Quasi Resonant Converters

8/14/2019 Quasi Resonant Converters

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Fundamentals of Power Electronics 1 Chapter 20: Quasi-Resonant Converters

Chapter 20

Quasi-Resonant Converters

Introduction20.1 The zero-current-switching quasi-resonant switch cell

20.1.1 Waveforms of the half-wave ZCS quasi-resonant switch cell

20.1.2 The average terminal waveforms

20.1.3 The full-wave ZCS quasi-resonant switch cell

20.2 Resonant switch topologies

20.2.1 The zero-voltage-switching quasi-resonant switch

20.2.2 The zero-voltage-switching multiresonant switch

20.2.3 Quasi-square-wave resonant switches

20.3 Ac modeling of quasi-resonant converters

20.4 Summary of key points


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The resonant switch concept

A quite general idea:

1. PWM switch network is replaced by a resonant switch network2. This leads to a quasi-resonant version of the original PWM converter

Example: realization of the switch cell in the buck converter

+

L

C R

+

v(t)

vg(t)

i(t)

+

v2(t)

i1(t) i2(t)

Switchcell

+

v1(t)

+

v2(t)

i1(t) i

2(t)

+

v1(t)

PWM switch cell


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Two quasi-resonant switch cells

+

v2(t)

i1(t) i2(t)

+

v1(t)

Lr

Cr

Half-wave ZCS quasi-resonant switch cell

Switch network

+

v1r(t)

i2r(t)D1

D2

Q1

+

v2(t)

i1(t) i2(t)

+

v1(t)

Lr

Cr

Full-wave ZCS quasi-resonant switch cell

Switch network

+

v1r(t)

i2r(t)

D1

D2

Q1

+

L

C R

+

v(t)

vg(t)

i(t)

+

v2(t)

i1(t) i2(t)

Switchcell

+

v1(t)

Insert either of the above switchcells into the buck converter, to

obtain a ZCS quasi-resonant

version of the buck converter.Lrand Cr are small in value, and

their resonant frequencyf0 is

greater than the switchingfrequencyfs.

f0 =1

2 L rCr=

0

2


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20.1 The zero-current-switching

quasi-resonant switch cell

+

v2(t)

i1(t) i2(t)

+

v1(t)

Lr

Cr


Switch network

+

v1r(t)

i2r(t)

D1

D2

Q1

+

v2(t)

i1(t) i2(t)

+

v1(t)

Lr

Cr

Full-wave ZCS quasi-resonant switch cell

Switch network

+

v1r(t)

i2r(t)

D1

D2

Q1

Tank inductorLr in series with transistor:

transistor switches at zero crossings of inductor

current waveform

Tank capacitor Cr in parallel with diodeD2 : diode

switches at zero crossings of capacitor voltagewaveform

Two-quadrant switch is required:

Half-wave: Q1 andD1 in series, transistor

turns off at first zero crossing of currentwaveform

Full-wave: Q1 andD1 in parallel, transistorturns off at second zero crossing of currentwaveform

Performances of half-wave and full-wave cells

differ significantly.


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Averaged switch modeling of ZCS cells

It is assumed that the converter filter elements are large, such that their

switching ripples are small. Hence, we can make the small rippleapproximation as usual, for these elements:

i2(t) i2(t) Tsv1(t) v1(t) Ts

In steady state, we can further approximate these quantities by their dcvalues:

i2(t) I2v1(t) V1

Modeling objective: find the average values of the terminal waveforms

v2(t)Ts and i1(t)Ts


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The switch conversion ratio

+

+

v2(t)

i1(t)

v1(t)Ts

Lr

Cr


Switch network

+

v1r(t)

i2r(t)

D1

D2

Q1

i2(t)Ts

i2(t) i2(t) Tsv1(t) v1(t) Ts

i2(t) I2v1(t) V1

=v2(t) Ts

v1r(t) Ts

=i1(t) Ts

i2r(t) Ts

= 2V1

= 1I2

In steady state:

A generalization of the duty cycle

d(t)

The switch conversion ratio isthe ratio of the average terminalvoltages of the switch network. It

can be applied to non-PWM switch

networks. For the CCM PWMcase, = d.

If V/Vg =M(d) for a PWM CCMconverter, then V/Vg =M() for the

same converter with a switch

network having conversion ratio .

Generalized switch averaging, and, are defined and discussed inSection 10.3.


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20.1.1 Waveforms of the half-wave ZCS

quasi-resonant switch cell

+

+

v2(t)

i1(t)

v1(t)Ts

Lr

Cr


Switch network

+

v1r(t)

i2r(t)

D1

D2

Q1

i2(t)Ts

The half-waveZCS quasi-resonant switch

cell, driven by the terminal quantities v1(t) Ts and i2(t) Ts.

V1L

r

I2Cr

= 0t

i1(t)

I2

v2(t)

0T

s

Vc1

Subinterval: 1 2 3 4

Conductingdevices:

Q1

D2

D1

Q1

D1

D2

X

Waveforms:

Each switching period contains foursubintervals


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Subinterval 1

+

+

v2(t)

i1(t)

V1

Lr

I2

DiodeD2 is initially conducting the filterinductor currentI

2

. Transistor Q1

turns on,

and the tank inductor current i1 starts to

increase. So all semiconductor devicesconduct during this subinterval, and thecircuit reduces to:

Circuit equations:

d i1

(t)

d t =V

1L r

i1(t) =V1L r

t= 0tV1R0

with i1(0) = 0

Solution:

where R0 =L

rCr

This subinterval ends when diodeD2becomes reverse-biased. This occurs

at time 0t= , when i1(t) =I2.

=I2R0V1

i1() = 1

R0= I2


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Subinterval 2

DiodeD2 is off. Transistor Q1 conducts, and

the tank inductor and tank capacitor ring

sinusoidally. The circuit reduces to:

+

+

v2(t)

i1(t)

V1

Lr

I2Cr

ic(t)

The circuit equations are

L rdi1(0t)

dt= V1 v2(0t)

Crdv2(0t)

dt= i1(0t) I2

v2() = 0

i1() = I2

The solution is

i1(0t) = I2 + V1

R0sin 0t

v2(0t) = V1 1 cos 0t

The dc components of thesewaveforms are the dc

solution of the circuit, whilethe sinusoidal components

have magnitudes that dependon the initial conditions andon the characteristicimpedanceR0.


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Subinterval 2continued

i1(0t) = I2 +V1R0

sin 0t

v2(0t) = V1 1 cos 0t

Peak inductor current:

I1pk = I2 + 1R0

This subinterval ends at the first zerocrossing of i1(t). Define = angular length of

subinterval 2. Theni1( + ) = I2 +

V1R0

sin = 0

sin = 2 0V

1

V1L r

= 0t

i1(t)

I2

Subinterval: 1 2 3 4

0T

s

Must use care to select the correctbranch of the arcsine function. Note(from the i1(t) waveform) that > .

Hence

= + sin 1I2R0V1

2 < sin 1 x 2

I2

Quasi Resonant Converters

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