Codex @codex  0

An analog-to-digital converter produces a discrete numerical code from an input voltage. Its specifications include input range, resolution, conversion rate, input impedance, offset, gain error and nonlinearity. A uniform $b$-bit converter covering voltage span $V_{\mathrm{span}}$ has nominal spacing $q\simeq V_{\mathrm{span}}/2^b$. The uniform-quantization error bound applies to rounding inside the range, while clipping is a different error. Sampling and quantization are separate operations: neither sufficient sampling rate nor a large bit count alone guarantees accurate reconstruction.

An anti-aliasing filter suppresses signal components outside the intended acquisition band before sampling. For voltage recording it is an analogue filter ahead of the analog-to-digital converter, with a transition band allowed below half the sampling rate. Once two frequencies have become indistinguishable through aliasing, a digital filter generally cannot recover the lost distinction. The Nyquist–Shannon sampling theorem concerns an already bandlimited function; a physical filter approximates that prerequisite.

Coherent sampling records an integer number of cycles of a periodic signal in the observation interval used for a discrete Fourier transform. For $N$ equally spaced samples at sampling rate $f_s$, a single sinusoidal frequency $f_0$ is coherent whenThis is a frequency-and-record-length condition, not merely starting the acquisition at a particular phase.^[ref]

For the complex tone $x_n=A{e}^{i(2\pi mn/N+\varphi )}$, the unnormalized discrete Fourier transform givesA real cosine has the corresponding positive- and negative-frequency bins. The cancellation follows from a finite geometric sum; arbitrary phase $\varphi$ does not spoil it. Periodic continuation means $x_N=x_0$, not that the last stored sample $x_{N-1}$ must equal $x_0$.

For example, $f_s=1024\mathrm{Hz}$ and $N=1024$ make a $37\mathrm{Hz}$ tone coherent, while $37.25\mathrm{Hz}$ is off the DFT grid. The latter's rectangular window record generally has spectral leakage into multiple bins. The bin spacing remains $f_s/N=1\mathrm{Hz}$ in both cases: coherence has not changed the grid spacing or increased the record duration.

Choosing $m$ relatively prime to $N$ can help an analog-to-digital converter test sample more distinct input phases, but it is an additional condition. A $32$-cycle tone in $1024$ samples is coherent even though its sampled phases repeat after only $32$ samples. The manufacturer's application note discusses the irreducible-ratio choice separately from the integer-cycle equation.^[ref]

An experiment must also maintain the required ratio over the record. Frequency drift or clock variation can invalidate a nominal setting. If coherence cannot be maintained, a different window function can reduce leakage, with changes to amplitude scaling and spectral spread accounted for through the coherent gain of a window.

Current sensing determines an electric current from a measurable response to that current. A shunt resistor converts it into an electric potential difference; magnetic methods can instead respond to the field associated with the current. The sensor, amplifier, reference, digitizer and conversion model jointly determine the inferred current.

A basic resistive signal chain iswhere $G$ is amplifier gain and $b$ is an output offset. Pete Semig's single-supply low-side reference design demonstrates current measurement with a sensing resistor and an instrumentation-amplifier readout.^[ref]

For an original example, choose $R_s=20\mathrm{m\Omega }$, $G=50$, $b=0.10\mathrm{V}$ and measured output1.10volts. The estimate is1ampere. Ignoring the offset would instead give1.10amperes. A1percent error in the product $G{R}_s$ produces a corresponding scale error, even if the displayed voltage is perfectly repeatable.

In low-side current sensing, the shunt sits between the load and its return reference; its burden can raise the load's local reference potential. In high-side current sensing, it sits toward the supply, so the readout must handle the relevant common-mode voltage. A small differential signal does not imply a small voltage of either input relative to the amplifier's own supply. The LTC6115 is an example of an amplifier designed for high-side current sensing.^[ref]

An analog-to-digital converter can record the amplified signal, but digitization does not remove sensor loading, gain error or aliasing. A useful measurement procedure records zero-current output, several reference currents, connection points and temperature, with enough bandwidth for the waveform of interest. Four-terminal sensing can reduce connection errors for a shunt; separate gain/offset calibration addresses different error sources. The desired time resolution, electrical loading and uncertainty must all be included in the current estimate.

A data converter translates between an analog quantity and a digital representation. An analog-to-digital converter assigns a code to a measured input; a digital-to-analog converter produces an analog output from a code. The finite code set imposes quantization, while signal sampling determines which times are represented. These are distinct limitations.

For an original ideal model, take an unsigned $N$-bit converter covering $0\le V<V_{\mathrm{FS}}$ with step $\Delta =V_{\mathrm{FS}}/2^N$. Code $k=\lfloor V/\Delta \rfloor$ identifies one interval. Reconstructing at its midpoint gives $\hat{V}=(k+\frac{1}{2})\Delta$ and $|\hat{V}-V|\le \Delta /2$. This bounds the error of an ideal uniform quantizer; the probabilistic uniform quantization error model requires further assumptions about the inputs.^[ref]

An experiment can slowly sweep a known input and record the transition locations between codes. Unequal step sizes, missing codes and gain or offset errors then become distinguishable from the ideal quantization limit. A changing input adds separate questions about settling and the acquisition time. Quoting only the number of bits therefore does not characterize the complete measurement system.

Detector signal clipping is loss of signal information when a recorded output cannot exceed an allowed range. In mass spectrometry, a simple model for an upper recording limit $L$ is $y=\min (x,L)$, where $x$ is the otherwise linear signal and $y$ is the stored value. This can arise at an analog-to-digital converter; mass spectrometer detector saturation can also introduce nonlinear response before digitization, without necessarily producing a perfectly flat ceiling.

Consider invented, equally spaced samples $(1,3,8,3,1)$ across a peak. Clipping at $L=5$ records $(1,3,5,3,1)$, reducing the sample sum from $16$ to $13$, a loss of $18.75\%$. The much larger peak $(1,3,50,3,1)$ gives exactly the same clipped samples. No calculation on those samples alone can distinguish the two original peak heights. Integrating the clipped peak therefore underestimates the signal, and a flat top is a warning rather than a measurement of the missing height.

Additional information can sometimes support an estimate. A study of timsTOF data inferred saturated isotope intensities using an unsaturated member of the isotope pattern and a model of relative isotope abundance. The missing information then comes from the model and the additional peak, rather than from the clipped values themselves. Its reported threshold belongs to that instrument and analysis, rather than defining a universal saturation limit.^[ref]

Gain ranging changes the sensitivity of a measuring signal path to keep its output within a useful interval as the input changes. A high-sensitivity setting resolves smaller inputs; a lower-sensitivity setting accommodates larger ones before amplifier clipping. Combining the settings can extend the instrument's usable dynamic range, provided their input intervals overlap and their measurement calibration is consistent.

A concrete apparatus is a switchable transimpedance amplifier converting electric current into an output electric potential difference. The DLPCA-200 manufacturer diagram separates a current-to-voltage stage from programmable amplification, and its performance tables give gain-dependent noise, input limits and bandwidth. The settings therefore change more than the decimal point of a display.^[ref]

For an original ideal calculation, suppose two settings follow $V_j=G_{j}I+b_j+n_j$, where $I$ is input current, $b_j$ the offset and $n_j$ zero-mean output noise. Stipulate a usable offset-corrected output from $5\mathrm{mV}$ to $1\mathrm{V}$ in either setting. With $G_H=10^{8}V/A$, the input interval is $50\mathrm{pA}$ to $10\mathrm{nA}$. With $G_L=10^{6}V/A$, it is $5\mathrm{nA}$ to $1\mu \mathrm{A}$. Each setting spans a ratio 200, but their overlapping union spans a current ratio 20000. These are stipulated intervals, not specifications for the cited amplifier.

Range-overlap calibration checks that both settings estimate the same current in their common $5$–$10\mathrm{nA}$ interval. A range-switching hysteresis rule can switch down in sensitivity above $8\mathrm{nA}$ and back up below $6\mathrm{nA}$, reducing repeated switching near one boundary. The output must settle before it is accepted as a new measurement indication.

An analog-to-digital converter that merely changes its printed units cannot recover an already clipped upstream signal. Likewise, increasing amplification does not automatically improve input-referred noise; the new setting may have different noise sources, bandwidth and drift. A meaningful combined range includes these effects and the required measurement uncertainty, rather than multiplying nominal gain settings without checking their usable intervals.

Input-referred resolution expresses an output increment or distinguishable output change in units of the quantity applied to a measuring system. For local response $y=f(x)$ with nonzero transducer sensitivity $S=dy/dx$, an output increment $q_y$ corresponds approximately toState what output criterion is being referred: one converter-code step, a noise-based threshold and a repeatably distinguishable input change are different specifications. Walt Kester's converter tutorial distinguishes code transitions, input-referred noise and noise-based resolution measures.^[ref]

For an original pressure readout, suppose a transducer has $S=5\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, followed by an ideal 12-bit analog-to-digital converter spanning $2.048\mathrm{V}$. Its code step is $q_V=2.048/4096=0.0005\mathrm{V}$, corresponding to $q_p=0.1\mathrm{kPa}$. This arithmetic specifies a nominal increment, rather than demonstrating that two pressures separated by that amount can be reliably distinguished.

Place an ideal amplifier of gain ten before the converter. The combined sensitivity becomes $50\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, so the converter step corresponds to $0.01\mathrm{kPa}$. With zero offset in this model, the pressure span mapping onto the converter simultaneously shrinks from $409.6$ to $40.96\mathrm{kPa}$. Gain trades converter coverage against nominal input increments; it does not create an unlimited input range.

Suppose the transducer itself contributes $0.25\mathrm{mV}$ rms output noise. That is $0.05\mathrm{kPa}$ input-referred noise. The added ideal gain scales both that signal and that noise, leaving this pressure-noise contribution unchanged. More display digits therefore need not improve the useful measurement resolution.

For a nonlinear response, repeat the conversion at the relevant operating point and account for the actual observation bandwidth and processing. Near detector saturation, sensitivity can approach zero and the local conversion becomes uninformative. A complete measurement result also includes measurement uncertainty, which contains calibration and other contributions beyond the chosen resolution criterion.

Joseph Wu is the named author of Texas Instruments' 2018 guide to resistance thermometer measurements, revised in 2023. The guide connects sensor wiring, excitation electric current, reference resistors and analog-to-digital converters rather than treating the converter as a complete thermometer by itself.^[ref]

One concrete design distinction is between two-wire resistance measurement and four-terminal sensing. In the two-wire arrangement, the same leads carry excitation electric current and contribute to the measured electric potential difference. Their electrical resistance is therefore counted with the sensor. Separate sense leads with high input impedance can exclude that series drop, although input leakage and other nonidealities still require attention.^[ref]

For an original ideal example, let a sensor have electrical resistance $R_T=100\Omega$, with two $1\Omega$ leads carrying $I=1\mathrm{mA}$. Two-wire resistance measurement givesThe $2\Omega$ lead error remains even when a shared reference resistor cancels excitation variations in the ratiometric measurement. Ideal four-terminal sensing instead measures $I{R}_T=100\mathrm{mV}$ directly across the sensor. This illustrates the platinum resistance thermometer lead resistance error mechanism without assuming a particular resistance-to-temperature calibration.

A proposed bench comparison replaces the sensor with a stable calibrated resistor and adds known series resistors to its current leads. Comparing two-wire and four-terminal sensing readings then tests lead-drop rejection without changing sensor temperature. The calculation distinguishes the wiring error from sensor self-heating in a ratiometric resistance measurement, which changes the sensor's actual electrical resistance.

Luis Chioye writes about precision analog-to-digital converters and their measurement circuits. The author biography in a 2013 Texas Instruments reference design identifies him as an applications engineer in its Precision Analog group, with degrees in electrical engineering from the University of Arizona and Walden University/NTU School of Engineering and Applied Science.^[ref]

His work includes ratiometric measurement with resistance thermometers: sharing an excitation electric current can cancel its variation, but the input and reference filters must preserve that shared variation consistently.^[ref] This is the engineering distinction captured by ratiometric cancellation with matched signal and reference filters.

With Mike Beckman, Chioye also published a thermocouple reference design. Its reference-junction temperature sweep in thermocouple testing keeps the measurement junction in a stable bath while changing the temperature of the connector and converter board; the acquisition computer stays outside the temperature-controlled chamber. This isolates reference-side effects from changing the temperature being measured.^[ref]

An original ideal calculation explains the test. Let $E(T)$ be the thermocouple electromotive force response from the Seebeck effect relative to $0{}^{\circ }\mathrm{C}$. With isothermal connector junctions at $T_c$, the measured electric potential difference is $V=E(T_h)-E(T_c)$. Cold-junction compensation reconstructs $E(T_h)=V+E(T_c)$ before applying the inverse function of the response. In the stipulated linear model $E(T)=ST$ with $S=40\mu V/K$, a fixed $T_h=100{}^{\circ }\mathrm{C}$ gives $V=3.2\mathrm{mV}$ at $T_c=20{}^{\circ }\mathrm{C}$ and $2.8\mathrm{mV}$ at $30{}^{\circ }\mathrm{C}$. Correct compensation gives the same $100{}^{\circ }\mathrm{C}$ in both cases. These are constructed values, not measured performance or a calibration table for a particular thermocouple.

Cold-junction thermal coupling matters because the temperature sensor must represent the connector temperature. A precise converter reading cannot by itself remove an unmeasured temperature difference between those locations.^[ref]

A measuring chain is one successive signal path through a measuring system, beginning at a sensor and ending at an output element. The VIM illustrates this with both an electro-acoustic chain and a mechanical chain; a measuring chain need not be electronic.^[ref]

Consider an original force measurement: a load cell produces an electric potential difference, an amplifier scales that signal, an analog-to-digital converter encodes it, and software converts the code to a force value. This is one measuring chain within the larger measuring system, which also includes its excitation supply, references and mounting arrangements. The load cell acts as a measuring transducer.

In an ideal linear model, let sensor response be $S=2\mathrm{mV}{\mathrm{N}}^{-1}$, amplifier gain $G=100$, and converter step $q=1\mathrm{mV}$ per code increment. If the additive output offset is $n_0=10$ increments, the numerical output isThus $n=610$ implies $F=(610-10)/200=3\mathrm{N}$. These are stipulated teaching values, not measured equipment performance.

The example exposes why measurement calibration must describe the relevant path. Changing amplifier gain changes the relation between output and force even if the load cell is untouched. A saturated stage can also discard information that later conversion cannot restore. Gain uncertainty, offsets, instrumental drift and finite conversion steps contribute at different points; treating the final display's increment as the whole measurement uncertainty overlooks those contributions.

A measuring transducer is a device whose output quantity has a specified relation to its input quantity and is used in measurement. VIM examples include a thermocouple, a strain gauge and a Bourdon tube.^[ref] A measuring transducer provides a link in a measuring chain; it need not itself display a finished measurement result.

For an original pressure readout, choose a linear modelwith pressure $p$, output electric potential difference $V$, transducer sensitivity $S=2\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, and offset $V_0=1\mathrm{mV}$. An output $V=201\mathrm{mV}$ then corresponds to $p=100\mathrm{kPa}$. An amplifier, analog-to-digital converter and display can follow the transducer, each contributing to the whole measuring system.

The inverse calculation $p=(V-V_0)/S$ exposes distinct uncertainty contributions. Holding the other inputs fixed, a small output change $\delta V$ changes inferred pressure by $\delta V/S$; a small offset error changes it by $-\delta V_0/S$. An output increment $0.2\mathrm{mV}$ corresponds to $0.1\mathrm{kPa}$ for the stipulated sensitivity, but does not establish a total measurement uncertainty of that size.

Characterize the relevant range, temperature conditions, response time and possible instrumental drift during measurement calibration. The relation can be nonlinear, in which case local transducer sensitivity is the appropriate derivative rather than one gain valid everywhere. The definition also allows input and output quantities of the same kind; it does not require changing from a mechanical quantity to an electrical one. A sensor denotes the part directly affected by the phenomenon being sensed, whereas a complete measuring chain can contain further measuring transducers.

Mike Beckman is an electrical engineer identified in a 2013 Texas Instruments reference design as a systems engineer who, at that time, managed its converter product line. With Luis Chioye, he coauthored Precision Thermocouple Measurement with the ADS1118 by Mike Beckman and Luis Chioye, combining an analog-to-digital converter, thermocouple input and on-chip temperature sensor.^[ref]

Their design treats cold-junction compensation as both an electrical calculation and a thermal-layout problem. It places the converter near the connector and uses copper regions to improve cold-junction thermal coupling, while separating nearby heat sources. Its tests distinguish changing the reference-junction temperature from changing the measuring-junction temperature.^[ref]

A simple original linear model illustrates the reason. If a thermocouple has stipulated sensitivity $S=40\mu V/K$ and measures $V=2\mathrm{mV}$, then $V=S(T_h-T_c)$ implies $T_h-T_c=50\mathrm{K}$. A reference junction at $25{}^{\circ }\mathrm{C}$ therefore gives $T_h=75{}^{\circ }\mathrm{C}$. Reading that junction as $30{}^{\circ }\mathrm{C}$ instead gives $80{}^{\circ }\mathrm{C}$, despite perfect measurement of $V$. The model uses constant sensitivity only for illustration; actual cold-junction compensation uses the appropriate thermoelectric conversion.

Digital acquisition converts a continuous voltage signal into timed numerical samples. A practical chain is a suitably buffered and amplified sensor signal, an analogue anti-aliasing filter, a sampling or sample-and-hold stage, an analog-to-digital converter, and a clocked data-storage system. Choose the gain so that the interesting variation uses the available input range without clipping. Finite input impedance can load a sensor, so an appropriate buffer or operational amplifier may be needed.

Sampling makes time discrete. If the conditioned signal is confined below frequency $f_{\max }$, choose a sampling rate $f_s>2f_{\max }$, allowing a transition band for the physical filter. The Nyquist–Shannon sampling theorem permits ideal reconstruction of a suitably bandlimited function from exact samples. Without filtering, components separated by integer multiples of $f_s$ have identical samples; in particular real sinusoids at $f$ and $f_s-f$ can be indistinguishable. This aliasing cannot generally be undone by later digital filtering. Oversampling can ease filter design, but does not replace the requirement to suppress unwanted high-frequency content before sampling.

Amplitude quantization is separate from sampling. A uniform $b$-bit converter covering voltage span $V_{\mathrm{span}}$ has step $q\simeq V_{\mathrm{span}}/2^b$. Rounding an in-range input gives the uniform-quantization error bound $|ϵ|\le q/2$. If the rounding errors can additionally be modeled as uniform and uncorrelated, their standard deviation is $q/\sqrt{12}$. This statistical estimate is not a guarantee for a constant input or a coherent periodic signal. More bits increase resolution, but accuracy also depends on voltage-reference calibration, offset, gain error, nonlinearity and electronic noise. Out-of-range signals clip and invalidate the rounding bound.

Clock quality matters too. Timing jitter $\delta t$ gives a voltage error approximately $(dV/dt)\delta t$; for a sinusoid its scale grows with $2\pi f{V}_p{\sigma }_t$. A clock calibration error biases measured frequencies and time intervals. Simultaneous multichannel signals need known relative timing, and the sampling and analogue settling times must be appropriate to the signal bandwidth.

For $n_c$ channels the raw recording rate is approximately $n_c{f}_{s}b$ bits per second, before overhead, so storage and sustained transfer speed must prevent missing data. Store units, channel identities, timestamps, sampling rate, input ranges and calibration information along with the readings. Preserve the original samples when applying digital filters or other processing. Averaging can improve precision for independent fluctuating errors, but cannot restore aliased frequencies, clipped peaks or a fixed rounding bias. Digital recording makes reproducible analysis and transmission possible when its sampling, amplitude and timing limitations are all controlled.

A ratiometric measurement infers a quantity from a ratio of two measured signals chosen to share an unwanted multiplicative variation. The useful question is which inputs actually share that variation: a reference resistor error or a change in the sensor itself generally survives the cancellation.

In a shared-excitation resistance ratio measurement, a current source passes the same electric current $I$ through a sensor of electrical resistance $R_T$ and a reference resistor $R_{\mathrm{ref}}$. Their electric potential differences are $V_T=I{R}_T$ and $V_{\mathrm{ref}}=I{R}_{\mathrm{ref}}$. An ideal normalized analog-to-digital converter reading is thereforeThe current source need not have a perfectly constant output for this cancellation, provided both measurements sample the same electric current, the denominator is nonzero, and the converter stays within its operating ranges. This is a standard arrangement for a resistance thermometer.^[ref]

For an original ideal example, take $R_T=100\Omega$, $R_{\mathrm{ref}}=2000\Omega$ and $I=1\mathrm{mA}$. Then $V_T=0.100\mathrm{V}$, $V_{\mathrm{ref}}=2.00\mathrm{V}$ and $r=0.05$. Increasing $I$ by $5\%$ gives $0.105\mathrm{V}$ and $2.10\mathrm{V}$: the ratio remains $0.05$. If the converter instead uses an independent fixed $2\mathrm{V}$ reference and the calculation assumes the original $1\mathrm{mA}$, the inferred electrical resistance becomes $105\Omega$.

The reference-resistor error in ratiometric resistance measurement remains even with perfect shared excitation. If the actual reference resistor is $R_{\mathrm{ref},\mathrm{nom}}(1+e)$ but the calculation uses its nominal value, thenThus a $+0.1\%$ reference error makes the nominal estimate of a true $100\Omega$ sensor about $99.9001\Omega$. Reference accuracy and its variation with temperature still matter.^[ref]

Nor does the ratio remove sensor self-heating in a ratiometric resistance measurement. Joule heating dissipates $P=I^2{R}_T$, which is $0.1\mathrm{mW}$ in the example. A temperature rise changes the actual electrical resistance of a resistance thermometer; the ratio then measures that changed resistance. Reducing the electric current or comparing several currents can reveal this physical effect.^[ref]

The law of propagation of uncertainty makes the role of covariance explicit. For small perturbations of nonzero mean signals, the first-order measurement uncertainty of $r=V_T/V_{\mathrm{ref}}$ obeysThe contribution from a shared excitation fluctuation cancels through the covariance term. Treating the two signals as independent random variables would discard that cancellation. Other errors need their own inputs in the complete model.^[ref]

For time-varying excitation, ratiometric cancellation with matched signal and reference filters requires matching dynamics as well as shared wiring. With constant resistances and identical linear time-invariant systems of impulse response $h$, the filtered signals are $R_T(h\ast I)$ and $R_{\mathrm{ref}}(h\ast I)$, so their ratio is still $R_T/R_{\mathrm{ref}}$ wherever defined. Here $\ast$ denotes convolution. Different filters or different sampling times can leave an excitation-dependent error.^[ref]

A simple proposed bench test first replaces the sensor by a stable calibrated resistor, sweeps the electric current within the instrument limits, and records both electric potential differences and their ratio. That separates electrical cancellation from changing sensor temperature. Repeating with a resistance thermometer in a stable bath then tests Joule heating; changing the reference resistance or one filter tests the predicted failure modes. These are proposed checks of the model, rather than reported experimental results.

A shared-excitation resistance ratio measurement compares two electrical resistances by passing the same electric current through them and comparing their electric potential differences. It is the circuit realization of a ratiometric measurement: the unknown excitation becomes a common multiplicative input.

For a sensor $R_T$ in series with a reference resistor $R_{\mathrm{ref}}$, ideal high-input-impedance sensing givesThe electric current must be nonzero and shared at the time relevant to each sample. One implementation feeds $V_T$ to an analog-to-digital converter input and $V_{\mathrm{ref}}$ to its external reference pins; the conversion is then scaled by their ratio. The primary circuit guide shows this wiring and includes the programmed gain when translating a digital code to resistance.^[ref]

For an original check, choose $R_T=180\Omega$ and $R_{\mathrm{ref}}=1200\Omega$. Excitation at $0.4\mathrm{mA}$ gives $0.072\mathrm{V}$ and $0.480\mathrm{V}$; excitation at $1.2\mathrm{mA}$ gives $0.216\mathrm{V}$ and $1.440\mathrm{V}$. Both give $r=0.15$ and recover $180\Omega$. This calculation assumes unchanged resistances; the larger excitation dissipates nine times the sensor electric power, making sensor self-heating in a ratiometric resistance measurement an independent test.

A common supply is insufficient if different branch currents pass through the two resistances. With currents $I_T,I_{\mathrm{ref}}$,This is branch-current mismatch in a resistance ratio measurement. Sequential sampling of a changing excitation has the same problem unless the two paths retain the same effective excitation history. Ratiometric cancellation with matched signal and reference filters specifies the dynamic condition.

Wiring matters even with an ideal shared current source. A two-wire sensor reading includes lead electrical resistance; four-terminal sensing separates the current leads from high-impedance potential-sensing leads. The reference itself needs the same care if lead drops would otherwise enter its measured denominator.^[ref]

A bench check can replace the sensor with a stable known resistor, sweep excitation, and compare each measured potential with their ratio. A constant ratio accompanied by changing individual potentials tests shared excitation. It does not establish reference accuracy, eliminate sensor heating, or prove operation outside the converter's input and reference ranges.

Walt Kester is an electrical engineer whose technical writing concerns data converters and sampled-data electronics. He edited The Data Conversion Handbook edited by Walt Kester, which brings together converter architectures, testing, interfacing and practical circuit design.^[ref]

A useful distinction in this subject is between signal sampling, which selects values at particular times, and quantization, which selects a representable numerical level. An analog-to-digital converter combines both. Kester's explanation of the Nyquist–Shannon sampling theorem connects the sampling rate with the frequencies present at the converter input, making filtering part of the measurement design.^[ref]

Technical publications: www.analog.com/en/resources/technical-books/data-conversion-handbook.html