Opti MOS™ and Co ol M O S™ The Opt im al S olut io ns Su it abl e f or D C/ D C Con ver ter Used in H V D C S ys tem Application Note About this document This application note analyze two cascaded solutions: Buck followed by LLC and Boost followed by LLC. Both suitable for wide input range DC/DC converters used in ICT HVDC systems. The optimal solution in terms of power loss, occupation of PCB and MOSFETs costs is being presented. Scope and purpose Guide the users select proper solution and power MOSFETs in DC/DC converter of ICT HVDC system. Intended audience Experienced power supply designers who want to optimize their solution and power MOSFETs selection. Table of Contents About this document ................................................................................................................... 1 Table of Contents ........................................................................................................................ 1 1 Introduction ............................................................................................................... 2 2 DC/DC Converter ......................................................................................................... 5 3 3.1 3.2 3.3 Solutions analysis ....................................................................................................... 8 Buck converter .................................................................................................................................... 8 Boost converter ................................................................................................................................. 11 LLC converter .................................................................................................................................... 13 4 4.1 4.2 Inductors and transformer ......................................................................................... 17 Inductors............................................................................................................................................ 17 LLC transformers ............................................................................................................................... 18 5 5.1 5.2 5.3 Conclusion ............................................................................................................... 20 Occupations of PCB by MOSFETs and magnetic elements .............................................................. 20 Power loss of MOSFETs and magnetic elements ............................................................................. 20 Cost of MOSFETs................................................................................................................................ 23 6 Reference ................................................................................................................. 25 Revision History ........................................................................................................................ 25 1 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Introduction 1 Introduction A need for improved and more efficiency power distribution for mission critical application is a result of continuous increases in global power consumption and a shift in power profile of modern loads[1]. About 1.3% of world electricity energy is taken over by equipment in data center and the number is about 2% in United States. The higher efficiency power distribution in data center is meaningful for reducing the consumption of resources and reducing CO2 emission; at the same time the higher efficiency power distribution in data center means IT companies or telecom carriers can reduce CAPEX and OPEX, which in return is beneficial to IT consumers. Most traditional data centers use alternative current (AC) power system as shown in the Figure 1: threephase AC voltage main power is handled by UPS (uninterruptible power supply) firstly, a better voltage waveform and backup power provided by battery group are obtained. The output single phase or threephase AC voltage is distributed by PDU (power distribution unit) to each cabinet or rack, where servers or other IT equipment is installed. The power supplies in a server rectify AC input voltage to 12 VDC and then convert it to a much lower voltage such as 1 VDC, which is ultimately consumed by CPUs or other ICs. Figure 1 AC power supply system in data centers It is easy to be found that there are two redundant parts in the AC power distribution system, one is the inverter (DC/AC) in UPS and the other is the rectifier (AC/DC) in sever, the redundant parts decrease the power system efficiency and reliability, also increase the cost of equipment. There are other shortcomings in AC power system such as the difficulty in UPS paralleling, large area occupation. HVDC system is promoted at the end of last century to cope with these problems, the term ”higher voltage DC (HVDC)” is used to identify voltage in an information and communication technology equipment(ICTE) space that are higher than 200 VDC and lower than 600 VDC[2]. Figure 2 illustrates the architecture of HVDC system. Compared with Figure 2, UPS is replaced by HVDC rectifier whose output voltage is a higher DC value compared to 48 VDC, the DC voltage is then distributed by PDU to power supplies in severs, and the followed conversions units are same with those of traditional power system. Figure 2 HVDC power supply system in data centers The HVDC system is much simpler and is composed of less power conversion parts compared to UPS showed in Figure 1, therefore higher efficiency, higher reliability and lower cost can be obtained. Application Note 2 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Introduction Figure 3 shows the advantages of HVDC system compared with traditional power distribution system in data center provided by HP[3]. Figure 3 Advantage of HVDC power system over traditional power system The output voltage of HVDC rectifier is specified differently in different countries, Figure 4 shows some of world-wide DC deployments [4]. 380 VDC HVDC system is widely adopted in many counties and groups, in China, however, an additional much lower voltage classs, 240 VDC is implemented in many data centers. As as result, associated standards, which specify the requirements for HVDC rectifier, PDU, protections, components and so on, have been published in some countries and international group such as China and Europe Union and ITU (International Telecommunication Union). Application Note 3 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Introduction Figure 4 World-wide HVDC deployment In the following, in section 2, the basic information of DC/DC converter of HVDC power system is introduced and the configuration and working conditions of proposed DC/DC converter solutions that are discussed further in the following sections are presented. The detailed calculations of Buck, Boost and LLC converters are shown in section 3. Section 4 compares the inductors and transformers of Buck, Boost and LLC converters in copper loss and magnetic loss. The conclusions of comparisons of different DC/DC converter solutions are shown in section 5, which is intended as an aid for power electonics engineers to choose suitable solutions when designing DC/DC converter of HVDC power system. Application Note 4 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System DC/DC Converter 2 DC/DC Converter As illustrated in the Figure 2, DC/DC converter in a server is connected to the output of HVDC rectifier through PDU, the input voltage of the converter is equivalent to the output voltage of HVDC rectifier excluding the voltage drops caused by PDU and conduction lines. Normal value of output voltage of HVDC rectifier is showed in Figure 4 in world-wide range, which ranges from 240 VDC to 400 VDC. In China, two kinds of HVDC voltage class, 240 VDC and 336 VDC, are piloted in some data centers in recent years. Actually 336 VDC HVDC system in China is termed as 380 VDC system in Europe or America, though there are some differences in detailed specifications. The output voltages and numbers of VRLA (Valve Regulated Lead Acid) battery of 240 VDC and 336 VDC HVDC rectifier are listed in the Table 1 and Table 2 according to Chinese standard and company specification [5][6]. Table 1 Main specifications of 240 VDC HVDC rectifier HVDC voltage class Normal rectifier output voltage Range of rectifier output voltage Input range of DC/DC converter Numbers of 2 VDC VRLA battery 240 VDC 204 VDC ~ 288 VDC 192 VDC ~ 288 VDC 120 Table 2 268 VDC Main specifications of 336V HVDC rectifier HVDC voltage class Normal rectifier output voltage Input range of DC/DC converter Numbers of 2 VDC VRLA battery 336 VDC 378 VDC 300 VDC ~ 400 VDC 168 Table 1 and Table 2 list the numbers of VRLA, which is very important because it plays a decisive role in the output voltage variety range of HVDC rectifier. The input voltage range of DC/DC converter is about 100 V for the two HVDC systems as showed in Table 1 and Table 2, and more challenging for many energy conversion companies is that they have to develop the HVDC DC/DC converter that can be compatible to both HVDC systems for cost down and short time to market. In this application the input voltage will be from 190 VDC to 400 VDC. It is very hard to obtain a high conversion efficiency using single topology for such a wide input range during the load range with acceptable cost. Therefore cascaded topology is promoted, on the one hand to increase the efficiency during the whole input and load range, on the other hand to simplify the control strategy. In this application note two cascaded topology solutions- Buck and Boost followed by LLCare analyzed in a 1200 W(12 V/100 A) server DC/DC converter that suitable for Chinese 240 V VDC and 336 VDC HVDC system. Buck and Boost are selected for its simplification in architecture and control strategy and well researched. Certainly other topologies such as Buckboost can also be implemented in cascaded topology for its possibility to realize ZVS, flexible output voltage and other merits, but the cost of the cascaded topology will be higher than Buck or Boost so it isn’t feasible to be applied. LLC is welcome for its excellent performance in high efficiency during the load range and low cost compared with other resonant converters such as ZVS full-bridge PWM converter. The configuration of the cascaded topology can be Buck/Boost followed by LLC or LLC followed by Buck/Boost, the former, as shown in Figure 5and Figure 6, is arbitrarily chosen in this paper because the analysis method and procedure are same for both configurations. One converter (for example Buck) of cascaded configuration should be closed-loop control to get a high-precision output voltage over the input and output range, the other converter (for example LLC) can be closed-loop, semiclosed-loop or open-loop control, thus the whole control strategy of cascaded topology converter is simpler than that of single topology converter. Application Note 5 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System DC/DC Converter Q3 Q1 Lr L_buck DC Q2 C_buck Co Q4 Cr Figure 5 Q5 Rload Q6 The cascaded topology of Buck+LLC Q3 L_boost Lr DC Q1 Q2 Co Q4 Rload C_boost Cr Figure 6 Q5 Q6 The cascaded topology of Boost+LLC The comparison of different cascaded topologies is implemented in a converter that output is 12 V/1200 W, the analysis is based on the same loss for each MOSFET of the converter, TO-220 package MOSFETs are chosen from Infineon Technologies for Buck, Boost and primary-side of LLC converter switches and SuperSO8 package MOSFETs are selected from Infineon Technologies for secondary-side of LLC converter switches for its low power loss and high thermal dissipation capability. While half-bridge LLC converter is selected and is controlled to make sure that the resonant converters always work at resonant frequency fres, the two resonant frequencies are set to be equivalent to each other for the two solutions. In order to make it easier to comparison, the inductors of Buck and Boost converter perform at continuous mode and the max. ripple currents through Buck inductor and Boost inductor are assigned to 25% of its average value. Some other presettable working conditions of cascaded topologies are: (1) Working frequency of Buck/Boost: (2) Resonant frequency of LLC: Application Note 𝑓𝑊_𝑃𝑊𝑀 = 80𝐾 (1) 𝑓𝑟𝑒𝑠_𝐿𝐿𝐶 = 130𝐾 (2) 6 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System DC/DC Converter The two working frequencies are chosen arbitrarily differently in case of resonating at high frequencies between front and end converters in a cascaded solution and causing system instability and severe EMI noise. (3) The calculation and comparisons between two solutions will be made at five input voltage points according to Table 1 and Table 2, those are: 190 VDC (min. input voltage), 268 VDC (normal input voltage for 240 V HVDC system), 300 VDC (max input voltage for 240 VDC HVDC system and min input voltage for 336 V HVDC system), 378 VDC (normal input voltage for 336 VDC HVDC system), 400 VDC (max. input voltage). (4) The comparison between two solutions will be made at three kinds of output load: 20% load (light load); 50% load (medium load) and 100% load (full load). In the following parts, the performance of Buck converter, Boost converter and two LLC converters following Buck and Boost respectively are analyzed according to these conditions. Application Note 7 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis 3 Solutions analysis 3.1 Buck converter The illustration of Buck converter is shown in Figure 7, Q1 and Q2 are high-side and low-side MOSFETs respectively and L_buck is the Buck inductor. Q1 DC L_buck Q2 Figure 7 R_buck C_buck Topology of Buck converter The output voltage of buck converter is arbitrarily assigned to 150 VDC , 𝑉𝑜𝑢𝑡_𝑏𝑢𝑐𝑘 = 150 𝑉 (3) It is supposed that efficiency of LLC is 98%, η𝐿𝐿𝐶 = 0.98 (4) Then the output current (also the average current through the inductor) of Buck converter at full load is: 𝑃 100 𝐼𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 = η ∗𝑉𝑜𝑢𝑡 = 0.98∗150 = 8.2𝐴 (5) 𝐿𝐿𝐶 The inductor of Buck converter is calculated as: 𝐿𝑏𝑢𝑐𝑘 ≥ 𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 𝑉𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗𝑇𝑜𝑓𝑓−𝑏𝑢𝑐𝑘 𝛥𝐼𝐿−𝑏𝑢𝑐𝑘 𝑉 ∗(1−𝐷) = 𝛥𝐼𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗𝑓 𝐿−𝑏𝑢𝑐𝑘 Where D is the duty cycle ratio and for Buck converter: 𝑉 𝐷 = 𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 𝑉 (6) 𝑊_𝑃𝑊𝑀 (7) 𝑖𝑛 As the range of input voltage of Buck converter (𝑉𝑖𝑛−𝑏𝑢𝑐𝑘 ) is from 190 VDC to 400 VDC, the duty cycle of the Buck converter is from 0.375 to 0.79 according to equation (3) and (7). So the minimum inductance of Buck converter inductor is 𝐿𝑏𝑢𝑐𝑘−𝑚𝑖𝑛 = 𝑉𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗(1−𝐷min) 𝛥𝐼𝐿−𝑏𝑢𝑐𝑘 ∗𝑓𝑊_𝑃𝑊𝑀 = 𝑉𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗(1−0.375) 0.25∗𝐼𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗80𝐾 ≈ 574 uH (8) The inductance of the Buck inductor is assigned to 720uH, that is (9) 𝐿𝑏𝑢𝑐𝑘 = 720 𝑢𝐻 Concerning the material and manufacture errors of inductor (generally ±20%), then the current ripple through the inductor and the minimum and maximum current through the inductor can be obtained according to: Application Note 8 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis ΔIL_buck = 𝑉𝑜𝑢𝑡−𝑏𝑢𝑐𝑘 ∗(1−𝐷) 𝐿𝑏𝑢𝑐𝑘 ∗𝐹𝑤𝑝𝑤𝑚 (10) 𝐼𝐿_𝑚𝑖𝑛 = 𝐼𝐿−𝑎𝑣𝑔 − 0.5 ∗ 𝛥𝐼𝐿_𝑏𝑢𝑐𝑘 (11) 𝐼𝐿_𝑚𝑎𝑥 = 𝐼𝐿−𝑎𝑣𝑔 + 0.5 ∗ 𝛥𝐼𝐿_𝑏𝑢𝑐𝑘 (12) The results from equation (9)~(12) are listed in Table 3. Table 3 Ripple, min. and max. current through Buck inductor Vin_1=190 VDC Vin2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC ΔIL_buck [A] 0.548 1.147 1.302 1.571 1.628 IL_buckmin@20%load [A] 1.359 1.059 0.982 0.847 0.819 IL_buckmax@20%load [A] 1.907 2.206 2.284 2.418 2.446 IL_buckmin@50%load [A] 3.808 3.508 3.431 3.296 3.268 IL_buckmax@50%load [A] 4.356 4.655 4.733 4.867 4.895 IL_buckmin@100%load [A] 7.889 7.59 7.512 7.378 7.349 IL_buckmax@100%load [A] 8.437 8.737 8.814 8.949 8.977 It is feasible to suppose that max. power loss of high-side MOSFET of buck converter is about 6W concerning the package of MOSFETs and cooling condition for ICT servers. The power losses of high-side MOSFET of Buck converter include switching loss, conduction loss and Coss loss. The switching loss can be calculated as [7]: 𝑡𝑟𝑖+𝑡𝑓𝑢 𝑃𝑠𝑤 = 𝑉𝑖𝑛 ∗ 𝐼𝑜𝑢𝑡 ∗ 𝑓𝑤 ∗ ( ) (13) 2 Where tri and tfu are the current rise time and voltage fall time during turn on and turn off respectively. Conduction loss is calculated as: 𝑃𝑐𝑛 = 𝐼𝑟𝑚𝑠_ℎ𝑠 2 ∗ 𝑅𝐷𝑆(𝑜𝑛) (14) Where RDS(on) is the conduction resistor of MOSFET at some junction temperature such as 120°C, 𝐼𝑟𝑚𝑠_ℎ𝑠 is the rms current through the high-side MOSFETs of Buck converter and is calculated as: 1 𝐼𝑟𝑚𝑠−ℎ𝑠 2 = 3 ∗ 𝐷 ∗ (𝐼𝑚𝑖𝑛 2 + 𝐼𝑚𝑎𝑥 2 + 𝐼𝑚𝑖𝑛 ∗ 𝐼𝑚𝑎𝑥 ) (15) As the current through the inductor is illustrated by Figure 8. Figure 8 Waveform illustration of high-side MOSFET of Buck converter Coss loss can be calculated as: 𝑃𝐶𝑜𝑠𝑠 = 𝐸𝑜𝑠𝑠 ∗ 𝑓𝑊_𝑃𝑊𝑀 (16) However, when we calculate the RDS(on) suitable for the application Coss loss is omitted for it is related to the specific MOSFET. Application Note 9 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis It is supposed that: 𝑡𝑟𝑖 = 𝑡𝑓𝑢 = 10 ∗ 10−9 (17) Then, we can get the different RDS(on) of high-side MOSFET at different input voltage that can meet the loss requirement according to: 𝑃 −𝑃 𝑅𝐷𝑆(𝑜𝑛) = 𝑡𝑜𝑡𝑎𝑙 𝑠𝑤 (18) 2 𝐼𝑟𝑚𝑠−ℎ𝑠 From equation (13) to (18), the RDS(on) can be obtained, as shown in the following table Table 4 RDS(on) [Ω] RDS(on) of high-side MOSFET of Buck converter suitable for the application Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 0.09 0.114 0.121 0.133 0.135 From Table 4, it is known that the RDS(on) of the high-side MOSFET suitable for the application should be smaller than 0.09Ω The maximum total power loss of low-side MOSFET of Buck converter is also supposed to be 6 W, the power loss of low-side MOSFET includes conduction loss caused by MOSFET and by body diode, which can be calculated 𝑃𝑐𝑛_𝑚𝑜𝑠_𝑙𝑠 = 𝐼𝑟𝑚𝑠_𝑙𝑠 2 ∗ 𝑅𝐷𝑆(𝑜𝑛) 𝑃𝑐𝑛_𝑏𝑑_𝑙𝑠 = 𝐹𝑤 ∗ 𝑉𝑠𝑑−𝑏𝑜𝑑𝑦 ∗ 𝐼𝑜𝑢𝑡 ∗ 𝑇𝑑𝑡 Where 𝐼𝑟𝑚𝑠_𝑙𝑠 is the rms current through the low-side MOSFETs of Buck converter, and: 1 𝐼𝑟𝑚𝑠_𝑙𝑠 2 = 3 ∗ (1 − 𝐷) ∗ (𝐼𝑚𝑖𝑛 2 + 𝐼𝑚𝑎𝑥 2 + 𝐼𝑚𝑖𝑛 ∗ 𝐼𝑚𝑎𝑥 ) (19) (20) (21) 𝑉𝑠𝑑−𝑏𝑜𝑑𝑦 is the forward voltage drop of body diode of low-side MOSFET, 𝑇𝑑𝑡 is the dead time between the high-side and low-side driving signal. It is supposed that: (22) (23) 𝑉𝑠𝑑−𝑏𝑜𝑑𝑦 = 1𝑉 𝑇𝑑𝑡 = 200 ∗ 10−9 𝑆 Then we can get the different RDS(on) of low-side MOSFET at different input voltage that can meet the loss requirement according to equation (19)~(23) The results are shown in the following table: Table 5 RDS(on) of low-side MOSFET of Buck converter suitable for the application RDS(on) [Ω] Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 0.418 0.2 0.176 0.146 0.14 From Table 5 we can know that the RDS(on) of low-side MOSFET of Buck converter suitable for the application should be smaller than 0.14Ω. The max. voltage MOSFETs have to endure for Buck converter is the max. input voltage, which is 400 VDC for the application. Considering 80% or more voltage derating and voltage spike produced by parasitic parameters, the voltage class of 600V or 650V CoolMOSTM is suitable for the application. Therefore, two paralleled IPP60R099P6 and two paralleled IPP65R150CFD are chosen for high-side and low-side MOSFETs respectively concerning RDS(on) for high-side and low-side MOSFETs and excellent body diode requirement for low side MOSFETs. For IPP60R099P6 used as high side switch of Buck converter, RDS(on) is 0.165Ω at 120°C junction temperature and Eoss (Energy of Coss) is about 4 uJ[8]; for IPP65R150CFD used as low side switch of Buck converter, RDS(on) is 0.29Ω at 120°C junction temperature, and forward voltage drop of body diode is about 0.8V[9]. The power Application Note 10 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis loss of each MOSFET can be calculated at 120°Cjunction temperature of MOSFET at different input voltage and output load after the MOSFETs are selected, the results are shown from Table 6 to Table 8. Table 6 Each MOSFET loss of Buck converter at 20% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC High-side MOS[W] 0.532 0.559 0.574 0.614 0.626 Low-side MOS[W] 0.062 0.109 0.123 0.146 0.152 Table 7 Each MOSFET loss of Buck converter at 50% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC High-side MOS[W] 1.174 1.145 1.156 1.213 1.234 Low-side MOS[W] 0.307 0.588 0.661 0.79 0.817 Table 8 Each MOSFET loss of Buck converter at 100% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin-5=400 VDC High-side MOS[W] 3.111 2.736 2.677 2.648 2.66 Low-side MOS[W] 1.122 2.235 2.525 3.028 3.134 3.2 Boost converter The illustration of Boost converter is shown in Figure 9, Q1 is the main switch MOSFET and Q2 is the diode MOSFET, L_boost is the Boost inductor. L_boost DC Q1 Q2 R_boost C_boost Figure 9 Topology of Boost converter The output voltage of Boost converter is arbitrarily assigned to 460 VDC, it is supposed that efficiency of Boost converter and its followed LLC converter are both 98%, then average input current of the Boost converter is: 𝑃 𝐼𝑖𝑛_𝑏𝑜𝑜𝑠𝑡 = η ∗η 𝑜𝑢𝑡 ∗V LLC Application Note 11 boost in (24) Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis The ripple current through the Boost inductor is Δ𝐼𝐿_𝑏𝑜𝑜𝑠𝑡 = 𝑉𝑜𝑢𝑡−𝑏𝑜𝑜𝑠𝑡 ∗𝐷∗(1−𝐷) 𝐿𝑏𝑜𝑜𝑠𝑡 ∗𝐹𝑤𝑝𝑤𝑚 (25) 𝑉𝑖𝑛 𝑉𝑜𝑢𝑡_𝑏𝑜𝑜𝑠𝑡 (26) Where D is the duty cycle ratio and for Boost converter 𝐷 =1− So the maximum ripple current through the inductor appears when D is equal to 0.5 according to equation (25), then the input voltage when D=0.5 is 𝑉𝑖𝑛_𝐷0.5 = 𝑉𝑜𝑢𝑡_𝑏𝑜𝑜𝑠𝑡 ∗ (1 − 0.5) = 230𝑉 (27) And the average input current when D=0.5 is obtained according to equation (24) and (27) 𝑃 1000 𝐼𝑖𝑛_𝐷0.5= η ∗η 𝑜𝑢𝑡 ∗V = 0.98∗.098∗230 = 5.433 (28) LLC in_D0.5 boost The inductance of Boost inductor is calculated as: 𝑉𝑜𝑢𝑡−𝑏𝑜𝑜𝑠𝑡 ∗𝐷∗(1−𝐷) 𝐿𝑏𝑜𝑜𝑠𝑡 = ΔI ∗𝑓 𝐿_𝑏𝑜𝑜𝑠𝑡 (29) 𝑊_𝑃𝑊𝑀 Therefore the minimum inductance of the boost inductor is obtained when D is equal to 0.5: 460∗0.5∗0.5 𝐿𝑏𝑜𝑜𝑠𝑡 = 0.25∗5.433∗80∗103 = 1.06 ∗ 10−4 (30) Concerning the material and manufacture errors of inductor (generally ±20%) the inductance of Boost inductor is set to 1.33 mH, that is 𝐿𝑏𝑜𝑜𝑠𝑡 = 1.33 𝑚𝐻 (31) Then the current ripple through the inductor and the minimum and maximum current through the inductor can be obtained according to equation (25) and equation (11) and equation (12) Table 9 Ripple, min. and max. current through Boost inductor at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC ΔIL_boost[A] 1.048 1.051 0.981 0.633 0.49 IL_boost,min@20%load[A] 0.791 0.407 0.343 0.344 0.38 IL_boost,max@20%load[A] 1.839 1.458 1.323 0.978 0.87 IL_boost,min@50%load[A] 2.764 1.805 1.592 1.336 1.317 IL_boost,max@50%load[A] 3.812 2.857 2.573 1.969 1.807 IL_boost,min@100%load[A] 6.052 4.137 3.675 2.989 2.897 IL_boost,max@100%load[A] 7.1 5.188 4.655 3.622 3.369 Similar to high-side MOSFET of buck converter, the power loss of main switch MOSFET(Q1 in Figure 9) of Boost converter include switching loss, conduction loss and Coss loss, and calculation of these power loss are same to those of high-side MOSFET of Buck converter(equation (13)~(16)). Also it is feasible to suppose that max. power loss of main switch MOSFET of Boost converter is about 6W, then we can get the RDS(on) of the MOSFET suitable for the application, as shown in the Table 10. Table 10 RDS(on) of main switch MOSFET of Boost converter suitable for the application RDS(on) [Ω] Vin1=190 VDC Vin2=268 VDC Vin3=300 VDC Vin4=378 VDC Vin5=400 VDC 0.141 0.469 0.735 2.445 3.8 From Table 10 we know that the RDS(on) of the main switch MOSFET suitable for the application should be smaller than 0.141 Ω. Application Note 12 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis For boost diode MOSFET (Q2 in Figure 9), the power loss include conduction loss of MOSFET and its body diode, the calculation of the two loss is also same with that of low-side MOSFET of Buck converter (equation (19)~(21)), the assumptions of equation (22) and (23) of low-side MOSFET are applicable to the calculation of boost diode MOSFET, then we can get the RDS(on) of the boost diode MOSFET suitable for the application, as shown in the Table 11. Table 11 RDS(on) of diode MOSFET of Boost converter suitable for the application RDS(on) [Ω] Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 0.329 0.465 0.521 2.445 3.8 The max. voltage MOSFETs have to endure for Boost converter is the max. output voltage, which is 460 VDC for the application. Considering 80% or more voltage derating and voltage spike produced by parasitic parameters, the voltage class of 600V or 650V CoolMOSTM is suitable for the application. As a result, two paralleled IPP60R125P6 and two paralleled IPP65R310CFD are chosen for main switch and diode MOSFETs respectively concerning RDS(on) for main switch and diode MOSFETs and excellent body diode requirement for diode MOSFET. The power loss of each MOSFET then can be calculated. For main switch MOSFET RDS(on) of IPP60R125P6 at 120°C junction temperature is 0.22Ω and Eoss at 460V is about 8.3uC[10]. For diode MOSFET, RDS(on) of IPP65R310CFD at 120°C junction temperature is 0.58Ω and forward voltage drop of the body diode is 0.8V, Eoss at 460 VDC is about 4 uC[11]. Then the power loss of each MOSFET is obtained at different input voltage and output load. Table 12 Each MOSFET loss of Boost converter at 20% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Main switch MOS[W] 0.965 0.786 0.779 0.769 0.767 Diode MOS[W] 0.446 0.413 0.404 0.385 0.38 Table 13 Each MOSFET loss of Boost converter at 50% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Main switch MOS[W] 1.621 1.041 0.998 0.941 0.932 Diode MOS[W] 1.015 0.817 0.764 0.671 0.65 Table 14 Each MOSFET loss of Boost converter at 100% load at different input voltage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Main switch MOS[W] 3.273 1.665 1.497 1.271 1.234 Diode MOS[W] 3 2.224 2.021 1.668 1.593 3.3 LLC converter The topology of half-bridge LLC converter with synchronous rectification following Buck/Boost converter is illustrated in Figure 10. Application Note 13 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis Q3 Lr DC Co Q4 Cr Figure 10 Q5 Rload Q6 Topology of half-bridge LLC converter As mentioned in the second part, the main specifications of LLC converter include: (1) Output voltage is 12 VDC and output full load is 100 A 𝑉𝑜𝑢𝑡_𝐿𝐿𝐶 = 12 𝑉, 𝐼𝑜𝑢𝑡_𝐿𝐿𝐶 = 100𝐴 (2) Resonant frequency (also working frequency) is 130 kHz, time of turn off is 20nS. 𝑓𝑟𝑒𝑠 = 130𝐾, 𝑇𝑜𝑓𝑓_𝐿𝐿𝐶 = 20 ∗ 10−9 𝑆 (32) (33) The LLC will always work at resonant frequency to get a high efficiency. For LLC converter following Buck converter, input voltage is 150 VDC, so the expected turn ratio of primary side to secondary side of transformer is 𝑁𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑒𝑥𝑝 = 𝑉𝑖𝑛_𝑏𝑢𝑐𝑘𝐿𝐿𝐶 2∗𝑉𝑜𝑢𝑡𝐿𝐿𝐶 150 (34) = 2∗12 = 6.25 The final turn ratio of transformer of LLC following Buck is determined as 6, that is 𝑁𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑇𝑥 = 6 For LLC converter following Boost converter, input voltage is 460Vdc, then the expected turn ratio is 𝑉𝑖𝑛_𝑏𝑜𝑜𝑠𝑡𝐿𝐿𝐶 460 𝑁𝑏𝑜𝑜𝑠𝐿𝐿𝐶_𝑒𝑥𝑝 = 2∗𝑉 = 2∗12 = 19.167 𝑜𝑢𝑡_𝐿𝐿𝐶 The final turn ratio of transformer of LLC following Boost is determined as 19, that is 𝑁𝑏𝑜𝑜𝑠𝑡𝐿𝐿𝐶_𝑇𝑥 = 19 It is supposed that magnetic cores of the two LLC transformers are same, which means the effective magnetic area and air gap are same. Another critical presupposed condition is that winding number of secondary side transformer is 1(total winding number is 2 for center-taped winding) for the two transformers, which is realized in many server power supplies to reduce the secondary-side winding conduction loss, so the ratio of primary winding inductance of two transformers is 𝑁 6 𝐿𝑚_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑇𝑥 = (𝑁 𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑇𝑋 )2 = (19)2 = 0.1 𝑏𝑜𝑜𝑠𝑡𝐿𝐿𝐶_𝑇𝑥 (35) (36) (37) (38) If the inductance of primary side transformer of LLC following Buck converter is assigned to 80µH, that is 𝐿𝑚_𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑇𝑥 = 80𝑢𝐻 (39) Then according to equation (38) the winding inductance of primary side transformer of LLC following Boost converter is 𝐿 80 𝐿𝑚𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑇𝑥 = 𝐿 𝑚_𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑇𝑥 = 0.1 = 800𝑢𝐻 (40) 𝑚_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑇𝑥 Application Note 14 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis So the peak values of magnetizing currents of two transformers are 𝑉 150 𝐼𝑝𝐿𝑚_𝑏𝑢𝑐𝑘 = 4𝑓 𝐿𝑖𝑛_𝑏𝑢𝑐𝑘𝐿𝐿𝐶 = 4∗130∗103 ∗80∗10−6 = 3.606 𝑟𝑒𝑠 𝑚_𝑏𝑢𝑐𝑘𝐿𝐿𝐶_𝑇𝑥 𝑉𝑖𝑛_𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐 𝐼𝑝𝐿𝑚_𝑏𝑜𝑜𝑠𝑡 = 4𝑓 𝑟𝑒𝑠 𝐿𝑚𝑏𝑜𝑜𝑠𝑡𝐿𝐿𝐶_𝑇𝑥 460 = 4∗130∗103 ∗800∗10−6 = 1.103 (41) (42) As it is known that the rms current of primary side of LLC converter can be calculated as 𝐼𝑟𝑚𝑠_𝑝𝑠_𝑙𝑙𝑐 = 4 1 𝑉𝑜𝑢𝑡 √𝑁 4 √2 𝑁∗𝑅𝑙𝑜𝑎𝑑 𝑅 ∗ 𝐿𝑚𝑙𝑜𝑎𝑑 2 ∗𝑓 2 𝑟𝑒𝑠 2 + 4π2 (43) Where N is the turn ratio of primary-side winding to secondary-side winding and Lm is the inductance of primary-side winding, 𝑅𝑙𝑜𝑎𝑑 is the resistor of output load and can be calculated as 𝑉 𝑅𝑙𝑜𝑎𝑑 = 𝐼 𝑜𝑢𝑡_𝐿𝐿𝐶 (44) 𝑜𝑢𝑡_𝐿𝐿𝐶 The rms current of primary-side LLC following Buck converter at different load can be obtained according to equation (43) and (44), as shown in the Table 15. Table 15 Primary-side rms current of LLC converter following Buck converter at different load rms current[A] 20% load 50% load 100% load 3.899 9.337 18.552 For LLC following Boost converter, the rms current of primary-side transformer at different load is Table 16 Primary-side rms current of LLC converter following Boost converter at different load 20% load 50% load 100% load rms current[A] 1.231 2.948 5.859 The power loss of MOSFET used in LLC converter includes conduction loss and turn off loss, the conduction loss is calculated as: 𝑃𝑐𝑜𝑛_𝑙𝑙𝑐 = 𝐼𝑟𝑚𝑠_𝑚𝑜𝑠 2 ∗ 𝑅𝐷𝑆(𝑜𝑛) (45) Where 𝐼𝑟𝑚𝑠−𝑚𝑜𝑠 is the rms current through MOSFET, for LLC converter 1 𝐼𝑟𝑚𝑠−𝑚𝑜𝑠 = 2 𝐼𝑟𝑚𝑠_𝑝𝑠_𝑙𝑙𝑐 (46) √ When LLC converter performs at its resonant frequency, turn off loss can be calculated as: 1 𝑃𝑡𝑜𝑓𝑓_𝑙𝑙𝑐 = 𝑉𝑖𝑛 ∗ 𝐼𝑝𝐿𝑚 ∗ 𝑇𝑜𝑓𝑓_𝑙𝑙𝑐 ∗ 𝐹𝑟 2 (47) Where Vin is the input voltage of LLC(output voltage of Buck or Boost converter), 𝐼𝑝𝐿𝑚 is the peak current of magnetic inductance of transformer as calculated in equation (41) or (42), 𝑇𝑜𝑓𝑓_𝑙𝑙𝑐 is the turn off time during which VDS (voltage between Drain and Source pin of MOSFET) of MOSFET increase from zero to Vin. We suppose that the power loss of high-side or low-side MOSFETs of LLC is 5W, the RDS(on) of high-side or lowside MOSFETs can be calculated 𝑅𝐷𝑆(𝑜𝑛) = 𝑃𝑡𝑜𝑡𝑎𝑙𝑙𝑜𝑠𝑠 −𝑃𝑡𝑜𝑓𝑓_𝑙𝑙𝑐 𝐼𝑟𝑚𝑠 2 (48) The max. RDS(on) of the MOSFETs used in the two LLC converters then can be obtained according to equation (33), (45)~(48): 𝑅𝐷𝑆(𝑜𝑛)_max _𝑏𝑢𝑐𝑘𝐿𝐿𝐶 = 0.025 (49) 𝑅𝐷𝑆(𝑜𝑛)_max _𝑏𝑜𝑜𝑠𝑡𝐿𝐿𝐶 = 0.253 50) Where RDS(on)_max_buckLLC and RDS(on)_max_boostLLC are the max. MOSFET RDS(on) of the LLC converter following Buck and Boost respectively. The max. voltage MOSFETs have to endure for LLC converter following Buck converter is 150 VDC in the application. Considering 80% or more voltage derating and voltage spike produced by parasitic parameters, the voltage class of 250 V OptiMOSTM is suitable for the application. However, the max. voltage MOSFETs Application Note 15 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Solutions analysis have to endure for LLC converter following Boost converter is 460 VDC in the application. Considering 80% or more voltage derating and voltage spike produced by parasitic parameters, the voltage class of 600 V or 650 V CoolMOSTM is suitable for the application. Therefore two paralleled IPP220N25NFD and two paralleled IPP65R190CFD are chose for LLCs following Buck converter and Boost converter respectively concerning power loss and excellent body diode requirement. RDS(on) is 0.0388Ω and 0.58Ωat 120°C for IPP220N25NFDand IPP65R190CFD respectively[12][13], then the power loss of each MOSFET using IPP220N25NFD and IPP65R190CFD for LLCs following Buck and Boost converter can be obtained according to equation (45)~(47), as shown in the following table. Table 17 Power loss of each MOSFET in the two LLC converters Power loss of each MOSFET of primary side of LLC following Buck[W] 20% load 50% load 100% load 0.777 1.126 2.372 Power loss of each MOSFET of primary side of 0.728 1.051 2.204 LLC following Boost[W] For secondary-side MOSFETs of the two LLC converters, the rms currents through any branch of synchronous rectifier (Q5 or Q6 in fig.10) of the two LLC converters are same and can be calculated 1 𝐼𝑟𝑚𝑠𝑠𝑠 = 4 ∗ 𝑉𝑜𝑢𝑡∗π 𝑅𝑙𝑜𝑎𝑑 2 𝑁 4 ∗𝑅𝑙𝑜𝑎𝑑 ∗ √ 𝐿2 2 𝑚 ∗𝑓𝑟𝑒𝑠 ∗ 5π2 −48 + 12π4 (52) 1 Because LLC converters work at resonant frequency, the power loss of secondary-side MOSFETs is mainly composed of conduction loss and is expressed as: 𝑃𝑐𝑙_𝑠𝑠 = 𝐼𝑟𝑚𝑠_𝑠𝑠 2 ∗ 𝑅𝐷𝑆(𝑜𝑛) (52) It is reasonable to choose SuperSO8 package of Infineon Technologies as the secondary-side MOSFET for its very low 𝑅𝐷𝑆(𝑜𝑛) and excellent heat dissipating capability. It is supposed that max. power loss for any branch of synchronous rectification(Q5 or Q6 in Figure 10) is about 4W. The 𝑅𝐷𝑆(𝑜𝑛) of the MOSFET than can meet the power loss requirement can be obtained according to equation (51) and (52) 𝑅𝐷𝑆(𝑜𝑛) = 𝐼 𝑃𝑐𝑙_𝑠𝑠 𝑟𝑚𝑠_𝑠𝑠² = 4 12 2 64 ∗( ) 1 12∗π 5π2 −48 100 ( ∗ 12 ∗√ ∗ +1)² 4 (80∗10−6 )²∗(130∗103 )² 12π4 100 = 0.65 ∗ 10−3 (53) The max. voltage MOSFETs have to endure for secondary side of LLC converter is 24 VDC in the application. Considering 80% or more voltage derating and voltage spike produced by parasitic parameters, the voltage class of 40 V OptiMOSTM is suitable for the application. The two paralleled BSC010N04LSI are used in any branch of synchronous rectification, 𝑅𝐷𝑆(𝑜𝑛) of the BSC010N04LS at 120°C junction temperature is about 1.35 mΩ [14], then the power loss of each MOSFETs of secondary side of LLC converter is calculated according to equation (51) and (52), the results at different load condition are shown in the Table 18. Table 18 Power loss of each MOSFETs of secondary side of LLC converter Power loss of each MOSFET [W] Application Note 20% load 50% load 100% load 0.084 0.521 2.082 16 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Inductors and transformer 4 Inductors and transformer 4.1 Inductors From calculation results in the previous parts, inductor of Buck converter is 720 µH and inductor of Boost converter is 1.33 mH, it is supposed that we choose the two magnetic cores with same dimension and material such as ferrite for the two inductors, and the airgap of the two cores are supposed to be same to each other so the ratio of winding number of Buck inductor to Boost inductor is 𝐿 720𝑢 𝑁𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝐿 = √𝐿 𝑏𝑢𝑐𝑘 = √1.33𝑚 = 0.736 (54) 𝑏𝑜𝑜𝑠𝑡 As the current through the Buck or Boost inductor is of saw-tooth waveform so the rms current is calculated 𝐼 𝐼𝑟𝑚𝑠_𝐿 = √ 𝑚𝑖𝑛 2 +𝐼 2 𝑚𝑖𝑛 ∗𝐼𝑚𝑎𝑥 +𝐼𝑚𝑎𝑥 (55) 3 For different input voltage, the rms current through the Buck inductor is nearly same so we can get the rms current at different load according to Table 3 and equation (55), results are shown in the following table Table 19 Rms current through the Buck inductor 20% load 50% load 100% load rms current through the Buck inductor [A] 1.7 4.1 8.2 Different from Buck inductor, however, the rms current through the Boost inductor is related not only to output load but also to input voltage, so the rms current through the Boost inductor is obtained in Table 9 and equation (55), results are shown in the Table 20. Table 20 Rms current through the Boost inductor Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 20% load 1.4 A 1.0 A 0.9 A 0.7 A 0.7 A 50% load 3.3 A 2.4 A 2.1 A 1.7 A 1.6 A 100% load 6.6 A 4. 7 A 4.2 A 3.3 A 3.1 A It is supposed that the maximum current density of the windings of two inductors is same, therefore the ratio of cross-section area of windings of Buck inductor to Boost inductor is 𝐼 8.2 𝐴𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝐿 = 𝐼 𝑟𝑚𝑠_𝑏𝑢𝑐𝑘_𝑚𝑎𝑥 = 6.6 = 1.242 (56) 𝑟𝑚𝑠_𝑏𝑜𝑜𝑠𝑡_𝑚𝑎𝑥 Then the ratio of DC winding resistance of buck inductor to that of boost inductor is 𝑁 0.736 𝑅𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 = 𝐴 𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝐿 = 1.242 = 0.592 (57) 𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝐿 The ratio of DC copper loss of Buck inductor to that of Boost inductor is calculated as 2 𝐼 𝑃𝑐𝑙_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 = 𝐼 𝑟𝑚𝑠_𝑏𝑢𝑐𝑘 2 ∗ 𝑅𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 (58) 𝑟𝑚𝑠_𝑏𝑜𝑜𝑠𝑡 The results of equation (58) at different input voltage and load are shown in the Table 21. Table 21 The ratio of DC copper loss of Buck inductor to that of Boost inductor Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 20% load 0.873 A 1.711 A 2.113 A 3.493 A 3.493 A 50% load 0.914 A 0.914 A 1.728 A 1.803 A 2.257 A 2.257 A 3.445 A 3.657 A 3.889 A 4.144 A 100% load Application Note 17 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Inductors and transformer The current change (ΔI) through Buck and Boost inductor, as calculated in the Table 3 and Table 9, are shown again in the Table 22. Table 22 Current change (ΔI) through Buck and Boost inductor Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 0.548 A 1.147 A 1.302 A 1.571 A 1.628 A ΔIL-boost[A] 1.048 A 1.051 A The inductance of inductor is expressed as 0.981 A 0.633 A 0.49 A ΔIL-buck[A] 𝑑Ψ 𝑁∗𝛥𝐵∗𝐴 𝐿 = 𝑑𝑖 = 𝛥𝐼 𝑒 (59) We choose the same magnetic cores for the two inductors so effective core area (Ae) is same, then the ratio of magnetic density change of the Buck inductors to Boost inductor is 𝐿 𝛥𝐼 𝛥𝐵𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 = 𝐿 𝑏𝑢𝑐𝑘 ∗ 𝛥𝐼 𝑏𝑢𝑐𝑘 ∗ 𝑁 𝑏𝑜𝑜𝑠𝑡 𝑏𝑜𝑜𝑠𝑡 1 (60) 𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 The results of equation (60) at different input voltage is obtained through equation(9), equation(31), equation(60) and Table22, as shown in the following table Table 23 The ratio of magnetic density change for the Buck and Boost inductor Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC 𝛥𝐵𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 0.385 0.803 0.977 1.826 2.445 According to magnetic core loss of Steinmetz equation, the magnetic loss is expressed as 𝑃𝑚𝑙 = 𝑉 ∗ 𝐾 ∗ 𝛥𝐵𝛼 ∗ 𝑓𝑊 𝛽 (61) Where V is the volume of the magnetic core, K,α,β are constant coefficients, ΔB is the magnetic density change and fw is the working frequency, as we have selected same magnetic cores for the two inductors V, K, fw, α and β are same for the two inductors, then the ratio of magnetic loss of the Buck inductor to Boost inductor can be obtained: 𝑃𝑚𝑙−𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 = 𝛥𝐵𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡 𝛼 (62) 4.2 LLC transformers We have supposed that the winding numbers of secondary-side transformers are same such as 1(each brach of synchronous rectification) for the two LLC transformers that following Buck and Boost converter respectively and the working frequencies are same for the two LLC converters. As a result the voltagesecond products of the two transformers are same, so the magnetic density change ΔB is equivalent to each other. The two transformers use identic magnetic core (equivalent in volume and Steinmetz coefficients), therefore the magnetic losses are same for the two transformers. If it is supposed that the maximum current density of the windings (include primary side and secondary side) of the two transformers are same, the ratio of cross-section area of primary-side windings of two transformers is 𝐴𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑝𝑠_𝑇𝑥 = 𝐼𝑟𝑚𝑠_𝑏𝑢𝑐𝑘𝑙𝑙𝑐_𝑝𝑠_𝑚𝑎𝑥 𝐼𝑟𝑚𝑠_𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑝𝑠_𝑚𝑎𝑥 (63) As it is known that the rms primary-side current of LLC converter is expressed by equation (43), and at most times the equation can be simplified as π 𝑉 ∗ 𝑜𝑢𝑡 √2 𝑁∗𝑅𝑙𝑜𝑎𝑑 Application Note 𝐼𝑟𝑚𝑠_𝑝𝑠_𝐿𝐿𝐶 = 2 (64) 18 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Inductors and transformer Thus according to equation (64), the ratio of rms current through primary-side windings of the two transformers is 𝐼𝑟𝑚𝑠_𝑝𝑠_𝑏𝑢𝑐𝑘𝑙𝑙𝑐 = 𝐼𝑟𝑚𝑠_𝑝𝑠_𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐 𝑁𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑇𝑥 (65) 𝑁𝑏𝑢𝑐𝑘𝑙𝑙𝑐_𝑇𝑥 Then the DC resistance ratio of primary-side windings of two transformers is obtained according to equation (63) and (65) 𝑁 1 𝑅𝐷𝐶_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑝𝑠_𝑇𝑥 = 𝑁 𝑏𝑢𝑐𝑘𝑙𝑙𝑐_𝑇𝑥 ∗ 𝐴 𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑇𝑥 𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡𝑝𝑠𝑇𝑥 = 𝐼𝑟𝑚𝑠_𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑝𝑠 2 (66) 𝐼𝑟𝑚𝑠_𝑏𝑢𝑐𝑘𝑙𝑙𝑐_𝑝𝑠 2 Therefore the ratio of primary-side winding copper loss of the two transformers is 𝐼𝑟𝑚𝑠𝑏𝑢𝑐𝑘𝑙𝑙𝑐 𝐼 𝑃𝑐𝑙_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑇𝑥 = (𝐼 𝑟𝑚𝑠_𝑏𝑢𝑐𝑘𝑙𝑙𝑐_𝑝𝑠 )2 ∗ 𝑅𝐷𝐶_𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑝𝑠_𝑇𝑥 = (𝐼 𝑟𝑚𝑠_𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐_𝑝𝑠 2 𝑝𝑠 𝑟𝑚𝑠𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐 𝑝𝑠 ) ∗ 2 𝑝𝑠 𝐼𝑟𝑚𝑠𝑏𝑢𝑐𝑘𝑙𝑙𝑐 2 𝑝𝑠 𝐼𝑟𝑚𝑠𝑏𝑜𝑜𝑠𝑡𝑙𝑙𝑐 =1 (67) We can know from equation (67) the copper loss of primary-side windings of the two transformers are same. As about copper loss of secondary-side windings, the winding numbers the current density of the windings and the currents through the windings are same and therefore the copper losses are same. It is concluded that the power loss of two transformers are same if we choose same magnetic core, current density for windings and same winding numbers for secondary side. Application Note 19 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Conclusion 5 Conclusion We compare the two solutions, Buck followed by LLC and Boost followed by LLC, in three dimensions: occupation of PCB, power loss and the cost of power MOSFETs 5.1 Occupations of PCB by MOSFETs and magnetic elements For the solution of Buck followed by LLC, total eight TO-220 package MOSFETs and four SuperSO8-package MOSFETs are chosen for Buck and its followed LLC converters. The same number and package of MOSFETs are chosen for Boost and its followed LLC converters, so the occupations of PCB by MOSFETs are same for the two solutions. However, for the LLC following Buck converter, the input voltage is only 150VDC, the MOSFETs used in the LLC belongs to the OptiMOSTM series of Infineon Technologies, in which there is more available SMD package such as SuperSO8, DPAK, therefore for high power density application the solution of Buck followed by LLC will be predominant. For the magnetic elements, the magnetic cores and current density of windings are same for inductors and transformers, so the dimensions of inductors and transformers for the two solutions are nearly same. 5.2 Power loss of MOSFETs and magnetic elements We can get the power loss of MOSFETs used in Buck, Boost and two LLC converters according to the previous calculation at different loads and input voltages, as shown in the followed tables. Table 24 MOSFETs loss of two solutions at 20% load Stage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Buck 1.188 W 1.336 W 1.394 W 1.52 W 1.556 W Boost 2.828 W 2.408 W 2.372 W 2.31 W 2.296 W LLC following Buck 3.108 W LLC following Boost 2.912 W Table 25 MOSFETs loss of two solutions at 50% load Stage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Buck 2.962 W 3.466 W 3.634 W 4.006 W 4.102 W Boost 5.28 W 3.724 W 3.534 W 3.226 W 3.166 W LLC following Buck 4.504 W LLC following Boost 4.204 W Table 26 MOSFETs loss of two solutions at 100% load Stage Vin_1=190 VDC Vin_2=268 VDC Vin_3=300 VDC Vin_4=378 VDC Vin_5=400 VDC Buck 8.466 W 9.942 W 10.404 W 11.352 W 11.588 W Boost 12.552 W 7.786 W 7.046 W 5.882 W 5.656 W LLC following Buck 4.744 W LLC following Boost 4.408 W Application Note 20 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Conclusion Based on previous data it is easy to get the comparison of MOSFETs loss in the two solutions (Buck followed by LLC and Boost followed by LLC) at different load and input voltage, as shown in the followed figures. At light load such as 20% load, the solution of Buck plus LLC will have a low MOSFETs loss compared with Boost plus LLC. At medium load such as 50% load, the solution of Buck plus LLC will have a low MOSFETs loss at low input voltage, with the increase of input voltage, however, the solution of Boost plus LLC will have a low MOSFETs loss. Similar to medium load, when the load is heavy such as full load, the solution of Boost plus LLC will have a low MOSFETs loss compared with Buck plus LLC solution. Figure 11 MOSFETs loss comparison at 20% load Figure 12 MOSFETs loss comparison at 50% load Application Note 21 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Conclusion Figure 13 MOSFETs loss comparison at 100% load Next is about the inductor power loss comparison, as we have calculated the DC copper loss ratio of Buck inductor to Boost inductor as shown in Table 21, the data can be transformed to curve to get a more clear comparison. Figure 14 Ratio of DC copper loss of Buck inductor to Boost inductor at different load and input voltage As show in the Figure 14, Buck converter will have a higher DC copper loss compared with Boost converter if the ripple current through the two inductors and current density of windings are same. And the higher input voltage the higher Buck inductor DC copper loss compared with Boost converter. We have obtained the ratio of magnetic loss of Buck inductor to that of Boost inductor in equation (62), for ferrite material such as 3C95 or PC95 that is widely used in SMPS(Switched Mode Power Supply), the range of is generally from 2.5 to 3 at about 100 kHz working frequency, so the ratio of magnetic loss of the two inductors as a function of α is shown in the following figure according to equation (62) and Table (23). Application Note 22 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Conclusion Figure 15 Ratio of magnetic loss of Buck inductor to Boost inductor 𝛥𝐵𝑏𝑢𝑐𝑘2𝑏𝑜𝑜𝑠𝑡_𝑉1𝛼 in Figure 15 represents the ratio of magnetic loss of Buck inductor to Boost inductor when input voltage is 190 VDC, and V2 to V5 represents input voltage of 268 VDC, 300 VDC, 378 VDC and 400 VDC respectively. When input voltage is smaller than 300 V (green, blue and red curve in Figure 15), Buck inductor will have a smaller magnetic loss compared to Boost inductor, as input voltage increase, however, Buck inductor will have a larger magnetic loss compared to Boost inductor, the higher input voltage, the higher Buck inductor magnetic loss compared to Boost inductor if the dimension of the magnetic cores and air gap are same for the two inductors. The two solutions will have same loss of transformers of LLC if magnetic core, winding current density and secondary-side winding number are same. 5.3 Cost of MOSFETs The cost of MOSFETs can be obtained according to the choice of MOSFETs and price listed in Infineon website, as shown in the following table Table 27 Cost of MOSFETs for the two solutions Buck+LLC Boost+LLC Application Note Part Items Number(PCS) Price per part(€) Total cost(€) IPP60R099P6 2 2.76 19.96 IPP65R150CFD 2 1.93 IPP220N25NFD 2 3.07 BSC010N04LSI 4 1.11 IPP60R125P6 2 1.91 IPP65R310CFD 2 1.3 23 14.08 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Conclusion Part Items Number(PCS) Price per part(€) IPP65R190CFD 2 1.61 BSC010N04LSI 4 1.11 Total cost(€) As shown in the Table 27, the cost of MOSFETs of Boost+LLC is smaller than that of Buck+LLC, about 30% cost down is realized according to the price listed in Infineon Technologies website. As a conclusion, the solution of Boost followed by LLC is predominant in the application of HVDC DC/DC converter that suitable for 240 VDC and 336 VDC HVDC system considering medium to high load efficiency and power MOSFETs cost. On the contrary, solution of Buck followed LLC will be good at high power density and high efficiency requirement at light load and low input voltage. Application Note 24 Revision 1.0, 2015-01-26 The Optimal Solutions Suitable for DC/DC Converter Used in HVDC System Reference 6 Reference [1] 380Vdc Architectures for the Modern Data Center, white paper, Emerge Allicance. [2] The Green Grid, Qualitative Analysis of Power Distribution Configuration for Data Centers (2007) [3] HVDC Demo Site and Future Trend, Netpower Labs [4] 380VDC Eco-system Development Present Status and Future Challenges, David E. Geary, David P. Mohr, David Owen, Maurizio Salato, BJ Sonenberg, Intelec 2013 [5] 240V Direct Current Power Supply System for telecommunications, YD/T 2378-2011 [6] 336V Direct Current Power System, QB-H-008-2012, China Mobile [7] MOSFET Power Losses Calculation Using the Datasheet Parameters, Dusan Graovac, Marco Purschel, Andreas Kiep, Application Note, Infineon Technologies co. Ltd. [8] IPX60R099P6, CoolMOSTM 600V P6 datasheet, www.infineon.com [9] IPX65R150CFD, CoolMOSTM 650V CFD datasheet, www.infineon.com [10] IPX60R125P6, CoolMOSTM 600V P6 datasheet, www.infineon.com [11] IPX65R310CFD, CoolMOSTM 650V CFD datasheet, www.infineon.com [12] IPP220N25NFD, OptiMOSTM FD power-transistor 250V datasheet, www.infineon.com [13] IPX65R190CFD, CoolMOSTM 650V CFD datasheet, www.infineon.com [14] BSC010N04LSI, datasheet, www.infineon.com Revision History Major changes since the last revision Page or Reference -- Application Note Description of change First Release 25 Revision 1.0, 2015-01-26 Trademarks of Infineon Technologies AG AURIX™, C166™, CanPAK™, CIPOS™, CIPURSE™, CoolGaN™, CoolMOS™, CoolSET™, CoolSiC™, CORECONTROL™, CROSSAVE™, DAVE™, DI-POL™, DrBLADE™, EasyPIM™, EconoBRIDGE™, EconoDUAL™, EconoPACK™, EconoPIM™, EiceDRIVER™, eupec™, FCOS™, HITFET™, HybridPACK™, ISOFACE™, IsoPACK™, iWafer™, MIPAQ™, ModSTACK™, my-d™, NovalithIC™, OmniTune™, OPTIGA™, OptiMOS™, ORIGA™, POWERCODE™, PRIMARION™, PrimePACK™, PrimeSTACK™, PROFET™, PRO-SIL™, RASIC™, REAL3™, ReverSave™, SatRIC™, SIEGET™, SIPMOS™, SmartLEWIS™, SOLID FLASH™, SPOC™, TEMPFET™, thinQ!™, TRENCHSTOP™, TriCore™. Other Trademarks Advance Design System™ (ADS) of Agilent Technologies, AMBA™, ARM™, MULTI-ICE™, KEIL™, PRIMECELL™, REALVIEW™, THUMB™, µVision™ of ARM Limited, UK. ANSI™ of American National Standards Institute. AUTOSAR™ of AUTOSAR development partnership. Bluetooth™ of Bluetooth SIG Inc. CATiq™ of DECT Forum. COLOSSUS™, FirstGPS™ of Trimble Navigation Ltd. EMV™ of EMVCo, LLC (Visa Holdings Inc.). EPCOS™ of Epcos AG. FLEXGO™ of Microsoft Corporation. HYPERTERMINAL™ of Hilgraeve Incorporated. MCS™ of Intel Corp. IEC™ of Commission Electrotechnique Internationale. IrDA™ of Infrared Data Association Corporation. ISO™ of INTERNATIONAL ORGANIZATION FOR STANDARDIZATION. MATLAB™ of MathWorks, Inc. MAXIM™ of Maxim Integrated Products, Inc. MICROTEC™, NUCLEUS™ of Mentor Graphics Corporation. MIPI™ of MIPI Alliance, Inc. MIPS™ of MIPS Technologies, Inc., USA. muRata™ of MURATA MANUFACTURING CO., MICROWAVE OFFICE™ (MWO) of Applied Wave Research Inc., OmniVision™ of OmniVision Technologies, Inc. Openwave™ of Openwave Systems Inc. RED HAT™ of Red Hat, Inc. RFMD™ of RF Micro Devices, Inc. SIRIUS™ of Sirius Satellite Radio Inc. SOLARIS™ of Sun Microsystems, Inc. SPANSION™ of Spansion LLC Ltd. Symbian™ of Symbian Software Limited. TAIYO YUDEN™ of Taiyo Yuden Co. TEAKLITE™ of CEVA, Inc. TEKTRONIX™ of Tektronix Inc. TOKO™ of TOKO KABUSHIKI KAISHA TA. UNIX™ of X/Open Company Limited. VERILOG™, PALLADIUM™ of Cadence Design Systems, Inc. VLYNQ™ of Texas Instruments Incorporated. VXWORKS™, WIND RIVER™ of WIND RIVER SYSTEMS, INC. ZETEX™ of Diodes Zetex Limited. Last Trademarks Update 2014-07-17 www.infineon.com Edition 2015-01-26 Published by Infineon Technologies AG 81726 Munich, Germany © 2015 Infineon Technologies AG. All Rights Reserved. Do you have a question about any aspect of this document? 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