Digital Signal Processing Reference
In-Depth Information
Figure 11.19
Reader with integral antenna and matching circuit (MIFARE
-reader, reproduced
by permission of Philips Electronics N.V.)
by a suitable layout (stripline). The matching circuit is clearly visible on the inside of
the antenna coil (SMD component).
Before we can dimension the circuit, we first need to determine the impedance
Z
A
of the antenna coil for the operating frequency by measurement. It is clear that
the impedance of a real antenna coil is generated by the serial connection of the coil
inductance
L
S
with the ohmic wire resistance
RL
S
of the wire. The serial connection
from
XL
S
and
RL
S
can also be represented in the impedance level.
The function of the matching circuit is the transformation of the complex coil
impedance
Z
A
to a value of 50
real. A reactance (capacitance, inductance) in series
with the coil impedance
Z
A
shifts the total impedance
Z
in the direction of the
j
X
axis, while a parallel reactance shifts the total impedance away from the origin in a
circular path (Figure 11.20).
The values of
C
2p
and
C
2s
are dimensioned such that the resulting coil impedance
Z
A
is transformed to the values desired to achieve 50
.
The matching circuit from Figure 11.18 can be mathematically represented by
equation 11.4:
1
Z
0
=
50
=
(
11
.
4
)
1
−
jωC
2p
+
1
−
jωC
1s
+
R
Ls
+
jωL
s
From the relationship between resistance and conductance in the complex impedance
plane (Z-level), we find the following relationship for
C
2p
:
Z
0
·
R
Ls
−
R
Ls
ωZ
0
R
LS
C
2p
=
(
11
.
5
)
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