圆形螺旋线圈自感和分布电容的计算

Calculation of Self-inductance and Distributed Capacitance of Spiral Inductor

提出了一种计算圆形螺旋线圈自感和分布电容的方法。在元件尺寸小于波长的准静态近似情况下用 Sommerfeld类型积分计算小段平面圆弧的自感和互感 ,然后用螺旋线方程对每一小段圆弧的自感和圆弧间的互感积分 ,算得螺旋线圈的自感。计算螺旋线圈分布电容时同样先计算出两小段同心圆弧间的电容 ,然后用螺旋线方程对其积分算得螺旋线圈的总分布电容。编制了相应的程序对多种情况下的螺旋线圈自感和分布电容进行了计算 ,计算与实验结果比较 ,有较好的一致性。与经验公式相比 ,计算自感的方法有更广的适用范围和对实验结果更好的逼近。而分布电容的计算方法比其它的方法大大减少了运算量。

A method for calculating the self inductance and distributed capacitance of the spiral inductor is described.At first, integral of Sommerfeld type is used to calculate the self and mutual inductance of per unit length of the arc under the quasi static approximation which is valid when the dimensions of the spiral are small than the wavelenth, then the self inductance of the spiral is obtained by doing the intergral of the self inductance and mutual inductance of per unit are length. The similar method is used to calculate the distributed capacitance,for example,calculating the distributed capacitance of per unit length between two rings and doing the integral for the total distribution of the spiral line.The calculated results were compared with experimental data,and a good agreement was shown.Compared with the empirical formula,this method for calculating the self inductance here has a wider applicable range and higher precision can be got.And compared with other method,the computation time can be sharply reduced using this method for calculating the distributed cappacitance of the spiral line.