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


Conventional phasor definition(sinusoidal steady state)


Equivalent device models in phasor domainin sinusoidal steady-state


Applying the conventional definition to amplitude and angle-modulated waveforms


Extending the phasor definition


Applying the generalized phasor definition to amplitude and angle-modulated waveforms


Equivalent device models in phasor domainusing generalized phasor definition


Equivalent device models in phasor domainusing generalized phasor definition


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


Linearizing the device models




Inductor equivalent circuit model








Small-signal phasor models of circuit elements

R

v̂

L jsL jsLIl^

1/( jsC)

jsCVc^

_

C

v(t)cos( t)dt)

R

L_


Some insight


Modelling the switch network

dtttdtv

tv sTg

ss )(cos

2

)(sin

)(4)(1


One way


More general – model the switch network with an equivalent transformer


Steps


Steps


Steps


The generalized phasor transformer model


Power balance in the phasor transformer model


Power balance in the phasor transformer model


Linearization of the transformer model

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

Documents

resonant conversion

insight slide

way slide

equivalent transformer

switch network slide

phasor domain

sinusoidal steadystate

equivalent circuit modeling