Design and application of high frequency low profile power transformer

zbz0529

Design and application of high frequency low profile power transformer [Copy link]

summary

The paper discusses the design issues of high-frequency low-profile power transformers, and gives the design and production method of flat-plate windings. This method can automatically connect the conductors of each layer of the winding in series, thereby solving the connection problem between the conductors of each layer of the winding, avoiding welding, and greatly improving the reliability of the device and the utilization rate of the winding to the core window. The experimental results show that the transformer made by this method has small leakage inductance and high efficiency, and is particularly suitable for use in distributed high-power density switching power supply modules. The paper also gives a computer-aided design method for high-frequency low-profile power transformers, which not only makes the design process more flexible and quick, but also makes the design results more reliable.

zbz0529

Keywords High-frequency and low-profile transformer winding production Computer-aided design Abstract: This paper discusses the issues related to high-frequency and low-profile power transformers. A new design and fabrication method for planar windingshas been presented. thewindowarea.Experimentalresultshaveshownthatthenewmethodcanresultinlowleakageinductance,highefficiency,andisparticularlyusefulforthedesignofinductorsandtranstformersusedinlow-profileandhigh-power-densityconvertermodules.Finally,acomputer-aideddesignofhigh- frequencyandlow-profilepowertranstormershasbeengiven,whichallowsthetransformerdesigntobefaster,moreflexibleandreliable. Keywords:HighfrequencyLowprofileTransformerwindingFobricationComputer-aideddesign

zbz0529

1 Introduction With the widespread application of switching power supplies, users have also put forward higher requirements for power modules, such as high efficiency, reliable performance, and small size. In addition, there are often restrictions on the overall height of the module. Therefore, the research on high-frequency and low-profile magnetic components has received increasing attention. The core of this new type of magnetic component is flat and very small (less than 1 cm). The winding is no longer wound with traditional solid round wires or stranded wires, but is realized with flexible or rigid printed circuit boards, and the conductor is flat. This unique structure not only saves the winding fixing frame and improves the utilization rate of the window, but also facilitates heat dissipation, reduces leakage inductance, and realizes automated production. In addition, since the current is distributed along the width of the conductor, the loss caused by the skin effect can be reduced. The disadvantage is that when using printed circuit boards to make multi-layer windings, additional welding holes are often required to connect adjacent conductors. When the number of turns is large, the design and production is very complicated. AJYerman et al. in the United States invented a winding production method without welding, but this method requires two layers of conductors to form a turn, so it does not effectively utilize the limited core window height. The design of the transformer also involves the determination of the geometric structural parameters of the core and winding and the arrangement of the winding. The traditional transformer design generally calculates the product of the core window area and the core cross-sectional area according to the design requirements, and then selects a suitable core, determines the number of winding turns, excitation inductance, etc., but this method is limited to low-frequency applications. When the switching frequency is very high (above 100kHz), the iron loss and copper loss of the transformer will increase significantly, and are closely related to the structure and relative arrangement of the transformer core and winding. Today's users have requirements for the volume, especially the height, of the power module, which makes designers tend to use low-profile power transformers. If the traditional method is still used, it will be difficult for the designed transformer to meet the requirements, and even if it meets the requirements, it may not be the best design. This article will give a novel folded winding design and production method. First, the copper sheet is processed into the required shape, and then folded into a winding. The number of turns formed by each layer of copper conductor is increased to 5/6 turns. In addition, the specific application and test results of the low-profile transformer and inductor made of windings in this way in the switching power supply are given. Finally, based on the relationship between the copper loss and iron loss of the high-frequency transformer and the geometric structure parameters and frequency, computer-aided design is used to find the optimal design solution for the power transformer with the smallest volume and the highest power density according to the user's requirements. This method is not only fast, but also allows designers to easily adjust the design parameters until a satisfactory design result is obtained.

zbz0529

2高频低造型电源变压器的研制与应用 2.1多层印刷电路板型及“z”字形折叠式绕组 　　D．V．D．Linde等人于1991年报导了用印刷电路板工艺制作多层绕组及应用，图1所示的是其采用的绕组导体串连方法，图中的端1和端2是绕组的引出端。图中所示的是一“匝数为6”（当然可以更大）的绕组，它实际上是由三个双面PCB组成，每个双面PCB的上下层导体则由“局部焊孔”相连。每层导体都有向外伸出的“连接铜片”，相邻的双面PCB正是靠这些“连接铜片”上的焊孔相连。如果要求的绕组匝数较多，连接点和连接线就会很多，例如当绕组匝数仅为10时就得有20个连接点和11条连接线。当绕组匝数较多时也未必能实现绕组的制作，因为“连接铜片”的多少受磁心尺寸的限制。连接点增多不仅给制作带来难度，同时也影响可靠性。为了解决连线以及焊接问题，A.J.Yerman等人发明了“z”字折叠式绕组，先用柔性PCB腐蚀制成一定形状的铜片，见图2，然后再折叠成绕组。图中的绕组是以“z”字折叠4个半匝的柔性PCB而成，总匝数为2。它实际上是由位于顶层以实线表示的导体7和底层以虚线表示的导体8折叠而成，而绕组的一匝实质上是由顶层的半匝和底层的半匝形成。端5和端6是引线端，虚线1、2和3为折叠线，9为绝缘材料，4为留给磁心心柱的通孔。这种方法的好处是避免了焊接，提高了整个元件的可靠性，但由于需要两层铜箔才形成整一匝，当匝数要求较多，而磁心高度又有要求时，绕组的高度便满足不了要求。 图1多层PCB型绕组的连接 图2“Z”字型折叠4个半匝的 柔性PCB而成的匝数为2的绕组 2.2一种折叠式绕组的新设计 图3所示的即是一种新的折叠式绕组设计图样，虚线为折叠线。可以看出，由于相邻环形导体中心连线之间有一定的夹角α，每一环形导体所形成的匝数实际上只有（1－α/360），最大数值为5/6（α=60o）。与前面所介绍的折叠式绕组设计相比，这种新方案使得设计者在磁心窗口高度受到限制时有可能得到较多的线圈匝数，或并联绕组以减小损耗和提高电流容量。为了与“z”字形绕组折叠方法相区别，称新的设计方法为“5/6匝”绕组折叠法。新设计除了可省去焊接程序，减少连接电阻，还提高了磁心窗口高度的利用率，缺点是相邻折叠线不平行，交错布置初级和次级绕组以减小漏感和高频损耗不是很方便。 当然，对于E型磁心，也可以用类似的方法来设计其绕组。图4即为适合E型磁心的方形绕组展开图。端1和端2为电流流入和流出端。该图样经折叠后形成匝数为5的绕组。 　 　 图3折叠式绕组新设计 　 图4适合E型磁心的方形绕组展片图 　 2.3低造型变压器的研制与测试结果 　　为了验证新的绕组设计方法的可行性和可靠性，作者设计制作了低造型变压器和滤波电感器，并将其用于一有源箝位同步整流正激式DC/DC变换器当中，见图7。其额定功率为50W，输入、输出电压各为48V和5V，开关频率为200kHz。图中的C2为箝位电容，其作用是在主开关关断期间，将主开关两端的电压Uds箝在一定的数值水平上，保持不变，从而避免了开关管V2上过大的电压应力。另外，采用有源箝位技术，不仅可实现变压器磁心的自动复位，无须另加复位措施，还可使得激磁电流正负方向流动，使磁心在磁化曲线第一和第三象限上运行，从而提高了磁心的利用率。 　　变压器所用的磁心结构参数如图5所示，其材料为MnZn铁氧体，磁导率为1000。初级和次级绕组导体的厚度分别为0.1mm、0.15mm（频率为200kHz时铜导体的趋肤深度约为0.2mm），层数分别为12和4，实际匝数比为10：4。先用CAD软件设计画好绕组的展开图样，然后用数控切割机加工铜片得到所要求的绕组图样。当然，在批量生产时，应考虑用冲床等设备来加工铜片绕组。图3和图6分别为初级绕组和次级绕组的展开图样。沿着折叠线依次折叠便成绕组。如果忽略引线和折叠的影响，绕组的直流电阻即为各层圆环导体的直流电阻之和。绕组的直流电阻可按下式计算： Rdc=2πρNl/twln(r0/r1)(1) 式中:Rdc——绕组的直流电阻； Nl——铜导体层数； ρ——铜导体的电阻率; 　　tw——铜导体厚度； 　　r0——绕组的外半径； r1——绕组的内半径。 　 　 图5Q型磁心结构尺寸 图6电源变压器副边绕组展开图 　　相邻导体用介电常数小、耐压性能好的绝缘胶带实现电气隔离。次级绕组被夹于初级绕组中间，因而漏感很小，为0.464μH，仅占激磁电感的1.5％。交流电阻（见表1）可根据Dowell模型来计算：　　(2) 式中：Rac——绕组的交流电阻； 　　M=△(sinh2△＋sin2△)/(cosh2△－cos2△) 　　D=2△(sinh△－sin△)/(cosh△＋cos△)　　△=tw/δ;δ（趋肤深度）= 　　f——开关频率； 　　μo——真空磁导率，μo=4π×10－7。 　　滤波电感器也采用相同的磁心，只是留了约1mm的气隙以防止磁心饱和及减小由于直流偏置所引起的损耗。电感器的绕组由两个具有相同匝数的绕组并联而成，以减少铜损。所制作的变压器和电感器整个磁心高度仅为8mm。 　　变压器的输入和输出功率测量方法是这样的：先将实测到的绕组两端的电压和流过的电流瞬时值相乘，然后再算得乘积在一个或多个周期内的平均值，即为变压器的输入或输出功率。这个过程通过TektronixA6302数字示波器来完成。为了避免高频对测量的影响，绕组两端分别接示波器的两个输入通道，之间的电压差即为绕组两端的电压。示波器的第三个通道则输入通过电流探头（TektronixA6302）测得的电流波形。 　　表1低造型电源变压器和电感器的参数 滤波电感器 匝数 5 电感量 4.1μH 总气隙 1mm 绕组直流电阻 2.25mΩ 电源变压器 工作频率 200kHz 初级匝数 10 次级匝数 4 激磁电感量 30.38μH 漏感量 0.46μH 绕组内径 6mm 绕组外径 13.5mm 初级直流电阻 16.0mΩ 初级交流电阻 29.3mΩ 次级直流电阻 3.56mΩ 次级交流电阻 5.09mΩ 　　图8所示的为该变压器效率与输入功率之间的关系。可以看出，该变压器具有很高的转换效率。当变换器的输出功率为50W时，即使是在自然通风冷却情况下，该变压器也没有明显温升（<50℃），这主要取决于它小的功耗和良好的散热性能。整个变换器效率与输出功率的关系见图9。由于采用了同步整流技术，该变换器具有较高的变换频率，在输出功率 为50W时的效率接近90％。 概括起来，“5/6匝”低造型变压器绕组折叠制作法具有下列优点： （1）避免了相邻导体之间的焊接； 图7有源箝位同步整流正激式DC/DC变换器 图8变压器效率和输入功率关系 图9变换器效率与输出功率关系 （2）可以在最大程度上利用磁心窗口高度，提高窗口填充系数； （3）使得加工过程中的铜材料损耗为最少； （4）制作方法简单、快捷，而且干净、不污染环境； （5）使设计者可以根据具体应用，选用不同厚度的铜片材料； （6）特别适合应用于高频高功率密度的开关电源模块中。

zbz0529

3 Optimization design of high-frequency low-profile power transformer 3.1 High-frequency transformer loss model (1) Core loss model The iron loss of the transformer is mainly caused by hysteresis and eddy current effects. Hysteresis loss is generally considered to be caused by the movement and friction of magnetic domains of magnetic materials. Hysteresis loss is proportional to frequency, while eddy current loss is proportional to the square of frequency. The most commonly used magnetic loss power density (unit volume) calculation formula will be used here: Pc=kBmfn(3) Where k is the loss coefficient, B is the peak-to-peak value of magnetic flux density, f is the magnetic field alternating frequency, k, m, and n are related to the characteristics of magnetic materials and can be obtained from the loss curve provided by the magnetic material supplier. At high frequencies, due to the influence of eddy current effects, the magnetic lines of force in the core are unevenly distributed. However, when ferrite soft magnetic materials with high resistivity are used as core materials, the eddy current is very small and the influence on the distribution of magnetic lines of force can be ignored. Therefore, it can be considered that the distribution of magnetic lines of force on the cross section of the core is uniform. For the E-E type magnetic core shown in Figure 10, its loss is: Pc=kfnΦm(2W2L)1-m(2Hw+W)(4) (2) Winding loss model Although PLDowell established a simple transformer copper loss and leakage inductance calculation model under a one-dimensional approximation of the electromagnetic field, the model is very convenient to use. It can be used to predict the copper loss and leakage inductance of high-frequency transformers and achieve the optimal design of high-frequency transformers. In high-frequency applications, in order to reduce copper loss and increase current capacity, the winding conductor is usually made of flat copper sheets, and each layer has only one circle of conductor, as shown in Figures 10 and 12. This allows the current to be distributed along the width of the conductor, reducing the loss caused by the skin effect. It is also beneficial to reduce the overall height of the transformer. If the influence of the connection points of each layer of conductors is ignored, for a winding with N turns, its DC resistance is: Rdc=2Nρ(L+Wc+2Ww)/(Ww-2dw)tw(5) where tw and dw are the conductor thickness and the gap between the winding and the core respectively. Due to the high-frequency effect, the resistance of the winding will increase significantly. The AC resistance of the winding can be expressed as: Rac=FrRdc(6) where Fr is the ratio of AC to DC resistance, which is related to the core and winding (a) Transformer cross-section (b) Core top view Figure 10: The geometric dimensions and layout of a high-frequency, low-profile power transformer with an E-E type core. Based on the PLDowell model, when the primary and secondary windings are arranged separately, the Fr value is: Fr=M＋[D(N2－1)]/3(7) Where: N——The number of winding layers starting from the zero leakage magnetic field; M=△(sinh2△＋sin2△)/(cosh2△－cos2△) D=2△(sinh△－sin△)/(cosh△＋cos△) △=tw/δ, δ is the skin depth at frequency f. The calculation of Fr when the primary and secondary windings are staggered is more complicated, and an example is given to illustrate. When one winding is sandwiched by another winding and the number of turns is an even number, the zero leakage magnetic field line just divides the winding into two halves (that is, the number of conductor layers on both sides is an integer), Fr can be calculated according to formula (7), but N should be half of the actual number of winding turns; when the number of winding conductor layers is an odd number, see Figure 11, the corresponding AC and DC resistance proportional coefficient Fr is: (8) Where: N0.5=N/2-0.5 M0.5=△1(sinh2△1＋sin2△1)/(cosh2△1－cos2△1) △1=tw/2δ Figure 11 Leakage magnetic field distribution when the primary and secondary windings are staggered (the number of turns of the winding sandwiched in the middle is 3, and the zero leakage magnetic field line is located on the horizontal center line of the second turn conductor of the winding) Figure 12 E-type magnetic core with flat winding (only one turn of conductor is drawn in the figure) In practical applications, the shape of the magnetic core is not necessarily limited to the E type. If other shapes are selected, the copper loss and iron loss can be calculated according to the corresponding calculation formula. When the transformer is used in a switching power supply, the current waveform flowing through the winding is not a sine wave, but contains high-order harmonics. Therefore, it is not enough to only consider the influence of the fundamental wave. The appropriate approach should be to first obtain the harmonic components of the current waveform, and then obtain the winding loss for each current harmonic component. In order to calculate the winding loss for the current harmonic component, it is necessary to calculate the AC/DC resistance proportionality coefficient Fr at each harmonic frequency, which can be obtained using formula (7) or (8). For the winding current i (t) that changes periodically, its Fourier expansion formula is: (9) Where Io is the DC component and In is the effective value of the nth harmonic component. Therefore, the total loss of the winding is: (10) Where Rn is the AC resistance of the winding at a frequency of nf. In actual calculations, the value of n can be larger, such as 15. In order to make more reasonable use of limited space, the core can also adopt the structure shown in Figure 13, so that the winding is completely surrounded by the core, which can effectively reduce electromagnetic interference. Figure 13 Another structure of low-profile core (a) Core structure (b) Arrangement of winding in the core 3.2 Algorithm design Based on the transformer loss model introduced above, a program for finding the minimum effective volume core can be written, and its process is shown in Figure 14. When the converter topology, transformer efficiency, core height, material, input and output voltage, power and other parameters are input, the program will automatically change the geometric structure size of the transformer, and then calculate the corresponding loss and efficiency, find the smallest volume core that meets the given maximum magnetic flux density, minimum excitation inductance and core height requirements, and give the corresponding core geometric structure size and copper loss, iron loss, etc. In the figure, ηo, Bsat, Ve, Ae, Le and Hco represent the target efficiency of the transformer, the saturation magnetic flux density of the magnetic material, the effective volume of the core, the effective cross-sectional area, the magnetic path length and the allowable height of the core. The specific design steps are as follows: (1) Select the switching power supply topology, such as forward or flyback. (2) Determine the primary-to-secondary winding turns ratio based on the input and output voltages and the switch control square wave pulse duty cycle. For a forward switching power supply: nps=Np/Ns=DUi/Uo(11) Where: nps is the primary-to-secondary winding turns ratio, Np is the primary winding turns, Ns is the secondary winding turns, D is the switch control square wave pulse duty cycle, Ui is the primary input voltage, and Uo is the power supply output voltage. (3) Set the primary winding turns Np to a certain value, and the secondary winding turns Ns can be obtained at the same time. (4) Select the layout of the primary and secondary windings: separate independent layout or staggered layout of the primary and secondary windings. After the winding layout is determined, the AC and DC resistance proportional coefficient Fr of the primary and secondary windings at different harmonic frequencies can be calculated. (5) Calculate the current ip (t), is (s) of the primary and secondary windings and the amplitude of each harmonic to calculate the loss of the winding, including high-frequency loss. (6) Within the set range, change the geometric structure parameters of the core and winding in turn, such as the core height hc, width W, window depth L, window width Ww and conductor thickness tw, and then calculate the core loss Pc and winding loss Pw under a certain geometric structure. (7) Calculate the efficiency η and flux density Bmax of the transformer. The efficiency of the transformer is: η=P0/(P0＋Pc＋Pw)(12) For the forward active clamp switching power supply: Bmax=UiDT/4NpAe(13) Where T is the control square wave pulse period. (8) Find the core and winding geometric structure parameters with the smallest volume and meet the efficiency requirements (> target efficiency ηo) and flux density requirements (<0.5Bsat). If the efficiency requirements are not met, repeat the process from (3) to (8). If the efficiency and other requirements are met, the search process ends and the structural parameters of the transformer are output. Based on the above conditions and requirements, the mathematical model for solving the minimum core volume can be written: minVe=2AeLe subHc≤Hco, Bmax≤0.5Bsat, η≥ηo Table 2 lists the transformer design results for active clamp forward converters obtained using the design program. The input voltage of the converter is 48V and 5V, the rated power is 200W, the operating frequency is 200kHz, the transformer winding turns ratio Np:Ns=6:2, each layer has only one conductor, and the core material is MnZn ferrite. In order to reduce high-frequency loss and leakage inductance, the primary and secondary windings are arranged in an interlaced manner, and the two secondary windings are first connected in parallel and then the primary is sandwiched in the middle. Of course, in order to fully ensure the reliability of the transformer, the allowable temperature rise limit of the transformer and the maximum allowable current density of the conductor should also be added to the constraints of the optimization program. The calculation of the transformer temperature rise involves the establishment of the transformer thermodynamic model, and the traditional transformer thermodynamic empirical model is not necessarily suitable for high-frequency low-profile transformers. This will be studied in depth in subsequent work. Table 2 High-frequency low-profile transformer design results Core width 25.5mm Effective volume 1260mm3 Core depth 11mm Excitation inductance 26μH Core height 6.2mm Leakage inductance 1μH Window width 8.65mm Copper loss 1.256W Window height 2.1mm Iron loss 1.782W Conductor thickness 0.1mm Efficiency 98.5% 3.3 Further discussion of factors affecting core volume In order to obtain a more satisfactory high-frequency low-profile transformer design, it is necessary to have a deep understanding of the factors affecting transformer performance and their degree of influence. In view of this, the author used the above design procedure to further study the relationship between core volume, core height, frequency, efficiency, etc. The converter topology used is the same as that introduced in Section 2.3, and the transformer winding turns ratio is 6:2. When the primary winding is sandwiched between two parallel secondary windings, the relationship between the minimum transformer core volume and frequency is shown in Figure 15. The volume of the core decreases significantly with the increase of frequency at first, and after reaching the minimum value, it increases with the increase of frequency. The greater the output power, the faster the increase. There are two reasons why the volume of the core increases with the increase of frequency. First, when the frequency increases, the skin effect becomes more severe. Therefore, in order to achieve the same efficiency, the width of the conductor is required to be widened to reduce the high-frequency loss, which increases the lateral size of the core and the volume. On the other hand, the core loss is related to the frequency and the core size. The higher the frequency, the smaller the size, and the greater the loss. Therefore, when the frequency increases, in order to keep the loss unchanged, the size of the core must be increased, and the volume naturally increases. Figure 15 shows the relationship between the minimum volume of the transformer core and the frequency. Figure 16 shows the minimum volume and efficiency curve of the transformer. Obviously, the transformer with high efficiency is also large in volume, but the two are not linearly related. As can be seen from the figure, the efficiency of the transformer is not the greater the better, because when the efficiency is very high, the volume increases rapidly, and the most suitable efficiency should be taken at the knee of the curve. For a transformer with an output power of 100W, an efficiency of 98.5% is more appropriate. When there are many conductor layers, the thickness of the conductor does not take a skin depth or a larger value to improve efficiency and reduce the volume of the core. In fact, when a skin depth is taken as the thickness of the conductor, not only is the volume of the core larger than when the conductor thickness takes the optimized value (the conductor optimized thickness is determined by the optimization program), but the core height is also larger, as shown in Figures 17 and 18. Because when there are many conductor layers, the loss of the winding will be more severe due to the leakage magnetic effect. Only by reducing the thickness of the conductor and increasing its lateral size can the copper loss be guaranteed not to be too high, so the volume of the core also increases. 4 Conclusion This paper introduces the design and production method of low-profile high-frequency magnetic component windings, and gives a new winding design and production scheme. The specific design and test results show that the use of magnetic components with this new type of winding in switching power supplies not only has low power consumption and temperature rise (<50℃), but also reduces the volume and height of the entire power module. The new winding design and production method can also greatly save copper materials, so it is very practical. This paper also gives the optimization design of the transformer used in high-frequency switching power supplies. Unlike traditional design methods, this design algorithm takes into account the impact of high frequency on copper loss and iron loss, and can easily adjust the design parameters of the transformer, such as height, bottom area, etc., as needed. Ultimately, it gives the structure of the minimum magnetic core with the minimum effective volume and parameters such as the thickness of the winding conductor, which can be used in specific designs. In addition, the design program was also used to further study the relationship between the core volume, core height, frequency and efficiency. Figure 16 Relationship between the minimum core volume and efficiency of the transformerFigure 17 Comparison of the minimum core volume and frequency curves of the transformer when the conductor thickness is fixed at a skin depth and replaced by the optimized valueFigure 18 Comparison of the core height and frequency curves of the transformer when the conductor thickness is fixed at a skin depth and replaced by the optimized value