The Characteristic Impedance of Trough and Slab Lines
The Characteristic Impedance of Trough and Slab Lines
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槽式和板式线路的特性阻抗
DOI：
10.1109/tmtt.1956.1125045
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发表时间：
1956
影响因子：
4.3
通讯作者：
R. Chisholm
中科院分区：
文献类型：
--
作者：
R. Chisholm
用变分法推导了由一个圆柱体组成的“槽线”的特征阻抗表达式，该圆柱体安装在与槽壁平行的半无限矩形槽内。“平板线”由无限个平行板之间的圆柱体组成，被视为槽线的一种特殊情况，其中槽的底部被认为与圆柱体无限远。该解决方案并不局限于安装在槽平行壁之间正好一半的圆柱体；对于给定的特性阻抗允许误差，给出了一个简单的公式来计算必须放在中心导体“定心”上的公差。特性阻抗的表达式为三项之和。第一个是“零阶”对数项，第二个是“二阶”修正项，当中心导体变得无限小时，它就消失了，第三个是“偏离中心”修正项，当圆柱体不在槽平行壁之间的正中间时，它就出现了。当特性阻抗为50欧姆时，二阶校正项约为0.3欧姆。用同样的方法进行四阶近似，会使其改变约0.001欧姆。
A variational method is used to develop an expression for the characteristic impedance of a "trough line" consisting of a circular cylinder mounted inside and parallel to the walls of a semi-infinate rectangular trough. The "slab line" consisting of a circular cylinder between infinite, parallel plates is treated as a special case of the trough line in which the bottom of the trough is taken to be infinitely remote from the circular cylinder. The solution has not been restricted to cylinders that are mounted exactly half way between the parallel walls of the trough; a simple formula is presented for calculating the tolerances which must be placed on the "centering" of the center conductor for a given allowable error in the characteristic impedance. The expression for the characteristic impedance is presented as the sum of three terms. The first is a "zero order" logarithmic term, the second a "second order" correction term which vanishes as the center conductor becomes infinitely small, and the third is an "off-center" correction term which arises when the cylinder is not exactly half way between the parallel walls of the trough. The second order correction term amounts to about 0.3 ohms when the characteristic impedance is of the order of 50 ohms. A fourth order approximation using the same method changes this by about 0.001 ohm.