rc4200 Fairchild Semiconductor, rc4200 Datasheet - Page 15

• Manufacturer Part Number: rc4200
• Description: Analog Multiplier
• Manufacturer: Fairchild Semiconductor

PRODUCT SPECIFICATION
Appendix 2—Applications
Design Considerations for RMS-to-DC Circuits
Average Value
Consider V
Where T = Period
ω = 2πf
RMS Value
Again, consider V
REV. 1.2.1 6/14/01
V
V
V
V
V
V
V
V
V
AG
AG
rms
rms
rms
rms
rms
rms
rms
=
Average Value of Asinωt is
2π
----- -
=
T
for Asinωtdt:
=
=
=
=
=
=
=
=
=
2A
------ -
∫
-- -
T
T
2
2A
------ -
2π
T
-- -
0
V
2
∫
in
-- -
T
A
------
1
A
------
A
------
A
------
V
IN
V
0
2
T
2
2
[
T
-- -
2
–
∫
2
2
2
2
AVG
= Asinωτ. By definition,
–
A
IN
0
T
0
--- -
ω
1
∫
cos
A
T
0
T
-- -
2
T
-- -
2
sin
t d
cos
2
–
IN
1
-- -
2
sin
ωt
π ( )
=
------ - sin2 ωt
4ω
–
ωt
1
= Asinωt
2
1
-- - cos 2 cos 2 ωt
2
t d
ωt dt
+
-- -
T
1
T
-- -
2
0
cos
∫
T
2
A
T
0
[
0 ( )
V
IN
]
0
T
]
2
-- - A
π
2
t d
T
dt
65-1873
t
Therefore, the rms value of Asinωt becomes:
RMS Value for Rectified Sine Waves
Consider V
integrate of each half cycle.
Practical Consideration: |Asinωt| has high-order harmonics;
Asinωt does not. Therefore, non-ideal integrators may cause
different errors for two approaches.
V
i.e.
This is the same as
so, |Asinωt|
V
Avg
implies V
1
-- -
T
(a)
(b)
rms
V
V
0
IN
IN
∫
1
-- - TV
T
=
0
T
-- -
2
∫
=
0
A
V
--------- -
V
Absolute
a
2
IN
Avg V
Value
2
------ -
0
sin
A
2
0
in
2
in
2
rms
2
=
= |A sin ωt|, a rectified wave. To solve,
dt =
ωt dt+
=
IN
V
=
Avg V
Low Pass
V
IN
2
Filter
0
Asinωt
1
-- - TA
1
∫
∫
0
a
(
b
T
T
-- -
2
2
– (
Figure 14.
IN
2
Asinωt
rms
V
sin
V
2
IN
O
)
2
2
ωt t d
Low Pass
)
Filter
2
dt
V = V
O
IN
V =
O
rms
65-4200-09
A
RC4200
VG
V
IN
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