MCP3909RD-3PH1 Microchip Technology, MCP3909RD-3PH1 Datasheet - Page 82

• 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
C.3
DS51723A-page 82
THE HARMONIC ANALYSIS ALGORITHM OF QUASI-SYNCHRONOUS
SAMPLING
Periodic signal can be expressed as trigonometric Fourier series or exponential Fourier
series. A periodic signal with a period of T can be expressed as :
EQUATION C-11:
where:
EQUATION C-12:
EQUATION C-13:
or as:
EQUATION C-14:
where the relationship between a
EQUATION C-15:
EQUATION C-16:
EQUATION C-17:
f t ( )
=
f t ( )
α
------ -
2
0
+
a
=
k
k
b
∑
k
∞
=
a
=
k
0
=
, b
1
+
-- -
T
(
2
α
-- -
T
2
k
c
k
⋅
a
k
ϕ
∑
， c
k
T
∫
0
∞
=
⋅
k
cos
k
f t ( )
T
∫
0
=
1
=
f t ( )
=
c
(
k
k
k
c
⋅
sin
and ϕ
atan
⋅
a
k
cos
⋅
ω
2
k
sin
sin
(
+
⋅
k
t
(
a
---- -
b
ϕ
)
k
(
⋅
b
k
k
k
k
+
ω
k
2
k
⋅
⋅
ω
is:
β
⋅
ω
cos
t
⋅
⋅
+
t
)dt
t
(
)
ϕ
k
dt
k
⋅
)
ω
⋅
© 2009 Microchip Technology Inc.
t
)
)