Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion
Outline of discussion
DIRECT MODELING APPROACH
1. How small-signal variations in the switching frequency affect the spectrum of the switch network output voltage vs1(t)
2. Passing the frequency-modulated voltage vs1(t) through the tank transfer function H(s) leads to amplitude modulation of the output voltage v(t)
3. How to recover the envelope of the output voltage and determine the small-signal control-to-output-envelope transfer function Genv(s)
PHASOR TRANSFORMATION APPROACH
• Equivalent circuit modeling via the phasor transform
• PSPICE simulation of Genv(s) using the phasor transform
Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion
Conventional phasor definition(sinusoidal steady state)
Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion
Equivalent device models in phasor domainin sinusoidal steady-state
Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion
Applying the conventional definition to amplitude and angle-modulated waveforms
Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion
Extending the phasor definition
Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion
Applying the generalized phasor definition to amplitude and angle-modulated waveforms
Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion
Equivalent device models in phasor domainusing generalized phasor definition
Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion
Equivalent device models in phasor domainusing generalized phasor definition
Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion
Large signal phasor models of circuit elements
v(t)cos( t)dt) v(t)
R R
L L js(t)L
C
1/( js(t)C)
C
Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion
Linearizing the device models
Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion
Linearizing the device models
Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion
Inductor equivalent circuit model
Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion
Inductor equivalent circuit model
Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion
Inductor equivalent circuit model
Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion
Linearizing the device models
Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion
Small-signal phasor models of circuit elements
R
v̂
L jsL jsLIl^
1/( jsC)
jsCVc^
_
C
v(t)cos( t)dt)
R
L_
Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion
Some insight
Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion
Modelling the switch network
dtttdtv
tv sTg
ss )(cos
2
)(sin
)(4)(1
Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion
One way
Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion
More general – model the switch network with an equivalent transformer
Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion
Steps
Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion
Steps
Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion
Steps
Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion
The generalized phasor transformer model
Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion
Power balance in the phasor transformer model
Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion
Power balance in the phasor transformer model
Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion
Linearization of the transformer model
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