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WO2008101367A1 - Magnetic integration structure - Google Patents

Magnetic integration structure Download PDF

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Publication number
WO2008101367A1
WO2008101367A1 PCT/CN2007/000592 CN2007000592W WO2008101367A1 WO 2008101367 A1 WO2008101367 A1 WO 2008101367A1 CN 2007000592 W CN2007000592 W CN 2007000592W WO 2008101367 A1 WO2008101367 A1 WO 2008101367A1
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WO
WIPO (PCT)
Prior art keywords
transformer
parameter
resonant
llc resonant
resonant converter
Prior art date
Application number
PCT/CN2007/000592
Other languages
French (fr)
Inventor
Yanjun Zhang
Dehong Xu
Kazuaki Mino
Kiyoaki Sasagawa
Original Assignee
Zhejiang University
Fuji Electric Systems Co., Ltd.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang University, Fuji Electric Systems Co., Ltd. filed Critical Zhejiang University
Priority to PCT/CN2007/000592 priority Critical patent/WO2008101367A1/en
Priority to CN200710186467XA priority patent/CN101308724B/en
Priority to JP2008033779A priority patent/JP2008205466A/en
Priority to US12/033,888 priority patent/US20080224809A1/en
Publication of WO2008101367A1 publication Critical patent/WO2008101367A1/en

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Classifications

    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F29/00Variable transformers or inductances not covered by group H01F21/00
    • H01F29/14Variable transformers or inductances not covered by group H01F21/00 with variable magnetic bias
    • H01F29/146Constructional details
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F38/00Adaptations of transformers or inductances for specific applications or functions
    • H01F38/02Adaptations of transformers or inductances for specific applications or functions for non-linear operation
    • H01F38/023Adaptations of transformers or inductances for specific applications or functions for non-linear operation of inductances
    • H01F2038/026Adaptations of transformers or inductances for specific applications or functions for non-linear operation of inductances non-linear inductive arrangements for converters, e.g. with additional windings
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F27/00Details of transformers or inductances, in general
    • H01F27/34Special means for preventing or reducing unwanted electric or magnetic effects, e.g. no-load losses, reactive currents, harmonics, oscillations, leakage fields
    • H01F27/38Auxiliary core members; Auxiliary coils or windings
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F3/00Cores, Yokes, or armatures
    • H01F3/10Composite arrangements of magnetic circuits
    • H01F3/12Magnetic shunt paths
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00Details of apparatus for conversion
    • H02M1/0064Magnetic structures combining different functions, e.g. storage, filtering or transformation
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00Conversion of DC power input into DC power output
    • H02M3/22Conversion of DC power input into DC power output with intermediate conversion into AC
    • H02M3/24Conversion of DC power input into DC power output with intermediate conversion into AC by static converters
    • H02M3/28Conversion of DC power input into DC power output with intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate AC

Definitions

  • the present invention relates to a magnetic integration structure, especially to 1 MHz-IkW LLC resonant converter with integrated magnetics.
  • LLC resonant converter can avoid both of these two problems. It has higher conversion efficiency at higher input voltage [3-4], which makes it an excellent candidate for the front end dc-dc converter. And if it is properly designed, LLC resonant converter can realize the ZCS OFF of the rectification diodes, which eliminates the reverse recovery of rectification diodes and improves efficiency. Another advantage of LLC resonant converter is the ZVS ON of the main switches, so that the converter can work at higher switching frequency and the power density is increased.
  • LLC resonant converter There are three magnetic components in LLC resonant converter: resonant inductor, parallel inductor and transformer. All the magnetic components can be integrated together [4-10]. Therefore, the power density of LLC resonant converter can be further increased.
  • Magnetic integration structure wherein the window area for the transformer is larger than the window area for the resonant inductance.
  • FIG. 1 is LLC resonant converter
  • Figure 2 is DC voltage gain curve of LLC resonant converter
  • Figure 3 is DC voltage gain of LLC resonant converter when parameter k is variable and parameter Q is constant;
  • Figure 4 is power factor angle curve when parameter k is variable and parameter Q is constant;
  • Figure 5 is DC voltage gain of LLC resonant converter when parameter k is constant and parameter Q is variable;
  • Figure 6 is power factor angle curve when parameter k is constant and parameter Q is variable
  • Figure 7 is some main waveforms of LLC resonant converter
  • Figure 8 is equivalent circuit of LLC resonant converter in half switching cycle
  • Figure 9 is the loss breakdown of LLC resonant converter
  • Figure 10 is forward voltage comparison of two different rectification diodes
  • Figure 11 is efficiency improvement when schottky diode is used to replace fast recovery diode
  • Figure 12 is the first presented integrated magnetic structure and its corresponding magnetic circuit model
  • Figure 13 is the second presented integrated magnetic structure and its corresponding magnetic circuit model
  • Figure 14 is the proposed magnetic integration structure
  • Figure 15 is practical integrated magnetic structure
  • Figure 16 is prototype of IMHz- IKW LLC resonant converter
  • Figure 17 is the resonant tank voltage V ab and the resonant current i p , v a b: 100V/div, i p : 20A/div, t: 500ns/div;
  • Figure 18 is the voltage on the rectification diodes, V DI : 50V/div, V D2 : 50V/div, t: 500ns/div;
  • Figure 19 is efficiency of LLC resonant converter
  • Figure 20 is switching frequency of LLC resonant converter.
  • T, k is defined as the ratio of parallel inductance to series inductance L * , f s is the l
  • : series resonant frequency and is defined as J ' , f is the switching frequency
  • the converter In the design we expect the converter to operate higher than the frequency f s i and lower than the series resonant frequency f s .
  • the frequency f s] is defined as # This is because when LLC resonant converter works in this region, the following excellent characteristic can be gained
  • circuit parameters can be expressed as another set of parameters: n, f s , k and Q, and design according to this set of parameters is more general and meaningful. Therefore, we'll firstly discuss the selection principles for the parameters n, f s , k and Q. After these parameters are decided the circuit parameters are also decided.
  • Vj n _max is the maximum input voltage 400V.
  • transformer turn ratio 8.5:2:2.
  • the switching frequency is below the series resonant frequency f s .
  • the switching frequency of LLC resonant converter is required to be around IMHz, we should choose the series resonant frequency f s to be a little bit larger than IMHz.
  • the series resonant frequency f s to be 1.1MHz.
  • Power factor angle is defined as the angle between the input voltage and the input current of the resonant tank. With a larger power factor angle the reactive power flowing into the resonant tank is increased so that the efficiency is impaired. Power factor angle can be expressed as
  • the circuit parameters can be calculated as Transformer turn ratio : 8.5 : 2 : 2 Resonant inductor Ls: 1.78uH Resonant capacitdr Cs: 11.8nF Parallel inductor Lp: 17.8uH.
  • v a b is the voltage applied to the resonant tank
  • i p and i LP are the current flowing through the resonant tank and the parallel inductor respectively
  • ioi and ⁇ D2 are the current flowing through the rectification diodes
  • v c is the voltage across the resonant capacitor.
  • the following current values must be derived firstly: (1) the rms value of the current flowing through the resonant tank, (2) the rms value of the current flowing through the transformer primary side, (3) the rms value of the current flowing through the transformer secondary side.
  • FIG. 7 Some main waveforms of LLC resonant converter Since the waveforms in Fig.7 are symmetric in a switching cycle, analyzing them in half a switching cycle is enough. In half a switching cycle (neglecting the switching process), the operation of LLC resonant converter can be divided into two stages [3-4]. The equivalent circuits of the two stages are shown in Fig.8 (a) and (b) respectively.
  • nV L, dt O)
  • V 1n is the input voltage
  • v c (t) is the voltage across the resonant capacitor
  • L s is the resonant inductor
  • i p (t) is the current flowing through the resonant tank
  • n is the transformer turn ratio
  • V 0 is the output voltage
  • C s is the resonant capacitor
  • L p is the parallel inductor
  • iLp(t) is the current flowing through it.
  • the initial value of i p (t), v c (t) and ⁇ LP (t) is given as nV.
  • ⁇ s is the angle frequency and is defined as 9 .
  • the parallel inductor is integrated with the transformer by utilizing the magnetizing inductance, the losses of the parallel inductor and transformer are analyzed together.
  • Q g is the gate charge of the main MOSFET
  • V gs is the gate drive voltage
  • f is the switching frequency
  • I o ff is the current through the main MOSFET when it is turned off and I Of r is equal nV a A f L to * " , tf is the fall time of the main MOSFET, f is the switching frequency, C 0Ss is the output capacitance of the main MOSFET.
  • C m , ⁇ , ⁇ are some empirical parameters related to the magnetic material
  • f is the switching frequency
  • 5 Ls is the maximum flux density
  • V e _Ls is the volume of the resonant inductor magnetic core.
  • Equation (18) where l pjms is the rms value of the resonant current i p and is given in equation (18), R- Ls _ac is the ac resistance of resonant inductor winding and can be measured through an impedance analyzer.
  • C m , ⁇ , ⁇ are some empirical parameters related to the magnetic material
  • f eq is the equivalent frequency and is defined as [12]
  • x is the maximum flux density
  • f is the switching frequency
  • V e _ ⁇ is the volume of the transformer magnetic core.
  • I p rm s is the rms value of the resonant current i p and is given in equation (18)
  • R Pr i_ac is the ac resistance of transformer primary winding and can be measured
  • I sec _rms is the rms value of the current through transformer secondary side and given in equation (20)
  • R sec ac is the ac resistance of transformer secondary winding and also can be measured through an impedance analyzer.
  • V F is the forward voltage drop of the rectification diodes
  • I D _ ⁇ S is the rms value of the current through the rectification diodes
  • I D _ ⁇ S is equal to I se c_rm s -
  • the parallel inductor L p and transformer T can be integrated together by inserting an air gap into the transformer magnetic core and reducing the magnetizing inductance to the parallel inductance [4,9].
  • the transformer leakage inductor As the resonant inductor [6-10].
  • the transformer inherent leakage inductance is smaller than the needed resonant inductance. Therefore the transformer leakage inductance is increased by inserting a "leakage layer" between the primary winding and secondary winding.
  • the material for the leakage layer is usually low permeability magnetic material, such as C302 (EPCOS) etc.
  • the presented structure 1 is to build the transformer windings on the left outer leg and build the resonant inductor winding on the right outer leg of the magnetic core. There are air gaps on both the outer legs and no air gap on the center leg. Therefore the fluxes generated by the transformer and the resonant inductor are short-circuited through the center leg. And the fluxes on the center leg can be cancelled.
  • the advantage of structure 1 is that the window area for transformer winding is the same as the discrete transformer.
  • the disadvantage is that the flux density on the left outer leg is doubled compared to the discrete transformer because the cross sectional area of the left outer leg is only half of the center leg. Therefore the magnetic core loss is increased.
  • Another disadvantage of structure 1 is that it's mechanical unstable [4-5].
  • the presented structure2 and its corresponding magnetic circuit model are shown in Fig. 13.
  • the advantage of structure2 is that the flux density for the transformer is the same as the discrete transformer, so that the transformer magnetic core loss is not increased. Another benefit is that it's a mechanical stable structure because the air gap is on all the legs.
  • the disadvantage of structure 2 is the decreased window area for transformer winding so that the transformer copper loss may increase.
  • the proposed magnetic integration structure is shown in Fig. 14. It's derived from the second structure as shown in Fig. 13 (a). But the window area for the transformer winding is increased so that the transformer copper loss increase is no so much as structure2.
  • the resonant inductance is only 1.78uH.
  • the Ansoft PEMage simulation result for the resonant inductance is 2.12uH. Because we need only three turns to realize the resonant inductor, the decrease of the window area for the resonant inductor is not a problem.
  • Fig. 15 shows the practical integrated magnetic structure.
  • Fig. 17 shows the experimental waveform of the voltage applied to the resonant tank V a b and the current flowing through the resonant tank i p .
  • the operation condition is: input voltage 400V 5 output 48V/20A, switching frequency 875 KHz. From Fig. 17 we can find that the experimental waveform corresponds well with the theoretical waveform shown in Fig.7.
  • Fig. 18 shows the experimental waveform of the voltage on the rectification diodes. The operation condition is the same as in Fig. 17. From Fig. 18 we can see that the waveform is clean which indicates the ZCS OFF of the rectification diodes.
  • Fig. 19 and Fig.20 shows the efficiency and switching frequency curve of LLC resonant converter. From Fig. 19 and Fig.20 we can see that the efficiency at 400V input voltage full load output is 93.95% at the switching frequency of 875 KHz.
  • Integrated magnetic structure is adopted. It can further reduce the magnetic component size and increase the power density.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Dc-Dc Converters (AREA)

Abstract

The copper loss lost in winding is reduced by making the winding area of the trans side larger than the winding area of the inductor side.

Description

Magnetic Integration Structure
Field of the Invention
The present invention relates to a magnetic integration structure, especially to 1 MHz-IkW LLC resonant converter with integrated magnetics.
Background of the Invention
In traditional Buck-type dc-dc converters such as forward, half bridge and full bridge converter, there exists a compromise between the input voltage range and the efficiency. The turn ratio of transformer is decided by the minimum input voltage. When the input voltage increases, the duty cycle decreases to keep the output voltage constant. But with the duty cycle decreasing the conversion efficiency also decreases [1-2]. This problem is especially severe in front end dc-dc converters in which the rated input voltage is 400V (Output voltage of PFC converter). To ensure 20ms holdup time, the input voltage range of the front end dc-dc converter is generally 300V-400V. If Buck-type dc-dc converter is used as the front end dc-dc converter, the conversion efficiency will be the lowest in the nominal operation condition.
Another problem with the Buck-type dc-dc converter is the reverse recovery of the rectification diodes. Reverse recovery generates losses on the rectification diodes. Besides, reverse recovery causes parasitic oscillation on the rectification diodes and thus increase their voltage stress. The diodes with higher voltage rating generally have larger forward voltage. Therefore the conduction loss of the rectification diodes is also increased and the conversion efficiency is impaired.
LLC resonant converter can avoid both of these two problems. It has higher conversion efficiency at higher input voltage [3-4], which makes it an excellent candidate for the front end dc-dc converter. And if it is properly designed, LLC resonant converter can realize the ZCS OFF of the rectification diodes, which eliminates the reverse recovery of rectification diodes and improves efficiency. Another advantage of LLC resonant converter is the ZVS ON of the main switches, so that the converter can work at higher switching frequency and the power density is increased.
There are three magnetic components in LLC resonant converter: resonant inductor, parallel inductor and transformer. All the magnetic components can be integrated together [4-10]. Therefore, the power density of LLC resonant converter can be further increased.
In this paper the parameter design for LLC resonant converter is presented. The loss analysis based on theoretical derivation is performed. Integrated magnetic structure is also adopted in the prototype to further increase the power density. Two different integrated magnetic structures are compared and improvement is made on one of them.
References are :
[1] Loveday H. Mweene, Chris A. Wright, Martin E Schlecht, "A IkW, 500kHz Front-End Converter for a Distributed Power Supply System," in Proc. IEEE Appl. Power Electron Conf., 1989, pp. 423-432.
[2] Koji Yoshida, Tatsuo Maeoka, Takuya Ishii, Tamotsu Ninomiya, "ZVS-PWM Half-Bridge Converter using Active Current Clamping with an Auxiliary Winding of a Transformer," in Proc. IEEE Power Electron.Spec. Conf., 1998, pp. 942-947.
[3] B. Yang, RC Lee, A.J. Zhang, and G. Huang, "LLC resonant converter for front end DC/DC conversion," in Proc. IEEE Appl. Power Electron Conf., 2002, pp. 1108-1112.
[4] Bo Yang, "Topology Investigation for Front End DC/DC Power Conversion for Distributed Power System," Ph.D Dissertation of Virginia Polytechnic Institute and State University, US, Sep 2003.
[5] Bo Yang, Rengang Chen, F.C.Lee, "Integrated Magnetic for LLC Resonant Converter," in Proc. IEEE Appl. Power Electron Conf, 2002, pp. 346-351.
[6] Marthinus C. Smit, Jan A. Ferreria, Jacobus D. Van Wyk, M. Ehsani, "An Ultrasonic Series Resonant Converter with Integrated L-C-T," IEEE Trans. Power Electron., vol.10, no. 1, pp. 25-31, Jan 1995,.
[7] Wenduo Liu, J.D. Van Wyk, "Design of Integrated LLCT Module for LLC Resonant Converter," in Proc. IEEE Appl. Power Electron Conf., 2005, pp. 362-368.
[8] Yah Liang, Wenduo Liu, Bing Lu, J.D. Van Wyk, "Design of Integrated Passive Component for a IMHz IkW Half-Bridge LLC Resonant Convener," in Proc. IEEE Ind. Appl. Conf., 2005, pp. 2223-2228.
[9] Johan T. Strydom, "Electromagnetic Design of Integrated Resonator- Transformers," Ph.D Dissertation, Rand Afrikaans University, South Africa, 2001.
[10] J. Biela, J.W. Kolar, "Electromagnetic Integration of High Power Resonant Circuits Comprising High Leakage Inductance Transformers," in Proc. IEEE Ind. Appl. Conf, 2005, pp. 4537-4545.
[! 1] Yanjun Zhang, Dehong Xu, Min Chen, Yu Han, Zhong Du, "LLC Resonant Converter for 48V-0.9V VRM," in Proc. IEEE Power Electron Spec. Conf, 2004, pp. 1848-1854.
[12] J. Reinert, A. Brockmeyer, and R. W. A. A. De Doncker, "Calculation of Losses in Ferro- and Ferrimagnetic Matericals Based on the Modified Steinmetz Equation," IEEE Trans. Ind. Appl., vol. 37, pp. 1055-1061, 2001.
Summary of the Invention
Magnetic integration structure wherein the window area for the transformer is larger than the window area for the resonant inductance.
Brief Description of the Drawing
Figure 1 is LLC resonant converter;
Figure 2 is DC voltage gain curve of LLC resonant converter;
Figure 3 is DC voltage gain of LLC resonant converter when parameter k is variable and parameter Q is constant; Figure 4 is power factor angle curve when parameter k is variable and parameter Q is constant;
Figure 5 is DC voltage gain of LLC resonant converter when parameter k is constant and parameter Q is variable;
Figure 6 is power factor angle curve when parameter k is constant and parameter Q is variable;
Figure 7 is some main waveforms of LLC resonant converter;
Figure 8 is equivalent circuit of LLC resonant converter in half switching cycle;
Figure 9 is the loss breakdown of LLC resonant converter;
Figure 10 is forward voltage comparison of two different rectification diodes;
Figure 11 is efficiency improvement when schottky diode is used to replace fast recovery diode;
Figure 12 is the first presented integrated magnetic structure and its corresponding magnetic circuit model;
Figure 13 is the second presented integrated magnetic structure and its corresponding magnetic circuit model;
Figure 14 is the proposed magnetic integration structure;
Figure 15 is practical integrated magnetic structure;
Figure 16 is prototype of IMHz- IKW LLC resonant converter;
Figure 17 is the resonant tank voltage Vab and the resonant current ip, vab: 100V/div, ip: 20A/div, t: 500ns/div;
Figure 18 is the voltage on the rectification diodes, VDI : 50V/div, VD2: 50V/div, t: 500ns/div;
Figure 19 is efficiency of LLC resonant converter; and
Figure 20 is switching frequency of LLC resonant converter.
Detailed Description of Embodiments
I. DC CHARACTERISTIC OF LLC RESONANT CONVERTER The LLC resonant converter is shown in Fig. 1.
Figure imgf000004_0001
Figure 1. LLC resonant converter
Using Fundamental Element Simplification (FES) method we can get the dc voltage gain Gdc of LLC resonant converter as following [11]
Figure imgf000005_0001
where V0 is the output voltage, Vjn is the input voltage, n is the turn ratio of transformer
T, k is defined as the ratio of parallel inductance to series inductance L* , fs is the l
Λ =: series resonant frequency and is defined as J ' , f is the switching frequency,
Q is defined as
Figure imgf000005_0002
From equation (1) we can draw the dc voltage gain curve of LLC resonant converter as shown in Fig.2 where the different curves correspond to different values of Q.
Figure imgf000005_0003
Figure 2. DC voltage gain curve of LLC resonant converter
In the design we expect the converter to operate higher than the frequency fsi and lower than the series resonant frequency fs. Here the frequency fs] is defined as
Figure imgf000005_0004
# This is because when LLC resonant converter works in this region, the following excellent characteristic can be gained
• ZVS ON for the main switches which minimizes the switching loss of the main switches
• ZCS OFF for the rectification diodes which minimizes the reverse recovery loss of the rectification diodes.
II. PARAMETER DESIGN OF LLC RESONANT CONVERTER
Before designing the circuit parameters of LLC resonant converter, we must know the specifications of the circuit firstly. The specifications for the LLC resonant converter are listed as below
• Input voltage: 300V-400V, rated input voltage: 400V
• Output voltage: 48V Output current: 2OA Switching frequency: IMHz The circuit parameters to be designed are Transformer turn ratio: n Resonant inductor: Ls Resonant capacitor: Cs Parallel inductor: Lp
As mentioned in section II, the above circuit parameters can be expressed as another set of parameters: n, fs, k and Q, and design according to this set of parameters is more general and meaningful. Therefore, we'll firstly discuss the selection principles for the parameters n, fs, k and Q. After these parameters are decided the circuit parameters are also decided.
A. Design of transformer turn ratio n
Since LLC resonant converter is expected to work in the desired operation region as shown in Fig.2. The following condition should be satisfied
» ι,ι _ max 2π Λ?) where Vjn_max is the maximum input voltage 400V.
From equation (2) the following condition for transformer turn ratio is derived
n ≥ WK _ max ^
2VΛ (3)
Therefore we choose the transformer turn ratio to be 8.5:2:2.
B. Design of the series resonant frequency fs
In the desired operation region as shown in Fig.2, the switching frequency is below the series resonant frequency fs. And because the switching frequency of LLC resonant converter is required to be around IMHz, we should choose the series resonant frequency fs to be a little bit larger than IMHz. Here we choose the series resonant frequency fs to be 1.1MHz.
C. Discussion of parameter k
From equation (1) we can again draw the DC voltage gain of LLC resonant converter as shown in Fig.3 where parameter k is variable and parameter Q is constant. From Fig.3 we can find that the smaller the parameter k is, the higher is the peak voltage gain and the narrower the switching frequency range. Therefore, a smaller parameter k is beneficial for increasing the voltage gain range and compressing the switching frequency range. However, the parameter k cannot be too small, because a smaller k means a comparatively smaller parallel inductance to resonant inductance ratio-and if the parallel inductance Lp is too small, the current flowing through it is large, and then the loss on it is increased, so is the main switch turn-off loss. Therefore, the selection of parameter k must make a balance between the voltage gain range, the switching frequency range and the loss.
Figure imgf000007_0001
Figure 3. DC voltage gain of LLC resonant converter when parameter k is variable and parameter Q is constant
Another point we should concern is the power factor angle (I). Power factor angle is defined as the angle between the input voltage and the input current of the resonant tank. With a larger power factor angle the reactive power flowing into the resonant tank is increased so that the efficiency is impaired. Power factor angle can be expressed as
Figure imgf000007_0002
From equation (4) we can draw the curves of the power factor angle when the parameter k is variable and parameter Q is constant as shown in Fig.4. From Fig.4 we can find that the power factor angle is larger when the parameter k is smaller in the switching frequency range. It also demonstrates that the parameter k cannot be too small. As a result we choose the parameter k to be 10.
Figure imgf000007_0003
Figure 4. Power factor angle curve when parameter k is variable and parameter Q is constant D. Discussion of parameter Q
From equation (1) we can also draw the voltage gain curves when the parameter k is constant while parameter Q is variable as shown in Fig.5. From Fig.5 we can find that the smaller the parameter Q is, the higher is the peak voltage gain and the narrower the switching frequency range. Therefore, from the angle of the voltage gain range and the switching frequency range, it seems that smaller parameter Q is better. However, from Fig.6 which shows the curves of the power factor angle when parameter k is constant and parameter Q is variable, smaller Q will cause a larger power factor angle, which will increase the reactive power flowing into the resonant tank and the decrease the efficiency. Therefore, we should also make a balance between the voltage gain range, the switching frequency range and the loss when selecting the parameter Q. The final choice of parameter Q is 0.35.
' 1O6
Figure imgf000008_0001
Figure 5. DC voltage gain of LLC resonant converter when parameter k is constant and parameter Q is variable
Figure imgf000008_0002
Figure 6. Power factor angle curve when parameter k is constant and parameter Q is variable
When those parameters are all decided, the circuit parameters can be calculated as Transformer turn ratio : 8.5 : 2 : 2 Resonant inductor Ls: 1.78uH Resonant capacitdr Cs: 11.8nF Parallel inductor Lp: 17.8uH.
III. THEORETICAL CALCULATION OF CURRENTS IN LLC RESONANT CONVERTER
When LLC resonant converter works in the desired operation region as shown in Fig.2, some of the main waveforms are shown in Fig.7 where vab is the voltage applied to the resonant tank, ip and iLP are the current flowing through the resonant tank and the parallel inductor respectively, ioi and ΪD2 are the current flowing through the rectification diodes and vc is the voltage across the resonant capacitor.
In order to analyze the losses in LLC resonant converter, the following current values must be derived firstly: (1) the rms value of the current flowing through the resonant tank, (2) the rms value of the current flowing through the transformer primary side, (3) the rms value of the current flowing through the transformer secondary side.
Figure imgf000009_0001
Figure 7. Some main waveforms of LLC resonant converter Since the waveforms in Fig.7 are symmetric in a switching cycle, analyzing them in half a switching cycle is enough. In half a switching cycle (neglecting the switching process), the operation of LLC resonant converter can be divided into two stages [3-4]. The equivalent circuits of the two stages are shown in Fig.8 (a) and (b) respectively.
Figure imgf000009_0002
(a) Stagel (0<t<Ts/2)
Figure imgf000009_0003
(b) Stage2 (Ts/2<t<T/2)
Figure 8. Equivalent circuit of LLC resonant converter in half switching cycle Before calculation of the currents we assume that the parallel inductance is far larger than the resonant inductance, so that the resonant current ip is almost constant in stage2. The assumption is not mathematically precise, but for loss analysis the accuracy is enough. A. Stage 1 (0< t < Ts/2)
The following differential equations can be written
V^ vtf+^^+nV. (5)
Figure imgf000010_0001
nV =L, dt O) where V1n is the input voltage, vc(t) is the voltage across the resonant capacitor, Ls is the resonant inductor, ip(t) is the current flowing through the resonant tank, n is the transformer turn ratio, V0 is the output voltage, Cs is the resonant capacitor, Lp is the parallel inductor and iLp(t) is the current flowing through it. And the initial value of ip(t), vc(t) and ΪLP(t) is given as nV.
',,(O)
Figure imgf000010_0002
nV.,
<u, (Q) = -
4/Λ where fs is the series resonant frequency, Io is the output current and f is the switching frequency.
Therefore the differential equations can be solved as
V,,, C /J K.
'^τir''Si+w^{τW^' -w:,cosaJ (8)
•.W-v.-v. n
Figure imgf000010_0003
Zv,,-fc fir* ,** nV nV lt (t) ~ A «Jf<hT + L h ' (10)
Co — In 'f Where ωs is the angle frequency and is defined as 9 .
From equation (8) the peak value of the current ip(t) can be calculated to be
Figure imgf000010_0004
And the current flowing through the transformer primary side and secondary side is given
V, Kf) =»„(0-^(0 (12)
LΛO = nipfl(t) where isec(t) is the current flowing through the transformer primary side and ip(t) is the current flowing through the transformer secondary side. B. Stage 2 (Ts/2 ≤ t ≤ T/2)
Following our assumption, in stage 2 the current ip(t), iLP(t), ipri(t) and isec(t) are as following respectively n Vl
''^ 4/.*Ls1 (14)
Figure imgf000011_0001
V-(O = O (16) ςcω=o (l7)
Therefore, from equation (8), (10), (12), (13) and equation (14) - (17) we can calculate the rms value of current ip(t), iprj(t) and isec(t) in half a switching cycle as
Figure imgf000011_0002
where φ is defined as
Figure imgf000011_0003
IV. LOSS ANALYSIS OF LLC RESONANT CONVERTER
Because in the design of LLC resonant converter the parallel inductor is integrated with the transformer by utilizing the magnetizing inductance, the losses of the parallel inductor and transformer are analyzed together.
Therefore, the total losses can be divided into the following eight parts:
1. Driving loss of main MOSFET Pdrjotai
where Qg is the gate charge of the main MOSFET, Vgs is the gate drive voltage, f is the switching frequency.
2. Conduction loss of main MOSFET P00n
P con - I />_ Λfij 2R tf.j_»ιt /O'2\ where IPJ-mS is the rms value of the resonant current ip and is given in equation (18), Rds on is the drain-source on resistance of the main MOSFET. 3. Turn-off loss of main MOSFET POff total p — I P —- 0-> LLILL
48Cn,,
(24) where Ioff is the current through the main MOSFET when it is turned off and IOfr is equal nVa A f L to * " , tf is the fall time of the main MOSFET, f is the switching frequency, C0Ss is the output capacitance of the main MOSFET.
4. Core loss of resonant inductor Pf6 Ls
~ . (25) where Cm, α, β are some empirical parameters related to the magnetic material, f is the switching frequency, 5Ls is the maximum flux density, Ve_Ls is the volume of the resonant inductor magnetic core.
5. Copper loss of resonant inductor Pcu Ls
0
P = ϊ R
(26) where lpjms is the rms value of the resonant current ip and is given in equation (18), R-Ls_ac is the ac resistance of resonant inductor winding and can be measured through an impedance analyzer.
6. Core loss of transformer Pfe
where Cm, α, β are some empirical parameters related to the magnetic material, feq is the
Figure imgf000012_0001
equivalent frequency and is defined as [12], " x is the maximum flux density, f is the switching frequency, Ve_τ is the volume of the transformer magnetic core.
7. Copper loss of transformer Pcu_τ
P — J ^R ■+• / ^ R cu_T ~~ p_nns />;i_<κ sec.,ntM sct_r(c
(28) where Ip rms is the rms value of the resonant current ip and is given in equation (18), RPri_ac is the ac resistance of transformer primary winding and can be measured, Isec_rms is the rms value of the current through transformer secondary side and given in equation (20), Rsec ac is the ac resistance of transformer secondary winding and also can be measured through an impedance analyzer.
8. Conduction loss of rectification diodes Pdiode P -= V I
where VF is the forward voltage drop of the rectification diodes, ID_ΠΠS is the rms value of the current through the rectification diodes and ID_ΠΠS is equal to Isec_rms- From the above analysis the loss breakdown is performed and the result is shown in Fig.9. The operation condition of LLC resonant converter is: input voltage .400V, output 48V/20A, switching frequency 875 KHz. We can find that the rectification diodes conduction loss takes a major part in the total losses.
Figure imgf000013_0001
Figure 9. Loss breakdown of LLC resonant converter
Therefore, we change the rectification diodes from DSEK60-02A (Fast recovery diode, IXYS) to DSSK60-015A (Schottky diode, IXYS). The comparison of their forward voltage is shown in Fig. 10, and the improvement of the conversion efficiency is shown in Fig. 11. From Fig. 11 we can find that when Schottky diode is used to replace fast recovery diode, the conversion efficiency is increased over full load range.
Figure imgf000013_0002
1 5 10 15 20 25 30 35 40 AS 50 55 60 Forwaid cunent \. (A)
Figure 10. Forward voltage comparison of two different rectification diodes
vohnge 48V
Figure imgf000013_0003
I 2 1 4 5 6 7 8 9 If) I l 12 I! U 15 16 17 18 19 21) Output UU ix nt (A)
Figure 11. Efficiency improvement when schottky diode is used to replace fast recovery diode V. INTEGRATED MAGNETIC OF LLC RESONANT CONVERTER
In LLC resonant converter, the parallel inductor Lp and transformer T can be integrated together by inserting an air gap into the transformer magnetic core and reducing the magnetizing inductance to the parallel inductance [4,9].
For the integration of the resonant inductor Ls, there are different kinds of methods. One of them is to utilize the transformer leakage inductor as the resonant inductor [6-10]. Generally the transformer inherent leakage inductance is smaller than the needed resonant inductance. Therefore the transformer leakage inductance is increased by inserting a "leakage layer" between the primary winding and secondary winding. The material for the leakage layer is usually low permeability magnetic material, such as C302 (EPCOS) etc.
Here we present another magnetic integration method. We integrate the discrete resonant inductor with the transformer by sharing some common magnetic paths. Two different structures and their corresponding magnetic circuit models are shown in Fig. 12 and Fig. 13 respectively.
The presented structure 1 is to build the transformer windings on the left outer leg and build the resonant inductor winding on the right outer leg of the magnetic core. There are air gaps on both the outer legs and no air gap on the center leg. Therefore the fluxes generated by the transformer and the resonant inductor are short-circuited through the center leg. And the fluxes on the center leg can be cancelled. The advantage of structure 1 is that the window area for transformer winding is the same as the discrete transformer. The disadvantage is that the flux density on the left outer leg is doubled compared to the discrete transformer because the cross sectional area of the left outer leg is only half of the center leg. Therefore the magnetic core loss is increased. Another disadvantage of structure 1 is that it's mechanical unstable [4-5].
The presented structure2 and its corresponding magnetic circuit model are shown in Fig. 13. We build the transformer winding on the upper E-core and build the resonant inductor winding on the lower E-core. There are air gaps on both the upper and lower center legs and outer legs. The fluxes generated by the transformer and the resonant inductor are short-circuited through the middle I-core. Also the flux on the I-core can be cancelled. The advantage of structure2 is that the flux density for the transformer is the same as the discrete transformer, so that the transformer magnetic core loss is not increased. Another benefit is that it's a mechanical stable structure because the air gap is on all the legs. However, the disadvantage of structure 2 is the decreased window area for transformer winding so that the transformer copper loss may increase.
Figure imgf000015_0001
(a) Strucrurel
Figure imgf000015_0002
(b) Magnetic circuit model
Figure 12. The first presented integrated magnetic structure and its corresponding magnetic circuit model
Figure imgf000015_0003
(a) Slructure2
Figure imgf000015_0004
(b) Magnetic circuit model
Figure 13. The second presented integrated magnetic structure and its corresponding magnetic circuit model
The proposed magnetic integration structure is shown in Fig. 14. It's derived from the second structure as shown in Fig. 13 (a). But the window area for the transformer winding is increased so that the transformer copper loss increase is no so much as structure2. The resonant inductance is only 1.78uH. The design results for the turns and the air gap of the resonant inductor is: nL=3, lg2=0.53mm. The Ansoft PEMage simulation result for the resonant inductance is 2.12uH. Because we need only three turns to realize the resonant inductor, the decrease of the window area for the resonant inductor is not a problem.
Fig. 15 shows the practical integrated magnetic structure.
Figure imgf000016_0001
Figure 14. The proposed magnetic integration structure
Figure imgf000016_0002
Figure 15. Practical integrated magnetic structure VI. EXPERIMENTAL RESULTS
A IMHz- IKW LLC resonant converter prototype is built and shown in Fig. 16. The specification for the converter is listed below
• Input voltage: 300V-400V
• Output voltage: 48V
• Output current: 2OA. The circuit parameters are:
• Resonant inductor L3: 1.8uH
• Resonant capacitor C5: 11.2nF
• Parallel inductor Lp: 2OuH
• Turn ratio of transformer T: 8.5:2:2, EE32/16/9 (Ferroxcube 3f35). The devices we use are:
• Main switches S l-S2:STW20NM50 (ST)
• Rectification diodes DI-D2: DSSK60-015A (IXYS).
Fig. 17 shows the experimental waveform of the voltage applied to the resonant tank Vab and the current flowing through the resonant tank ip. The operation condition is: input voltage 400V5 output 48V/20A, switching frequency 875 KHz. From Fig. 17 we can find that the experimental waveform corresponds well with the theoretical waveform shown in Fig.7.
Fig. 18 shows the experimental waveform of the voltage on the rectification diodes. The operation condition is the same as in Fig. 17. From Fig. 18 we can see that the waveform is clean which indicates the ZCS OFF of the rectification diodes.
Fig. 19 and Fig.20 shows the efficiency and switching frequency curve of LLC resonant converter. From Fig. 19 and Fig.20 we can see that the efficiency at 400V input voltage full load output is 93.95% at the switching frequency of 875 KHz.
The experimental results verify the possibility of high efficiency and high frequency operation of IkW LLC resonant converter.
Figure imgf000017_0001
Figure 16. Prototype of IMHz- IKW LLC resonant converter
i ;
Vj IOUWdM • • ■ ■ '
> I' liUAΛIiv)
SOOiuΛliv himi'ft; ,I.ΛI r,«n« i . ...
Figure 17. The resonant tank voltage Vab and the resonant current ip, vab: 100V/div, ip: 20A/div, t: 500ns/div
Figure imgf000017_0002
Figure 18. The voltage on the rectification diodes, VDI : 50V/div, vO2: 50V/div, t: 500ns/div
96.00
94 00 92.00 90.00
£ 88.00
Input voltage 400V
86.00
Output voltage 48V 84.00 82.00
1 2 3 4 5 6 7 8 9 IU 1 1 12 13 14 15 16 17 18 1920 Output Cuirenl (A)
Figure 19. Efficiency of LLC resonant converter
Figure imgf000018_0001
17 18 1920 Output Current (A)
Figure 20. Switching frequency of LLC resonant converter
VII. CONCLUSION
A IMHz-IKW LLC resonant converter is presented in this paper.
The parameter design method for LLC resonant converter is discussed.
The loss analysis based on theoretical derivation is performed and we find that the rectification diodes conduction loss is the highest among all the losses. Therefore we use Schottky diode to replace fast recovery diode to improve the conversion efficiency.
Integrated magnetic structure is adopted. It can further reduce the magnetic component size and increase the power density.
Experimental results show that IkW LLC resonant converter is capable of operating at MHz switching frequency with high efficiency.
ACKNOWLEDGEMENT
This work was supported by National Natural Science Foundation of China with Project Number 50237030 and 50377037, and was also supported by Fuji Electric Advanced Technology Co., Ltd.

Claims

Claims
1. Magnetic integration structure wherein the window area for the transformer is larger than the window area for the resonant inductance.
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WO2016022966A1 (en) * 2014-08-07 2016-02-11 The Trustees Of Dartmouth College Magnetic devices including low ac resistance foil windings and gapped magnetic cores
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CN112687454A (en) * 2020-12-21 2021-04-20 中南大学 Transformer magnetic integration structure integrating leakage inductance and excitation inductance and integration method thereof
CN112687454B (en) * 2020-12-21 2022-08-09 中南大学 Transformer magnetic integration structure integrating leakage inductance and excitation inductance and integration method thereof
CN118299162A (en) * 2024-03-29 2024-07-05 西安电子科技大学 Orthogonal magnetic flux core structure for improving power density of Sigma converter

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