfs.
Output can be controlled byvariation of switchingfrequency, closer to oraway from the tank
resonant frequency
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Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion
An electronic ballast
+Half-bridge, driving LCC tank circuit and gasdischarge lamp
Must producecontrollable high-frequency (50 kHz)ac to drive gas
discharge lamp
DC input istypically producedby a low-harmonicrectifier
Similar to resonantdc-dc converter,but output-siderectifier is omitted
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Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion
Derivation of a resonant dc-dc converter
vR(t)++
(t)
Resonanttanknetwork
csourcevg(t) vs(t)+
Switchnetworks
NSNTRectifiernetworkNR
Lo
-p
ss
ilternet
or
l
Rectify and filter the output of a dc-high-frequency-ac inverter
The series resonant dc-dc converter
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7/27Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion
A series resonant link inverter
+ (t)Resonanttanknetworkcsourcevg(t)SwitchnetworksLo-pssilternetorlSwitchnetwork
Same as dc-dc series resonant converter, except output rectifiers arereplaced with four-quadrant switches:
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Resonant conversion: advantages
The chief advantage of resonant converters: reduced switching loss
Zero-current switching
Zero-voltage switching
Turn-on or turn-off transitions of semiconductor devices can occur atzero crossings of tank voltage or current waveforms, thereby reducingor eliminating some of the switching loss mechanisms. Henceresonant converters can operate at higher switching frequencies thancomparable PWM converters
Zero-voltage switching also reduces converter-generated EMIZero-current switching can be used to commutate SCRs
In specialized applications, resonant networks may be unavoidable
High voltage converters: significant transformer leakageinductance and winding capacitance leads to resonant network
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Resonant conversion: disadvantages
Can optimize performance at one operating point, but not with widerange of input voltage and load power variations
Significant currents may circulate through the tank elements, evenwhen the load is disconnected, leading to poor efficiency at light load
Quasi-sinusoidal waveforms exhibit higher peak values than equivalentrectangular waveforms
These considerations lead to increased conduction losses, which canoffset the reduction in switching loss
Resonant converters are usually controlled by variation of switchingfrequency. In some schemes, the range of switching frequencies canbe very large
Complexity of analysis
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Resonant conversion: Outline of discussion
Simple steady-state analysis via sinusoidal approximation
Simple and exact results for the series and parallel resonantconverters
Mechanisms of soft switching
Resonant inverter design techniques. Circulating currents, and thedependence (or lack thereof) of conduction loss on load power
Following this chapter: extension of sinusoidal analysis techniques to
model control system dynamics and small-signal transfer functions
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19.1 Sinusoidal analysis of resonant converters
vR(t)++
(t)Resonanttanknetwork
csourcevg(t) vs(t)+Switchnetworks
NSNTRectifiernetworkNRLo-pssilternetorl
A resonant dc-dc converter:
If tank responds primarily to fundamental component of switch networkoutput voltage waveform, then harmonics can be neglected.
Let us model all ac waveforms by their fundamental components.
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The sinusoidal approximation
ResonanttankresponseTankcurrentspectrums3ss
sssfs3fss
Tank current and outputvoltage are essentiallysinusoids at the switching
frequencyfs.
Neglect harmonics ofswitch output voltagewaveform, and model onlythe fundamentalcomponent.
Remaining ac waveformscan be found via phasoranalysis.
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19.1.1 Controlled switch network model
vgSwitchnet1If the switch network produces asquare wave, then its outputvoltage has the following Fourierseries:
The fundamental component is
So model switch network output portwith voltage source of valuevs1(t)
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Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion
Model of switch network input port
vgSwitchnet1Assume that switch network
output current is
It is desired to model the dccomponent (average value) ofthe switch network inputcurrent.
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Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion
Switch network: equivalent circuit
Switch network converts dc to ac
Dc components of input port waveforms are modeledFundamental ac components of output port waveforms are modeled
Model is power conservative: predicted average input and outputpowers are equal
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Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion
19.1.2 Modeling the rectifier and capacitivefilter networks
RectifiernetworkNRLo-iltenet
Assume large output filter
capacitor, having small ripple.
vR(t)is a square wave, having
zero crossings in phase with tankoutput currentiR(t).
IfiR(t)is a sinusoid:
ThenvR(t)has the following
Fourier series:
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Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion
Sinusoidal approximation: rectifier
Again, since tank responds only to fundamental components of appliedwaveforms, harmonics invR(t)can be neglected.vR(t)becomes
Actual waveforms with harmonics ignored
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Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion
Rectifier dc output port model
RectifiernetworkNRLo-iltenet Output capacitor charge balance: dc
load current is equal to averagerectified tank output current
Hence
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Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion
Equivalent circuit of rectifier
Rectifier input port:
Fundamental components ofcurrent and voltage aresinusoids that are in phase
Hence rectifier presents aresistive load to tank network
Effective resistanceReis
With a resistive loadR, this becomes
Rectifier equivalent circuit
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Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion
19.1.3 Resonant tank network
Model of ac waveforms is now reduced to a linear circuit. Tank networkis 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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Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion
Solution of tank network waveforms
Transfer function:
Ratio of peak values of input and
output voltages:
Solution for tank output current:
which has peak magnitude
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Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion
19.1.4 Solution of convertervoltage conversion ratioM=V/Vg
EliminateRe:
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Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion
Conversion ratioM
So we have shown that the conversion ratio of a resonant converter,
having switch and rectifier networks as in previous slides, is equal tothe magnitude of the tank network transfer function. This transferfunction is evaluated with the tank loaded by the effective rectifier inputresistanceRe.
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Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion
19.2 Examples19.2.1 Series resonant converter
vR(t)++
(t)resonanttanknetwork
csourcevg(t) vs(t)+switchnetworks
NSNTrectifiernetworkNRlo-pssilternetorl
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Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion
Model: series resonant converter
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Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion
Construction ofZi
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F d t l f P El t i 27 Ch t 19 R t C i
Construction ofH