Digital Signal Processing Reference
In-Depth Information
•
intentional variation of the capacitance of
C
2
for the purpose of data transmis-
sion (we will deal with so-called 'capacitive load modulation' in more detail in
Section 4.1.10.3).
•
detuning due to environmental influences such as metal, temperature, moisture, and
'hand capacitance' when the smart card is touched.
Figure 4.33 shows the locus curve for
Z
T
(C
2
)
in the complex impedance plane. As
expected, the locus curve obtained is the circle in the complex
Z
plane that is typical
of a parallel resonant circuit. Let us now consider the extreme values for
C
2
:
C
2
=
1
/ω
TX
L
2
: The resonant frequency of the transponder in this case precisely
corresponds with the transmission frequency of the reader (see equation (4.25)).
The current
i
2
in the transponder coil reaches a maximum at this value due to
resonance step-up and is real. Because
Z
T
∼
jωM
·
i
2
the value for impedance
Z
T
also reaches a maximum — the locus curve intersects the real axis in the complex
Z
plane. The following applies:
|
Z
T
(C
2
)
|
max
=|
Z
T
(C
2
=
1
/ω
TX
)
2
•
·
L
2
)
|
.
C
2
=
1
/ω
2
L
2
: If the capacitance
C
2
is less than or greater than
C
2
=
1
/ω
TX
L
2
then
the resonant frequency of the transponder will be detuned and will vary significantly
from the transmission frequency of the reader. The polarity of the current
i
2
in the
resonant circuit of the transponder varies when the resonant frequency is exceeded,
•
90
Im in
Ω
120
60
150
f
RES
>
f
TX
: inductive
30
180
0
0
20
40
60
Re in
Ω
210
330
f
RES
<
f
TX
: capacitive
240
300
270
k
=
6%
k
10%
k
=
20%
=
Figure 4.33
10 - 110 pF) in the complex impedance plane as
a function of the capacitance
C
2
in the transponder is a circle in the complex
Z
plane. The
diameter of the circle is proportional to
k
2
The locus curve of
Z
T
(
C
2
=
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