Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion
Announcements
• Prof. Erickson PDF slides on AC modeling posted on website.
• Some comments on handwritten notes / slides
• Some comments on HW #4 (due for on-campus students Mon. Feb 18)
• Genv = Genv,vin
• “Root Locus”
• Salient features
• Algebra
Fundamentals of Power Electronics 2 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 3 Chapter 19: Resonant Conversion
Phasor analysis
Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion
3. Extract expression for envelope
Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion
Square and linearization
Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion
Square root and linearization
Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion
Result:Small-signal expression for envelope
Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion
What is Genv(s)?
Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion
The poles of Genv(s)
Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion
The poles of Genv(s)
Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion
The numerator of Genv(s)
Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion
The DC gain Genv(s)
Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion
Phasor representation of amplitude and frequency modulated signals
dttmj
dttmjtj
eaAtx
eeaAtx S
)(_
)(
)()(
})Re{()(
aAtx
eaAtx tj S
)(
})Re{()(_
For amplitude modulation:
For frequency and amplitude modulation(traditional phasor definition):
aAtx
eeaAtx dttmjtj S
)(
})Re{()(_
)(For frequency and amplitude modulation(modified phasor definition):
Fundamentals of Power Electronics 18 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
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