Environmental Engineering Reference
In-Depth Information
Figure 10.3.1
Sinusoidal voltage perturbation and resulting sinusoidal current response, phase-shifted
by
φ
.
V
0
- amplitude of the voltage signal;
I
0
- amplitude of the current signal;
V
oc
-
open-circuit voltage;
I
oc
- open-circuit current (Andrade et al., 2010).
indicative of the capacitive and inductive character of the cell, vs the real impedance of
the cell,
Z
Real
. Nyquist plots have the advantage that activation-controlled processes
with distinct time-constants show up as unique impedance arcs and the shape of the
curve provides insight into possible mechanisms or governing phenomena. However,
this format of representing impedance data has the disadvantage that the frequency-
dependence is implicit; therefore, the AC frequency of selected data points should be
indicated. Because both data formats have their advantages, it is usually best to present
both Bode and Nyquist plots - Figure 10.3.2.
It is important to note that impedance analysis is based on the assumption that the
system under study behaves linearly. Since linear systems typically exhibit features and
properties that are much simpler than the general nonlinear cases, the analysis becomes
less complex. A system is linear if it complies with both homogeneity and additivity
principles, which state that: i) when a perturbation is imposed to a system, the response
will be proportional and of the same type as the input signal (for instance, if a tensile
strength applied to a sample increases twofold, the corresponding strain will double);
ii) if the perturbation imposed on a system consists of the weighted sum of several
signals, then, the output is simply the weighted sum of the system's responses to each
input signal. Mathematically, let us consider
y
1
(
t
) the response of a continuous time
system
x
1
(
t
) and
y
2
(
t
) the output corresponding to the input
x
2
(
t
). Then the system is
linear if:
i
)
Principle of homogeneity
: the response to
a
·
x
1
(
t
)is
a
·
y
1
(
t
)
ii
)
Principle of additivity:
the response to
x
1
(
t
)
+
x
2
(
t
)is
y
1
(
t
)
+
y
2
(
t
)
Search WWH ::
Custom Search