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7/29/2019 Resonant converstion
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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 converter
Parallel 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
Resonant tank network
ResistiveloadR
is(t) i(t)
v(t)
+
+
dcsource
vg(t)vs(t)
+
Switch network
L Cs
Cp
NS NT
Series tank network
L Cs
Basic circuit
Several resonant tank networks
Parallel tank network
L
Cp
LCC tank ne twork
L Cs
Cp
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Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion
Tank network responds only to fundamental
component of switched waveforms
f
Switch
output
voltage
spectrum
Resonant
tank
response
Tank
current
spectrum
ffs 3fs 5fs
ffs 3fs 5fs
fs 3fs 5fs
Tank current and outputvoltage are essentiallysinusoids at the switching
frequencyfs.Output can be controlledby variation of switchingfrequency, closer to oraway from the tankresonant 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
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
+
R
+
v(t)
Resonant tank network
dcsource
vg(t)
Switch network
L Cs
i(t)
Low-passfilter
network
acload
Switch network
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 EMI
Zero-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 thanequivalent rectangular 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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10/27Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion
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
A resonant dc-dc converter:
If tank responds primarily to fundamental component of switchnetwork output voltage waveform, then harmonics can be neglected.
Let us model all ac waveforms by their fundamental components.
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12/27Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion
The sinusoidal approximation
f
Switch
output
voltage
spectrum
Resonant
tank
response
Tank
current
spectrum
ffs 3fs 5fs
ffs 3fs 5fs
fs 3fs 5fs
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
is(t)
+
vg vs(t)
+
Switch network
NS
1
2
1
2
If 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 value vs1(t)
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Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion
Model of switch network input port
is(t)
+
vg vs(t)
+
Switch network
NS
1
2
1
2
Assume that switch network
output current is
It is desired to model the dccomponent (average value)of the 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 modeled Fundamental 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 capacitive
filter networks
Assume large output filter
capacitor, having small ripple.
vR(t) is a square wave, havingzero crossings in phase with tankoutput current iR(t).
If iR(t) is a sinusoid:
Then vR(t) has the followingFourier 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 in vR(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
Output capacitor charge balance: dcload 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 resistanceRe is
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. Tanknetwork is excited by effective sinusoidal voltage (switch networkoutput 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 converter
voltage conversion ratio M= V/Vg
EliminateRe:
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Fundamentals of Power Electronics 23 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 tothe magnitude of the tank network transfer function. This transferfunction is evaluated with the tank loaded by the effective rectifierinput resistanceRe.
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Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion
19.2 Examples
19.2.1 Series resonant converter
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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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Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion
Construction ofH