Page 477 - Engineering Electromagnetics, 8th Edition

CHAPTER 13 Guided Waves 459

D13.2. The dimensions of a coaxial transmission line are a = 4 mm, b =
17.5 mm, and c = 20 mm. The conductivity of the inner and outer conductors
7

is 2 × 10 S/m, and the dielectric properties are µ r = 1, = 3, and σ/ω =
r
0.025. Assume that the loss tangent is constant with frequency. Determine:
(a) L, C, R, G, and Z 0 at 150 MHz; (b) L and R at 60 Hz.
Ans. 0.30 µH/m, 113 pF/m, 0.27 /m, 2.7 mS/m, 51 ; 0.36 µH/m, 1.16 m /m

13.1.4 Two-Wire (High Frequencies)
For the two-wire transmission line of Figure 13.4 with conductors of radius a and
conductivity σ c with center-to-center separation d in a medium of permeability µ,
permittivity , and conductivity σ c , the capacitance per unit length is found using the

results of Section 6.4:
π
C = −1 (20)
cosh (d/2a)
or
. π
C = (a d)
ln(d/a)
The external inductance may be found from L ext C = µ .Itis

µ −1
L ext = cosh (d/2a) (21)
π
or
. µ
L ext = ln(d/a) (a d)
π
The conductance per unit length may be written immediately from an inspection of
the capacitance expression, and using the relation RC = /σ:
πσ
G = (22)
−1
cosh (d/2a)
The resistance per unit length is twice that of the center conductor of the coax,
1
R = (23)
πaδσ c

Figure 13.4 The geometry of the
two-wire transmission line.