Biomedical Engineering Reference
In-Depth Information
meshes. The M plot permits the agreement between an experi-
mental impedance spectrum and the corresponding fit to a series of
RC meshes to be verified in detail. In this respect, it differs from
the Bode plot, which is often almost featureless.
A plot that has been frequently adopted in the literature to dis-
play an impedance spectrum richer in features than the Bode plot
is the
Y
'/Z vs.
Y
”/Z plot, sometimes called Cole-Cole plot.
4-6
Here
Y
' and
Y
” are the in-phase and quadrature component of the elec-
trode admittance. However, this plot yields a semicircle for a se-
ries combination of a resistance and a capacitance, and not for
their parallel combination. Thus, the impedance
Z
of a RC series is
given by:
Z
R
i
/
Z
C
(5)
Noting that
Y
{
Y
'-i
Y
”=1/
Z
, rearrangement of Eq. (5) yields:
1
2
2
2
Y
"
Z
C
Z
R
C
(6a)
Z
Y
'
Z
Z
RC
Y
"
(6b)
Eliminating Z
RC
from Eqs. (6a) and (6b) we get:
2
2
2
2
2
Y
"
Y
'
Y
"
Y
"
C
Y
'
C
§
·
§
·
§
·
§
·
§
·
§
·
(7)
¨
©
¸
¹
¨
©
¸
¹
C
¨
©
¸
¹
0
o
¨
©
¸
¹
¨
©
¸
¹
¨
©
¸
¹
Z
Z
Z
Z
2
Z
2
On a Cole-Cole plot, this equation yields a semicircle of di-
ameter
C
and center of coordinates (
C
/2,0). Here too, from Eq.
(6b) it follows that Z at the maximum of the semicircle equals
1/
RC
. Strictly speaking, a Cole-Cole plot is not suitable for verify-
ing the fitting of a series of RC meshes to an experimental imped-
ance spectrum. Thus, the admittance of a single RC mesh is given
by:
1
1
Y
R
i
Z
C
o
Y
'
Z
Z
R
(8)
Y
"
Z
C
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