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