Transient analysis of coaxial cables using the skin effect approximationA+Bsqrt{s}

The purpose of this paper is to demonstrate the utility of the function
A +B \sqrt{s}
for approximating the coaxial line series impedance (skin effect) in applications to transient analysis. The time domain response expansions of Holt are modified in terms of two adjustable parameters which replace the physical parameters
R
and
K
. The modified expansions are truncated to yield condensed expressions useful for analysis and design. Two types of terminations are considered: 1) nonreflective, terminated in the characteristic impedance
Z_{0}(s)
, and 2) doubly reflective, sending and receiving ends each terminated in the nominal characteristic impedance
R_{0} = \lim_{s \rightarrow \infty} Z_{0}(s) = \sqrt{L/C}
. Experimental data are presented on the frequency and time domain insertion responses of three commercial cables: RG 5B/U-68.6 m (225 ft), RG 21/U-96.8 m (317 ft), and RG 58A/U-137 m (450 ft). Theoretical and experimental time domain responses for the sending- and receiving-end voltages are compared over the time interval from the order of 10 ns to that of 10
\mu
s. It is demonstrated that the parameters
A
and
B
can be adjusted to provide functions of time which closely approximate the actual time domain response over different intervals.