MCP3909-I/SS Microchip Technology, MCP3909-I/SS Datasheet - Page 84

• 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
C.4
DS51723A-page 84
MEASURING THE VOLTAGE/CURRENT RMS VALUE AND POWER USING
QUASI-SYNCHRONOUS SAMPLING ALGORITHM
From Equation C-11, a periodic voltage can be expressed as:
EQUATION C-25:
So the voltage fundamental and the voltage of each harmonic can be expressed as:
EQUATION C-26:
From Equation C-25, the fundamental voltage and voltage of each harmonic can also
be expressed as:
EQUATION C-27:
Where:
EQUATION C-28:
EQUATION C-29:
The voltage RMS value of each harmonic, then can be expressed as shown in
Equation C-31 with its initial phase angle shown in Equation C-29.
EQUATION C-30:
U t ( )
U
=
k
t ( )
U a0
---------- -
2
U
U
=
+
k
k
t ( )
u
k
=
∑
ak
∞
=
u
=
ck
1
------ - u
cos
ϕ
1
(
2
u ak
uk
u
=
⋅
(
ck
k
=
cos
sin
ck
⋅
u
ω
=
atan
ak
(
(
k
⋅
k
2
t
⋅
⋅
)
ω
+
u
--------------------------- -
ω
u
-------
u
+
ak
⋅
u
ak
bk
⋅
t
u
bk
2
)
t
k
+
+
+
2
2
sin
u bk
u
ϕ
bk
(
uk
k
sin
2
)
⋅
ω
(
k
© 2009 Microchip Technology Inc.
⋅
⋅
t
ω
)
⋅
t
)
)