Environmental Engineering Reference
In-Depth Information
2.776441 × 10
3
0.0025
Z
uc
(
i
)
10
3
2.097003
×
0.002
0
2
4
6
8
10
12
14
16
0.628319
15.707963
w
(
i
)
Figure 10.53 Simulation of ultra-capacitor model - magnitude of
Z
uc
(
j
w
)
versus frequency
1.5
1.442554
1
10
3
-
I
m
Z
uc
(
i
)
0.5
0.204442
0
2.05
2.1
2.15
2.2
2.25
2.3
2.35
2.4
2.087013
2.37227
R
e
Z
uc
(
i
)
10
3
Figure 10.54 Imaginary versus real part of
Z
uc
(
j
w
)
2.044416
10
4
0.0024
0
10
3
2.37227
5
10
4
Im
Z
uc
(
i
)
R
e
Z
uc
(
i
)
0.0022
0.001
2.087013
10
3
0.002
1.442554
10
3
0.0015
0
5
10
15
20
0
5
10
15
20
0.628319
w
(
i
)
15.707963
0.628319
w
(
i
)
15.707963
(a)
(b)
Figure 10.55 Real and imaginary components of
Z
uc
(
j
w
): (a) real part of
Z
uc
(
j
w
),
(b) imaginary part of
Z
uc
(
j
w
)
In Reference 40, Buller
et al
. describe a transformation of (10.69) from the
frequency domain into the time domain. The interesting contribution is that the four
characteristic frequency domain parameters are adequate to define the time domain
model of arbitrary complexity. In the time domain, the model represented by
