MCP3909-I/SS Microchip Technology, MCP3909-I/SS Datasheet - Page 88

• Manufacturer Part Number: MCP3909-I/SS
• Description: IC POWER METERING-1 PHASE 24SSOP
• Manufacturer: Microchip Technology

Specifications of MCP3909-I/SS

• Package / Case: 24-SSOP (0.200", 5.30mm Width)
• Input Impedance: 390 KOhm
• Measurement Error: 0.1%
• Voltage - I/o High: 2.4V
• Voltage - I/o Low: 0.85V
• Current - Supply: 2.3mA
• Voltage - Supply: 4.5 V ~ 5.5 V
• Operating Temperature: -40°C ~ 85°C
• Mounting Type: Surface Mount
• Meter Type: Single Phase
• Operating Temperature Range: - 40 C to + 85 C
• Mounting Style: SMD/SMT
• Supply Voltage Range: 4.5V To 5.5V
• Digital Ic Case Style: SSOP
• No. Of Pins: 24
• Interface Type: Serial, SPI
• Supply Voltage Max: 5.5V
• Rohs Compliant: Yes
• Lead Free Status / RoHS Status: Lead free / RoHS Compliant
• For Use With: MCP3909EV-MCU16 - EVALUATION BOARD FOR MCP3909MCP3909RD-3PH1 - REF DESIGN MCP3909 3PH ENGY MTR
• Lead Free Status / Rohs Status: Lead free / RoHS Compliant

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