ADE7761B
Rev. 0 | Page 13 of 24
ANALOG-TO-DIGITAL CONVERSION
The analog-to-digital conversion in the ADE7761B is carried
out using second-order, Σ-Δ ADCs.
Figure 19 shows a first-
order, Σ-Δ ADC (for simplicity). The converter is made up of
two parts: the Σ-Δ modulator and the digital low-pass filter.
....10100101....
1-BIT DAC
LATCHED
COMPAR-
ATOR
INTEGRATOR
V
REF
MCLK
C
R
ANALOG
LOW-PASS FILTER
DIGITAL
LOW-PASS FILTER
1 24
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Figure 19. First-Order, Σ-Δ ADC
A Σ-Δ modulator converts the input signal into a continuous
serial stream of 1s and 0s at a rate determined by the sampling
clock. In the ADE7761B, the sampling clock is equal to CLKIN.
The 1-bit DAC in the feedback loop is driven by the serial data
stream. The DAC output is subtracted from the input signal.
If the loop gain is high enough, the average value of the DAC
output (and, therefore, the bit stream) approaches that of the
input signal level. For any given input value in a single sampling
interval, the data from the 1-bit ADC is virtually meaningless.
Only when a large number of samples are averaged is a meaningful
result obtained. This averaging is carried out in the second part
of the ADC, the digital low-pass filter. By averaging a large
number of bits from the modulator, the low-pass filter can
produce 24-bit data-words that are proportional to the input
signal level.
The Σ-Δ converter uses two techniques to achieve high resolution
from what is essentially a 1-bit conversion technique. The first is
oversampling, which means that the signal is sampled at a rate
(frequency) that is many times higher than the bandwidth of
interest. For example, the sampling rate in the ADE7761B is
CLKIN (450 kHz) and the band of interest is 40 Hz to 1 kHz.
Oversampling has the effect of spreading the quantization noise
(noise due to sampling) over a wider bandwidth. With the noise
spread more thinly over a wider bandwidth, the quantization
noise in the band of interest is lowered (see
Figure 20).
However, oversampling alone is not an efficient enough method
to improve the signal-to-noise ratio (SNR) in the band of interest.
For example, an oversampling ratio of 4 is required just to increase
the SNR by only 6 dB (1 bit). To keep the oversampling ratio at
a reasonable level, it is possible to shape the quantization noise so
the majority of the noise lies at the higher frequencies. This is what
happens in the Σ-Δ modulator; the noise is shaped by the inte-
grator, which has a high-pass type response for the quantization
noise. The result is that most of the noise is at higher frequencies,
where it can be removed by the digital low-pass filter. This noise
shaping is also shown in
Figure 20.
SHAPED NOISE
HIGH RESOLUTION
OUTPUT FROM
DIGITAL LFP
NOISE
IGNAL
NOISE
IGNAL
0 1 225 450
FREQUENCY (kHz)
0 1 225 450
FREQUENCY (kHz)
DIGITAL FILTER
NTIALIAS FILTER (RC)
SAMPLING FREQUENCY
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Figure 20. Noise Reduction Due to Oversampling and
Noise Shaping in the Analog Modulator
Antialias Filter
Figure 20 also shows an analog low-pass filter, RC, on input to
the modulator. This filter is present to prevent aliasing. Aliasing
is an artifact of all sampled systems, which means that frequency
components in the input signal to the ADC that are higher than
half the sampling rate of the ADC appear in the sampled signal
frequency below half the sampling rate.
Figure 21 illustrates
the effect.
0 1 225 450
FREQUENCY (kHz)
IMAGE
FREQUENCIES
SAMPLING
FREQUENCY
NTIALIASING EFFECTS
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Figure 21. ADC and Signal Processing in Current Channel or Voltage Channel
In Figure 21, frequency components (arrows shown in black)
above half the sampling frequency (also known as the Nyquist
frequency), that is, 225 kHz, are imaged or folded back down
below 225 kHz (arrows shown in gray). This happens with all
ADCs, no matter what the architecture. In
Figure 21, only
frequencies near the sampling frequency (450 kHz) move into
the band of interest for metering (40 Hz to 1 kHz). This fact
allows the use of a very simple low-pass filter to attenuate these
frequencies (near 250 kHz) and, thereby, prevent distortion in the
band of interest. A simple RC filter (single pole) with a corner
frequency of 10 kHz produces an attenuation of approximately
33 dB at 450 kHz (see
Figure 21). This is sufficient to eliminate
the effects of aliasing.
