192 5. PLANAR TRANSMISSION LINES
where q
tan ı
"
is the filling factor of the dielectric loss. is should not be confused with the
filling factors .q
"
q/ adopted for the definition of the effective dielectric constant. A good
approximation for q
tan ı
"
is given in [3] for printed lines. In these lines, the dielectric boundary
and the electric field are parallel in regions of high field, but not over the entire circuit, which
includes microstrip lines, as:
q
tan ı
"
D
"
r
"
reff
q
"
: (5.26a)
e filling factor .q
"
D q/ for a multilayer structure is related to the equivalent dielec-
tric constant ."
req
! "
r
/ and its corresponding effective value ."
reff
/ through Eq. (5.18). us,
substituting Eq.(5.18) in (5.26a) yields:
q
"
D q D
"
reff
1
=
"
reff
1
(5.26b)
and
q
tan ı
"
D
"
r
"
reff
"
reff
1
"
r
1
D
1 .1="
reff
/
1 .1="
r
/
: (5.26c)
Equations (5.25) and (5.26b) can be used through this chapter for the estimation of an
effective dielectric loss tangent and, through that, the associated attenuation constant .˛
d
/. Since
a quasi TEM mode can be treated as an ordinary TEM mode propagating in a transmission line
with a dielectric constant ."
reff
/, the .˛
d
/ can be readily adapted from this propagation mode,
e.g., Pozar [1]:
˛
d
D
k tan ı
";eff
2
D
k
0
p
"
reff
tan ı
";eff
2
; (5.27)
where k
0
is the free-space wavenumber.
5.9 COPLANAR TRANSMISSION LINES
e coplanar transmission lines are composed of strip conductors printed on the same plane, usu-
ally on the top surface of a dielectric substrate. eir established representatives are the coplanar
waveguide (CPW), the Slotline, and the coplanar strip (CPS). All three of them offer a con-
venient shunt connection of microwave components, while CPW and CPS support both series
and shunt connections.
Slotlines can be realized by etching a longitudinal slot (or the entire slotline circuit) on
the metalized surface of a dielectric substrate, while its opposite side is left free (unmetallized).
Its most interesting application refers to the hybrid microstrip-slotline circuits, where the slot-
line circuit is etched on the ground plane of the microstrip. In this manner, high characteristic
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