Can you please explain, simply, as to a Bear of Little Brain¹, how sigma-delta converters work?
A. By over-sampling, noise shaping and digital filtering.
Athens is a beautiful city, with the ambiance of many millennia of history. I was walking round the Acropolis with Spiros, one of our Greek distributors, when he asked me how sigma-delta (S-?) converters work. "Sigma and delta are letters of our Greek alphabet," he exclaimed, "but every article I have seen about their operation is double dutch² to me. They all start with several pages of partial differential equations and then go downhill from there."
If a voltage is measured many times, the average of the measurements will be more accurate than most individual measurements. This is "over-sampling." (Dither³ may be necessary to randomize the errors in the individual measurements.)
There is a definite theoretical minimum limit to the possible noise of an analog-to-digital converter (ADC). When an ADC samples a signal at a frequency of fs the digital output contains the signal and this "quantization noise" is usually spread evenly from dc to fs/2. By sampling at a higher rate of Kfs, the noise is spread over the wider band from dc to Kfs/2. If we then remove all the noise above fs/2 with a digital filter the signal-to-noise ratio (SNR) of the digital output is improved — effectively improving the ADC resolution.
Normally the SNR increases with the square root of K, so very high sampling rates are necessary for useful increases in SNR. But a S-? modulator does not produce uniformly distributed quantization noise. Although the total noise is unaltered in a S-? system, most of it is at high frequencies (HF). This is known as noise shaping and permits much lower values of K.
If the digital output from the S-? modulator is filtered to remove HF, leaving the frequencies from dc to fs/2 (where the wanted signals are) then the SNR and resolution of the digital output are improved.
A S-? ADC simply consists of a S-? modulator and a digital low-pass filter, both of which are easily made with modern high-density digital technology. The principle of S-? ADCs has been known for more than 40 years, but the ability to build one on a chip is relatively recent.
"When you are a Bear of Very Little Brain and you think of Things, you find sometimes that a Thing which seemed very Thingish inside you is quite different when it gets out into the open and has other people looking at it." — AA Milne, "The House at Pooh Corner"
Double dutch means gobbledygook
Dither — the addition of noise or some other AC signal in order to randomize errors.
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