A comparison of two recently proposed formulas for end capacitance in open circuited, two wire transmission lines [and reply]

For the original article see ibid., vol. 41, no. 4, p. 666-72 (1993). In the aforementioned paper, W.J. Getsinger has provided a solution to the problem of the excess end capacitance which results from open circuit termination of a parallel, two wire transmission line. He references some earlier work by King (1955) based on a thin wire approximation to which his solution is asymptotically equivalent in the limit of a large conductor spacing to diameter ratio. In a previous paper by H. E. Green and J.D. Cashman (see ibid., vol. 34, no. 1, p. 180-82, 1986) a solution to this problem derived by the quite different procedure of fitting an empirical relationship to a set of data derived from conductivity measurements on an analogous system of conductors in an electrolytic tank was published. In a later paper, these authors used this formula to calculate a correction term in the radiation pattern of a transmission line antenna which they also confirmed by experiment (see IEEE Trans. Antenna and Propag., vol. 38, no. 4, p. 575-8, 1990). Getsinger does not reference Green and Cashman who, at the time of carrying out their work, were equally unaware of King's earlier attack on the problem. It is interesting to compare the Getsinger and Green and Cashman solutions for the light which it throws on expectations of their likely accuracy. The two solutions use different notation and require algebraic manipulation to bring them into a form for comparison. This is done in a form which conforms essentially to the notation used by Getsinger. In reply Getsinger considers that the authors of the above letter seem to have observed that the end capacitance formulas apply to quite different physical structures, and would not be expected to yield the same values. Nevertheless, he thinks the letter serves a valuable purpose in introducing for discussion a little appreciated distinction (for end capacitance considerations) between two-conductor lines, and in leading to a new and useful result: an expression for the end capacitance of a two conductor line made of thick-walled hollow tubing. >