A 16-bit ADC on the label. How much information reaches the measurement?

An ADC returns a 16-bit word, and the application displays voltage to five decimal places. Connected to a stable source, the last digits still fluctuate. The team considers averaging, a more expensive ADC, or truncating the displayed result. Each addresses a different issue, so first establish what limits the useful measurement.

Code count, repeatability, accuracy, and reproduction of a changing signal are different properties. A very stable reading can be displaced by reference error. A correct average can come from a path that strongly distorts dynamic signals. One “effective bits” figure cannot describe all these behaviors.

We will construct two deterministic examples: a DC-input histogram and a sine-wave spectrum containing noise and harmonics. The data are synthetic. It does not characterize an actual ADC or BBest24 product. It does let us reproduce the calculations and see why different assessment methods support different conclusions.

What 16 bits actually means

Assume a unipolar range from 0 to 4.096 V and 65536 codes. The nominal step is 4.096 / 65536 = 62.5 µV. This is the ideal quantization step in our model, not a guarantee that a 62.5 µV input change can be reliably detected under every condition.

The model rounds voltage to the nearest code. A real converter has specified coding, transition levels, and endpoint behavior. Before converting data, establish whether the output is signed, unsigned, offset, aligned within a wider word, or affected by input gain. Misreading the format can overwhelm every subtle noise consideration.

An ideal quantization model often uses RMS noise of q / √12, approximately 18.0 µV here. Analog Devices MT-001 explains the assumptions behind this approximation and the 6.02N + 1.76 dB relationship for a full-scale sine wave. Do not apply an uncorrelated-error model unconditionally to every DC input or periodic code sequence.

Nominal 16-bit resolution therefore describes representation and an ideal reference point. Useful performance also depends on source, amplifier, filters, reference, clock, supply, and acquisition method. Replacing the ADC alone may accomplish little when the dominant error originates upstream.

A histogram answers a spread question

For a constant 2.048 V input, generate 4096 samples with Gaussian noise whose specified standard deviation is 0.5 mV. Quantize them in 62.5 µV steps. A fixed random seed reproduces the same record. Its actual finite-record standard deviation is approximately 0.490 mV, or 7.84 LSB.

Codes range from 32742 to 32794 in this record. The extremes span 52 steps, but that is not a guaranteed bound on future noise. Gaussian extremes depend on observation length. One histogram cannot support an absolute promise that the reading will never move farther.

A histogram retains spread but discards sample order. Slow drift and independent noise can produce similar shapes while responding differently to averaging. For real measurements, also inspect the time trace, temperature dependence, and periodic interference. A stable mean over one short window does not establish day-long stability.

Specify input conditions. “Shorted input” may mean ground, midscale, or a source with defined impedance. Behavior can differ near a rail or at a high common-mode voltage. Without the operating point, another person’s measurement is difficult to compare meaningfully.

Averaging helps under a particular assumption

Divide the same record into nonoverlapping groups of 16 samples. The standard deviation of group means is approximately 0.124 mV. Independent noise with constant variance should improve by a factor of four because √16 = 4. This result agrees with that assumption within finite-record variation.

It does not automatically add two bits of total measurement accuracy. Averaging reduces random spread but does not remove fixed offset, gain error, or reference error. More digits after averaging may describe an incorrect value with greater precision. Separate random uncertainty from systematic components.

Correlation changes the calculation. If successive samples contain almost the same slow drift, averaging 16 points does not provide a fourfold improvement. With periodic interference, the outcome depends on sample rate and window length. Samples are not independent merely because they occupy separate rows in a file.

Averaging also changes bandwidth and delay. At 8192 samples/s, a group of 16 spans approximately 1.95 ms. Producing one value per group yields 512 results/s. This is a new data stream with different properties. Check whether it still exposes short events important to the application.

Reference error can hide beneath a quiet reading

Consider a separate variant: the actual reference is 0.1% higher than the conversion assumes, or 4.100096 V. With an ideal path and 2.048 V input, converting the code using the nominal range yields approximately 2.048 / 1.001 = 2.045954 V, before quantization. The error is approximately −2.046 mV.

That error greatly exceeds the nominal 62.5 µV step, and averaging any number of samples will not remove it. A histogram can be narrow and repeatable yet displaced. Resolution assessment therefore needs a known reference input and an error budget for the path.

This reference-error variant is not included in either plotted dataset. Keeping it separate makes the mechanism behind each result explicit. In hardware, components can coexist and vary with temperature and time. Correcting one point does not necessarily remove error across the full range.

A dynamic signal asks a different question

The second record contains 4096 samples at 8192 samples/s. Input consists of a 2.048 V offset and a 346 Hz sine wave with 1.8 V peak amplitude. Add a 692 Hz second harmonic of 0.8 mV peak, a 1038 Hz third harmonic of 0.4 mV peak, and independent noise with specified 0.5 mV RMS. Finally, apply the same 16-bit quantization.

Harmonic amplitudes are peak values, while noise is specified by standard deviation. Do not add them directly as equivalent quantities. Sine-wave RMS is peak amplitude divided by √2; independent component powers add. An approximate calculation before the FFT helps detect implementation scaling errors.

Exactly 173 fundamental cycles fit in the record. This is coherent sampling: 346 / 8192 = 173 / 4096. The Analog Devices article on coherent and window sampling describes this relationship. We can use a rectangular window without tone spreading caused by a discontinuity at the record boundary.

Calculate SINAD without losing energy

An FFT produces complex coefficients. A one-sided spectrum combines positive and negative frequency powers, while DC and the Nyquist bin are counted once. Dividing by the square of the sample count makes summed power equal the time-domain mean square. A script test checks this relationship instead of trusting the plot’s appearance.

Fundamental power comes from bin 173. The SINAD denominator contains every other positive-frequency bin through Nyquist, including harmonics but excluding DC. Compute 10 × log10(Psignal / Perror). This record produces 63.966 dB, rounded to 63.97 dB.

Do not remove harmonics as components that “are not noise”: SINAD includes both noise and distortion. SNR with harmonics excluded answers another question. MT-003 organizes these definitions and notes inconsistent terminology in documentation. Comparing numbers requires comparing their calculation methods too.

The plot shows each bin’s power relative to the fundamental, in dBc per bin. It is not noise spectral density in dB/Hz. A longer FFT can lower the visible level of individual bins without improving total noise power over the same bandwidth. Do not judge performance solely from the visual height of the noise floor.

ENOB needs the input level

Without amplitude correction, substitution into (SINAD − 1.76) / 6.02 gives 10.33. This is the direct conversion at the applied signal level. Full-scale peak amplitude for our range is 2.048 V, while the test uses 1.8 V, approximately 1.12 dB below full scale.

Following the correction described in MT-003, add 20 × log10(2.048 / 1.8) before dividing by 6.02. Full-scale-normalized ENOB is approximately 10.52. Both values are shown with their definitions to prevent an unqualified comparison between a reduced-level result and a datasheet specification.

Normalization is not a measurement at a larger amplitude. A real path’s distortion may change closer to full scale. The correction does not prove identical behavior at another operating point. It is a reporting convention whose assumptions belong beside the result.

Input frequency matters as well. ENOB can differ between a slow sine wave and a signal near the bandwidth limit. One 346 Hz result does not describe every application. A specification should include frequency range, amplitude, analysis bandwidth, sample rate, and input configuration rather than merely demanding “at least 12 effective bits.”

Removing harmonics changes the decision

Remove the synthetic harmonics while retaining noise, seed, and all other conditions. SINAD rises to approximately 68.11 dB, an improvement of about 4.14 dB without changing nominal resolution or averaging. Part of this example’s limitation came from distortion, so improving linearity could be more useful than increasing code width.

This does not establish that a real ADC would be responsible. Harmonics can originate in the test generator, amplifier, filter, or inappropriate input loading. Attribution requires knowing test-source quality and making controlled changes. A spectrum of the complete path does not automatically assign responsibility to individual components.

Averaging does not repair arbitrary nonlinearity. Filtering can attenuate selected frequencies, but changes measurement bandwidth. Improved SINAD after bandwidth reduction is useful when it matches application needs; it should not be presented as improved full-band converter performance. Comparisons must preserve the same energy-integration range.

When coherence disappears

If the actual generator frequency does not fit the record, tone energy spreads across several bins. Counting one bin as signal and everything else as error underestimates performance. An appropriate window, integration around the tone, and window-related corrections are required. Adding an arbitrary window while retaining the original calculation is insufficient.

Windows have main-lobe width and equivalent noise bandwidth. Selection depends on separating nearby tones, controlling leakage, or measuring amplitude. Our script is not a universal laboratory analyzer. It uses a coherent record for which the single-bin rule is explicitly justified.

Check clipping too. Even isolated samples at the coding limit can introduce distortion that later analysis cannot remove. The model has headroom and does not reach range endpoints. A physical test must consider offset, amplitude tolerance, and transients rather than only the generator’s nominal setting.

What these examples do not establish

A histogram at one input level does not measure integral or differential nonlinearity across the range. One sine-wave spectrum does not establish settling after channel changes or behavior with a high-impedance source. Those questions require other stimuli, conditions, and criteria.

We omit clock jitter, temperature drift, supply interference, out-of-band aliasing, and actual input-filter behavior. Their absence is a generator assumption, not hardware evidence that they were excluded. Synthetic data is useful for checking calculations but cannot replace path measurements.

Also distinguish display resolution from decision criteria. An application may show fewer digits for readability while retaining full data for analysis. Truncating fluctuating digits does not reduce measurement error. If a decision depends on a small difference, assess uncertainty and margin rather than merely quieting the display.

Similar numbers can have different definitions

The histogram’s observed peak-to-peak span can support an illustrative noise-free-bit indicator. Here, it is 52 × 62.5 µV = 3.25 mV, and log2(4.096 V / 3.25 mV) is approximately 10.30. This uses observed peak-to-peak spread, not dynamic ENOB from SINAD. Its resemblance to the second example’s 10.33 is coincidental.

Changing record length can change the extremes and this indicator even when the underlying noise distribution is unchanged. Read noise-free-bit claims together with method, bandwidth, and observation time. Do not compare them directly with sine-derived ENOB that includes harmonics.

A standard-deviation-based bit count also needs a definition. Converting full range to RMS noise without specifying the coefficient produces a different value from a peak-to-peak criterion. A clear report retains original quantities in volts and gives bit-based summaries alongside them. Readers can then apply criteria suitable for their own decisions.

A good sine test does not verify channel switching

Imagine a separate idealized first-order path with a 100 µs time constant. Switching between channels 2 V apart leaves a settling error of 2 V × exp(−t / 100 µs). After 1 ms, approximately 90.8 µV remains, or 1.45 nominal LSB for our range. A steady sine-wave test under other conditions might have looked satisfactory.

To reduce that error below half an LSB, or 31.25 µV, the model needs approximately 1.107 ms. This is a calculation for an assumed response, not an actual ADC acquisition-time specification. It illustrates how acquisition timing and channel order can limit useful resolution independently of a steady-state FFT result.

A real circuit needs checks of input drive, source impedance, and available time after multiplexer switching. Repeatedly reading one channel can hide an error exposed by alternating between widely separated levels. Select that test from intended use rather than nominal bit count alone.

An ADC assessment record

In our example, a 16-bit representation coexists with approximately 7.84 LSB of spread and full-scale-normalized dynamic ENOB of 10.52. These numbers are consistent because they describe different properties of the same model. A useful design decision starts by identifying which property limits the application and which experiment can establish that limitation.

Reducing output rate requires reconsidering aliasing. A 16-sample average is a particular filter with a particular response, not an ideal rejection of every frequency above the new Nyquist limit. At 512 results/s, that limit is 256 Hz. Our 346 Hz sine wave therefore cannot be represented correctly in that stream without accounting for filtering and a changed measurement objective. The averaging example concerns DC input, not improvement of that sine-wave spectrum.

This distinction prevents a misleading optimization: software can smooth a display while removing information the application needs. Requirements should identify both the smallest important change and the fastest important change. Together they determine a useful trade-off among noise, bandwidth, and delay. Retain before-filter and after-filter results so the cost of improved repeatability remains visible. A better metric calculated over a narrower bandwidth must not be silently attributed to the original full-rate stream.

Sources

• Analog Devices MT-001, Rev. A, 10/2008; quantization model and assumptions behind the SNR-to-bit relationship.
• Analog Devices MT-003, Rev. A, 10/2008; SINAD, SNR, harmonics, ENOB, and input-level correction.
• Analog Devices: Coherent Sampling vs. Window Sampling, 29 March 2002; record coherence and spectrum analysis.

Sources checked on 21 October 2026. Data and one-sided FFT powers come from the model described above. The generator uses fixed seeds 24 and 25. Results are an educational simulation, not a physical converter characterization.