PRODUCT SPECIFICATION
RC4200
Therefore, the rms value of Asinωt becomes:
Appendix 2—Applications
A
Vrms = ------
Design Considerations for RMS-to-DC Circuits
Average Value
2
Consider V = Asinωτ. By definition,
in
RMS Value for Rectified Sine Waves
Consider V = |A sin ωt|, a rectified wave. To solve,
in
T
---
integrate of each half cycle.
VAG
=
2 VINdt
∫
0
1
T
---
i.e.
TVin2 dt =
∫
Where T = Period
0
ω = 2πf
T
T
1
---
T
2π
= ------
T
-2--A2sin2ωt dt+ T (–Asinωt)2dt
∫
∫
---
0
2
1
1
This is the same as TA2sin2ωt dt
--
∫
VIN
A
0
so, |Asinωt|rms = Asinωtrms
t
Practical Consideration: |Asinωt| has high-order harmonics;
Asinωt does not. Therefore, non-ideal integrators may cause
different errors for two approaches.
0
T
2
T
65-1873
T
---
2
(a)
---
VAG
=
2Asinωt dt
∫
T
Low Pass
2
0
V
IN
a
VO = VIN
rms
Filter
T
2
---
2
(b)
V
IN
2A
T
1
ω
------- ---
=
–
cos ωt
V
IN
VO
2
a
Absolute
Value
Low Pass
Filter
2
0
V
IN
VO
=
A VGVIN
b
2A
-------
2π
=
[– cos(π) + cos(0)]
65-4200-09
2
--
π
Average Value of Asinωt is
A
Figure 14.
2
RMS Value
Again, consider V = Asinωt
VIN
---------
V0
Avg
= V0
IN
T [VIN]2dt
1
T
---
Vrms
=
VAVG
=
2
∫
0
implies V0
=
Avg( V
)
IN
Vrms for Asinωtdt:
2
V0 Avg V
=
IN
T
1
T
Vrms
=
=
A2sin2ωt dt
---
∫
0
A2
------
T
1
1
T
--
-- – cos 2 cos 2 ωt dt
Vrms
∫
2
2
0
A2
------
2
1
4ω
T
0
T
------
sin2 ωt
Vrms
Vrms
Vrms
=
=
=
--- –
2
A2
T
2
------ ---
2
A2
------
2
REV. 1.2.1 6/14/01
15
FAIRCHILD [ FAIRCHILD SEMICONDUCTOR ]
