Digital Signal Processing Reference
In-Depth Information
90
120
60
Im in
Ω
150
30
f
RES
>
f
TX
: inductive
Z
′
T
(k
=
1)
Re in
Ω
Z
′
T
(k
=
0)
180
0
0
500
1000
Z
′
T
(k
=
1)
Z
′
T
(k
1)
=
f
RES
f
TX
: capacitive
<
210
330
240
300
270
f
RES
=
f
TX
f
RES
=
f
TX
+
3%
f
RES
=
f
TX
−
1%
Figure 4.32
The locus curve of
Z
T
(k
=
0-1
)
in the complex impedance plane as a function
of the coupling coefficient
k
is a straight line
corresponds with
f
RES
,
Z
T
(k)
remains real for all values of
k
.
4
Given a detun-
ing of the transponder resonant frequency (
f
RES
=
f
TX
), on the other hand,
Z
T
also has an inductive or capacitive component.
•
k
=
1: This case only occurs if both coils are identical in format, so that the
windings of the two coils
L
1
and
L
2
lie directly on top of each other at distance
d
=
0.
Z
T
(k)
reaches a maximum in this case. In general the following applies:
|
Z
T
(k)
max
|=|
Z
T
(K
max
)
|
.
Transponder capacitance
C
2
We will now change the value of transponder capac-
itance
C
2
, while keeping all other parameters constant. This naturally detunes the
resonant frequency
f
RES
of the transponder in relation to the transmission frequency
f
TX
of the reader. In practice, different factors may be responsible for a change in
C
2
:
•
manufacturing tolerances, leading to a static deviation from the target value;
•
a dependence of the data carrier's input capacitance on the input voltage
u
2
due to
effects in the semiconductor:
C
2
=
f(u
2
)
;
4
The low angular deviation in the locus curve in Figure 4.32 where
f
RES
=
f
TX
is therefore due to the
fact that the resonant frequency calculated according to equation (4.34) is only valid without limitations for
the undamped parallel resonant circuit. Given damping by
R
L
and
R
2
, on the other hand, there is a slight
detuning of the resonant frequency. However, this effect can be largely disregarded in practice and thus
will not be considered further here.
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