Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 52

1.10. The dimensions of some standard 50-W semiflexible coaxial cables are
given in the following table (dimensions in millimeters):

Outer diameter 2.20 3.58 1.19 0.58

2 b 1.68 2.98 0.94 0.42

2 a 0.51 0.92 0.29 0.13

2a

2b

The dielectric is Teflon (e c = 2.1 and tan d = 0.0001). At 915 MHz and
2.4 GHz, find the dielectric, conductive, and total loss if the conductors
are copper.

1.11. The 2.2-mm coaxial cable of problem 1.10 is terminated to muscle (as
shown in Fig. P1.11).
An approximate model of the system is shown in Figure P1.11 b , where
C f is the fringing capacitance on the left side of the z = 0 boundary and
C 0 is the open-end capacitance on the right side of the z = 0 boundary,

where the line is air terminated. The values C 0 = 0.05 pF and C f = 0.01

pF are given.
(a) Show that when the cable is terminated to the tissue, the ratio of the
real to the imaginary part of the admittance associated with the
external capacitance is the loss tangent of the medium.
(b) Calculate the input admittance and the reflection coefficient at z =

0 for f values of 915 MHz and 2.45 GHz.
(c) Calculate the input reflection coefficient seen at a source located at
the input of a 100-cm coaxial line terminated at the tissue
(d) If the source provides an available power of 10 W (50 W source
impedance), how much is the power absorbed in the tissue?

z = 0 e

e c

z

Z c = 50 W C f

C 0 e

z = 0

(a) (b)

FIGURE P1.11 Coaxial probe terminated to lossy medium with complex permittivity
e:( a ) schematic of the probe; ( b ) equivalent circuit model.