Biomedical Engineering Reference
In-Depth Information
the treatment site. Another important electrical parameter in a coaxial cable
is the characteristic impedance, which is determined by the dimensions and
the dielectric material. Imperfections in the cable or connectors, or antenna
mismatch, produce power reflections that reduces the radiated power as well
as introduce hot spots in the cable itself.
Design Consideration
The first consideration in the design of a coaxial trans-
mission line is the maximum allowable outer conductor diameter, which, for
MBA application, is 0.022 in. or less. Next, the dielectric material must be
chosen with consideration of its dielectric loss and physical properties. The
optimum choice (lowest loss) dielectric is air; however, foam dielectric
materials are available that approach the dielectric constant of air. The center
conductor's diameter is then adjusted to achieve the desired impedance char-
acteristics. An optimum geometry exists for achieving minimum attenuation
in a coaxial transmission line. The
characteristic impedance
of the cable is
directly related to the geometry of the conductor's diameter.
Power Loss
Power loss in a coaxial cable is related to the attenuation con-
stant a. This constant has two components: a
c
, due to conductor loss, and a
d
,
due to dielectric losses, where a = a
c
+ a
d
. For those low-loss dielectrics used
in microwave cables, the dielectric loss is negligible (
2%) compared to the
conductor losses. For copper conductors surrounded by an insulator having a
dielectric constant e, the losses in decibels per 100 ft or in decibels per meter
can be determined from
<
0 214
.
F
ZD
1
D
d
Ê
Ë
ˆ
¯
a
=
1
+
dB 100 ft
c
0
or
(6.1)
0 023
.
F
ZD
1
D
d
Ê
Ë
ˆ
¯
a
=
1
+
dB m
c
0
where
F
is the frequency in megahertz,
D
is in inches or meters, and
a
=
=
277
0 0909
.
F
e
tan
d
dB 100 ft
dB m
d
a
.
F
e
tan
d
(6.2)
d
where
D
is the inner diameter (i.d.) of the outer conductor,
d
is the outer diam-
eter (o.d.) of the inner conductor in inches, and tan d is the dielectric loss
factor.
If the outer diameter is held constant because of mechanical size con-
straints, as is the case considered here, it can be determined from the above
expressions that [5].
1. The loss has a broad minimum at a
D/d
ratio of 3.59 for any dielectric
at any frequency.
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