Computation of Impedance and Attenuation of TEM-Lines by Finite Difference Methods

The characteristic impedance and the attenuation of transmission lines supporting TEM modes can be computed by using finite difference methods for solving the Laplace equation for the domain defined by the inner and the outer conductor. The difference equations can be solved by machine computation and the impedance and the attenuation is obtained by integrating the field gradients and the squares of field gradients over both boundaries. The case of a shielded strip transmission line is treated as a numerical example. A computation time of approximately 0.015 hour on the IBM 7094 is required for achieving an accuracy of 0.5 percent for the impedance and 2 percent for the attenuation. The finite difference method is also used for lines which are partially filled with dielectric material and it is concluded that low attenuations are obtained by placing the dielectric material in such a way that high field regions are avoided.

[1]  Parry Moon,et al.  Field Theory Handbook , 1961 .

[2]  Heinrich Weber,et al.  Die partiellen Differentialgleichungen der mathematischen Physik , 1901 .

[3]  H. E. Green.  The Numerical Solution of Some Important Transmission-Line Problems , 1965 .

[4]  S. Frankel.  Convergence rates of iterative treatments of partial differential equations , 1950 .

[5]  L. Richardson.  The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[6]  L. Richardson,et al.  On the Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1910 .

[7]  R. V. Garver,et al.  Characteristic Impedance of Rectangular Coaxial Transmission Lines , 1964 .

[8]  H. A. Wheeler.  Transmission-Line Properties of Parallel Strips Separated by a Dielectric Sheet , 1965 .

[9]  Characteristic impedance of two special forms of transmission line , 1964 .

[10]  J. W. Duncan,et al.  Characteristic Impedances of Multiconductor Strip Transmission Lines , 1965 .

[11]  W. Getsinger.  Coupled Rectangular Bars Between Parallel Plates , 1962 .

[12]  E. G. Cristal.  Coupled Circular Cylindrical Rods Between Parallel Ground Planes , 1964 .

[13]  H. Kober,et al.  Dictionary of conformal representations , 1957 .

[14]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .