ST AN2644 Application note

AN2644

Application note

An introduction to LLC resonant

half-bridge converter

Introduction

Although in existence for many years, only recently has the LLC resonant converter, in particular in its half-bridge implementation, gained in the popularity it certainly deserves. In many applications, such as flat panel TVs, 85+ ATX PCs or small form factor PCs, where the requirements on efficiency and power density of their SMPS are getting tougher and tougher, the LLC resonant half-bridge with its many benefits and very few drawbacks is an excellent solution. One of the major difficulties that engineers are facing with this topology is the lack of information concerning the way it operates. The purpose of this application note is to provide insight into the topology and help familiarize the reader with it, therefore, the approach is essentially descriptive.

Figure 1. LLC resonant topology schematics and waveforms

September 2008 Rev 2 1/64

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Contents AN2644

Contents

1 Classification of resonant converters . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 The LLC resonant half-bridge converter . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 General overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 The switching mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Fundamental operating modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.1 Operation at resonance (f = fR1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

2.3.2 Operation above resonance (f > fR1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

CCMA operation at heavy load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

DCMA at medium load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

DCMAB at light load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

2.3.3 Operation below resonance (fR2 < f < fR1, R>R

DCMAB at medium-light load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

DCMB at heavy load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

2.3.4 Capacitive-mode operation below resonance (fR2 < f < fR1, R<R

Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36

) . . . . . . . . . . . . . . . . 30

crit

) . . . 34

crit

2.4 No-load operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.5 Overload and short circuit operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.6 Converter's startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.7 Analysis of power losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.8 Small-signal behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.8.1 Operation above resonance (f > fR1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.8.2 Operation below resonance (f

2.8.3 Operation at resonance (f = f

< f < fR1, R>R

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

) . . . . . . . . . . . . . . . . 44

crit

3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Appendix A Power MOSFET driving energy in ZVS operation . . . . . . . . . . . . . . 48

2/64

AN2644 Contents

Appendix B Resonant transitions of half-bridge midpoint . . . . . . . . . . . . . . . . . 50

Appendix C Power MOSFET effective C

and half-bridge midpoint's transition

oss

times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Appendix D Power MOSFETs switching losses at turn-off. . . . . . . . . . . . . . . . . 59

Appendix E Input current in LLC resonant half-bridge with split resonant

capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3/64

List of figures AN2644

List of figures

Figure 1. LLC resonant topology schematics and waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Figure 2. General block diagram of a resonant inverter, the core of resonant converters. . . . . . . . . . 5

Figure 3. LLC resonant half-bridge schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 4. LLC resonant half-bridge with split resonant capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 5. Equivalent schematic of a real transformer (left, tapped secondary; right, single

secondary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Figure 6. Example of high-leakage magnetic structures (cross-section) . . . . . . . . . . . . . . . . . . . . . . . 9

Figure 7. Equivalent schematic of a transformer including parasitic capacitance . . . . . . . . . . . . . . . 12

Figure 8. Power MOSFET totem-pole network driving a resonant tank circuit in a half-bridge

converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 9. Detail of Q1 ON-OFF and Q2 OFF-ON transitions with soft-switching for Q2 . . . . . . . . . . 14

Figure 10. Q2 gate voltage at turn-on: with soft-switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 11. Q2 gate voltage at turn-on: with hard-switching (no ZVS) . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 12. Q1 ON-OFF and Q2 OFF-ON transitions with hard switching for Q2 and recovery for

DQ1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 13. Bridge leg transitions in the neighborhood of inductive-capacitive regions boundary . . . . 17

Figure 14. Bridge leg transitions under no-load conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Figure 15. Reference LLC converter for the analysis of the fundamental operating modes . . . . . . . . 21

Figure 16. Operation at resonance (f = f Figure 17. Operation above resonance (f > f Figure 18. Operation above resonance (f > f

load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 19. Operation above resonance (f > f

load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 20. Operation below resonance (f

operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 21. Operation below resonance (f Figure 22. Capacitive mode operation below resonance (f

Figure 23. No-load operation (cutoff): main waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 24. Circuit's equivalent schematic under: no-load conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 25. Circuit's equivalent schematic under: short-circuit conditions. . . . . . . . . . . . . . . . . . . . . . . 38

Figure 26. Converter's startup: main waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 27. High-side driving with bootstrap approach and bootstrap capacitor charge path. . . . . . . . 41

Figure 28. Frequency compensation with an isolated type 3 amplifier (3 poles + 2 zeros) . . . . . . . . 45

Figure 29. Comparison of gate-charge characteristics with and without ZVS . . . . . . . . . . . . . . . . . . . 48

Figure 30. Equivalent circuit to analyze the transitions of the half-bridge midpoint node when Q2

turns off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 31. Voltage of HB node vs time (see Equation 32). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 32. Resonant current vs time (see Equation 34) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 33. Capacitance associated to the half-bridge midpoint node . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 34. C

capacitances vs. half-bridge midpoint's voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

oss

Figure 35. Simplified schematic to analyze transition times of the node HB when Q2 turns off . . . . . 56

Figure 36. Schematization of Q2 turn-off transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Figure 37. Input current components in a split-capacitor LLC resonant half-bridge. . . . . . . . . . . . . . . 61

Figure 38. Timing diagram showing currents flow in the converter of Figure 37 . . . . . . . . . . . . . . . . . 61

): main waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

): main waveforms in CCMA operation at heavy load 25

): main waveforms in DCMA operation at medium

): main waveforms in DCMAB operation at light

< f < fR1 , R>R

< f < fR1, R>R

): main waveforms in DCMAB

crit

): main waveforms in DCMB2 operation 32

crit

< f < fR1, R<R

): main waveforms . . . 35

crit

4/64

AN2644 Classification of resonant converters

1 Classification of resonant converters

Resonant conversion is a topic that is at least thirty years old and where much effort has

been spent in research in universities and industry because of its attractive features: smooth

waveforms, high efficiency and high power density. Yet the use of this technique in off-line

powered equipment has been confined for a long time to niche applications: high-voltage

power supplies or audio systems, to name a few. Quite recently, emerging applications such

as flat panel TVs on one hand, and the introduction of new regulations, both voluntary and

mandatory, concerning an efficient use of energy on the other hand, are pushing power

designers to find more and more efficient AC-DC conversion systems. This has revamped

and broadened the interest in resonant conversion. Generally speaking, resonant

converters are switching converters that include a tank circuit actively participating in

determining input-to-output power flow. The family of resonant converters is extremely vast

and it is not an easy task to provide a comprehensive picture. To help find one's way, it is

possible to refer to a property shared by most, if not all, of the members of the family. They

are based on a "resonant inverter", i.e. a system that converts a DC voltage into a sinusoidal

voltage (more generally, into a low harmonic content ac voltage), and provides ac power to a

load. To do so, a switch network typically produces a square-wave voltage that is applied to

a resonant tank tuned to the fundamental component of the square wave. In this way, the

tank will respond primarily to this component and negligibly to the higher order harmonics,

so that its voltage and/or current, as well as those of the load, will be essentially sinusoidal

or piecewise sinusoidal. As shown in Figure 2, a resonant DC-DC converter able to provide

DC power to a load can be obtained by rectifying and filtering the ac output of a resonant

inverter.

Figure 2. General block diagram of a resonant inverter, the core of resonant

converters

Resonant

tank circuit

Rectifier

Vout

Low-pass

filter

Vout

Vin

Resonant Inverter

Switch

network

Switch

network

Resonant Inverter

Resonant

tank circuit

Resonant Converter

Different types of DC-AC inverters can be built, depending on the type of switch network and

on the characteristics of the resonant tank, i.e. the number of its reactive elements and their

configuration [1].

As to switch networks, we will limit our attention to those that drive the resonant tank

symmetrically in both voltage and time, and act as a voltage source, namely the half-bridge

and the full-bridge switch networks. Borrowing the terminology from power amplifiers,

5/64

Classification of resonant converters AN2644

switching inverters driven by this kind of switch network are considered part of the group

called "class D resonant inverters".

As to resonant tanks, with two reactive elements (one L and one C) there are a total of eight

different possible configurations, but only four of them are practically usable with a voltage

source input. Two of them generate the well-known series resonant converter and parallel

resonant converter considered in [2] and thoroughly treated in literature.

With three reactive elements the number of different tank circuit configurations is thirty-six,

but only fifteen can be used in practice with a voltage source input. One of these, commonly

called LCC because it uses one inductor and two capacitors, with the load connected in

parallel to one C, generates the LCC resonant inverter commonly used in electronic lamp

ballast for gas-discharge lamps. Its dual configuration, using two inductors and one

capacitor, with the load connected in parallel to one L, generates the LLC inverter.

As previously stated, for any resonant inverter there is one associated DC-DC resonant

converter, obtained by rectification and filtering of the inverter output. Predictably, the above-

mentioned class of inverters will originate the "class D resonant converters". Considering

off-line applications, in most cases the rectifier block will be coupled to the resonant inverter

through a transformer to guarantee the isolation required by safety regulations. To maximize

the usage of the energy handled by the inverter, the rectifier block can be configured as

either a full-wave rectifier, which needs a center tap arrangement of transformer's secondary

winding, or a bridge rectifier, in which case tapping is not needed. The first option is

preferable with a low voltage / high current output; the second option with a high voltage /

low current output. As to the low-pass filter, depending on the configuration of the tank

circuit, it will be made by capacitors only or by an L-C type smoothing filter. The so-called

"series-parallel" converter described in [2], typically used in high-voltage power supply, is

derived from the previously mentioned LCC resonant inverter. Its dual configuration, the LLC

inverter, generates the homonymous converter, addressed in [3], [4] and [5], that will be the

subject of the following discussion. In particular we will consider the half-bridge

implementation, illustrated in Figure 3, but the extension to the full-bridge version is quite

straightforward.

Figure 3. LLC resonant half-bridge schematic

VinVin

Preferably integrated into a single

Driver

Half-bridge

magnetic structure

LLC tank circuit

6/64

a:1

Center-tapped output with full-wave

(low voltage and high current)

a:1:1

rectification

Single-ended output with bridge

rectification

(high voltage and low current)

Vout

VoutVout

AN2644 The LLC resonant half-bridge converter

In resonant inverters (and converters too) power flow can be controlled by the switch

network either by changing the frequency of the square wave voltage, or its duty cycle, or

both, or by special control schemes such as phase-shift control. In this context we will focus

on power flow control by frequency modulation, that is, by changing the frequency of the

square wave closer to or further from the tank circuit's resonant frequency while keeping its

duty cycle fixed.

2 The LLC resonant half-bridge converter

2.1 General overview

According to another way of designating resonant converters, the LLC resonant half-bridge

belongs to the family of multiresonant converters. Actually, since the resonant tank includes

three reactive elements (Cr, Ls and Lp, shown in Figure 3), there are two resonant

frequencies associated to this circuit. One is related to the condition of the secondary

winding(s) conducting, where the inductance Lp disappears because dynamically shorted

out by the low-pass filter and the load (there is a constant voltage a V

Equation 1

---------------------------- -=

2π Ls Cr⋅

across it):

out

the other resonant frequency is relevant to the condition of the secondary winding(s) open,

where the tank circuit turns from LLC to LC because Ls and Lp can be unified in a single

inductor:

Equation 2

It will be of course f

LLC resonant tank, while f

> fR2. Normally, fR1 is referred to as the resonance frequency of the

is sometimes called the second (or lower) resonance

frequency. The separation between f

-------------------------------------------=

2π Ls Lp+()Cr

and fR2 depends on the ratio of Lp to Ls. The larger

this ratio is, the further the two frequencies will be and vice versa. The value of Lp/Ls

(typically > 1) is an important design parameter.

It is possible to show that for frequencies f > f

tank is inductive and that for frequencies f < f

frequency region f

< f < fR1 the impedance can be either inductive or capacitive depending

on the load resistance R. A critical value R

impedance will be capacitive, inductive for R> R

the input impedance of the loaded resonant

the input impedance is capacitive. In the

exists such that if R < R

crit

. For a given tank circuit the value of R

crit

then the

crit

depends on f. More precisely, in [6] it is shown that for any tank circuit configuration (then for

the LLC in particular):

Equation 3

where Zo

crit

and Zo∞ are the resonant tank output impedances with the source input short-

Zo0Zo∞⋅=

circuited and open-circuited, respectively.

7/64

The LLC resonant half-bridge converter AN2644

For certain reasons that will be clarified in the following sections, the LLC resonant

converter is normally operated in the region where the input impedance of the resonant tank

has inductive nature, i.e. it increases with frequency. This implies that power flow can be

controlled by changing the operating frequency of the converter in such a way that a

reduced power demand from the load produces a frequency rise, while an increased power

demand causes a frequency reduction.

The Half-bridge Driver switches the two power MOSFETs Q1 and Q2 on and off in phase

opposition symmetrically, that is, for exactly the same time. This is commonly referred to as

"50% duty cycle" operation even if the conduction time of either power MOSFET is slightly

shorter than 50% of the switching period. In fact, a small deadtime is inserted between the

turn-off of either switch and the turn-on of the complementary one. The role of this deadtime

is essential for the operation of the converter. It goes beyond ensuring that Q1 and Q2 will

never cross-conduct and will be clarified in the next sections as well. For the moment it will

be neglected, and the voltage applied to the resonant tank will be a square-wave with 50%

duty cycle that swings all the way from 0 to V

. Before going any further, however, it is

important to make one concept clear.

Figure 4. LLC resonant half-bridge with split resonant capacitor

Cr / 2

a:1:1

Vin

Half-bridge

Driver

a:1:1

Cr / 2

A few paragraphs above, the impedance of the tank circuit was mentioned. Impedance is a

concept related to linear circuits under sinusoidal excitation, whereas in this case the

excitation voltage is a square wave.

However, as a consequence of the selective nature of resonant tanks, most power

processing properties of resonant converters are associated with the fundamental

component of the Fourier expansion of voltages and currents in the circuit. This applies in

particular to the input square wave and is the foundation of the First Harmonic

Approximation (FHA) modeling methodology presented in [2] as a general approach and

used in [4] and [5] for the LLC resonant converter specifically. This approach justifies the

usage of the concept of impedance as well as those coming from complex ac circuit

analysis.

Coming back to the input square wave excitation, it has a DC component equal to V

/2. In

the LLC resonant tank the resonant capacitor Cr is in series to the voltage source and under

steady state conditions the average voltage across inductors must be zero. As a result, the

DC component V

/2 of the input voltage must be found across Cr which consequently plays

the double role of resonant capacitor and DC blocking capacitor.

It is possible to see, especially at higher power levels, a slightly modified version of the LLC

resonant half-bridge converter, where the resonant capacitor is split as illustrated in

Figure 4. This configuration can be useful to reduce the current stress in each capacitor

8/64

AN2644 The LLC resonant half-bridge converter

and, in certain conditions, the initial imbalance of the V·s applied to the transformer at start

up (see "Converter's start-up" section). Additionally, it makes the input current to the

converter look like that of a full-bridge converter, as shown in Appendix E, with a resulting

reduction in both the input differential mode noise and the stress of the input capacitor.

Obviously, the currents through Q1 and Q2 will be unchanged. It is easy to recognize that

the two Cr/2 capacitors are dynamically in parallel, so that the total resonant tank's

capacitance is again Cr.

The system appears quite bulky, with its three magnetic components. However, the LLC

resonant topology lends itself well to magnetic integration. With this technique inductors and

transformers are combined into a single physical device to reduce component count, usually

with little or no penalty to the converter's characteristics, sometimes even enhancing its

operation. To understand how magnetic integration can be done, it is worth looking at the

well-known equivalent schematics of a real transformer in Figure 5 and comparing them to

the inductive component set of Figure 3.

Lp occupies the same place as the magnetizing inductance L

primary leakage inductance L

. Then, assuming that we are going to use a ferrite core plus

, Ls the same place as the

bobbin assembly, Lp can be used as the magnetizing inductance of the transformer with the

addition of an air gap into the magnetic circuit and leakage inductance can be used to make

Ls.

Figure 5. Equivalent schematic of a real transformer (left, tapped secondary; right,

single secondary)

i1(t)

iM(t)

n : 1

ideal

i2(t)

v2(t)

v2(t)v2(t)

v1(t)

v1(t)v1(t)

i1(t)

iM(t)

n : 1 : 1

ideal

i2(t)

v2(t)

v2(t)v2(t)

v1(t)

v1(t)v1(t)

v2(t)

v2(t)v2(t)

To do so, however, a leaky magnetic structure is needed, which is contrary to the traditional

transformer design practice that aims at minimizing leakage inductance. The usual

concentric winding arrangement is not recommended here, although higher leakage

inductance values can be achieved by increasing the space between the windings.

Figure 6. Example of high-leakage magnetic structures (cross-section)

Primary

Primary winding

winding

Primary

Primary winding

winding

Secondary

winding

Windings on separate legs of an EE core

Secondary

winding

Side-by-side windings (EE or pot core)Windings on separate legs of an EE core

Side-by-side windings (EE or pot core)

9/64

The LLC resonant half-bridge converter AN2644

It is difficult, however to obtain reproducible values, because they depend on parameters

(such as winding surface irregularities or spacer thickness) difficult to control. Other fashions

are recommended, such as placing the windings on separate core legs (using E or U cores)

or side by side on the same leg which is possible with both E and pot cores and shown in

Figure 6. They permit reproducible leakage inductance values, because related to the

geometry and the mechanical tolerances of the bobbin, which are quite well controlled. In

addition, these structures possess geometric symmetry, so they lead to magnetic devices

with an excellent magnetic symmetry.

However, in the real transformer model of Figure 5 there is the secondary leakage

inductance L

that is not considered in the model of Figure 3. The presence of LL2 is not a

problem from the modeling point of view because the transformer's equivalent schematic

can be manipulated so that L

incorporated in L

). This is exactly what has been done in the transformer model shown in

disappears (it is transferred to the primary side and

Figure 3. Then, it is important to underline that Ls and Lp are not real physical inductances

, LM and LL2 are), their numerical values are different (Ls ≠ LL1, Lp ≠ LM), and, finally, the

turn ratio a is not the physical turn ratio n=N

interpretation. L

is the inductance of the primary winding measured with the secondary

. Ls and Lp can be given a physical

1/N2

winding(s) shorted, while Lp is the difference between the inductance of the primary winding

measured with the secondary windings open and L

However, L

is not free from side effects. For a given impressed voltage, LL2 decreases the

voltage available on the secondary winding, which carries a current i

, by the drop LL2·di2/dt.

This is an effect that is taken into account by the above mentioned manipulation of the

transformer model. In addition, in multioutput converters, where there is leakage inductance

associated to each output winding, cross-regulation between the various outputs will be

adversely affected because of their decoupling effect.

Finally, there is one more adverse effect to consider in the center-tapped output

configuration. With reference to Figure 3 and 5, when one half-winding is conducting, the

voltage v

(t) externally applied to that half-winding is V

(VF is the rectifier forward drop

out+VF

of the conducting diode). With no secondary leakage inductance, this voltage will be found

across the secondary winding of the ideal transformer and then coupled one-to-one to the

nonconducting half-winding. Consequently, the reverse voltage applied to the reverse-

biased rectifier will be 2·V

·di2/dt adds up to V

out+VF

the reverse voltage applied to the nonconducting rectifier will be increased by L

. If now we introduce the leakage inductance LL2, the drop

out+VF

. and is reflected to the other half-winding as well. As a result,

·di2/dt.

Note that in case of single-winding secondary with bridge rectification, the voltage applied to

reverse-biased diodes of the bridge is only V

that the negative voltage of the secondary winding is fixed at -V

and is not affected by LL2. The reason is

out+VF

externally and is not

determined by internal coupling like in the case of tapped secondary.

It is worth pointing out that the 50% duty cycle operation of the LLC half-bridge equalizes

the stress of secondary rectifiers both in terms of reverse voltage - as just seen - and

forward conduction current. In fact, each rectifier carries half the total output current under

all operating conditions. Then, if compared to similar PWM converters (such as the ZVS

Asymmetrical Half-bridge, or the Forward converter), in the center-tapped output

configuration the equal reverse voltage typically allows the use of lower blocking voltage

rating diodes. This is especially true when using common cathode diodes housed in a single

package. A lower blocking voltage means also a lower forward drop for the same current

rating, and then lower losses.

It must be said, however, that in the LLC resonant converter the output current form factor is

worse, so the output capacitor bank is stressed more. Although the stress level is

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AN2644 The LLC resonant half-bridge converter

considerably lower than that in a flyback converter, as shown in Ta bl e 1 , this is one of the

few real drawbacks of the topology.

Table 1. Output stress for LLC resonant half-bridge vs. PWM topologies @ 50% duty cycle

Output current form factors Forward - ZVS AHB LLC resonant HB Flyback (CCM-DCM boundary)

Peak-to-DC ratio ≈1.05÷1.15

Rms-to-DC ratio ≈1

AC-to-DC ratio ≈0.03÷0.09

-- -

≈ 1.57=

---------- -

≈ 1.11=

----- - 1–≈ 0.48= 8

-- - 1.63≈ 3

-- - 1– 1.29≈ 3

Additional details concerning power losses will be discussed in Analysis of power losses on

page 41.

To complete the general picture on the LLC resonant converter, there is another aspect that needs to be addressed concerning parasitic components which affect the behavior of the circuit.

The first parasitic element to consider is the capacitance of the midpoint of the half-bridge structure, the node common to the source of the high-side power MOSFET and to the drain of the low-side power MOSFET. Its effect is that the transitions of the half-bridge midpoint will require some energy and take a finite time to complete. This is linked to the previously mentioned deadtime inserted between the turn-off of either switch and the turn-on of the complementary one, and will be discussed in more detail in Section 2.2.

The second parasitic element to consider is the distributed capacitance of transformer's windings. This capacitance, which exists for both the primary and the secondary windings, in combination with windings' inductance, originates what is commonly designated as the transformer "self-resonance". In addition to this capacitance one needs to consider also the junction capacitance of the secondary rectifiers, which adds up to that of the secondary windings and lowers the resulting self-resonance frequency (loaded self-resonance).

The effect of all this parasitic capacitance can be modeled with a single capacitor C connected in parallel to L turns from LLC to LLCC. This 4 the transformer's loaded self-resonance (f considerably lower than f than f

and if the load impedance is high enough, its effect starts making itself felt,

as illustrated in Figure 7. The resonant tank, as a consequence,

- order tank circuit features a third resonance frequency at > fR1). When the operating frequency is

the effect of CP is negligible. However, at frequencies greater

LSR

eventually resulting in reversing the transferable power vs. frequency relationship as frequency approaches f

. Power now increases with the switching frequency, feedback

LSR

becomes positive and the converter loses control of the output voltage. The onset of this "feedback reversal" in closed-loop operation is revealed by a sudden frequency jump to its maximum value as the load falls below a critical value (i.e. the frequency exceeds a critical value) and a simultaneous output voltage rise.

In some way, either appropriately choosing the operating frequency range (<< f increasing f

, the converter must work away from feedback reversal. This usually sets the

LSR

) or

practical upper limit to a converter's operating frequency range.

11/64

The LLC resonant half-bridge converter AN2644

Figure 7. Equivalent schematic of a transformer including parasitic capacitance

2.2 The switching mechanism

Still another way of classifying resonant converters would include the LLC resonant halfbridge in the family of "resonant-transition" converters. This nomenclature refers to the fact that in this class of converters power switches are driven in such a way that a resonant tank circuit is stimulated to create a zero-voltage condition for them to turn-on.

To understand how this can be achieved in the LLC half-bridge, it is instructive to consider the circuits illustrated in Figure 8 where the switches Q1 and Q2 that generate the square wave input voltage to the resonant tank are power MOSFETs. Their body diodes DQ1, DQ2 are pointed out because they play an important role. In circuit a), the drain-to-source parasitic capacitances C changes of the node HB are concerned, the parasitic capacitances Cgd and Cds are effectively in parallel, then Cgd+Cds=C

Additionally, other contributors to the parasitic capacitance of the node HB (e.g. that formed between the case of the power MOSFETs and the heat sink, the intrawinding capacitance of the resonant inductor, etc.) are lumped together in the capacitor C C

, is connected between the node HB and a node having a fixed voltage (Vin for C

oss2

ground for C

). Then, as far as voltage changes of the node HB are concerned, C

oss2

effectively connected in parallel to C together in a single capacitor C

oss1

, C

are pointed out as well. In fact, as far as voltage

oss2

has to be considered.

oss

. Note that C

Stray

and C

oss2

from the node HB to ground, as shown in the circuit b):

. It is convenient to lump all of them

Stray

oss1

, like

oss1

Equation 4

which we will refer to in the following discussion. Note also that C linear capacitors, i.e. their value is a function of the drain-to-source voltage. It is intended that their time-related equivalent value will be considered (see Appendix A).

12/64

++=

OSS1COSS2CStray

oss1

and C

oss2

are non-

AN2644 The LLC resonant half-bridge converter

Figure 8. Power MOSFET totem-pole network driving a resonant tank circuit in a

half-bridge converter

Coss

DQ1

Vin

Node

HB Driver

DQ1

DQ2

Coss

Stray

IRI

Resonant

Tank &

Load

Vin

DQ1

Node

HB Driver

DQ2

IRI

Resonant

Tank &

Load

As previously stated, there is no overlap between the conduction of Q1 and Q2. Additionally, a deadtime T

between the transitions from one state to the other of either

switch, where they both are open, is intentionally inserted. It is intended that when Q1 is closed and Q2 is open, the voltage applied to the resonant tank circuit is positive. Similarly we will define as negative the voltage applied to the resonant tank circuit when Q1 is open and Q2 is closed. Consistently with two-port circuits sign convention, the input current to the resonant tank, I

Let us assume Q1 closed and Q2 open. It is then I to the circuit is positive (V reactive elements. Let us suppose that I instant t

when Q1 opens, and refer to the timing diagram of Figure 9.

The current through Q1 falls quickly and becomes zero at t = t

, will be positive if entering the circuit, negative otherwise.

= I(Q1). Despite that the voltage applied

= Vin), IR can flow in either direction since we are in presence of

is entering the tank circuit (positive current) in the

. Q2 is still open and IR must

keep on flowing almost unchanged because of the inductance of the resonant tank that acts as a current flywheel. The electrical charge necessary to sustain I C

, initially charged at Vin, which will be now discharged. Provided IR(t1) is large enough,

the voltage of the node HB will then fall at a certain rate until t = t

will come initially from

, when its voltage

becomes negative and the body diode of Q2, DQ2, becomes forward biased, thus clamping the voltage at a diode forward drop V the remaining part of the deadtime T DQ2. When this occurs, the voltage across Q2 is -V input voltage V

. In the end, this is what is called zero-voltage switching (ZVS): the turn-on

below ground. IR will go on flowing through DQ2 for

until t = t3, when Q2 turns on and its R

, a value negligible as compared to the

DS(on)

shunts

transition of Q2 is done with negligible dissipation due to voltage-current overlap and with C

already discharged, there will be no significant capacitive loss either. Note, however,

that there will be nonnegligible power dissipation associated to Q1's turn-off because there will be some voltage-current overlap during the time interval t

- t1.

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The LLC resonant half-bridge converter AN2644

Figure 9. Detail of Q1 ON-OFF and Q2 OFF-ON transitions with soft-switching for

Dead-time

Dead-timeDead-time

t0–t1Q1 current fall time;

voltage-current overlap for Q1

Node HB transition time

0–t2

Q2’ body diode conduction time

2–t3

Vc = Resonant capacitor voltage

VHB= Node HB voltage

IR= Tank circuit’s current

I(Lp) = Lp (magnetizing) current

I(Q1) = MOSFET Q1 current

I(CHB) = CHBcurrent

Q2 OFF

Q1’s current

falls to zero

Q1 ON

Low turn-off losses

I(Q1)

I(CHB)

I(Q1)

I(CHB)

Q1 OFF

Q2 OFF

Tank circuit’s current

is positive

0 t1t2 t3

Q1 OFF

Q2 ON

Q2 is switched on with essentially

zero drain-to-source volt age: ZVS!

Magnetizing current equals

tank circuit’s current

HB node’s parasitic capa-

HB node’s parasitic capacitance discharge current

citance discharge current

There is an additional positive side effect in turning on Q2 with zero drain-to-source voltage. It is the absence of the Miller effect, normally present in power MOSFETs at turn-on when hard-switched. In fact, as the drain-to-source voltage is already zero when the gate is supplied, the drain-to-gate capacitance Cgd cannot "steal" the charge provided to the gate. The so-called "Miller plateau", the flat portion in the gate voltage waveform, as well as the associated gate charge, is missing here and less driving energy is therefore required. Note that this property provides a method to check if the converter is running with soft-switching or not by looking at the gate waveform of Q2 (which is more convenient because it is sourcegrounded), as shown in Figure 10 and 11.

Figure 10. Q2 gate voltage at turn-on: with

soft-switching

HB node is falling down

here; current due to Cgd

With similar reasoning it is possible to understand that the same ZVS mechanism occurs to Q1 when it turns on if I

is flowing out of the resonant tank circuit (negative current).

In the end we can conclude that, if the tank current at the instant of half-bridge transitions has the same sign as the impressed voltage, both switches will be "soft-switched" at turn-on, i.e. turned on with zero voltage across them (ZVS). It is intuitive that this sign coincidence

Figure 11. Q2 gate voltage at turn-on: with

hard-switching (no ZVS)

Current injection through

Cgd due to hard-switching

Miller effect

14/64

AN2644 The LLC resonant half-bridge converter

occurs if the tank current lags the impressed voltage (e.g. it is still positive while voltage has already gone to zero), which is a condition typical of inductors. In other words, ZVS occurs if the resonant tank input impedance is inductive. The frequency range where tank current lags the impressed voltage is therefore called the "inductive region".

It is worth emphasizing the essential role of DQ1 and DQ2 in ensuring continuity to current flow and clamping the voltage swing of the node HB at V

and -VF respectively (the LLC

in+VF

resonant half-bridge belongs to the family of ZVS clamped-voltage topologies). Power MOSFETs, with their inherent body diodes are therefore the best suited power switches to be used in this converter topology. Other types of switches, such as BJT or IGBT, would need the addition of external diodes.

Going back to the state when Q1 is closed and Q2 open, let us now assume that at the instant t

when Q1 opens, current is flowing out of the resonant tank towards the input

source, i.e. it is negative. This operation is shown in the timing diagrams of Figure 12.

With Q1 now open the current will go on flowing through DQ1 throughout the deadtime, and will eventually be diverted through Q2 only when Q2 closes at t = t

, the end of the

deadtime. As far as Q1 is concerned, then, there will be no loss associated to turn-off because the voltage across it does not change significantly (it is essentially the same situation seen at turn-on when the converter works in the inductive region).

Q2, instead, will experience now a totally different situation. As DQ1 is conducting during the deadtime, the voltage across Q2 at t = t considerable voltage-current overlap but the energy of C R happens in PWM-controlled converters at turn-on. The associated power dissipation ½C

as well. In this respect, it is a "hard-switching" condition identical to what normally

DS(on)

f may be considerably higher than that normally dissipated under "soft-switching"

HBVin

equals Vin+VF so that there will be not only a

will be dissipated inside its

conditions and this may easily lead to Q1 overheating, since heat sinking is not usually sized to handle this abnormal condition.

In addition to that, at t = t

the body diode of Q1, DQ1, is conducting current and its voltage

is abruptly reversed by the node HB being forced to ground by Q2. Hence, DQ1 will keep its low impedance and there will be a condition equivalent to a shoot-through between Q1 and Q2 until it recovers (at t = t

It is well-known the power MOSFET's body diodes do not have brilliant reverse recovery characteristics. Hence DQ1 will undergo a reverse current spike large in amplitude (it can be much larger than the forward current it was carrying at t=t

) and relatively long in duration

(in the hundred ns) that will go through Q2 as well. This spike, in fact, cannot flow through the resonant tank because Ls does not allow for abrupt current changes.

This is a potentially destructive condition not only because of the associated power dissipation that adds up to the others previously considered, but also due to the current and voltage of DQ1 which are simultaneously high during part of its recovery. In fact, there will be an extremely high dv/dt (many tens of V/ns!) experienced by Q1 as DQ1 recovers and the voltage of the node HB goes to zero. This dv/dt may exceed Q1 rating and lead to an immediate failure because of the second breakdown of the parasitic bipolar transistor intrinsic in power MOSFET structure. Finally, it is also possible that Q1 is parasitically turned on if the current injected through its Cgd and flowing through the gate driver's pull down, which is holding the gate of Q1 low, is large enough to raise the gate voltage close to the turn-on threshold (see the spike after turn-off in the graph of Figure 11). This would cause a lethal shoot-through condition for the half-bridge leg.

An additional drawback of this operation is the large and energetic negative voltage spikes induced by the recovery of DQ1 because of the unavoidable parasitic inductance of the PCB

15/64

The LLC resonant half-bridge converter AN2644

subject to its di/dt, which may damage any control IC coupled to the half-bridge leg, not to mention the big EMI generation.

Similarly, it is possible to show that the same series of adverse events will happen to Q1 and Q2, with exchanged roles, when Q2 is turned off if I

is flowing into the resonant tank circuit

(positive current).

The obvious conclusion is that, if the tank current and the impressed voltage at the instant of half-bridge transitions have opposite signs, both switches will be hard-switched and the reverse recovery of their body diodes will be invoked, with all the resulting negative effects. It is intuitive that this sign opposition occurs if the tank current leads the impressed voltage, which is typical of capacitors and then occurs if the resonant tank input impedance is capacitive. This kind of operation is often termed "capacitive mode" and the frequency range where tank current leads the impressed voltage is called the "capacitive region".

Figure 12. Q1 ON-OFF and Q2 OFF-ON transitions with hard switching for Q2 and

recovery for DQ1

Dead-time

t0–t1Q2’ body diode conduction time;

coinciding with dead-time

Q1’s body diode recovery time

1–t2

Vc = Resonant capacitor voltag e

VHB= Node HB voltage

IR= Tank circuit’s current

I(Lp) = Lp (magnetizing) c urrent

I(Q1) = MOSFET Q1 current

Node HB voltage

Q1 ON

Q2 OFF

I(Q1)

I(Q2)

I(Q1)

I(Q2)

Tank circuit’s current

is negative

Q1 OFF

Q2 OFF

0 t1t2

Q1 OFF

Q2 ON

Q2 is hard-switchedQ1 has soft turn-off

Resonant capacitor voltage

High dv/dt

Q1’s body diode

is recovered

Current is circulating

through Q1’s body diode

Then, the converter must be operated in the region where the input impedance is inductive (the inductive region), that is, for frequencies f > f load resistance R is such that R> R

. This is a necessary condition in order for Q1 and Q2

crit

to achieve ZVS, which is evidently a crucial point for the good operation of the LLC resonant half-bridge.

To summarize, ZVS brings the following benefits:

1. low switching losses: either high efficiency can be achieved if the half-bridge is operated at a not too high switching frequency (for example < 100 kHz) or high switching frequency operation is possible with a still acceptably high efficiency (definitely out of reach with a hard-switched converter);

2. reduction of the energy needed to drive Q1 and Q2, thanks to the absence of Miller effect at turn-on. Not only is turn-on speed unimportant because there is no voltagecurrent overlap but also gate charge is reduced, then a small source capability is required from the gate drivers.

3. low noise and EMI generation, which minimizes filtering requirements and makes this converter extremely attractive in noise-sensitive applications.

4. all of the above-mentioned adverse effects of capacitive mode, which not only impair efficiency but also jeopardize the converter, are prevented.

16/64

or in the range fR2 < f < fR1 provided the

AN2644 The LLC resonant half-bridge converter

Note, however, that working in the inductive region is not a sufficient condition in order for ZVS to occur.

In the above discussion, it has been said that the voltage of the node HB could swing from V

to zero "provided IR is large enough". Of course the same holds if we consider node HB's

swing from zero up to V is that the associated inductive energy level of the resonant tank circuit is maintained at the expense of the energy contained in the capacitance C greater than that owned by C the node HB will be able to reach -V

. What actually happens when Q1 turns off with positive IR current

) is

. If the inductive energy (∝ I

(∝ V

) CHB will be completely depleted and the voltage of

, injecting DQ2 and allowing Q2 to turn-on with

essentially zero drain-to-source voltage. Similarly, when Q2 turns off with negative current, part or all of the associated inductive energy will be transferred to C inductive energy is greater than that needed to charge C

up to Vin+VF, the node HB will be

. If the available

allowed to swing all the way up until DQ1 is injected, thus clamping the voltage, and Q1 will be able to turn-on with essentially zero drain-to-source voltage.

Seen from a different perspective, the inductive part of the tank circuit resonates with C and this is the origin of the term "resonant transition" used for designating resonant converters having this property. This "parasitic" tank circuit active during transitions is formed by C

with the series inductance Ls if during the half-bridge transition there is

current circulating on the secondary side (so that Lp is shorted out) or with the total inductance Ls + Lp if there is no current conduction on the secondary side.

Figure 13. Bridge leg transitions in the neighborhood of inductive-capacitive

Q1 ON

Q2 OFF

IRI(Lp)

regions boundary

Q1 OFF

Q2 OFF

Q2 ON

Q1’s body diode conduction

Q2 is hard switched

Q2 is hard switched Q1’s body diode is recovered

Q1’s body diode is recovered

IR = 0

Q1 ON

Q1 OFF

Q2 OFF

Q1 OFF

Q2 OFF

Q2 is hard switched

Q1 OFF

Q2 ON

IR = 0

VHB= Node HB

voltage

IR= Tank circuit’s

current

I(Lp) = Lp (magnetizing)

current

VHB= Node HB

voltage

IR= Tank circuit’s

current

I(Lp) = Lp (magnetizing)

current

IRI(Lp)

Q1 ON

Q2 OFF

Q1 ON

Q2 OFF

Q1 OFF

Q2 ON

Q2 OFF

Q1’s body diode conduction

Q2 is hard switched

Q2 is hard switched Q1’s body diode is recovered

Q1’s body diode is recovered

Q1 OFF

Q2 ON

Q2 OFF

Q2 is soft switched

IR = 0

The above mentioned energy balance considerations, however, are not still sufficient to guarantee ZVS under all operating conditions. There is an additional element that needs to be considered, the duration of the deadtime T

The first obvious consideration is that the duration of the deadtime represents an upper limit to the time the node HB takes to swing from one rail to the other: in order for the mosfet that is about to turn on to achieve ZVS (i.e. to be turned on with zero drain-to-source voltage), the transition has to be completed within T

as depicted in Figure 9. However, the way the

17/64

The LLC resonant half-bridge converter AN2644

deadtime and ZVS are related is actually more complex and depends on converter's operating conditions.

It is instructive to see this in Figure 13, which shows typical node HB waveforms occurring when working in the inductive region but too close to the capacitive region, so that ZVS is not achieved. They refer to the Q1 →OFF, Q2 → ON transition; those related to the opposite transition are obviously turned upside down.

● Case a) is very close to the boundary between inductive and capacitive regions. Tank

current reverses just after Q1 is switched off, a portion of node HB ringing appears as a small "dip", then the tank current becomes negative enough to let the body diode of Q1 start conducting. When Q2 turns on there are capacitive losses and the recovery of the Q1's body diode with all the related issues.

● Case b) is slightly more in the inductive region but still I

crosses zero within the

deadtime. The node HB ringing becomes larger and the body diode of Q1 still conducts for a short time and its recovery is invoked as Q2 turns on.

● Case c) Is even more in the inductive region but still not sufficiently away from the

capacitive-inductive boundary. The ringing of the node HB is large enough to reach zero but I

reverses within the deadtime and the voltage goes up again. At the end of

the deadtime the voltage does not reach Vin, hence the body diode of Q1 does not conduct and Q2, when turned on, will experience only capacitive losses.

● Case d) Is further in the inductive region and I

crosses zero nearly at the end of the

deadtime. Q2 is now almost soft-switched with no losses. This can be considered as the boundary of the operating region where ZVS can be achieved with the given duration of T

Note that the resonant tank's current during node HB ringing is lower than the one flowing through Lp. This means that their difference is flowing into the transformer and, consequently, that one of the secondary half-windings is conducting. Therefore, C

resonating with Ls only.

This analysis shows that there is a "border belt" in the inductive region, close to the boundary with the capacitive region (f

< f < fR1, R = R

) and that as converter's operation

crit

is moved away from the capacitive-inductive boundary and pushed more deeply in the inductive region there is a progressive behavior change from hard-switching to softswitching. In the cases a and b the inductive energy in the resonant tank is too small to let the node HB even swing "rail-to-rail"; moving away from the boundary, as shown in case c, the energy is higher and allows a rail-to-rail swing, but it is not large enough to keep the node HB "hooked" to the rail throughout the deadtime T

. If the converter is operated in this

border belt, Q1 and Q2 will be hard-switched at turn-on and, in cases such as case a and case b, the body diode of the just turned off power MOSFET is injected and then recovered as the other power MOSFET turns on.

Case b and, especially, case c highlight that it is possible to look at the deadtime T from another standpoint: looking at those waveforms, one might conclude that the current I

also

at the beginning of the deadtime is too low or, conversely, that the deadtime is too long. In case c, for example, if the dead-time had been approximately half the value actually shown, Q2 would have been soft-switched at turn-on. Of course, the more appropriate interpretation depends on whether T

is fixed or not.

These cases are related to heavy load conditions.

Figure 14 shows a case typical of no-load conditions, where ZVS is not achieved because of

a too slow transition of the node HB so that it does not swing completely within the deadtime T

. In this case the situation seems less stressful than operating in the capacitive region.

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AN2644 The LLC resonant half-bridge converter

There is no body diode conduction and, consequently, no recovery. Q1 will be almost softswitched at turn-off, while Q2 will have capacitive losses at turn-on. It is true that the turn-on voltage is lower than V

, thus the associated energy of CHB is lower, but at no-load the

operating frequency is usually considerably higher than in the capacitive region, then these power losses may easily overheat Q1 and Q2. Finally, note in Figure 14 that I(Lp) is exactly superimposed on I

, then the secondary side of the transformer is open and CHB is

resonating with the total inductance Ls+Lp.

Figure 14. Bridge leg transitions under no-load conditions

IRI(Lp)

Q1 ON

Q2 OFF

Q1 OFF

Q2 OFF

Q1 OFF

Q2 ON

Q2 is hard switched

VHB= Node HB voltage

IR= Tank circuit’s current

I(Lp) = Lp (magnetizing) current

From what we have seen we can conclude that the conditions in order for the half-bridge switches to achieve ZVS are:

1. Under heavy load conditions, as one switch turns off, the tank current must have the same sign as the impressed voltage and be large enough so that both the rail-to-rail transition of the node HB is completed and the current itself does not reverse before the end of the deadtime, when the other switch turns on.

2. With no-load, the tank current at the moment one switch turns off (which has definitely the same sign as the impressed voltage) must be large enough to complete the node HB transition within the deadtime, before the other switch turns on.

Both conditions can be translated into specifying a minimum current value I to be switched when either power MOSFET turns off. In general, different I

that needs

Rmin

values are

Rmin

needed to ensure ZVS at heavy load and at no-load. One can simply pick the greater one to ensure ZVS under any operating condition by design. On the other hand, this minimum required amount of current is to the detriment of efficiency.

At light or no-load a significant current must be kept circulating in the tank circuit, just to maintain ZVS, in spite of the current delivered to the load that is close to zero or zero. Using ac-analysis terminology, a certain amount of reactive energy is required even with no active energy.

Finally, also at heavy load the value of I

to be specified is the result of a trade-off. In fact,

Rmin

its value is directly related to the turn-off losses of both Q1 and Q2. The higher the switched current is, the larger the switching loss due to voltage-current overlap will be.

The discussion on the switching mechanism has been focused on the primary-side switches, and the conditions in order for them to achieve soft-switching (ZVS at turn-on, precisely) have been found. One important merit of the LLC resonant converter is that also the rectifiers on the secondary side are soft-switched. They feature zero-current switching (ZCS) at both turn-on and turn-off. In fact, at turn-on the initial current is always zero and ramps up with a relatively low di/dt, so that forward recovery does not come into play. At turn-off they become reverse biased when their forward current is already zero, so that their

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The LLC resonant half-bridge converter AN2644

reverse recovery is not invoked. This topic will be addressed in Section 2.3, where it will be shown that this property is inherent in the topology, hence it occurs regardless of converter's design or operating conditions.

2.3 Fundamental operating modes

The LLC resonant half-bridge converter features a considerable number of different operating modes, which stem from its multiresonant nature. Essentially, the term "multiresonant" means that the configuration of the resonant tank may change within a single switching cycle. We have seen that there are two resonant frequencies, one (the higher) associated to either of the secondary rectifiers conducting, the lower one associated to both rectifiers non-conducting. Then, depending on the input-to-output voltage ratio, the output load and the characteristics of the resonant tank circuit, the secondary rectifiers can be always conducting (with the exception of a single point in time), which is referred to as CCM (Continuous Conduction Mode) like in PWM converters, or there can be finite time intervals during which neither of the secondary rectifiers is conducting. This will obviously be called a DCM (Discontinuous Conduction Mode) operating mode.

Different kinds of CCM and DCM operating modes exist, although not all of them can be seen in a given converter, some are not even recommended, like those associated with capacitive mode operation. However, in all CCM modes the parallel inductance Lp is always shunted by the load resistance reflected back to the primary side, so that it never participates in resonance, rather it acts as an additional load to the remaining LC resonant circuit. Similarly, in all DCM modes, there will be some finite time intervals where Lp, being no longer shunted from the secondary side, becomes part of resonance.

In the following we will consider four fundamental operating modes and use the nomenclature defined in [3]:

1. Operation at resonance, when the converter works exactly at f = f

2. Above-resonance operation, when the converter works at a frequency f > f

;

. Moving

away from resonance, we will consider three sub-modes:

a) CCMA operation at heavy load;

b) DCMA operation at medium load;

c) DCMAB operation at light load;

3. Below-resonance operation, when the converter works at a frequency f a load resistor R > R

. Moving away from resonance, we will consider two sub-modes:

crit

< f < fR1 with

a) DCMAB operation at medium-light load;

b) DCMB operation at heavy load;

4. Below-resonance operation, when the converter works at a frequency f a load resistor R < R

(capacitive mode), corresponding to the CCMB operating mode

crit

< f < fR1 with

defined in [3];

In addition, two extreme operating conditions will be considered:

1. No-load operation (cutoff)

2. Output short-circuit operation

It is interesting to point out that, unlike PWM converters where DCM operation is invariably associated to light load operation and CCM to heavy load operation, in the LLC resonant converter this combination does not hold.

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