A 16-Bit ADC Output Does Not Promise 16 Effective Dynamic Bits

Start with what the 16-bit code space represents

A nominal N-bit ADC represents its input with 2^N possible codes. The ideal code width, or least significant bit (LSB), divides the full input span by that count. For a 16-bit space spanning 4.096 V, 2^16 = 65,536 and 4.096 V / 65,536 = 0.0000625 V: 62.5 microvolts per ideal LSB. This uses the span divided into code bins, rather than treating the first and last code centers as the span's endpoints.

Quantization assigns a continuous input to discrete levels. MT-001's ideal model has quantization error within half an LSB for an in-range input, and rms error q / sqrt(12) under its stated approximation, where q is the ideal LSB. The familiar ideal SNR = 6.02N + 1.76 dB additionally assumes a full-scale sine and integration over the Nyquist bandwidth, dc to half the sample rate. For N = 16, that expression gives 98.08 dB.

Those are ideal-model statements. A physical acquisition can also have noise, offset, gain and nonlinearity contributions. The calculated 62.5 microvolt code width does not bound their combined effect.

References: [TI1][AD2]

Noise and harmonic distortion answer different questions

Input-referred noise can spread repeated output values even for a steady input. Harmonic distortion describes another effect: a nonlinear response to a sine can add components at integer multiples of its frequency. A report that removes those harmonics from its residual can look better than one that includes them.

In the convention used here, SNR compares the fundamental signal with noise, excluding harmonics and dc. SINAD compares it with the combined noise and distortion, including harmonics but excluding dc. In rms-amplitude terms, SINAD in dB is 20 log10(S / R), where S is the fundamental's rms amplitude and R is the root-sum-square residual over the declared band.

ENOB expresses that dynamic performance on an ideal-converter bit scale. It is different from the essentially dc noise measures called effective resolution or noise-free code resolution in MT-004. A bit-valued headline needs its definition.

References: [TI1][AD4]

AD-51: equal code widths, different SINAD outcomes

AD-51 is a fictional comparison of two acquisition offers, A and B. Both provide nominal 16-bit output words over an ideal unipolar span of 0 V to 4.096 V. Each therefore has 65,536 possible codes and the same calculated 62.5 microvolt ideal LSB.

Stipulate a full-scale sine centered at midspan, with 4.096 V peak-to-peak amplitude, a 1 kHz input frequency and 100,000 samples/s for each offer. Both declared SINAD values cover the same Nyquist band, dc to 50 kHz, excluding the fundamental and dc from the residual. Both figures describe the same offered acquisition boundary with the same reporting convention and no different filtering basis. These are invented analytical premises, not measurements of actual equipment.

A supplies SINAD = 74.00 dB. B supplies SINAD = 61.96 dB. At the stipulated full-scale amplitude, ENOB = (SINAD in dB - 1.76) / 6.02. Thus A gives (74.00 - 1.76) / 6.02 = 12.00 bits, while B gives (61.96 - 1.76) / 6.02 = 10.00 bits.

Now stipulate a separate requirement of at least 70 dB SINAD under exactly those conditions. This threshold is fictional, not an industry rule. A clears the numerical comparison by 4.00 dB. B falls short by 8.04 dB. Their identical nominal resolution cannot settle that requirement.

The SINAD gap is 12.04 dB. Because the signal amplitudes match, B's combined residual rms amplitude is approximately 10^(12.04 / 20), or four times A's. This is a comparison of residual amplitude, not four times the absolute measurement error.

Both outputs remain 16-bit words. Twelve or ten ENOB does not identify a set of individually trustworthy upper bits or order the recipient to discard lower bits. It expresses the supplied noise-and-distortion ratio on another scale.

References: [AD2][TI1]

Keep the conditions attached to the number

AD-51 is decidable because its premises match. For actual offers, retain the input frequency and amplitude, input span, sampling rate, integrated bandwidth and any stated filtering with the reported SINAD. A low-frequency figure does not establish performance at a higher frequency. A reduced bandwidth can change the included noise population.

Also identify the object covered by the evidence. A converter's component specification and a complete acquisition product's input-to-output performance describe different boundaries. The buyer needs evidence applicable to the offered boundary and to the requirement's conditions. Preserve whether a value is a minimum, typical value or illustrative curve.

A low-looking noise floor in a spectrum is insufficient by itself. MT-003 distinguishes noise in individual spectral bins from noise integrated over the comparison band. A plot's vertical floor cannot simply replace the residual in the SINAD calculation.

References: [AD1][AD3]

Normalize reduced amplitude without changing the measured ratio

MT-003 gives an amplitude correction when SINAD is referenced to the actual sine amplitude: ENOB = [SINAD_measured - 1.76 + 20 log10(A_full-scale / A_signal)] / 6.02. The two amplitudes must use the same convention. Establish the decibel reference first; a value already referred to full scale must not receive that correction again.

For an additional invented example, let a sine be 6.00 dB below full scale and its signal-referenced SINAD be 68.00 dB. The amplitude correction is 6.00 dB, giving (68.00 - 1.76 + 6.00) / 6.02 = 12.00 normalized ENOB.

Its measured signal-to-residual ratio remains 68.00 dB. It would not meet a fictional 70 dB signal-referenced SINAD requirement at that reduced amplitude. Normalization changes the reference for the bit comparison. It does not improve the supplied waveform or establish the distortion that would occur at a different amplitude.

References: [AD1][TI1]

Read the AD7902's nominal resolution and SINAD separately

Analog Devices' AD7902 data sheet, Rev. B, August 2015, provides a concrete historical example. Its cover lists 16-bit resolution and 91 dB SINAD at 1 kHz. Table 2 separates resolution from AC accuracy: at a 1 kHz input and 5 V reference, SINAD is 89 dB minimum and 91 dB typical. At the stated 2.5 V reference, the corresponding values are 84 dB minimum and 86 dB typical.

Footnote 5 matters: the decibel specifications are referred to full-scale input range, while testing normally uses an input 0.5 dB below full scale. Page 13 defines SINAD, SNR and ENOB. Read the terminology together with the table's reference convention; do not treat the 91 dB headline as an unexplained actual-signal ratio or automatically add another 0.5 dB.

This example demonstrates separately specified properties. Its values are not AD-51's figures or a specification for a complete acquisition product.

References: [AD3]

Carry the dynamic comparison into the actual input decision

For AD-51, the supported conclusion is narrow and useful: A meets the stipulated SINAD requirement and B does not, while both retain the requested 16-bit representation. A buyer can retain both fields in the comparison instead of replacing one with the other.

For an industrial AI input, that still leaves the physical meaning of the supplied signal and the task's evidence requirements to resolve. More ENOB alone proves no improvement in model accuracy. The related sampling-and-aliasing article addresses which original frequencies a stream can distinguish. The measurement-resolution article addresses uncertainty and conformity decisions. Neither question is answered by the SINAD-to-ENOB conversion.

The acquisition supplier and appointed technical owners should resolve missing performance conditions and product suitability. This article explains supplied specifications and fictional arithmetic; it supplies no acquisition-design, measurement, calibration or field procedure.

Connect selected equipment through a separate physical scope

If the customer-selected acquisition or compute equipment also needs physical network connections, Leviathan's Structured Cabling & Fiber Installation service is the relevant starting point for an agreed cabling scope. Use the service and project-inquiry links below with a nonconfidential equipment list, approved endpoints and routes, and required labels and handoff records.

That inquiry concerns separately agreed physical equipment work and availability. ADC characterization, acquisition software and industrial AI evaluation remain with the appointed specialists.

References: [L1]