Page 30 - Antennas for Base Stations in Wireless Communications

Fundamentals of Antennas 3

of the radiation resistance (R r ) and the antenna losses (R l ). The input
impedance can then be used to determine the reflection coefficient (Γ)
and related parameters, such as voltage standing wave ratio (VSWR)
and return loss (RL), as a function of frequency as given in 1–4

Γ = Z in − Z o (1.1)
Z in + Z o
where Z is the normalizing impedance of the port. If Z is complex, the
o
o
reflection coefficient can be modified to be
Z − Z ∗
Γ = in o (1.2)
Z in + Z o
*
where Z is the conjugate of the nominal impedance. The VSWR is
o
given as
1 + Γ
VSWR = (1.3)
1 − Γ
And the return loss is defined as

Γ
RL = −20log| | (1.4)
Input impedance is usually plotted using a Smith chart. The Smith
chart is a tool that shows the reflection coefficient and the antenna’s
frequency behavior (inductive or capacitive). One would also determine
any of the antenna’s resonance frequencies. These frequencies are those
at which the input impedance is purely real; conveniently, this corre-
sponds to locations on the Smith chart where the antenna’s impedance
locus crosses the real axis.
Impedance of an antenna is complex and a function of frequency. The
impedance of the antenna can be adjusted through the design process
to be matched with the feed line and have less reflection to the source.
If that is not possible for some antennas, the impedance of the antenna
can be matched to the feed line and radio by adjusting the feed line’s
impedance, thus using the feed line as an impedance transformer.

1.1.2 Matching and Bandwidth
In some cases, the impedance is adjusted at the load by inserting a
matching transformer, matching networks composed of lumped ele-
ments such as inductors and capacitors for low-frequency applications,
or implementing such a matching circuit using transmission-line tech-
nology as a matching section for high-frequency applications where
lumped elements cannot be used.