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ADE7755 Datasheet(PDF) 13 Page  Analog Devices 

ADE7755 Datasheet(HTML) 13 Page  Analog Devices 
13 / 20 page ADE7755 Rev. A  Page 13 of 20 NONSINUSOIDAL VOLTAGE AND CURRENT The active 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 operation, instantaneous voltage and current waveforms can be expressed in terms of their harmonic content. ( ∑ ∞ ≠ + × × + = 0 t sin 2 ) ( h h h O a hω V V t v ) (1) where: v(t) is the instantaneous voltage. VO is the average voltage value. Vh is the rms value of the voltage harmonic, h. ah is the phase angle of the voltage harmonic. ∑ ∞ ≠ + × × + = 0 ) t sin( 2 ) ( h h h O β hω I I t i (2) where: i(t) is the instantaneous current. IO is the current dc component. Ih is the rms value of the current harmonic, h. βh is the phase angle of the current harmonic. Using Equation 1 and Equation 2, the active power (P) can be expressed in terms of its fundamental active power (P1) and harmonic active power (PH). P = P1 + PH (3) where: P1 is the active power of the fundamental component: P1 = V1 × I1 cosΦ1 Φ1 = α1 – β1 and PH is the active power of all harmonic components: ∑ ∞ ≠ Φ × = 1 cos h h h h H I V P Φh = αh – βh A harmonic active power component is generated for every harmonic, provided that the harmonic is present in both the voltage and current waveforms. The power factor calculation previously shown is accurate in the case of a pure sinusoid; therefore, the harmonic active power must also correctly account for the power factor because it is made up of a series of pure sinusoids. Note that the input bandwidth of the analog inputs is 14 kHz with a master clock frequency of 3.5795 MHz. ANALOG INPUTS Channel 1 (Current Channel) The voltage output from the current transducer is connected to the ADE7755 at Channel 1. Channel 1 is a fully differential voltage input. V1P is the positive input with respect to V1N. The maximum peak differential signal on Channel 1 should be less than ±470 mV (330 mV rms for a pure sinusoidal signal) for specified operation. Note that Channel 1 has a programmable gain amplifier (PGA) with userselectable gain of 1, 2, 8, or 16 (see Table 5). These gains facilitate easy transducer interfacing. +470mV –470mV VCM V1 DIFFERENTIAL INPUT ±470mV MAX PEAK COMMONMODE ±100mV MAX V1P V1N V1 VCM AGND Figure 24. Maximum Signal Levels, Channel 1, Gain = 1 Figure 24 illustrates the maximum signal levels on V1P and V1N. The maximum differential voltage is ±470 mV divided by the gain selection. The differential voltage signal on the inputs must be referenced to a common mode, for example, AGND. The maximum commonmode signal is ±100 mV, as shown in Figure 24. Table 5. Gain Selection for Channel 1 G1 G0 Gain Maximum Differential Signal (mV) 0 0 1 ±470 0 1 2 ±235 1 0 8 ±60 1 1 16 ±30 
