It may be Greek to you, but sigma delta converters are not really hard to understand.

DN Staff

July 17, 2006

3 Min Read
It may be Greek to you, but sigma delta converters are not really hard to understand.

Q. Can you please explain, simply, as to a Bear of Little Brain 1, 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 dutch 2 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." (Dither 3 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.

  1. "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"

  2. Double dutch means gobbledygook

  3. Dither - the addition of noise or some other AC signal in order to randomize errors.

  1. To learn more about sigma delta converters, Go to:
    Have a question involving a perplexing or unusual analog problem? Submit your question to: [email protected]

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