Image Processing Reference
In-Depth Information
where
L is the charging nip length
j(x) is the current pro
le of the bare plate current that satis
es
ð
L
1
L
j
(
x
)d
x
¼
(
:
)
1
10
3
0
When the photoconductor is moved by a distance x at a velocity v m
=
is Equation 10.2
becomes
Cv
d
V
p
1
L
j
(
x
)
d
x
¼
S
(
V
g
V
p
)
(
10
:
4
)
By rewriting Equation 10.4, we get
d
V
p
V
g
V
p
¼
S
Cv
1
L
j
(
x
)d
x
(
10
:
5
)
Integrating Equation 10.5 (the left-hand side from V
p
(0) to V
p
(L) and the right-hand
side from 0 to L), we get
V
p
(
L
)
ð
ð
L
d
V
p
V
g
V
p
¼
S
Cv
1
L
S
Cv
j
(
x
)d
x
¼
(
10
:
6
)
V
p
(
0
)
0
Therefore,
V
p
(
L
)
V
p
(
S
Cv
ln (
V
g
V
p
)
)
¼
(
10
:
7
)
0
Applying the upper and lower limits, we have
V
g
V
p
(
)
V
g
V
p
(
L
)
¼
0
S
Cv
ln
(
10
:
8
)
Solving Equation 10.8 for V
p
(L) results in
e
a
)
e
a
V
p
(
L
) ¼
V
g
(
1
) þ
V
p
(
0
(
10
:
9
)
where
V
p
(0) is the initial plate voltage
a
¼
S
Cv
This model is linear with respect to the input voltage V
g
with a constant gain of
(1
-
e
a
). Moreover, there is no dependence on the charging nip length because
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