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15
PRODUCT SPECIFICATION
RC4200
Appendix 2—Applications
Design Considerations for RMS-to-DC Circuits
Average Value
Consider V
in
= Asin
wt
. By definition,
Where T = Period
w
= 2
p
f
RMS Value
Again, consider V
IN
= Asin
w
t
Therefore, the rms value of Asin
w
t becomes:
RMS Value for Rectified Sine Waves
Consider V
in
= |A sin
w
t|, a rectified wave. To solve,
integrate of each half cycle.
Practical Consideration: |Asin
w
t| has high-order harmonics;
Asin
w
t does not. Therefore, non-ideal integrators may cause
different errors for two approaches.
Figure 14.
V
AG
V
IN
t
0
T
2
ò
=
p
T
2
=
A
V
IN
0
T
2
T
t
65-1873
V
AG
2
T
---
A
w
t
sin
t
0
T
2
ò
=
T
2A
1
w
---
w
t
cos
–
0
T
2
=
2
p
2A
p
( )
cos
–
( )
cos
+
[
]
=
Average Value of Asin
w
t is 2
p
--A
V
rms
V
AVG
1
T
---
V
IN
[
]
2
t
0
T
ò
=
=
V
rms
for Asin
w
tdt:
V
rms
1
T
---
A
2
sin
2
w
t dt
0
T
ò
=
V
rms
2
T
A
1
2
1
w
t
–
dt
0
T
ò
=
V
rms
A
2
------T
2
4
w
-1
w
t
–
0
T
=
V
rms
A
2
------T
2
=
V
rms
2
2
A
=
V
rms
A
2
=
i.e. 1
T
--- TV
in
2
dt =
0
1
T
---
A
2
sin
2
w
t dt+
Asin
w
t
–
(
)
2
dt
T
2
T
ò
0
T
2
ò
This is the same as 1
1 TA
2
sin
2
w
t t
so, |Asin
w
t|
rms
Asin
w
t
rms
=
Low Pass
Filter
a
2
b
a
2
Absolute
Value
Low Pass
Filter
V
IN
V = A V
IN2
V = V
IN
rms
65-4200-09
(a)
V
IN
V
IN
(b)
O
V
V
IN
2
Avg
V
V
0
2
---------
V
0
=
implies V
0
Avg V
IN
2
)
=
V
0
Avg V
IN
2
=