I- Impedance or admittance Nyquist ’s diagrams
Impedance Z and admittance Y are two inver transfer functions linked by the following very simple relation:
Y
1Z
(1)
Let us consider the electrical circuit shown in Fig. 1 corresponding to circuit #1 of the Test Box-3 [1].
Fig. 1: Voigt circuit made of three Rs and two Cs.
The experimental Nyquist diagram of the impedance Z is show in Fig. 2 [1]. Since frequency values are lost in the Nyquist diagram, it is uful to indicate the frequency of some characteristic points (top of the mi-
Fig. 2: Nyquist impedance diagram of the electrical circuit shown in Fig. 1. Arrow always indicates increasing frequencies.
Obviously the high frequency mi-circle is smaller than the low frequency mi-circle.
To highlight the high frequency part of the diagram, it is better to plot the admittance diagram instead of the impedance diagram as it is shown in Fig. 3.
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The admittance diagram in Fig. 3 shows the high frequency mi-circle better. Does the graph of the admittance contain more information than the graph of the impedance? No, the admittance diagram only prents
Fig. 3: Nyquist admittance diagram of the electrical circuit shown in Fig. 1.
II- Impedance or admittance Bode diagrams
To be convinced of that, we can plot the impedance and admittance Bode diagrams as shown in Fig. 4. Let us recall that plotting the Bode diagram of a transfer function H consists of plotting the decimal logarithm of the magnitude of H given by:
22
H) (Im H) (Re H
and the pha of H given by:
H
Re H
Im arctan
H
具体表现φ versus the decimal logarithm of frequency or radial frequency.财务专员
Application note #8
Impedance, admittance, Nyquist, Bode, Black, etc …
沙漠绿洲According to Eq. (1), it is obvious that
Z log Y
log
and
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φ
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The graphs showing magnitude and phas on Fig. 4 are symmetrical with respect to the horizontal axis. There is no more information in an admittance diagram than in an impedance diagram.
II- Impedance or admittance Black diagrams
Fig. 4: Bode impedance and admittance diagrams of the electrical circuit shown in Fig. 1.
Electricians u other reprentations, such as Black diagrams, for example, where the decimal logarithm of the magnitude is plotted versus the pha (Fig. 5).
Fig. 5: Black impedance and admittance diagrams of the electrical circuit shown in Fig. 1.
As with the Nyquist diagram, frequency values are lost in Black Adiagram. Therefore, it is uful to indicate the frequency of some characteristic points.
Reference:
[1] Bio-Logic Application Note
#9
(www.bio-logic.info )
