Section 7.5 · Further exercises · 1 of 5
Exercise 7.5.1: Identifying a cable from two measurements
Five further exercises on the coaxial line, in the spirit of Problems 7.5.1–7.5.3, the worked example and the home exercise, graded from easy to harder. They use only the results listed at the head of this subsection. (Five more, on the circular guide, close Section 7.4.)
Identifying a cable from two measurements
#An unmarked m coil of coaxial cable with a solid dielectric is found in a laboratory. With the far end open, a capacitance meter at kHz reads nF. A time-domain reflectometer sees the echo from the open end ns after the launched step. The inner conductor has a diameter of mm. (a) Find the velocity, the relative permittivity and a likely material. (b) Find , and . (c) Find and the inner diameter of the outer conductor. (d) Up to which frequency is the cable single-mode?
The echo has travelled the cable twice. The capacitance per unit length and the velocity together give without any knowledge of the geometry, because and combine into .
One-way delay ns: m/s, : solid polyethylene.
pF/m and
, and mm.
mm: GHz.
From the geometry, pF/m and nH/m: the two measurements are consistent with a homogeneous filling.
These are the dimensions of an RG-58 type cable. The kHz capacitance is the static value, valid because the cable ( m) is far shorter than the wavelength ( km). The exact TE root is GHz, about above the estimate, and long before that the loss (about dB/m at GHz, Worked example 7.5.1) sets the practical limit.
cf. Problem 7.5.2