Digital Signal Processing Reference
In-Depth Information
4
3
2
1
0
0.01
0.1
1
10
100
R
T
/R
A
A
s
A
e
Figure 4.65
Graph of the relative effective aperture
A
e
and the relative scatter aperture
σ
in
relation to the ratio of the resistances
R
A
and
R
r
.Where
R
T
/R
A
=
1 the antenna is operated
using power matching (
R
T
=
R
r
). The case
R
T
/R
A
=
0 represents a short-circuit at the terminals
of the antenna
to calculate the reflected power
P
S
of an antenna (see Section 4.2.4.1) we need the
absolute value for
A
S
.The
effective aperture A
e
of an antenna is proportional to its
gain
G
(Kraus, 1988; Meinke and Gundlach, 1992). Since the gain is known for most
antenna designs, the effective aperture
A
e
, and thus also the scatter aperture
A
S
,is
simple to calculate for the case of matching
(Z
A
=
Z
T
)
. The following is true
5
:
λ
0
4
π
·
G
σ
=
A
e
=
(
4
.
86
)
From equation (4.75) it thus follows that:
λ
0
P
e
=
A
e
·
S
=
4
π
·
G
·
S
(
4
.
87
)
4.2.5.5 Effective length
As we have seen, a voltage
U
0
is induced in the antenna by an electromagnetic field.
The voltage
U
0
is proportional to the electric field strength
E
of the incoming wave.
5
The derivation of this relationship is not important for the understanding of RFID systems, but can be
found in Kraus (1988, chapter 2 - 22) if required.
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