中文摘要：

由于电感器的磁芯具有多值非线性以及方程难以求得有价值的数值解等原因,电感器的研发仍处于可行设计阶段。该文结合硅钢片有/无气隙状态下的极限磁滞回线,推导出平均脉冲磁导率,并用4维可视化求出能使铁心平均脉冲有效磁导率最大的气隙厚度与磁路长度的比值;从麦克斯韦（Maxwell）方程出发,以铁心截面、窗口面积和线圈匝数为自变量,分别演绎出以电感量、体积、损耗和温升等为因变量的表达式fi（Am,Aw,N）,并采用若干个因变量交集的4维可视化算法,实现了多目标诸约束条件的优化设计,提供了可供比较的设计方法分析。

英文摘要：

For a variety of reasons, such as multi-valued nonlinearity of the core and the difficulty to obtain some valuable numerical solutions of the optimization design equations, the inductor＇s research and development is often done by the feasible design so far. Based on magnetic hysteresis loops under the silicon steel＇s state with/without air-gap, this paper derives the expression of average incremental permeability and the ratio for the length of air-gap and the length of magnetic circuit to ensure maximum of the average pulse permeability using 4D visualization. Then, form Maxwell＇s equations, the paper solves the expression fi（N, Am, Aw） of each design objective like inductance, volume, loss, surface or temperature rise. In the expressions, Aw is the window area, and Ae is the core section, and N is the number of turns. Moreover, the paper realizes the optimization design based on the 4D visualization of multi-objective and provides the Comparison of results for the design.