Third Harmonics current injection scheme

7/21/2019 Third Harmonics current injection scheme

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The third harmonics current injection scheme for LLC

topology to reduce the RMS of the output current

Ren Ren, Fanghua Zhang, Zhiyuan Shen, Shuo Liu

Jiangsu Key Laboratory of New Energy Generation and Power Conversion

Nanjing University of Aeronautics and Astronautics Nanjing, China

[email protected], [email protected], [email protected], [email protected]

Abstract —The Intermediate Bus Converter (IBC) is a middle

stage converter in the distribution power architecture,

characterized with high efficiency, high frequency and high

power density, to realize the DC voltage transform and isolated

function. In this paper, the unregulated LLC DC transformer’s

(LLC-DCT) inherent problem which leads to a large conduction

loss in IBC application has been discussed. A new intuitive

topology with third order harmonic current injection has been

proposed to reduce the RMS of the resonant and secondary

current. At the end, the theoretical analysis and the proposedoptimal topology design are verified by an 800W, 100kHz,

400V/12.5V LLC-DCT prototype.

Keywords—LLC-DCT; third harmonics current injection;

conduction loss; resonant converter;

I. I NTRODUCTION

With the development of information technology and power electronic technology, the higher demand of the powermanagement has been proposed [1-2]. High efficiency, highfrequency and high power density are becoming a trend of theisolated DC/DC converters. The Intermediate Bus Converter(IBC) is a middle stage converter in the distribution powerarchitecture to realize the DC voltage transformation andisolation. Working as a key stone of the distribution powerarchitecture, the IBC has a more stringent requirement of thehigh power density. Basically, the IBC converter can bedivided into two categories. One is regulated. Another one isunregulated [3-5]. In this paper, the unregulated bus converteris discussed.

The resonant converter is one of promising substitutetopology of IBC candidate compared with traditional hard-switched converter

[6-7]. For instance, The LLC DC-

Transformer (LLC-DCT) is open-loop type of LLC converterwhose switching frequency is fixed at resonant frequency tomaximize the efficiency because nearly ZCS for primaryswitches can be obtained in this work condition. In themeanwhile, its switches of primary side and secondary side canachieve Zero-Voltage-Switching (ZVS) and Zero-Current-Switching (ZCS) respectively at any load condition.

On the other hand, most of resonant converters have someinherent problems to prevent them from improving the

performance. Since current in the telecommunication power

supply dramatically increased， like a server, the conduction

loss occupies the main loss in the IBC, especially fortransformer and synchronous rectification (SR) devices. Themain drawback of resonant converter is large RMS of rectifiedcurrent compared with PWM converter. The basic method is

paralleling SR devices [8-9], but the synchronous rectificationimitating diodes’ action in LLC is difficult to realize because ofthe SR devices’ package and circuit’s inductance. Too many

paralleling SR devices layout will make SR more difficult towork well and cause the reliability problems. For winding loss,

the paper [10] and [11] proposed the matrix transformerstructure to relieve eddy loss and conduction loss. The leakageinductance and ac resistance show a decrease by using matrixtransformer. Unfortunately, the costs of this structure willincrease on account of the usage of multiple magnetics. Inaddition to the above, the selection of switch should be keep alarge voltage and current margin since the resonant convertershave a large voltage and current stress in contrast to the PWMconverter.

To solve this issue, the paper [12] proposed novel multi-element resonant converters. Through the design of theresonant element, the third harmonic voltage gain also raise tothe same as the fundamental voltage gain. As a result, the thirdharmonic current injects to the total current making a much

reduced RMS of the secondary current. But its analysis onlyconsiders the voltage gain aspect and doesn’t illustrate how tocontrol the ratio of third current injection. Moreover, the paperalso doesn’t give the consideration about the influence of theleakage inductor on the multi-resonant elements and itsexperimental current waveform doesn’t realize best ratio ofthird current injection.

This paper focuses on how to reduce the RMS of theresonant and secondary current. A new intuitive topology has

been proposed and the methods to control the ratio of the thirdharmonic have been investigated. Also, the leakage inductancehaving an influence on the ratio and phase shift of the thirdharmonic is analyzed.

II.

NEW LLC TOPOLOGY BASED O N THIRD HARMONIC

CURRENT I NJECTION

A. Resonant tank of third harmonic current injection

Inherit from the resonant converter, band-passcharacteristic of the resonant tank eliminates high frequencycomponent in the current of resonant tank. As a result,

This paper is sponsored by Qing Lan Project.

978-1-4799-6735-3/15/$31.00 ©2015 IEEE 1435



1 Lr i

mi

m L

1r C

1r L

inV

3r L 3 Lr i3r

C

load R

secondary side rectified current of a LLC converter has a high peak-average ratio. Fig1 is an AC simplified equivalent circuit

of LLC converter. As the Fig1 shown, the resonant tank can beregarded as a band-pass current source. According to theFourier decomposition, symmetric periodic square wave can bedecomposed into the sum of a set of simple oscillatingfunctions. Fundamental harmonic is not affected sinceimpedance of the resonant tank is zero at resonant frequencies,while high order harmonic component in the current ofresonant tank is eliminated since impedance of the resonanttank is quite large. The form factor of full-wave rectified sinewave is 1.11 while form factor of square wave is1.Consequently, the secondary current which only keeps thefundamental component with high form factor causesadditional 23% conduction losses in synchronous rectificationdevices than square wave. Injecting high order harmonic

reduces conduction losses. However, at the turn off edge of theswitch cycle, the current is high. The switching performance ofmain devices is sacrificed. To reduce the conduction losswithout sacrificing switching performance, 3

rd harmonic is

injected.

The new resonant tank is shown in the Fig2. Resonant

frequency of the additional resonant tank is set as third orderharmonics’ frequency. At 3rd harmonic frequency, impedanceof the added resonant tank is zero, so 3rd harmonic current is

injected to the load and it acts as a 3rd harmonic current source.Form factor of secondary side rectified current is 1.05.

Conduction loss decreased by 10% compared with the LLCresonant converter.

The new topology based on third harmonics injection isshown in the Fig3. The resonant frequency of third harmonic

injection tank is triple resonant frequency of fundamentalcomponent tank. So, the resonant frequency express as:

1 3

1 1 3 3

1 1

2 2r r

r r r r

f f L C L C π π

= = (2.1)

where Lr1 and C r1 is the fundamental frequency resonantinductor and capacitor respectively and Lr3 and C r3 is the thirdorder harmonic resonant inductor and capacitor respectively.

Also, the correlation between the f r1 and f r3 should besatisfied as:

3 13r r f f = ⋅ (2.2)

The voltage gain of this new topology is illustrated inFigure 4. From the figure 4, the voltage gain in thefundamental frequency and third order frequency are the same,so the third order harmonic injection will not change the totalvoltage gain when the new converter works at its fundamentalresonant frequency. The other interesting point is the voltage

gain of specific frequency f r2 is zero just like one descripted in paper [13]. This character can be used to control the currentinrush in the process of the start-up and short-circuit condition.

Simulantian and Key Waveform of New Topology

In order to investigate the switching behavior andconverter’s characteristic of the proposed topology, thesimulation was run by Saber software.

Fig. 5 shows the key waveform of the proposed resonantconverter involving the Drain-Source voltage of primaryswitch VDS, its drive signal VGS, the primary side current of thetransformer I pri, the tank current I1 and the third order harmonicinjection resonant rank current I3. It can be seen that when thethird order harmonic current is injected into the total resonantcurrent, i.e. Transformer current at primary and secondary side,the total resonant current and secondary rectified current looklike the shape of a saddle. This feature makes the RMS and

peak value of the current much reduced. Although an extraresonant tank branch is added, the primary switch can stillobtain the ZVS because the whole magnetizing current doesnot change. The less switching loss means higher switchingfrequency available.

Lr i

mi

m L

load Rr C

r L

inV First order band-pass

current source

Fig. 1. AC equivalent circuit of LLC-DCT

1 Lr i

mi

m L

1r C 1r

L

inV

3r L 3 Lr i3r C

load R

Fig. 2. AC equivalent circuit of proposed LLC-DCT

0 1.5 105× 3 105

× 4.5 105× 6 105

×

0

1

2

3

4

Ggainf f 2,( )

Ggainf f 10,( )

Ggainf f 25,( )

Ggainf f 40,( )

Ggainf f 60,( )

Ggainf f 1 0 0,( )

f

1r f 3r f

2r f

Fig.4. The voltage gain of proposed topology

o RoC p

N 1 s

N

5 D

6 D2 s N

1r C 1r L

inV

1S

3 D

1 D

3S

1C

3C

2 D 2C 2

S

4S

4 D

4C

inC

3r C 3r L

Fig. 3.

AC equivalent circuit of proposed LLC-DCT

1436



III. THE A NALYSIS OF I NJECTION R ATIO AND PHASE SHIFT

OF THIRD HARMONICS CURRENT

The resonant component parameters are satisfied withequation (3.1) between fundamental frequency resonant rankand third order harmonic resonant tank. It can introduce ascaling factor k which makes the equation (3.2).

3 3 1 19r r r r L C L C ⋅ = ⋅ (3.1)

3 1 3 1

1

9r r r r L k L C C

k = ⋅ = ⋅ (3.2)

The choice of k will affect the third order harmonicscurrent injection ratio because of the existence of resonantfrequency f r2. The leakage inductance affects both injectionratio and phase shift of third harmonics current and the effectof phase. Also, the load condition affects injection ratio. All

these factors and design method of resonant parameters will bediscussed and analyzed in this chapter.

A. The effect of k on harmonic injection ratio

The resonant frequency f r2 can obtain a nearly zero voltagegain. This could be explained the resonant tank has the infiniteimpedance because the fundamental and third harmonicresonant tank built up a new parallel resonance. The parallelresonant frequency will affect the harmonic injection easily ifthe f r2 is too close to f r1 or f r3. In general implement, theswitching frequency always has a deviation for trackingresonant frequency, so the voltage gain will greatly changewhen the switching frequency drops into f r2 frequency trap.

The equation 3.3 can be obtained when parallel resonanceneglects the tiny influence caused by load and magnetizing

inductance：

2 1 2 3

2 1 2 3

1 1( ) ( ) 0r r

r r

j L j L j C j C

ω ω

ω ω

+ + + = (3.3)

where ωr2 is the corresponding angular frequency of f r2.

The f r2 can be derived from the equation 3.3, it expressed as:

1 32

1 3 1 3

1

2 ( )r r

r

r r r r

C C f

C C L Lπ

+= ⋅

+ (3.4)

Combining the equation 3.4 with 2.2 and 3.2, the relation between the f r2 and k can be inferred as follows:

2 3

9 1

9( 1)r r

k f f

k

+= ⋅

+ (3.5)

where f r3 sets 300kHz..

The Fig. 6 shows the curve of correlation between f r2 and k.From the curve, it concludes that if the k is set too high, thesecond resonance frequency f r2 will be close enough to f r3. So ifthe switching frequency has a little deviation comparing thefirst resonant frequency f r1, it will drop the secondaryresonance trap and third harmonic injection ratio will be so low.

The Fig. 7 displays this design work condition at k=10. Itcan be seen the secondary resonant frequency f r2 and thirdresonant frequency is so close. From above analysis, it shouldset f r2 in some specific range. The safe range is150kHz~250kHz. Through the Fig. 6, the range of k can be

decided as 0.18~1.86.

B. The effect of load on third harmonic injection

The impedance of load and magnetizing inductance willaffect the third harmonic injection ratio. When the load isextremely light, the third harmonic injection ratio will dropdown because the magnetizing inductance branch has the lowerimpedance. At the same time, the load condition will also

0 1.5 105

× 3 105

× 4.5 105

× 6 105

×

0

1

2

3

4

Ggainf f 2,( )

Ggainf f 10,( )

Ggainf f 25,( )

Ggainf f 40,( )

Ggainf f 60,( )

Ggainf f 1 00,( )

f

1r f

2r f

3r f

Fig.7. The voltage gain at k=10

( )kHz

0 2 4 6 8 10100

150

200

250

300

f r2 k ( )

k

Fig.6. The relaiton cruve between f r2 and k

DS V GS V

pri I

sec I

1 I

3 I

Figure 5: The key simulation waveform.

1437



introduce the phase difference between fundamental frequencycurrent and third harmonic current.

The analysis method is to decompose the excitation ofsquare wave into two components including first harmonic andthird harmonic. Then sinusoidal approximation analysis isapplied on first harmonic and third harmonic respectively.Some results will be given by relation curve as follows. Theanalysis specs are that input voltage is 400V, the output voltageis 12.5V and the power rating is 800W. Select the 10% of fullload to full load as analysis range.

The Fig. 8 shows the lighter the load is, the lower value of

the third harmonic current injection ratio will be, but it changesvery small in a wide range of load which keeps a stableinjection ratio. The Fig. 9 suggests that there is a small phaseshift when it works at light load condition. The phase shift will

be 2°when working at 10% load. The phase shift may cut

down the performance of the reduction of conduction loss butconsidering it happens in light condition, it can’t cause a largeloss.

C. The effect of leakage inductance on third harmonic

injection

The leakage inductance also has an effect on phase shift between the first harmonic and third harmonic. The analysismethod is the same with former section. The result is given in

Fig. 10 when working at full load condition.

From the Fig. 10, the phase shift can be positive or negativeon different leakage inductance values. This character can beused to compensate the phase shift caused by load with properleakage inductance value.

IV. EXPERIMENTAL VERIFICATION

The Fig. 11 shows the fundamental frequency current iLr1,third order harmonic current iLr3 and secondary side rectifiedcurrent isec at the full load condition. The Fig. 12 shows the isec and its synchronous rectifier’s driver signal Vdri_sec. The Fig. 13displays the driver signal and its Gate-Source voltage of

primary side switch and it can still achieve the ZVS switchingcondition. From the Fig. 14, the efficiency of LLC with thirdorder harmonics current injection is 96.2% in the full loadcondition compared with 95.11% without third order

harmonics current injection. In the light load condition, because the conduction loss doesn’t occupy the dominant loss,the efficiency doesn’t improve markedly. In Summary, owingto the third order harmonic injection branch, the current stressof switch at secondary side, conduction loss and transformerloss can be reduced, so the overall efficiency improved.

0 1 2 3 4 50

1

2

3

4

θdiff R al( )

R al Fig.9. The correlation curve between the phase shift θdiff and the load

resistance R al

0 5 10 15 200.326

0.328

0.33

0.332

0.334

ampratio R al( )

R al Fig.8. The correlation curve between the thid harmonic injection ratio ampratio

and the load resistance R al

[5 / ]t us div

_ sec [5 / ]driV V div

[20 / ] seci A div

Fig.12. The secondary rectified current and its driver signal

0 1 10 7−

× 2 10 7−

× 3 10 7−

× 4 10 7−

×

3−

2−

1−

0

1

2

3

θdiff Lk ( )

Lk Fig.10. The correlation curve between the phase shift θdiff and

[10 / ] seci A div

[2.5 / ]t us div1 [5 / ] Lr i A div

3

[5 / ] Lr

i A div

Fig.11. The waveform of first harmonic current and third harmonic

current

[5 / ]t us div

_ sec [5 / ]driV V div

[20 / ] seci A div

Fig.12. The secondary rectified current and its driver signal

1438



V. CONCLUSION

The paper proposes a new LLC topology with thirdharmonics injection. With third harmonics injection, theconduction loss can be reduced by 10%. The designconsiderations of resonant tank and operation of converter areillustrated in this paper. ZVS also can be achieved in the

primary side switches. The effects of leakage inductance and

load condition to injection ratio are analyzed. The validity ofthe proposed scheme has been tested and verified by theexperimental results of an 800W prototype.

R EFERENCES

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[5] W. Zhang, Y. Long, Z. Zhang, F. Wang, L. M. Tolbert, B. J. Blalock, S.Henning, C. Wilson, and R. Dean, “Evaluation and comparison ofsilicon and gallium nitride power transistors in LLC resonant converter,”in Proc. IEEE Energy Conversion Congress and Expo (ECCE), 2012, pp. 1362-1366.

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[10 / ]t us div

_ [5 / ]dri priV V div

[200 / ] DS V V div

Fig.13. The waveform of ZVS of primary switch

Fig.14. The efficiency comparison of traditional LLC-DCT and

proposed LLC-DCT

1439

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Third Harmonics current injection scheme