Page 525 - Engineering Electromagnetics, 8th Edition

CHAPTER 13 Guided Waves 507

CHAPTER 13 PROBLEMS
13.1 The conductors of a coaxial transmission line are copper (σ c = 5.8 ×
7
10 S/m), and the dielectric is polyethylene ( = 2.26, σ/ω = 0.0002). If

r
the inner radius of the outer conductor is 4 mm, find the radius of the inner
conductor so that (a) Z 0 = 50 ;(b) C = 100 pF/m; (c) L = 0.2 µH/m.
A lossless line can be assumed.
13.2 Find R, L, C, and G for a coaxial cable with a = 0.25 mm, b = 2.50 mm,
7
c = 3.30 mm, r = 2.0, µ r = 1, σ c = 1.0 × 10 S/m, σ = 1.0 × 10 −5 S/m,
and f = 300 MHz.
13.3 Two aluminum-clad steel conductors are used to construct a two-wire
6
7
transmission line. Let σ Al = 3.8 × 10 S/m, σ St = 5 × 10 S/m, and
µ St = 100 µH/m. The radius of the steel wire is 0.5 in., and the aluminum
coating is 0.05 in. thick. The dielectric is air, and the center-to-center wire
separation is 4 in. Find C, L, G, and R for the line at 10 MHz.
13.4 Find R, L, C, and G for a two-wire transmission line in polyethylene at
f = 800 MHz. Assume copper conductors of radius 0.50 mm and
separation 0.80 cm. Use r = 2.26 and σ/(ω ) = 4.0 × 10 .
−4

13.5 Each conductor of a two-wire transmission line has a radius of 0.5 mm;
their center-to-center separation is 0.8 cm. Let f = 150 MHz, and assume
σ and σ c are zero. Find the dielectric constant of the insulating medium
8
if (a) Z 0 = 300 ;(b) C = 20 pF/m; (c) ν p = 2.6 × 10 m/s.
13.6 The transmission line in Fig. 6.8 is filled with polyethylene. If it were filled
with air, the capacitance would be 57.6 pF/m. Assuming that the line is
lossless, find C, L, and Z 0 .
13.7 Pertinent dimensions for the transmission line shown in Figure 13.2 are b =
3mmand d = 0.2 mm. The conductors and the dielectric are nonmagnetic.
(a)If the characteristic impedance of the line is 15 , find . Assume a

r
low-loss dielectric. (b) Assume copper conductors and operation at 2 × 10 8
rad/s. If RC = GL, determine the loss tangent of the dielectric.
13.8 A transmission line constructed from perfect conductors and an air
dielectric is to have a maximum dimension of 8 mm for its cross section.
The line is to be used at high frequencies. Specify the dimensions if it is
(a)atwo-wire line with Z 0 = 300 ;(b)a planar line with Z 0 = 15 ;
(c)a72 coax having a zero-thickness outer conductor.
13.9 A microstrip line is to be constructed using a lossless dielectric for which
= 7.0. If the line is to have a 50 characteristic impedance, determine

r
(a) r,eff ;(b) w/d.
13.10 Two microstrip lines are fabricated end-to-end on a 2-mm-thick wafer of
lithium niobate ( = 4.8). Line 1 is of 4 mm width; line 2 (unfortunately)

r