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  1. 1. Metrics
    1. 1.1 Quantization Noise
    2. 1.2 Signal to Noise Ratio (SNR)
    3. 1.3 Effective Number of Bits (ENOB)

This page is for general design principles related to Analog to Digital (ADC) and Digital to Analog Converters (ADC).

1.  Metrics

1.1  Quantization Noise

  • For the quantization noise: E<V_{qnoise}> = 0 (Expected value) and \sigma_{qnoise} = \frac{V_{LSB}}{\sqrt{12}} (standard deviation)
    • ie. Quantiziation noise varies about 0 by +/- LSB/2
  • For signals evenly distributed between Vref and ground: E<V_{signal}> = \frac{V_{ref}}{2} (Expected value) and \sigma_{signal} = \frac{V_{ref}}{\sqrt{12}} (standard deviation)

1.2  Signal to Noise Ratio (SNR)

  • SNR = 10 \log \frac{ \sigma^2_{signal} }{ \sigma^2_{noise} }
    • If using standard deviation (σ) instead of variance (σ2), use 20log instead
  • Signal to Quantization Noise Ration
    SNQR = 20 \log \frac{ V_{ref} / \sqrt{12} }{ V_{LSB} / \sqrt{12} } = 20 \log \frac{ V_{ref} }{ V_{ref}/ 2^N } = 20N \log 2 = 6.02 N
    • Total SNR must exceed SNQR or ADC will just be digitizing noise.
    • Therefore SNR must increase by 6 dB for every additional bit
  • To measure SNR: SNR_{measured} = 10 \log \frac{ \sigma^2 of whitenoise in }{ \sigma^2 of white noise out }

1.3  Effective Number of Bits (ENOB)

  • For uniformly distributed signals: ENOB = \frac{ SNR_{measured} }{ 6.02 }
  • For sinusoidal signals: ENOB = \frac{ SNR_{measured} - 1.76 }{ 6.02 }

Backrefs:

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Last edited by DrLock. Originally by DrLock.