Digital Signal Processing Reference
In-Depth Information
200
|Z
1
|
arg(Z
1
)
150
100
50
0
10
6
10
7
10
7
10
7
10
7
5
×
1
×
1.5
×
2
×
2.5
×
Figure 4.48
The measurement of impedance and phase at the measuring coil permits no con-
clusion to be drawn regarding the frequency of the transponder
in the form of a line diagram it has a curved path, as shown in Figure 4.48. As the
measuring frequency rises the line diagram passes through various local maxima and
minima for the magnitude and phase of
Z
1
. The sequence of the individual maxima
and minima is always the same.
In the event of mutual inductance with a transponder the impedance
Z
1
of the
coupling coil
L
1
is made up of several individual impedances:
Z
1
=
R
1
+
jωL
1
+
Z
T
(
4
.
58
)
Apart from at the transponder resonant frequency
f
RES
,
Z
T
tends towards zero, so
Z
1
=
R
L
+
jωL
1
. The locus curve in this range is a line parallel to the imaginary
y
axis of the complex Z plane at a distance of
R
1
from it. If the measuring frequency
approaches the transponder resonant frequency this straight line becomes a circle as
a result of the influence of
Z
T
. The locus curve for this is shown in Figure 4.49.
The transponder resonant frequency corresponds with the maximum value of the real
component of
Z
1
(however this is not visible in the line diagram shown in Figure 4.48).
The appearance of the individual maxima and minima of the line diagram can also be
seen in the locus curve. A precise measurement of the transponder resonant frequency
is therefore only possible using measuring devices that permit a separate measurement
of
R
and
X
or can display a locus curve or line diagram.
4.1.12 Magnetic materials
Materials with a relative
permeability >
1 are termed ferromagnetic materials. These
materials are iron, cobalt, nickel, various alloys and ferrite.
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