Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion Outline of discussion DIRECT MODELING APPROACH 1.How small-signal variations in the.

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