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ADE7752A Datasheet(PDF) 18 Page  Analog Devices 

ADE7752A Datasheet(HTML) 18 Page  Analog Devices 
18 / 24 page ADE7752/ADE7752A Rev. C  Page 18 of 24 DIGITALTOFREQUENCY CONVERSION After multiplication, the digital output of the lowpass filter contains the real power information of each phase. Because this LPF is not an ideal brick wall filter implementation, however, the output signal also contains attenuated components at the line frequency and its harmonics (cos(hωt), where h = 1, 2, 3, and so on). power signal. The average value of a sinusoidal signal is zero. Thus, the frequency generated by the ADE7752 is proportional to the average real power. Figure 27 shows the digitalto frequency conversion for steady load conditions, constant voltage, and current. Figure 27 As can be seen in The magnitude response of the filter is given by () 2 8 1 1   ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + = f f H (8) , the frequency output CF varies over time, even under steady load conditions. This frequency variation is primarily due to the cos(2ωt) components in the instantaneous real power signal. The output frequency on CF can be up to 160 times higher than the frequency on F1 and F2. The higher output frequency is generated by accumulating the instantaneous real power signal over a much shorter time, while converting it to a frequency. This shorter accumulation period means less averaging of the cos(2ωt) component. As a conse quence, some of this instantaneous power signal passes through the digitaltofrequency conversion. This is not a problem in the application. Where CF is used for calibration purposes, the frequency should be averaged by the frequency counter. This removes any ripple. If CF is being used to measure energy, such as in a microprocessorbased application, the CF output should also be averaged to calculate power. Because the outputs F1 and F2 operate at a much lower frequency, much more averaging of the instantaneous real power signal is carried out. The result is a greatly attenuated sinusoidal content and a virtually ripplefree frequency output. where the −3 dB cutoff frequency of the lowpass filter is 8 Hz. For a line frequency of 50 Hz, this would give an attenuation of the 2ω(100 Hz) component of approximately –22 dB. The dominating harmonic is twice the line frequency, cos(2ωt), due to the instantaneous power signal. Figure 27 shows the instantaneous real power signal at the output of the CF, which still contains a significant amount of instantaneous power information, cos (2ωt). This signal is then passed to the digitaltofrequency converter where it is integrated (accumulated) over time to produce an output frequency. This accumulation of the signal suppresses or averages out any nondc component in the instantaneous real LPF TO EXTRACT REAL POWER (DC TERM) Σ Σ MULTIPLIER LPF MULTIPLIER LPF MULTIPLIER LPF Σ DIGITALTO FREQUENCY DIGITALTO FREQUENCY F1 F2 CF VA IA VB IB VC IC CF TIME F1 ω cos(2 ωt) ATTENUATED BY LPF 2 ω FREQUENCY – RAD/S 2 V × I 0 INSTANTANEOUS REAL POWER SIGNAL (FREQUENCY DOMAIN) X X X ABS TIME Figure 27. Real PowertoFrequency Conversion 
