具有U型线圈结构的高度可调节高频开关变压器的应用与分析
Application and Analysis of Adjustable Profile High Frequrncy Switchmode Transformer Having a U- Shaped Winding Structure

一、引 言
高频（HF）变压器在大部分HF开关电源中担任重要角色。不幸的是，由于材料性能和制造工艺的限制，很多形状和尺寸使它们没有商业价值。在高频下，可选择的材料包括铁粉芯，MnZn铁氧体和NiZn铁氧体。由于要确立诸如漏感，线圈间或线圈内的电容，趋肤效应和接近效应损耗和磁芯损耗这些数字值很困难，故实用的高频变压器设计还是个问题。
使用U型线圈和多个环形磁芯元件结构的高频变压器作为RF变压器在无线电发射机中已用了二十多年。1990′s年代引入功率电子学，已经在大量的DC/DC变换器中应用，并获得较大收益。在高频应用中，该类变压器表现出许多优点，比如:高功率密度，高效益，低漏感，高度可调和低的EMI（电磁干扰）。
这篇文章叙述新开发的一种具有多个环形磁芯元件结构的可调式U型线圈变压器。实验确定了与频率相关的磁化阻抗和漏磁阻抗。最后，确定了磁通分布与磁芯和线圈中的涡流数字值。
二、 U型线圈结构的设计
可调U型线圈变压器由一个小直径U型曲折铜管和环绕铜管的几个高μ环形磁芯组成。铜管的末端焊接在印刷电路板上，如图1所示。U型铜管代表一匝初级线圈。线圈匝数取决于所需的变压比值。对铜管厚度的基本考虑是:为了达到最高额定工作频率，选择外铜管的壁厚来优化厚度。然后，增大直径来减小电流密度，和加大热交换表面积。内部线圈应该用多层线或绞合线，来减小趋肤效应的影响。

图1 具有多个环形磁芯元件的可调式U型线圈变压器的结构图
（a）水平分布结构;
（b）具有较低漏磁的垂直分布结构
三、电压比和阻抗特性
图2表示输入电压V1和输出电压V2的电压比与频率的关系曲线。结果表明:由于良好的磁性耦合，电压比等于匝数比1:1，并且在有意义的频率范围内几乎是恒定的。该变压器的耦合效率比平面磁芯结构的要高得多。在较高频率下，电压比受线圈寄生电容的影响。

图2 电压比V1/V2——频率曲线图
在小信号的情况下，用TDK PC40高频环形磁芯试验研究了铜损和磁芯损耗。采用短路试验来获得漏感L1和电阻R1。用开路试验来得到磁化电感Lm和磁化分支等效磁芯的电阻Rm。采用HP4285A（75kHz~3
0MHz）精密LCR测量仪得到所有结果。结果见表1。
实验结果表明，在100kHz~2MHz频率范围内，漏感L1与频率无关。线圈电阻R1几乎也与频率无关。实验结果也显示，磁化电感Lm与磁导率μ有关，且电阻Rm与磁芯的磁滞损耗有关，并随频率发生重大变化。使用下列公式得到等效电路磁化阻抗:
(1)
(2)
四、 磁通和涡流分布的数字分析
图3表示，当忽略线圈末端效应的影响时，在次级线圈开路条件下，磁芯的磁通密度和线圈内涡流密度分布的计算机模拟结果。使用商用软件包可以得到模拟结果。磁通密度By沿x轴分布（如图3（b）所示），结果使磁芯的使用面积比平面磁芯的好，但比罐型磁芯的差。图3（c）显示涡流分布在初级线圈的内表面和次级线圈的外表面。这种不对称的分布是近接效应的结果。可以减小这种不对称的分布。所以，可以通过加大外管（初级线圈）的直径，让外管壁厚不变，使用绞合线作次级线圈，来减小铜损。



图3 在外管线圈上带励磁的磁场分布，r1=0.9mm，h=1.1mm，r2=3.2mm，TDK-PC40(T14×3.5×7)铁氧体
五、 涡流损耗的比较
U型变压器的磁通密度和涡流分布与罐型和平面型磁芯变压器的相比较。图4表示下列三种结构的变压器最大涡流密度的比较:MET U型初级线圈和绞合线次级线圈，并且有多个环形磁芯元件结构;具有分离的初次级线圈结构PCT Ⅰ罐型磁芯;初次级线圈绞合在一起的PCTⅡ罐型磁芯;弯曲型线圈结构的PSTⅠ平面磁芯;和螺旋形成线圈结构的PSTⅡ平面磁芯。新结构的最大归一化涡流分布比罐型磁芯或平面磁芯的小50%。所以，其损耗在较高频下应该比平面罐型磁芯结构的低。

图4 归一化涡流密度的比较
六、 结 论
本文叙述了一个新开发的，具有多个环形磁芯元件结构的，可调高度U型线圈变压器。试验和数字结果表明在高频下有如下优点:低铜损、低漏磁阻抗、高功率密度、高磁性耦合。新的设计也使制造成本低，并具有高度可调。使用边界元法来研究变压器磁芯的磁通密度分布和线圈的涡流分布。可以通过次级使用绞合线;初级使用大直径的同心中空管线来优化这些分布。将来的工作将集中在进一步优化受磁芯材料和周围环境热交换性能线来优化这些分布。将来的工作将集中在进一步优化受磁芯材料和周围环境热交换性能的约束的磁性系统的设计。还有，调查研究发生在线圈末端的EMI（电磁干扰），管线线圈的屏蔽效果，初次级线圈之间的耦合，以及线圈末端损耗效应。

Abstract- This paper introduces a newly developed high frequency switchmode transformer consisting of a U-shaped winding and a multiple toroidal magnetic core element structure. The new transformer with adjustable profile structure exhibits a utilization of the core area which is better than a planar core but worse than a pot core .The coupling efficien- cy of the transformer is much higher than a planar and core structure. The numerical results for the flux density and eddy current density have been compared with those of a planar and pot core transformer structure.The maximum normalized eddy current density of the new structure is 50% less than a pot core or a planar core .The experimental results at low current excitation indicate that the copper loss is lower at high frequency (10 MHz) when using the new winding structure .The core loss is primarily due to hysteresis and increases significantly if a Mnzn based material such as TDK PC 40 is used at frequencies above 2MHz.
Index Terms - Transformer， eddy-current， flux density copper and core losses ，leakage and magnit-izing impedances.
I. Introduction
H IGH frequency (HF) transformers play an important role in most HF switching power supplies.Unfortunately they are not commercially available in a wide range of shapes and sizes due to constraints imposed by material properties and manufacturing processes. The materials of choice at high frequencies include powder cores.MnZn ferrites and NiZn ferrites.The design of transformers for use at high frequencies is also problematic due to difficulties in establishing numerical values for leakage inductance， inter and intra winding capacitance ，skin and proximity effect losses and core losses.
A high frequency transformer with a U-shaped winding and multiple toroidal core element structure has been used in radio transmitters as a RF transformer for more than two decades.It was introduced into power electronics in the early 1990Ms[1] and has since gained greater acceptance in a number of DC/DC converter application [2]. This type of transformer exhibits many advantages in high frequency applications such as high power density， high efficiency， low leakage inductance， adjustable profile and low EMI.
This paper presents a newly developed adjustable U-shaped winding transformer with multiple toroidal core element structure. The frequency-dependent magnetizing impedance and leakage impedance are determined experimentally. Finally the distribution of magnetic flux and eddy current in the magnetic core and windings are determined numerically.
II. CONFIGURATION OF U-SHAPED WINDING STRUCTURE
A adjustable U-shaped winding transformer consists of a small diameter U-shaped meandering copper tube with several high m toroidal cores placed around the copper tube.The ends of the tube are soldered onto the printed circuit board as shown in Fig. 1. The U-shaped copper tube represents a one turn primary winding. An insulated copper wire is us passed through the tube and serves as the secondary winding of the transformer.The number of turns to be used depends on the desired transformation ratio The basic consideration of the copper tube thickness is the wall thickness of the outer tube is selected to have the optimun thickness for the highest nominal operating frequency.The diameter is then increased in order to decrease the current density and to increase the heat removal surface area.Multiple wire or litz wire should be used for the inner winding so as to reduce the impact of shin effect.
III. VOLTAGE RATIO AND IMPEDANCE CHARACTERISTICS
Fig.2 shows the voltage ratio of input voltage V1 and output voltage V2 versus frequency.The result indicates that the voltage ratio equals the turn ratio 1:1 and is almost constant over the frequency range of interest due to the good magnetic coupling.The coupling efficiency of the transformer is much higher than a planar core structure.At much higher frequencies，the voltage ratio is influenced by parasitic winding capacitances.
The copper losses and core losses of a TDK PC40 highfreq-uency toroidal manetic core were experimentally investigated under small signal conditions.The leakage inductance L1 and resistance R1 were obtained by using a short circuit test.The magnetising inductance Lm and magnetizing branch equivalent core loss resistance Rm were obtained by using an open circuit test.All results were obtained using a HP4285A(75KHz-30MHz) precision LCR meter.The results ane shown in Talbe I.
The experimental results indicate a frequency independent leakage inductance L1 over the frequency range 100KHz to 2MHz.The winding resistance R1 is also almost frequency independent. The experimental results also show that the magnetizing inductance Lm ，related to permeability m ，and the resistance Rm， related to the hysteresis core losses， change significantly with frequency.The equivalent circuit magnetizing impedance can be obtained by using the following formulas:
(1)
(2)
IV.NUMERICAL ANALYSIS OF MAGNETIC FLUX AND EDDY CURRENT DISTRIBUTION
Fig.3 shows the computer simulation results for the flux density in the core and eddy-current density distribution in the windings under open-circuit conditions for second winding，when ignoring the impact of end winding effects.The operating condition results in the worst case for core loss.The simulation results were obtained by using the commercial software package [3].The flux density distribution By along x axis shown in Fig.3(b) results in a core area uitilization which is better than a planar core but worse than a pot core [4].Fig.3 (c) shows that the eddy current is distributed on the inside surface of the primary winding and the outside surface of the secondary winding.The asymmetric distribution is a consequence of the proximity effect.The asymmetry distribution can be reduced and hence copper losses reduced by increasing the diameter of the outer tube (primary winding)， by leaving the thickness of the outer wall unchanged and by using litz wire for the secondary winding.
V. COMPARISON OF EDDY-CURRENT LOSSES
The flux density and eddy current distribution for the U-shaped transformer have been compared with those of a pot core and planar core transformers [4].Fig.4 shows the comparison of maximum eddy current density for the following three types of transformers:MET U-shaped primary winding and litz wire secondary with multiple toroidal core element structure;PCT I pot core with separated primary and secondary winding structure;PCT II pot core with twisted primary and secondary winding structure;PST I planar magnetic core with meander type winding structure and PST II planar magnetic core with spiral winding structure.The maximum normalized eddy current distribution of the new structure is 50% less than that of a pot core or a planar core.Consequently its losses at higher frequencies should be lower than the planar or pot core structure.
VI.CONCLUSIONS
The paper presented a newly developed adjustable profile U-shaped winding transformer with multiple toroidal core element structure.The experimental and numerical results have demonstrated the following advantages at high operating frequencies:low copper losses，low leakge impedance，high power density，high magnetic coupling.The new design should also be less costly to manufacture and has an adjustable profile.A boundary element method was used to investigate the magnetic flux density distribution in the transformer core and eddy current distribution in the windings.These distributions can be optimized by using a litz wire secondary and a large diameter concentric hollow tubular primary winding.Future work will concentrate on further optimizing the design of the magnetic system subject to constraints imposed by the heat transfer properties of the core material and surrounding environment.Also，EMI generated at the winding terminals，shielding effects of the tube winding，coupling between primary and secondary windings and winding end loss effects will be investigated.
ACKNOWLEDGMENT
The authors wish to thank Mr.F.Wong for his assistance during the work of the computer simulation and data analysis.

REFERENCES
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