Page 206 - Satellite Communications, Fourth Edition

186 Chapter Six

and control electrode provides the RF coupling between input and
output. Thus, this is basically a contactless switch.
As mentioned earlier, it is also possible to alter the phase shift by alter-
ing the propagation coefficient. By definition, a sinusoidal electromag-
netic wave experiences a phase change of 2 rad over distance of one
wavelength l, and therefore the phase change coefficient can be writ-
ten simply as

2
(6.45)
l
This will be in radians per meter with l in meters. As noted earlier, the
connection between wavelength l, frequency f, and phase velocity v p is
lf v p . It is also known that the phase velocity on a transmission line
c/2e , where c is
having a dielectric of relative permittivity r is v p r
the free space velocity of light. Substituting these relationships in Eq.
(6.43) gives:

2 f 2e r
l (6.46)
c
This shows that, for a fixed length of line, a phase change can be
obtained by changing the frequency f or by changing the relative per-
mittivity (dielectric constant) e . In one scheme (Nishio et al., 2004) a
r .
method is given for phasing a base station antenna array by means of
frequency change. The modulated subcarrier is fed in parallel to a
number of heterodyne frequency mixers. A common local oscillator (LO)
signal is fed to each mixer to change the subcarrier up to the assigned
carrier frequency, the output from each mixer feeding its own element
in the antenna array. The phase change is introduced into the LO cir-
cuit by having a different, fixed length of line in each branch of the LO
feed to the mixers. Thus the output from each mixer will have its own
fixed phase angle, determined by the phase shift in the oscillator
branch.
Phase change can also be effected by changing the relative permit-
tivity of a delay line. Efforts in this direction have concentrated on
using ferroelectric material as a dielectric substrate for the delay line.
Whereas the dielectric constant of a printed circuit board may range
from about 2 to 10, ferroelectrics have dielectric constants measured
in terms of several hundreds. The ferroelectric dielectric constant can
be changed by application of an electric field, which may be in the
order of 2000 kV/m. Thus to keep the applied voltage to reasonable
levels, a thin dielectric is needed. For example, for a dielectric thick-
ness of 0.15 mm and an electric field of 2000 kV/m the applied voltage