MCP3909-I/SS Microchip Technology, MCP3909-I/SS Datasheet - Page 77

• 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

© 2009 Microchip Technology Inc.
Assuming that the integral starts at β, then:
EQUATION C-5:
Likewise, as strict integration cannot be realized in the entire cycle, so:
EQUATION C-6:
Similarly, the integral value of above equation is related to β with 2π as its period, let’s
denote it as F
F
EQUATION C-7:
It can be proved that,
EQUATION C-8:
In practical applications, it is necessary to sample the continuous analog signals and
process the data obtained with discrete algorithms. The quasi-synchronous recursive
process mentioned above can be expressed as follows:
For Equation C-4, the integral interval [x
can be divided equally into n x N sections, which results in n x N + 1 sampled data,
f(x
2
(x), and a recurrence formula can be obtained as the following:
i
), (i=0,1,...,nxN), and we can iterate as follows:
2
(β). If it won't confuse people, we'll write F
f x ( )
F
f x ( )
n
=
( )
α
F
=
1
=
( )
F
α
1
---------------- -
2
n
( )
lim
Power Calculation Theory
π
–
α
≠
1
+
∞
---------------- -
2
π
Δ
F
=
0
1
n
+
, x
⋅
( )
----- -
2
(
1
α
Δ
x
0
π
+
+ n x (2π + Δ)] whose width is n x (2π + Δ)
⋅
⋅
2
(
=
(
∫
x
β
π
β
+
+
+
f x ( )
∫
β
2
Δ
2
∫
β
π
π
)
F
)
+
F
n 1
Δ
1
–
)
( )
F
α
x ( ) x d
1
( )
1
d
α
(α) and F
α
d
α
2
(β) as F
DS51723A-page 77
1
(x) and