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capacitor is defined as the ratio of the magnitude of the charge accumulated
on either of the plates divided by the potential difference across the plates.
Using the Gauss law of electrostatics, it can be shown that the capacitance
per unit length of an infinitely long coaxial cable is:

C = 2πε (3.12)
b a)
l ln( /
where a and b are the radius of the internal and external conductors, respec-
tively, and ε is the permittivity of the dielectric material sandwiched between
the conductors. (The permittivity of vacuum is approximately ε = 8.85 ×
0
10 –12 , while that of oil, polystyrene, glass, quartz, bakelite, and mica are,
respectively, 2.1, 2.6, 4.5–10, 3.8–5, 5, and 5.4-6 larger.)

In-Class Exercise

Pb. 3.18 Find the ratio of the capacitance of two coaxial cables with the
same dielectric material for, respectively: b/a = 5 and 50.

3.6.2 The Decibel Scale
In the SI units used by electrical engineers, the unit of power is the Watt.
However, in a number of applications, it is convenient to express the power
as a ratio of its value to a reference value. Because the value of this ratio can
vary over several orders of magnitude, it is often more convenient to repre-
sent this ratio on a logarithmic scale, called the decibel scale:

 P 
G[dB = 10 log   (3.13)
]
 P ref 
where the function log is the logarithm to base 10. The table below converts
the power ratio to its value in decibels (dB):

dB values
P/P ref
(10 ) (10 n)
n
4 6
2 3
1 0
0.5 –3
0.25 –6
0.1 –10
10 –3 –30

© 2001 by CRC Press LLC