Digital Signal Processing Reference
In-Depth Information
operating frequency of the RFID system in question.
1
The resonant frequency of the
parallel resonant circuit can be calculated using the Thomson equation:
1
2
π
√
L
2
·
C
2
f
=
(
4
.
25
)
In practice,
C
2
is made up of a parallel capacitor
C
2
and a parasitic capacitance
C
p
from the real circuit.
C
2
=
(C
2
+
C
p
)
. The required capacitance for the parallel
capacitor
C
2
is found using the Thomson equation, taking into account the parasitic
capacitance
C
p
:
1
(
2
πf )
2
L
2
−
C
p
C
2
=
(
4
.
26
)
Figure 4.13 shows the equivalent circuit diagram of a real transponder.
R
2
is the
natural resistance of the transponder coil
L
2
and the current consumption of the data
carrier (chip) is represented by the load resistor
R
L
.
If a voltage
u
Q2
=
u
i
is induced in the coil
L
2
, the following voltage
u
2
can be
measured at the data carrier load resistor
R
L
in the equivalent circuit diagram shown
in Figure 4.13:
u
Q2
1
R
L
+
jωC
2
u
2
=
(
4
.
27
)
1
+
(j ωL
2
+
R
2
)
·
We now replace the induced voltage
u
Q2
=
u
i
by the factor responsible for its
generation,
u
Q2
=
u
i
=
jωM
·
i
1
=
ω
·
k
·
√
L
1
·
L
2
·
i
1
, thus obtaining the relationship
R
2
C
2
=
C
p
+
C
′
2
M
i
1
i
2
u
2
L
1
L
2
C
p
C
′
2
R
L
u
Q2
∼
Parallel C ('tuning C')
Parasitic capacitor
Figure 4.13
Equivalent circuit diagram for magnetically coupled conductor loops. Transponder
coil
L
2
and parallel capacitor
C
2
form a parallel resonant circuit to improve the efficiency of
voltage transfer. The transponder's data carrier is represented by the grey box
1
However, in 13.56 MHz systems with anticollision procedures, the resonant frequency selected for the
transponder is often 1 - 5 MHz higher to minimise the effect of the interaction between transponders on
overall performance. This is because the overall resonant frequency of two transponders directly adjacent
to one another is always lower than the resonant frequency of a single transponder.
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