Practical_Antenna_Handbook_0071639586

C h a p t e r 4 : T r a n s m i s s i o n L i n e s a n d I m p e d a n c e M a t c h i n g 117
where Z 0 = characteristic impedance, in ohms
ε = dielectric constant of insulator between conductors
S = center-to-center spacing of conductors
d = diameter of (identical) conductors
(b) Coaxial line:
Z 0
⎛ D ⎞
= 138 log ⎜ ⎟
(4.8)
ε ⎝ d ⎠
where D = diameter of inside surface of outer conductor
d = diameter of inner conductor
(c) Shielded parallel line:
where A = s/d
B = s/D
(d) Stripline:
Z0
⎛
= 276 log ε ⎜
2A
⎝
2
( 1– B )
2
( 1 + B )
⎞
⎟
⎠
(4.9)
Z 0
= 377 εt
⎛ T ⎞
⎜ ⎟
⎝W
⎠
(4.10)
where ε t = relative dielectric constant of printed wiring board (PWB)
T = thickness of PWB
W = width of stripline conductor
The relative dielectric constant e t used here differs from the normal dielectric constant
of the material used in the PWB. The relative and normal dielectric constants
move closer together for larger values of the ratio W/T.
Example 4.2 A stripline transmission line is built on a 4-mm-thick printed wiring board
that has a relative dielectric constant of 5.5. Calculate the characteristic impedance of
the stripline if the width of the strip is 2 mm.
Solution
Z
0
377 ⎛ T ⎞
= ⎜ ⎟ ε ⎝W
⎠
t
377 ⎛ 4
= ⎜
⎞ 5.5 ⎝2
⎠ ⎟
377
= (
2.35 2 )
= 321 Ω