Digital Signal Processing Reference
In-Depth Information
As induced voltage
u
Q2
=
u
i
increases, the value of the shunt resistor
R
S
falls,
thus reducing the quality of the transponder resonant circuit to such a degree that the
voltage
u
2
remains constant. To calculate the value of the shunt resistor for differ-
ent variables, we refer back to equation (4.29) and introduce the parallel connection
of
R
L
and
R
S
in place of the constant load resistor
R
L
. The equation can now be
solved with respect to
R
S
. The variable voltage
u
2
is replaced by the constant voltage
u
Transp
— the desired input voltage of the data carrier — giving the following equation
for
R
S
:
1
jω
·
k
·
√
L
1
L
2
·
i
1
u
Transp
R
S
=
−
1
|
u
2-unreg
>u
Transp
(
4
.
32
)
1
R
L
−
jωC
2
−
jωL
2
+
R
2
Figure 4.18 shows the graph of voltage
u
2
when such an 'ideal' shunt regulator is
used. Voltage
u
2
initially increases in proportion with the coupling coefficient
k
.When
u
2
reaches its desired value, the value of the shunt resistor begins to fall in inverse
proportion to
k
, thus maintaining an almost constant value for voltage
u
2
.
Figure 4.19 shows the variable value of the shunt resistor
R
S
as a function of the
coupling coefficient. In this example the value range for the shunt resistor covers several
powers of ten. This can only be achieved using a semiconductor circuit, therefore
so-called
shunt
or
parallel regulators
are used in inductively coupled transponders.
These terms describe an electronic regulator circuit, the internal resistance of which
20
u
2
regulated
u
2
unregulated
15
10
5
0
0
0.05
0.1
0.15
0.2
0.25
0.3
k
Figure 4.18
Example of the path of voltage
u
2
with and without shunt regulation in the
transponder, where the coupling coefficient
k
is varied by altering the distance between transpon-
der and reader antenna. (The calculation is based upon the following parameters:
i
1
=
0
.
5A,
L
1
=
1
µ
H,
L
2
=
3
.
5
µ
H,
R
L
=
2k
,
C
2
=
1
/ω
2
L
2
)
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