MCP3909RD-3PH1 Microchip Technology, MCP3909RD-3PH1 Datasheet - Page 88

• Manufacturer Part Number: MCP3909RD-3PH1
• Description: REF DESIGN MCP3909 3PH ENGY MTR
• Manufacturer: Microchip Technology

Specifications of MCP3909RD-3PH1

• Main Purpose: Power Management, Energy/Power Meter
• Embedded: No
• Utilized Ic / Part: MCP3909, PIC18F2520, PIC18F4550
• Primary Attributes: 3-Ph, 220 VAC, In Case, LCD, USB, GUI
• Secondary Attributes: Opto-Isolated Interface for Safety
• Operating Voltage: 220 V
• Operating Current: 5 A
• Description/function: Energy Meter
• For Use With/related Products: MCP3909
• Lead Free Status / RoHS Status: Not applicable / Not applicable

MCP3909 / dsPIC33F 3-Phase Energy Meter Reference Design
DS51723A-page 88
We get:
EQUATION C-49:
EQUATION C-50:
As Δf << f, from Equation C-49 and C-50, we have:
EQUATION C-51:
Therefore,
EQUATION C-52:
Assuming that the signal's initial phase angle measured in the 1st cycle is
the N-th is
frequency is:
EQUATION C-53:
ϕ
N
, then the difference between actual frequency and the assumed
u
a
Δ
u
f
=
ϕ
b
≈
u
2u
---------- -
1
=
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
≈
T
(
c1
ϕ
(
2u
---------- -
⎧
⎪
⎪
⎪
⎪
⎪ ⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
ϕ
N
tg
(
T
N
tg
⋅
ϕ
c1
−
(
------------------------------------------------------------------------ -
−
tg
−
N
−
f
1
2
u
---- -
u
1
2
ϕ
(
2
⋅
π
ϕ
+
(
π
a
b
−
−
u
π
u
1
3
1
f
------------------------------------------------------- -
u
u
π
1
2
2
π
a
b
⋅
≈
(
ϕ
+
⋅
Δ
⋅
a
b
⋅
−
u
u
N
)
( ,
N
1
N
cos
( ,
)
2
f
--------------------- -
cos
π
π
sin
a
b
+
)
2
)
u
+
π
u
( ),
⋅
π
b
2
⋅
⋅
⋅
b
π
)
f
(
π
)
(
sin
(
(
(
=
⋅
u
ϕ
=
( ,
ϕ
⋅
2f
2f
( ,
ϕ
( ,
f
b
, 0
u
f
u1
u1
, 0
u1
u
ϕ
(
>
( ,
b
+
+
u
( ,
b
ϕ
)
u
N
)
ϕ
)
, 0
a
>
ϕ
u1
<
a
Δ
⋅
Δ
N
−
>
u
, 0
N
sin
<
, 0
f
f
)
ϕ
a
)
)
−
) 0
u
−
) 0
u
⋅
1
⋅
⋅
>
ϕ
a
⎛
⎝
a
ϕ
sin
Δ
Δ
1
πΔ
-------- -
<
) 0
<
1
>
f
f
<
f
π
) 0
>
⎛
⎝
) 0
f
)
−
πΔ
-------- -
⎞
⎠
π
π
f
)
© 2009 Microchip Technology Inc.
)
f
⎞
⎠
ϕ
1
and in