AN-1374: ADE7912/ADE7913 Front-End DSP Specifications

Introduction

This application note explains several aspects of the digital filtering associated with the Σ-Δ modulators used in the ADE7912/ ADE7913. The role of the filters is to decimate the outputs of the modulators to various rates, while eliminating high frequency noise. These rates start from a high of 8 kHz and go as low as 1 kHz, allowing the user to update the rates to the microcontroller processing bandwidth.

Digital Decimation Filtering

Functional Description

Figure 1 shows the block diagram of the decimation filtering implemented in the ADE7912/ADE7913. The Σ-Δ modulator provides a bit stream with a frequency of 1 MHz when the chip is clocked at CLKIN = 4.096 MHz. The SINC4 filter uses four decimation ratios—32, 64, 128, and 256—to provide outputs at 32 kHz, 16 kHz, 8 kHz and 4 kHz. To limit the bandwidth to meaningful frequencies while also keeping the data rate as low as possible, an extra low-pass filter (LPF) with 60 dB attenuation is used. This makes the subsequent rms and power calculations more precise, reducing the bandwidth a micro-controller must reserve for the metrology calculations.

The LPF performs another decimation by 4, and has internal flexibility, which leads to two different bandwidths. The LPF is implemented as two separate, sixth-order filters: one filter for the narrower bandwidths, one filter for the larger bandwidths.

The ADE7912/ADE7913 provide multiple output data rates (ODRs): 8 kHz, 4 kHz, 2 kHz, and 1 kHz, as well as two selectable bandwidths for each of these rates (see Table 1). The selectable ODRs help users address a wide range of scenarios to make their own trade-offs in the datapaths implemented in the microcontroller.

ODR and bandwidth selection is performed by Bit 7 (BW) and Bits[5:4] (ADC_FREQ) in the CONFIG register. Table 1 shows the different BW and ADC_FREQ settings required when the ADE7912/ADE7913 is clocked at CLKIN = 4.096 MHz. The bandwidth is indicated by the point at which the gain is attenuated by 3 dB.

Frequency Response and Time Delay Characteristics of the SINC4 + LPF Filters

The equivalent Z-domain formula of the SINC4 for various decimation ratios (DRs) is shown in the following equation:

The Z-domain formula of the LPF that corresponds to the narrower bandwidth (BW, Bit 7 of the CONFIG register, is set to 1) is shown in the following equation:

where LPF_BW1 is the LPF that corresponds to the narrower bandwidth.

The Z-domain formula of the LPF that corresponds to the larger bandwidth (BW, Bit 7 of the CONFIG register, is cleared to 0) is shown in the following equation:

where LPF_BW2 is the LPF that corresponds to the larger bandwidth.

Magnitude Frequency Response and Time Delays for Various Filters

Figure 2 through Figure 25 and Table 2 through Table 32 provide detailed information about the magnitude frequency response and the time delays introduced in the signal path by the various filters. The output data rate (ODR) is the output frequency at which the analog-to-digital converter (ADC) samples are provided by the ADE7912/ADE7913. The bandwidth of the filter (BW) is the point at which the gain is attenuated by 3 dB. The full frequency response, or the response up to the −3 dB point, and the flat-band response (from 0 dB down to −0.8 dB attenuation) are shown in all ODR and BW cases.

The phase delay defines the propagation delay in the phase of a sinusoidal signal passing through the filter. Tables showing the phase delay at various frequencies are shown for all ODR and BW cases.

From the perspective of power calculations, these time delays do not affect the final results because both voltage and current signals are subject to identical time delay propagation. However, in case of transient events or events synchronous to the zero crossings, it may be useful to know the time delays.

The frequency points are selected in such a way that the intermediate values can be obtained with accuracy by piecewise linear interpolation. These frequency points may be useful, for example, if amplitude corrections are necessary.

ODR = 8 kHz and BW = 3.338 kHz

Table 2. SINC4 + LPF Gain Response at Various Frequencies for ODR = 8 kHz and BW = 3.338 kHz; Frequency Range = 50 Hz to 450 Hz

	Frequency (Hz)
	50	100	150	200	250	300	350	400	450
Magnitude (milli_dB)	0	−0.32	−0.87	−1.66	−2.67	−3.93	−5.44	−7.21	−9.26

ODR = 8 kHz and BW = 2.137 kHz

ODR = 4 kHz and BW = 1.67 kHz

Table 14. SINC4 + LPF Gain Response at Various Frequencies for ODR = 4 kHz and BW = 1.67 kHz; Frequency Range = 50 Hz to 450 Hz

	Frequency (Hz)
	50	100	150	200	250	300	350	400	450
Magnitude (milli_dB)	0	−1.323	−3.589	−6.865	−11.234	−16.784	−23.596	−31.732	−41.222

ODR = 4 kHz and BW = 1.069 kHz

Table 19. SINC4 + LPF Gain Response at Various Frequencies for ODR = 4 kHz and BW = 1.069 kHz; Frequency Range = 50 Hz to 450 Hz

	Frequency (Hz)
	50	100	150	200	250	300	350	400	450
Magnitude (milli_dB)	0	−2.19	−5.60	−9.92	−14.85	−20.23	−26.10	−32.76	−40.68

ODR = 2 kHz and BW = 0.836 kHz

Table 23. SINC4 + LPF Gain Response at Various Frequencies for ODR = 2 kHz and BW = 0.836 kHz; Frequency Range = 50 Hz to 450 Hz

	Frequency (Hz)
	50	100	150	200	250	300	350	400	450
Magnitude (milli_dB)	0	−5.5	−15.37	−30.27	−50.55	−76	−106	−139	−176

ODR = 2 kHz and BW = 0.535 kHz

Table 26. SINC4 + LPF Gain Response at Various Frequencies for ODR = 2 kHz and BW = 0.535 kHz; Frequency Range = 50 Hz to 450 Hz

	Frequency (Hz)
	50	100	150	200	250	300	350	400	450
Magnitude (milli_dB)	0	−7.69	−17.99	−30.48	−48.05	−73.36	−102.34	−137.17	−305.62

ODR = 1 kHz and BW = 0.418 kHz

ODR = 1 kHz and BW = 0.268 kHz

Table 31. SINC4 + LPF Gain Response at Various Frequencies for ODR = 1 kHz and BW = 0.268 kHz; Frequency Range = 50 Hz to 400 Hz

	Frequency (Hz)
	50	100	150	200	250	268	300	350	400
Magnitude (dB)	0	−0.022	−0.065	−0.128	−1.20	−3.0	−8.615	−18.9	−28.91

Author

Gabriel Antonesei