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X T
April 1999
The functions to calculate the voltage on C1 and C2 after some time (t), with an applied current (I), with initial voltages on the
capacitors (V10 and V20, respectively):
v 1 t , V10, V20, I
C 1.
V1 0
C1
V2 0
C2
+ C 1.C 2 . V10
t
I.R.C 2 .e R .C s ...
C1 C2 2
V20 I.R C 1 C 2 .I.t
C1 C2 2
C
2
2
.V1
0
C
2
1
.V2
0
v 2 t , V10, V20, I
C 2.
V2 0
C1
V1 0
C2
t
I.R.C 2 .e R .C s ...
C1 C2 2
+ C 1.C 2. V10 V20
C1
C 2 .I.t
C
2
2
.V1
0
C1 C2 2
C
2
1
.V2
0
I
.C
2
2
.R
The function used to compute the area under the loop filter voltage curve (this will be used twice: once for the time the charge
pump is on and a second time when it is off):
a t , V10, V20, I
1 . 2.C s .R.C 2. V10 V20 . C 1 C 2
2
C1 C2 2
t
I.R.C 2 .e R .C s ...
+ 1 . t . t .I. C 1 C 2
2.C 1.C 2. V10 V20
2.C
2
2
.
V1 0
I.R
2
C1 C2 2
+ R.C s .C 2.
V2 0
V10 . C 1 C 2
C1 C2 2
I.R.C 2
2.C
2
1
.V2
0
..
sgn ( x) if( x<0, 1, 1)
4.5.99
,62
24