ADE7761ARS-REF datasheet(15/28 Pages) AD

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ADE7761

Rev. A | Page 15 of 28

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

ADE7761 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 18).

However, oversampling alone is not an efficient enough method

to improve the signal-to-noise ratio (SNR) in the band of inter-

est. 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 that the majority of the noise lies at the higher frequen-

cies. This is what happens in the Σ-Δ modulator; the noise is

shaped by the integrator, which has a high-pass type response

for the quantization noise. The result is that most of the noise is

at the higher frequencies where it can be removed by the digital

low-pass filter. This noise shaping is also shown in Figure 18.

SHAPED NOISE

HIGH RESOLUTION

OUTPUT FROM

DIGITAL LFP

NOISE

SIGNAL

NOISE

SIGNAL

1kHz

225kHz

450kHz

FREQUENCY (Hz)

1kHz

225kHz

450kHz

FREQUENCY (Hz)

DIGITAL FILTER

ANTIALIAS FILTER (RC)

SAMPLING FREQUENCY

Figure 18. Noise Reduction Due to Oversampling and

Noise Shaping in the Analog Modulator

Antialias Filter

Figure 18 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 fre-

quency 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 19 illustrates the effect.

In Figure 19, 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 the example shown,

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 19). This is

sufficient to eliminate the effects of aliasing.

1kHz

225kHz

450kHz

FREQUENCY (Hz)

IMAGE

FREQUENCIES

SAMPLING

FREQUENCY

ANTIALIASING EFFECTS

Figure 19. ADC and Signal Processing in Current Channel or Voltage Channel

ACTIVE POWER CALCULATION

The ADCs digitize the voltage signals from the current and

voltage transducers. A high-pass filter in the current channel

removes any dc component from the current signal. This

eliminates any inaccuracies in the active power calculation due

to offsets in the voltage or current signals (see the HPF and

Offset Effects section).

The active 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 active power component (dc component), the

instantaneous power signal is low-pass filtered. Figure 20

illustrates the instantaneous active power signal and shows how

the active power information can be extracted by low-pass

filtering the instantaneous power signal. This scheme correctly

calculates active 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.

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