# Chapter 20 Quasi-Resonant Converters

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```					                                            Chapter 20
Quasi-Resonant Converters

Introduction
20.1        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

Fundamentals of Power Electronics              1                Chapter 20: Quasi-Resonant Converters
Analysis result: switch conversion ratio µ

Switch conversion ratio:

with                          10

This is of the form                     8

6

4

2

0
0       0.2     0.4        0.6   0.8        1
Js

Fundamentals of Power Electronics   2                Chapter 20: Quasi-Resonant Converters
Characteristics of the half-wave ZCS resonant switch

Switch
characteristics:

Mode boundary:

Js ≤ 1

Fundamentals of Power Electronics    3           Chapter 20: Quasi-Resonant Converters
Buck converter containing half-wave ZCS quasi-resonant switch

Conversion ratio of the buck converter is (from inductor volt-second balance):

For the buck converter,

ZCS occurs when

Output voltage varies over the
range

Fundamentals of Power Electronics        5               Chapter 20: Quasi-Resonant Converters
Boost converter example

For the boost converter,

Half-wave ZCS equations:

Fundamentals of Power Electronics            7         Chapter 20: Quasi-Resonant Converters
Fundamentals of Power Electronics   8   Chapter 20: Quasi-Resonant Converters
Fundamentals of Power Electronics   9   Chapter 20: Quasi-Resonant Converters
20.1.3 The full-wave ZCS quasi-resonant switch cell

Half
i1 (t)
wave
I2

Subinterval:          1   2            3   4             = 0t

v2 (t)
V c1
Full
wave                                               i1 (t)                            

I2             0Ts
Conducting    Q1         Q1          X        D2
devices:    D1         D1
Subinterval: D 2
1        2                3        4     = 0t

v2 (t)

V
Fundamentals of Power Electronics   10                      Chapter 20: Quasi-Resonant Converters
c1
Fundamentals of Power Electronics   11   Chapter 20: Quasi-Resonant Converters
Analysis: full-wave ZCS

Analysis in the full-wave case is nearly the same as in the half-wave
case. The second subinterval ends at the second zero crossing of the
tank inductor current waveform. The following quantities differ:

In either case, µ is given by

Fundamentals of Power Electronics           12           Chapter 20: Quasi-Resonant Converters
Full-wave cell: switch conversion ratio µ

Full-wave case: P1 can be
approximated as

so

Fundamentals of Power Electronics    13        Chapter 20: Quasi-Resonant Converters
Half Wave                                               Full Wave

i1 (t)
i1 (t)

I2
I2

Subinterval:     1    2            3   4        = 0t
Subinterval:    1    2               3   4     = 0t
v2 (t)                                                  v2 (t)
V c1
Vc1

                                                                          
0Ts                                                      0Ts
Conducting      Q1   Q1          X    D2                Conducting      Q1   Q1        D1    X   D2
devices:      D1   D1                                   devices:      D2
D2
Hard switching at turn-off of diode
Conventional buck converter example (Fig. 20.1)

I
i(t)          I
Fast
transistor              –
Vg   +                         v(t)   Silicon               0
–                                diode
+                                                      t
i(t)                                   Area
Qr
v(t)
0

– Vg

Fundamentals of Power Electronics               15    Chapter 20: Quasi-Resonant Converters
Zero-current switching at turn-off of diode
ZVS quasi-resonant buck example (Fig. 20.2)

i(t)
Cr
I

0
Lr
+                                                                 Area          t
Vg
–                              i(t)                               Qr
–
v(t)                v(t)
+                              0

– Vg

Fundamentals of Power Electronics          16    Chapter 20: Quasi-Resonant Converters
Zero-voltage switching at turn-off of diode
ZVS quasi-squarewave buck example (Fig. 20.2)

i(t)
ir (t)

i(t)             Lr
–                                                             Area
Vg   +                               Cr                                                Qr
–                v(t)                                           0

+
v(t)
0

– Vg                         – Vg

Fundamentals of Power Electronics                 17          Chapter 20: Quasi-Resonant Converters
Zero-current and zero-voltage switching

ZCS quasi-resonant switch:
• Tank inductor is in series with
switch; hence SW switches at
zero current
• Tank capacitor is in parallel with
diode D2; hence D2 switches at
zero voltage
Discussion
• Zero voltage switching of D2 eliminates switching loss arising from D2
stored charge.
• Zero current switching of SW: device Q1 and D1 output capacitances lead
to switching loss. In full-wave case, stored charge of diode D1 leads to
switching loss.
• Peak transistor current is (1 + Js) Vg/R0, or more than twice the PWM value.
Fundamentals of Power Electronics          18            Chapter 20: Quasi-Resonant Converters
Fundamentals of Power Electronics   19   Chapter 20: Quasi-Resonant Converters
20.2 Resonant switch topologies

Basic ZCS switch cell:

SPST switch SW:

• Voltage-bidirectional two-quadrant switch for half-wave cell
• Current-bidirectional two-quadrant switch for full-wave cell

Connection of resonant elements:
Can be connected in other ways that preserve high-frequency
components of tank waveforms

Fundamentals of Power Electronics          20               Chapter 20: Quasi-Resonant Converters
Connection of tank capacitor

Connection of tank
capacitor to two
other points at ac
ground.
This simply
changes the dc
component of tank
capacitor voltage.
The ac high-
frequency
components of the
tank waveforms
are unchanged.

Fundamentals of Power Electronics        21         Chapter 20: Quasi-Resonant Converters
A test to determine the topology
of a resonant switch network

Replace converter elements by their high-frequency equivalents:
• Independent voltage source Vg: short circuit
• Filter capacitors: short circuits
• Filter inductors: open circuits
The resonant switch network remains.

If the converter contains a ZCS
quasi-resonant switch, then the
result of these operations is

Fundamentals of Power Electronics           22             Chapter 20: Quasi-Resonant Converters
20.2.1 The zero-voltage-switching
quasi-resonant switch cell

When the previously-described operations
are followed, then the converter reduces to

A full-wave version based on the
PWM buck converter:

Fundamentals of Power Electronics        23            Chapter 20: Quasi-Resonant Converters
ZVS quasi-resonant switch cell

Switch conversion ratio                     Tank waveforms
v Cr(t)
half-wave
V1

full-wave
Subinterval:    1   2           3    4         = 0t
iLr(t)                        I2
ZVS boundary

                      
0Ts
A problem with the quasi-resonant ZVS        Conducting                  D1 Q 1       Q1
devices:      X
D2       D2
switch cell: peak transistor voltage
becomes very large when zero voltage
switching is required for a large range of

Fundamentals of Power Electronics           24                 Chapter 20: Quasi-Resonant Converters
20.2.2 The ZVS multiresonant switch

When the previously-described operations
are followed, then the converter reduces to

A half-wave version based on the
PWM buck converter:

Fundamentals of Power Electronics        25            Chapter 20: Quasi-Resonant Converters
20.2.3 Quasi-square-wave resonant switches

When the previously-                 ZCS
described operations
are followed, then the
converter reduces to

ZVS

Fundamentals of Power Electronics   26         Chapter 20: Quasi-Resonant Converters
A quasi-square-wave ZCS buck with input filter

• The basic ZCS QSW switch cell is restricted to 0 ≤ µ ≤ 0.5
• Peak transistor current is equal to peak transistor current of PWM
cell
• Peak transistor voltage is increased
• Zero-current switching in all semiconductor devices

Fundamentals of Power Electronics        27              Chapter 20: Quasi-Resonant Converters
A quasi-square-wave ZVS buck

i2 (t)

v2 (t)
V1

0

0Ts            0t
Conducting
devices:     D1 Q1   X          D2   X

• The basic ZVS QSW switch cell is restricted to 0.5 ≤ µ ≤ 1
• Peak transistor voltage is equal to peak transistor voltage of PWM
cell
• Peak transistor current is increased
• Zero-voltage switching in all semiconductor devices

Fundamentals of Power Electronics        28                Chapter 20: Quasi-Resonant Converters

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