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J. A. Stratton于1941年在其名著《Electromagnetic Theory》中写道:“没有一般方法可用来求圆波导特征方程的根”。他写下这句话时,电子计算机尚未发明。对于由J. R. Carson、S. P. Mead、S. A. Schelkunoff最先导出的特征方程,用电子计算机作数值解的工作,已有美国人(1969年)和日本人(1981年)做过,但前者是针对介质圆管波导,后者虽是针对金属管波导但却引入了一些近似条件。本文在更为严格的条件下用Newton—Raphson法解了圆波导特征方程(HE_(11)模)。软件程序可用以计算全频域的传播常数(包括实部和虚部)。此外,讨论了波导内填充介质时对传播常数的影响。
J. A. Stratton wrote in his famous book “Electromagnetic Theory” in 1941: “There is no general method that can be used to find the root of a circular waveguide characteristic equation.” When he wrote this sentence, the computer had not been invented yet. For the eigenvalue equations first derived by JR Carson, SP Mead, and SA Schelkunoff, the numerical solution using a computer has been done by the Americans (1969) and the Japanese (1981) Tube waveguide, the latter although for the metal tube waveguide but introduced some approximate conditions. In this paper, the Newton-Raphson method is used to solve the circular waveguide characteristic equation (HE_ (11) mode) under more stringent conditions. Software programs can be used to calculate propagation constants (including real and imaginary parts) in the full frequency range. In addition, the influence on the propagation constant in the waveguide filled media is discussed.