THE WORKING CHARACTERISTICS OF A RECTANGULAR AND TROUGH LINE WITH INNER CIRCULAR CYLINDRICAL CONDUCTOR

By means of elliptical functions the rectangular line with inner central conductor of circular cylindrical shape is transformed into a coaxial line with circular outer conductor and nearly circular inner conductor, then by employing a finite number of terms of circular cylindrical harnomics we can fit the boundary conditions at the outer conductor and at a finite number of points at the inner conductor, thus the problem of the rectangular line with inner central circular conductor is solved. Similarly, by means of trigonometrical functions, the trough line with central inner conductor can be handled, i.e., it is transformed into a wire of nearly circular cross-section parallel to and in front of a grounded plane, then by means of the bipolar coordinate transformation, the problem of this trough line can be solved by using a finite number of rectangular harnomics. When the distance between the axis of the inner conductor and the bottom of the trough tends to infinity, the results obtained in this paper go into that of the well-known slab line.