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10 / 20 page AD71056 Rev. A | Page 10 of 20 THEORY OF OPERATION The two ADCs in the AD71056 digitize the voltage signals from the current and voltage sensors. These ADCs are 16-bit, Σ-Δ with an oversampling rate of 450 kHz. This analog input struc- ture greatly simplifies sensor interfacing by providing a wide dynamic range for direct connection to the sensor and also simplifies the antialiasing filter design. 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. 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. To extract the real power component (that is, the dc component), the instantaneous power signal is low-pass filtered. Figure 15 illustrates the instantaneous real power signal and shows how the real power information is extracted by low-pass filtering the instantaneous power signal. This scheme correctly calculates real power for sinusoidal 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. TIME TIME ADC ADC CH1 CH2 MULTIPLIER F1 F2 DIGITAL-TO- FREQUENCY CF DIGITAL-TO- FREQUENCY INSTANTANEOUS REAL POWER SIGNAL INSTANTANEOUS POWER SIGNAL – p(t) LPF HPF Figure 15. Signal Processing Block Diagram The low frequency outputs (F1, F2) of the AD71056 are generated by accumulating this real power information. This low frequency inherently means a long accumulation time between output pulses. Consequently, the resulting output frequency is proportional to the average real power. This average real power information is then accumulated (for example, by a counter) to generate real energy information. Conversely, due to its high output frequency and, hence, shorter integration time, the CF output frequency is proportional to the instantaneous real power. This is useful for system calibration that can be done faster under steady load conditions. POWER FACTOR CONSIDERATIONS The method used to extract the real power information from the instantaneous power signal (that is, by low-pass filtering) is valid even when the voltage and current signals are not in phase. Figure 16 displays the unity power factor condition and a displacement power factor (DPF) = 0.5; that is, the current signal lagging the voltage by 60°. Assuming the voltage and current waveforms are sinusoidal, the real power component of the instantaneous power signal (the dc term) is given by ( ° × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × 60 cos 2 I V ) (1) This is the correct real power calculation. V× I 2 0V POWER CURRENT AND VOLTAGE POWER TIME TIME VOLTAGE CURRENT V× I 2 COS (60°) 0V INSTANTANEOUS POWER SIGNAL INSTANTANEOUS REAL POWER SIGNAL INSTANTANEOUS POWER SIGNAL INSTANTANEOUS REAL POWER SIGNAL 60° Figure 16. 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 non- sinusoidal current and voltage waveforms. All voltage and current waveforms in practical applications have some harmonic content. Using the Fourier transform, instantaneous voltage and current waveforms can be expressed in terms of their harmonic content. ( h 0 h h 0 t h V V t v α ω + × × + = ∑ ∞ ≠ sin 2 ) ( ) (2) where: v(t) is the instantaneous voltage. V0 is the average value. Vh is the rms value of Voltage Harmonic h. is the phase angle of the voltage harmonic. h α |
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