DSPIC33FJ128GP706A-E/MR Microchip Technology, DSPIC33FJ128GP706A-E/MR Datasheet - Page 84

• Manufacturer Part Number: DSPIC33FJ128GP706A-E/MR
• Description: 16 Bit MCU/DSP 40MIPS 128KB FLASH 64 QFN 9x9x0.9mm TUBE
• Manufacturer: Microchip Technology
• Series: dsPIC™ 33Fr

Specifications of DSPIC33FJ128GP706A-E/MR

• Core Processor: dsPIC
• Core Size: 16-Bit
• Speed: 40 MIPs
• Connectivity: CAN, I²C, IrDA, LIN, SPI, UART/USART
• Peripherals: AC'97, Brown-out Detect/Reset, DMA, I²S, POR, PWM, WDT
• Number Of I /o: 53
• Program Memory Size: 128KB (128K x 8)
• Program Memory Type: FLASH
• Ram Size: 16K x 8
• Voltage - Supply (vcc/vdd): 3 V ~ 3.6 V
• Data Converters: A/D 18x10b/12b
• Oscillator Type: Internal
• Operating Temperature: -40°C ~ 125°C
• Package / Case: 64-VFQFN, Exposed Pad
• Lead Free Status / RoHS Status: Lead free / RoHS Compliant
• Eeprom Size: -
• 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
)
)