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AD7751ABRS Datasheet(PDF) 10 Page - Analog Devices |
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AD7751ABRS Datasheet(HTML) 10 Page - Analog Devices |
10 / 16 page REV. A AD7751 –10– THEORY OF OPERATION The two ADCs digitize the voltage and current signals from the current and voltage transducers. These ADCs are 16-bit second order sigma-delta converters with an oversampling rate of 900 kHz. This analog input structure greatly simplifies transducer interfacing by providing a wide dynamic range for direct connection to the transducer and also simplifying the antialiasing filter design. A programmable gain stage in the current channel further facili- tates easy transducer interfacing. A high-pass filter in the current channel removes any dc component from the current signal. This eliminates any inaccuracies in the real-power calculation due to offsets in the voltage or current signals—see HPF and Offset Effects section. The real-power calculation is derived from the instantaneous power signal. The instantaneous power signal is generated by a direct multiplication of the current and voltage signals. In order to extract the real-power component (i.e., the dc compo- nent) the instantaneous power signal is low-pass filtered. Figure 2 illustrates the instantaneous real-power signal and shows how the real-power information can be extracted by low-pass filtering the instantaneous power signal. This scheme correctly calculates real-power for nonsinusoidal current and voltage waveforms at all power factors. All signal processing is carried out in the digital domain for superior stability over temperature and time. LPF DIGITAL-TO- FREQUENCY F1 F2 CH1 MULTIPLIER PGA CH2 ADC V I 2 V I V I 2 p(t) = i(t) v(t) WHERE: v(t) = V cos( t) i(t) = I cos( t) p(t) = V I 2 {1+cos(2 t)} ADC TIME HPF DIGITAL-TO- FREQUENCY CF INSTANTANEOUS REAL- POWER SIGNAL INSTANTANEOUS POWER SIGNAL – p(t) Figure 2. Signal Processing Block Diagram The low frequency output of the AD7751 is generated by accumulating this real-power information. This low frequency inherently means a long accumulation time between output pulses. The output frequency is therefore proportional to the average real-power. This average real-power information can in turn be accumulated (e.g., by a counter) to generate real-energy information. Because of its high output frequency and hence shorter integration time, the CF output is proportional to the instantaneous real-power. This is useful for system calibration purposes that would take place under steady load conditions. Power Factor Considerations The method used to extract the real-power information from the instantaneous power signal (i.e., by low-pass filtering) is still valid even when the voltage and current signals are not in phase. Figure 3 displays the unity power factor condition and a DPF (Displacement Power Factor) = 0.5, i.e., current signal lagging the voltage by 60 °. If we assume the voltage and current waveforms are sinusoidal, the real-power component of the instantaneous power signal (i.e., the dc term) is given by: VI × ×° () 2 60 cos (1) This is the correct real-power calculation. INSTANTANEOUS REAL-POWER SIGNAL INSTANTANEOUS POWER SIGNAL V I 2 cos(60 ) V I 2 INSTANTANEOUS POWER SIGNAL INSTANTANEOUS REAL-POWER SIGNAL 60 CURRENT VOLTAGE CURRENT VOLTAGE 0V 0V Figure 3. DC Component of Instantaneous Power Signal Conveys Real-Power Information PF < 1 Nonsinusoidal Voltage and Current The real-power calculation method also holds true for nonsinu- soidal current and voltage waveforms. All voltage and current waveforms in practical applications will have some harmonic content. Using the Fourier Transform, instantaneous voltage and current waveforms can be expressed in terms of their harmonic content. vt V V h t Oh h h ( ) sin( ) =+ × ∑ ×+ ≠ ∞ 2 0 ωα (2) where: v(t) is the instantaneous voltage VO is the average value Vh is the rms value of voltage harmonic h and h is the phase angle of the voltage harmonic. it I I h t Oh h h ( ) sin( ) =+ × ∑ ×+ ≠ ∞ 2 0 ωβ (3) where: i(t) is the instantaneous current IO is the dc component Ih is the rms value of current harmonic h and h is the phase angle of the current harmonic. |
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