一种电流密度均匀分布的平面变压器绕线宽度优化方法  

A Winding Width Optimization Method for Planar Transformer with Uniform Distribution of Current Density

作　　者：安少亮[1] 吴庆 王博彦 徐义轩 吴红飞[2] An Shaoliang;Wu qing;Wang Boyan;Xu Yixuan;Wu Hongfei(School of Electrical Engineering Xi’an University of Technology,Xi’an 710000 China;College of Automation Engineering Nanjing University of Aeronautics and Astronautics,Nanjing 211106 China)

机构地区：[1]西安理工大学电气工程学院,西安710000 [2]南京航空航天大学自动化学院,南京211106

出　　处：《电工技术学报》2025年第6期1816-1827,共12页Transactions of China Electrotechnical Society

摘　　要：针对平面变压器印制电路板(PCB)绕组每层绕线温度分布不均与损耗大的问题,该文提出一种电流密度均匀分布的平面变压器绕线宽度优化方法。首先,详细讨论了PCB绕组电流密度有效值的时不变性与计算方法,分析了交直流电阻的数学关系。然后,推导了环形绕组直流电阻的表达式,利用数学归纳法详细证明了电流密度分布均匀时环形绕组内外径之比的约束条件,并给出了考虑绕组间隙的绕组宽度修正公式,揭示了电流密度有效值与绕组损耗同时最优的内在联系。最后,基于六路绕组输出反激变换器的标准型号磁心,采用两种绕组宽度排布方法对变压器的电流密度、绕组损耗和发热情况进行对比分析,通过有限元仿真与实验验证了所提的绕组电流密度分布均匀时PCB绕组宽度设计方法的正确性与普适性。In recent years,with the continuous expansion of the market demand for consumer electronic products,various types of small and medium-power switch-mode power supplies have emerged.Particularly in modern small-power switch-mode power supplies,topologies represented by flyback converters play a crucial role in practical applications.In such power systems,the transformer,as one of the core components,significantly affects the overall system efficiency and power density.Planar transformers have attracted considerable attention due to their low height and leakage inductance characteristics.When the transformer operates under high-frequency conditions,the skin effect and proximity effect prevent the current from distributing uniformly across its cross-section.In flyback converters,the primary winding has a large number of turns,and the intensified proximity effect further exacerbates the uneven distribution of current density in each winding,concurrently reducing the efficiency of the transformer.This paper proposes a winding-width optimization method for planar transformers to achieve uniform distribution of current density.First,a quantitative method for measuring the current density of windings is discussed.The root mean square(RMS)value of the winding current density within a single switching cycle is time-invariant,which leads to the use of Ohm's Law to calculate its RMS value.Subsequently,through theoretical analysis,it is determined that when the operating conditions of the transformer are constant,the main factors affecting the winding current density are its geometric parameters.The constraints on the inner and outer diameters of the winding are derived to achieve the most uniform current density distribution.Considering the inevitable presence of winding clearances in practical engineering,the formula is adjusted to calculate the optimal inner-to-outer diameter ratio.Furthermore,an in-depth analysis explores the inherent relationship between winding current density distribution and winding losses.A comparison

关 键 词：平面变压器 绕组内外径等比 电流密度 数学归纳法 

分 类 号：TM46[电气工程—电器]