高频单导体传输线模型及其乘积积分算法

低频情况下,可以使用经典传输线方程(电报方程)计算传输线网络沿线及负载上的电压和电流,由于采用了准TEM模近似,故经典传输线方程在处理更高频情况下的传输线问题时就不再适用.本文基于麦克斯韦方程和电磁散射理论,建立了高频单导体传输线方程,对该方程做低频近似即可得到经典方程;采用乘积积分方法对该高频方程进行数学变换,使其具有和经典方程类似的方程形式;根据边界条件和乘积积分解法最终计算出传输线沿线电流和电位分布.若干仿真算例证实,该模型及其方法可以给出和全波分析方法一致的计算结果,为精确分析高频传输线问题提供了全波分析之外的另一种途径.

High-frequency single-conductor transmission line model and its productintegral algorithm

At low frequencies, the classic transmission line equation (telegraph equation) is often applied to calculating the voltage and current along a line and load. Due to applying of the quasi TEM mode approximation, the classic transmission line equation is not available for transmission line problems at higher frequencies. Based on Maxwell's equations and electromagnetic scattering theory, the high frequency single conductor transmission line equation is established. The classic equations are obtained by employing low frequency approximation. Adopting the mathematical transformation of product integral method to the high frequency equation, it has the similar form of the classic transmission line equations. The current and potential distribution along the transmission line are obtained by combining boundary conditions and product integral solution. Simulations of the modal and method have a good agreement with full wave analysis method by a few examples. The study provides another way for accurate analysis of high frequency transmission line problems besides the full wave analysis.