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Technology / Technical guide
ADC Quantisation, Bit Count & Effective Number of Bits
An analogue-to-digital converter represents a range of inputs through finite codes. Its nominal bit count describes the number of possible labels, while dynamic effective resolution depends on an explicitly defined measurement. Quantisation error, analogue noise, distortion and sensor bias are distinct contributions rather than one universal bits-to-accuracy conversion.
Code count and physical information are different.
Follow the ideal step size into its conditional error model, then distinguish that model from a SINAD-derived figure.
01 / Code intervals
A nominal step follows the declared ideal model.
For an ideal N-bit uniform partition of span Vspan into 2^N equal code intervals, step size q = Vspan/2^N.
For an ideal N-bit uniform partition of span Vspan into 2^N equal code intervals, step size q = Vspan/2^N. This identifies interval width, not a guarantee that every actual transition or endpoint calibration uses that ideal relationship.
Hypothetical partition: N = 12 and span 4.096 V give q = 0.001 V, or 1 mV. These invented values are not a MARSTON sensor range. Adding display decimals after conversion does not create additional measured code intervals.
02 / Error model
A half-step bound needs ideal rounding and no clipping.
Within the represented range, ideal nearest-level quantisation can be described with error bounded by half a step under its stated endpoint convention.
Within the represented range, ideal nearest-level quantisation can be described with error bounded by half a step under its stated endpoint convention. Clipping outside the range is different and can exceed that bound.
If the error is modelled as zero-mean uniform over −q/2 to +q/2, its RMS is q/√12. Analog Devices derives this approximation. A constant or correlated input can produce repeatable code error rather than independent white noise.
03 / Ideal SNR
The familiar bit equation has waveform conditions.
For a full-scale pure sine, ideal quantisation alone with the stated uniform, uncorrelated noise interpretation gives approximately SNR = 6.02N+1.76 dB over the specified Nyquist bandwidth.
For a full-scale pure sine, ideal quantisation alone with the stated uniform, uncorrelated noise interpretation gives approximately SNR = 6.02N+1.76 dB over the specified Nyquist bandwidth. It is not a formula for every input amplitude or frequency condition.
An invented N = 10 gives 61.96 dB under that ideal model. Analogue noise, distortion, jitter and a reduced-amplitude signal change the problem. The step-size relation therefore cannot independently predict a complete measurement chain’s dynamic SNR.
04 / SINAD and ENOB
Effective bits describe a defined dynamic ratio.
SINAD includes noise and distortion relative to the stated signal, with DC and bandwidth treatment declared.
SINAD includes noise and distortion relative to the stated signal, with DC and bandwidth treatment declared. For the common full-scale-sine convention, ENOB = (SINAD_dB−1.76)/6.02. Analog Devices notes that reduced-amplitude reporting needs its corresponding amplitude convention.
A hypothetical SINAD of 61.96 dB maps to ten effective bits under that definition. This is not an instruction to truncate a digital word to ten bits, nor does it establish ten-bit absolute accuracy of a mechanical sensor.
05 / Different metrics
Noise-only resolution is not the same dynamic quantity.
A DC noise-based effective-resolution value can use a different denominator and omit distortion.
A DC noise-based effective-resolution value can use a different denominator and omit distortion. Nominal code width, noise-free counts and sine-based ENOB thus answer different questions. Comparing their numbers without definitions can imply an improvement that is only a changed metric.
The sensor-terms guide addresses mechanical and indication behaviour. A fine converter step cannot remove upstream bias, while a precise sensor can still be represented coarsely by later conversion or display.
06 / Scope
A converter model does not specify a product chain.
Input frequency, amplitude, represented bandwidth and included error contributions belong to a dynamic figure.
Input frequency, amplitude, represented bandwidth and included error contributions belong to a dynamic figure. The jitter guide explains one separate timing contribution rather than assuming quantisation is the only limitation.
No MARSTON ADC architecture, bit count, ENOB or accuracy is assigned. The equations provide no instrument settings, field test, reference-voltage change or controller modification; they explain why the numerical labels require their assumptions.
Related technical guides: Ratiometric Sensing: Common Reference & Residual Errors · Sampling Jitter: Timing Error, Signal Slope & SNR · Power Spectral Density: Units, Integration & RMS.
General background: Analog Devices MT-001: Ideal quantisation error and conditional SNR · Analog Devices MT-003: SINAD and full-scale ENOB conventions. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| N | Nominal code-bit count | Not a complete accuracy statement. |
| q | Vspan/2^N in the ideal partition | Actual transition behaviour is separate. |
| q/√12 | Ideal model RMS error | Uniform-error interpretation is explicit. |
| SINAD | Signal-to-noise-and-distortion ratio | Waveform, amplitude and bandwidth conventions matter. |
| ENOB | (SINAD_dB−1.76)/6.02 | Common full-scale-sine dynamic convention. |
Engineering questions.
Do extra printed decimals create additional codes?
No. Formatting cannot add measured conversion intervals.
Is quantisation error always white noise?
No. Input and sampling relationships can create correlated error.
Does 6.02N+1.76 cover every waveform?
No. The stated full-scale-sine and ideal-noise conditions matter.
Is ENOB the physical output-word length?
No. It is a derived dynamic performance figure.
Does ten effective bits prove sensor absolute accuracy?
No. The upstream quantity and error boundaries remain distinct.
Are 4.096 V and 12 bits equipment specifications?
No. They are hypothetical partition inputs.
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