Digital Signal Processing Reference
In-Depth Information
If the antenna is operated using power matching, i.e.
R
T
=
R
V
and
X
T
=−
X
A
,then
the following simplification can be used:
U
0
2
4
SR
r
A
e
=
(
4
.
80
)
As can be seen from Figure 4.63 the current
I
also flows through the radiation
resistance
R
r
of the antenna. The converted power
P
S
is emitted from the antenna and it
makes no difference whether the current
I
was caused by an incoming electromagnetic
field or by supply from a transmitter. The power
P
S
emitted from the antenna, i.e. the
reflected power in the received case, can be calculated from:
P
S
=
I
2
·
R
r
(
4
.
81
)
Like the derivation for equation (4.79), for the scatter aperture
A
s
we find:
I
2
U
0
2
P
S
S
=
·
R
r
R
r
S
·
[
(R
r
+
R
V
+
R
T
)
2
·
σ
=
A
S
=
=
(
4
.
82
)
+
(X
A
+
X
T
)
2
]
S
If the antenna is again operated using power matching and is also loss-free, i.e.
R
V
=
0,
R
T
=
R
r
and
X
T
=−
X
A
, then as a simplification:
U
0
4
SR
r
σ
=
A
S
=
(
4
.
83
)
Therefore, in the case of the power matched antenna
σ
=
A
s
=
A
e
.Thismeansthat
only half of the total power drawn from the electromagnetic field is supplied to the
terminating resistor
R
T
; the other half is reflected back into space by the antenna.
The behaviour of the scatter aperture
A
s
at different values of the terminating
impedance
Z
T
is interesting. Of particular significance for RFID technology is the
limit case
Z
T
=
0. This represents a short-circuit at the terminals of the antennas.
From equation (4.82) this is found to be:
U
0
2
SR
r
=
4
A
e
|
Z
T
=
0
σ
max
=
A
S-max
=
(
4
.
84
)
The opposite limit case consists of the connection of an infinitely high-ohmic ter-
minating resistor to the antenna, i.e.
Z
T
→∞
. From equation (4.82) it is easy to see
that the scatter aperture
A
s
, just like the current
I
, tends towards zero.
σ
min
=
A
S-min
=
0
|
Z
T
→∞
(
4
.
85
)
The scatter aperture can thus take on any desired value in the range 0 - 4
A
e
at var-
ious values of the terminating impedance
Z
T
(Figure 4.65). This property of antennas
is utilised for the data transmission from transponder to reader in backscatter RFID
systems (see Section 4.2.6.6).
Equation (4.82) shows only the relationship between the scatter aperture
A
S
and
the individual resistors of the equivalent circuit from Figure 4.63. However, if we are
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