A high performance 50
coaxial line is to be used, however little is known about its
performance. Basic measurements of the cable are made and it is discovered to have an
outer shield diameter of 30 mm, and a wall thickness of 3 mm where the inner conductor
is unable to be measured accurately at this time. All conductors are known to be copper,
and the cable is known to be filled with PTFE dielectric having a relative permittivity of
2.1 and a loss tangent of 0.0003. (The conductivity of copper is 5.8 × 107 Siemens per m).
Part (I) — 15 Marks
If this line is used in its ‘high frequency’ range, calculate;
(a) The diameter of the inner conductor;
(b) the inductance per unit length of line;
(c) the capacitance per unit length of line; and
(d) the signal velocity relative to the speed of light (velocity factor).
Part (II) — 25 Marks
This cable is to be used in equipment at a frequency of 620 MHz, hence calculate:
(e) The resistance per unit length of the conductors;
(f) the conductance per unit length between the conductors;
(g) the signal attenuation in both decibels and Nepers per metre; and
(h) the value of the complex propagation coefficient.
Part (III) — 10 Marks
If the line is terminated by a copper plate soldered across the ends of the conductors;
(i) Find the length of line which will give the maximum value of impedance at the input
end (at the operating frequency of 620 MHz);
(j) estimate the approximate value of this input impedance; and
(k) explain and discuss your assumptions.
. . . / 7
Fields and Waves Numerical Transmission Line Assignment Page 7
QUESTION 2 — 50 Marks
A 790 m. length of 50 Hz power transmission line is represented by a symmetrical ‘nominal-’
equivalent circuit. The series impedance Z consists of a resistance of 12.30
in series with
an inductance of 1.49 mH, and the parallel branches at each end consist of 1.8 nF capacitors.
Part (I) — 20 Marks
(a) The values of the four distributed parameters R, L, G, and C; and
(b) the approximate frequency beyond which this representation of the line would no longer
Part (III) — 30 Marks
For switching communications purposes it is intended to propagate a (carrier) wave of peak
amplitude 16 volts and frequency 170 kHz down a line of this type. Hence:
(c) Determine the propagation coefficient, stating the value of the attenuation coefficient
in Nepers/m, and the phase coefficient in radians/m.
(d) Determine the velocity of propagation.