Basic Physical Principles - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 14

where c =

10 8 ms − 1 3 × is the velocity of light in free space; μ r is the relative

permeability of the transmission line medium; and ε r is the relative permittivity

of the dielectric material.

2.1.2 Bifilar Transmission Line

The configuration of this TL comprises a pair of parallel conducting wires separated
by a constant distance (Fig. 2.3). For a bifilar transmission line [25],

πε

C bif = (2.11)

ln ( 2 D / d )

= μ
π

ln 2 D
d

L bif . (2.12)

Hence, the characteristic impedance of a bifilar TL is given by

120
√ ε ln 2 D

d

Z bif = (2.13)

r

where ε r is the relative permittivity of the dielectric between the wires/rods; D is

distance between the rods; and d is the diameter of each rod.

Fig. 2.3 Schematic of a
two-wire line

2.1.3 Microstrip Line

The geometry of microstrip lines is very simple: a thin conductor and a ground
plane separated by a low-loss dielectric material. The fabrication typically relies
on printed circuit techniques. The use of a substrate with a high dielectric constant
reduces the fringing field in the air region above the conductor. Because the electric
field lines remain partially in the air and partially in the substrate, microstrip lines
do not support pure TEM mode, but a quasi-TEM mode [3]. For 0

. < / <

05 w h 1,

the characteristic impedance is given by