Electronics & General Electrical

4–20 mA Measurement Chain Study

One process value followed from transmitter to ADC code — loop current, sense-resistor voltage, converter LSB and dynamic range, and the quantization error at the code the reading lands on.

linked calculations: 4linked calculations
inputs, entered once: 5inputs, entered once
values derived, not retyped: 2values derived, not retyped

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The system this study analyses

Drawn from the study’s own definition and annotated with the example values below. Every quantity on it is one the study entered or computed.

Measurement chain (example)

Measurement chain analysed by this study, annotated with the values it used and computed.

›Diagram values as a table

Measurement chain diagram: Transmitter (transmitter), then Sense resistor (resistor), then Converter (analogue-to-digital converter), then Digital value (digital readout).
Element	Quantity	Value
Transmitter	Process value	100 units
Transmitter	LRV	0 units
Transmitter	URV	200 units
Transmitter	Span position	50 %
Sense resistor	Resistance	250 Ω
Sense resistor	Dissipation	0.036 W
Converter	Reference	5 V
Converter	Full scale	5 V
Converter	Step size	0.001221 V
Converter	Codes	4096
Digital value	Code	2458
Digital value	Represents	3 V
Digital value	Range used	60 %
Transmitter to Sense resistor	Loop current	12 mA
Sense resistor to Converter	Sense voltage	3 V
Converter to Digital value	Quantization error	0.0006104 V

A process measurement changes form three times between the sensor and the number on a screen. It leaves the transmitter as a current, becomes a voltage across a sense resistor, and arrives at the converter as one of a fixed set of codes. Each of those conversions has its own arithmetic, and the errors people meet in the field are almost always at the joins rather than inside any one stage.

This study runs the whole chain from one process value. It reports the loop current the transmitter would produce, the voltage the sense resistor develops, the step size and dynamic range the converter's bit depth buys, and the code that voltage lands on together with the error at that point.

The numbers are not entered twice. The loop current is computed once and carried into the sense-resistor step; the sense voltage is computed once and carried into the conversion step. Changing the sense resistance moves the code, which is the physical relationship a spreadsheet usually loses.

Every shared value is entered once

The system voltage is not typed into four calculators. It is defined once for the study and carried into every step that needs it — so a change reaches all of them, and no two steps can describe different systems.

The study’s shared inputs and the steps each one reaches
Input	Example value	Used by
Process valueTransmitter	100 units	Step 01
Lower range value (LRV)Transmitter	0 units	Step 01
Upper range value (URV)Transmitter	200 units	Step 01
Sense resistanceSignal conditioning	250 ohm	Step 02
Converter reference voltageConverter	5 V	Step 03, Step 04
Loop currentDerived	12 mA	Computed by Step 01, used by Step 02
Sense voltageDerived	3 V	Computed by Step 02, used by Step 04

The 4 steps

Worked through below with an example measurement chain study (4–20 ma transmitter to digital value). Every number shown was produced by the same calculators the library already ships — nothing on this page is illustrative.

Step 01
Transmitter scaling
4–20 mA Loop Scaling Calculator
Converts the process value into the loop current a transmitter calibrated to this range would produce, and reports the position within the calibrated span.
Inputs and their sources
- ConvertProcess value → currentFixed by the study
- Lower range value (LRV)0 unitsYou enter
- Upper range value (URV)200 unitsYou enter
- Process value100 unitsYou enter
Example results
- Loop current12mA
- Percentage of span50%
- Calibrated span200units
- Process units per mA12.5units/mA
›Why this step is here
The chain starts here because everything downstream is a representation of this one number. The span of a 4–20 mA loop is 16 mA rather than 20 mA — the 4 mA offset is a live zero, which exists so that no current at all is distinguishable from a genuine reading of zero. Dividing by 20 instead of 16 is the classic arithmetic slip with these loops, and it gives an answer that looks plausible everywhere except the endpoints.
›Worked solution
1. Fraction of span from the process value
  $f = \dfrac{PV - PV_{LRV}}{PV_{URV} - PV_{LRV}}$
  $f = \dfrac{100 - 0}{200 - 0}$
  $f = 0.5 \;(50\%)$
2. Loop current from the fraction of span
  $I = 4\,\text{mA} + f \cdot 16\,\text{mA}$
  $I = 4 + 0.5 \cdot 16$
  $I = 12\ \text{mA}$
Calculator assumptions
- The transmitter's output is exactly linear between its calibrated 4 mA and 20 mA endpoints.
- The transmitter is correctly calibrated — 4 mA corresponds to the LRV entered and 20 mA to the URV.
- The loop is intact and the receiving input's impedance is within what the transmitter can drive.
References
- Standard practice for analogue current-loop transmission in process instrumentation; the 4–20 mA signal range and live-zero convention are defined in IEC 60381-1.
- Bela G. Liptak (ed.), Instrument Engineers' Handbook, Volume 1: Process Measurement and Analysis.
Step 02
Sense resistor
Ohm's Law Calculator & Power Wheel
Applies Ohm's law to the loop current and the sense resistance to give the voltage presented to the converter, and the power the resistor dissipates.
Inputs and their sources
- Current12 mADerivedStep 01 · Transmitter scaling
- Resistance250 ΩYou enter
Example results
- Voltage3V
- Power0.036W
›Why this step is here
A converter reads voltage; a loop carries current. The sense resistor is the whole of the conversion between them, and the resistance chosen is what sets the voltage span the converter sees — 250 Ω turns 4–20 mA into 1–5 V, which is why that value is so common. Current is used to carry the signal in the first place because the voltage dropped along a long cable run subtracts from a voltage signal and does nothing at all to a current one.
›Worked solution
1. Voltage from Ohm's law
  $V = I \times R$
  $V = 0.012 \times 250$
  $V = 3\ \text{V}$
2. Power from current and resistance
  $P = I^2 \times R$
  $P = 0.012^2 \times 250$
  $P = 0.036\ \text{W}$
Calculator assumptions
- DC circuit, or AC circuit at unity power factor (P = VI with no reactive component).
- All four quantities are treated as real, positive scalars.
- Resistance is treated as constant (no temperature dependence).
References
- Boylestad, R., Introductory Circuit Analysis, 13th ed., Chs. 2–4
- IEC 60027-1, Letter symbols for electrotechnology
Step 03
Converter resolution
ADC Resolution & LSB Calculator
Reports the number of codes, the size of one step and the dynamic range the chosen bit depth and reference voltage give the converter.
Inputs and their sources
- Resolution12 bitsYou enter
- Input rangeUnipolar — 0 to VrefYou enter
- Reference voltage5 VYou enter
Example results
- LSB (one step)0.001221V
- Number of codes4096
- Highest code4095
- Full-scale range5V
- Dynamic range72.25dB
- One LSB as a share of full scale0.02441%
- One LSB in parts per million244.1ppm
›Why this step is here
This step describes the ruler rather than the measurement: it takes no signal at all. One code is worth the full-scale range divided by 2^N, and nothing finer than that step is visible to the converter however quiet the rest of the chain is. Two details cause most of the confusion and are both reported here — a bipolar input spans twice the reference, and there are 2^N codes whose highest is 2^N − 1, because counting starts at zero. Resolution is a ceiling and not an accuracy: a real device adds non-linearity, offset, gain error and noise on top of it.
›Worked solution
1. Number of codes from the resolution
  $\text{codes} = 2^{N}$
  $\text{codes} = 2^{12}$
  $\text{codes} = 4096$
  There are 4096 codes, and the highest is 4095 — counting starts at zero.
2. Size of one step
  $V_{LSB} = \dfrac{FSR}{2^{N}}$
  $V_{LSB} = \dfrac{5}{4096}$
  $V_{LSB} = 0.0012207\ \text{V}$
  Dividing by 2^N gives the step between adjacent codes. Dividing by 2^N − 1 instead answers a different question — the volts per code of a converter whose top code sits exactly at full scale — and the two differ by one part in 2^N.
3. Dynamic range in decibels
  $DR = 20\log_{10}\left(2^{N}\right)$
  $DR = 20\log_{10}(4096)$
  $DR = 72.2472\ \text{dB}$
  The ratio of full scale to one LSB, expressed in dB. This is not the same quantity as signal-to-noise ratio, though the two are often confused — see the quantisation error and SNR calculator.
Calculator assumptions
- The converter is ideal: its only imperfection is the finite step size, and every step is exactly the same width.
- The full-scale range is exactly the reference voltage for a unipolar input, or twice it for a bipolar one, with no headroom lost at either end.
- The reference voltage is stable and accurate — its own error scales every code equally and appears as a gain error.
- LSB is defined as FSR divided by 2^N, the step between adjacent codes.
References
- Standard data-acquisition relations: the number of codes 2^N, the step size FSR/2^N, and dynamic range 20·log₁₀(2^N). These follow directly from the definition of uniform quantisation.
- Walt Kester (ed.), The Data Conversion Handbook, Analog Devices.
- Bela G. Liptak (ed.), Instrument Engineers' Handbook, Volume 1: Process Measurement and Analysis.
Step 04
Signal conversion
ADC Quantization Error & SNR Calculator
Converts the sense voltage to a code on that ruler, and reports the quantization step, the error at this point, the share of the converter's range the signal occupies and the ideal signal-to-noise ratio at that amplitude.
Inputs and their sources
- Resolution12 bitsYou enter
- Input rangeUnipolar — 0 to VrefYou enter
- Reference voltage5 VYou enter
- Input voltage3 VDerivedStep 02 · Sense resistor
Example results
- Maximum quantization error (±½ LSB)0.0006104V
- Quantization step (1 LSB)0.001221V
- Maximum error as a share of full scale0.01221%
- Ideal SNR, full-scale sine74dB
- Ideal SNR at this input amplitude69.56dB
- Output code2458
- Voltage that code represents3V
- Actual error for this input0.0004883V
- Range utilisation60%
›Why this step is here
The sense voltage is not re-entered here — it arrives from step 02, so changing the sense resistance moves the code without anyone retyping a number. The figure worth reading is the range utilisation. Quantization noise is fixed by the step size and does not shrink when the signal does, so every part of the converter's range the signal leaves unused is signal-to-noise ratio given away: a converter driven to a tenth of its range behaves like one with about three fewer bits. That is the relationship between the sense resistance chosen in step 02 and the reference voltage chosen here, expressed as a number.
›Worked solution
1. Size of one quantization step
  $V_{LSB} = \dfrac{FSR}{2^{N}}$
  $V_{LSB} = \dfrac{5}{2^{12}}$
  $V_{LSB} = 0.0012207\ \text{V}$
2. Maximum error of a rounding quantizer
  $e_{max} = \pm\dfrac{V_{LSB}}{2}$
  $e_{max} = \pm\dfrac{0.0012207}{2}$
  $e_{max} = \pm6.1035e-4\ \text{V}$
  True for a converter that rounds to the nearest code. One that truncates has an error of 0 to −1 LSB instead — the same width of uncertainty, but offset by half a step.
3. Ideal signal-to-quantization-noise ratio
  $SNR = 6.02N + 1.76\ \text{dB}$
  $SNR = 6.02 \cdot 12 + 1.76$
  $SNR = 74\ \text{dB}$
  A full-scale sine wave figure and nothing else. The 1.76 dB is 10·log₁₀(3/2), which comes from comparing a full-scale sinusoid against error spread uniformly over one LSB.
4. SNR actually available at this amplitude
  $SNR' = SNR + 20\log_{10}(k)$
  $SNR' = 74 + 20\log_{10}(0.6)$
  $SNR' = 69.563\ \text{dB}$
  Quantization noise is fixed by the step size, so a smaller signal does not bring quieter noise — every dB of unused range is a dB of SNR given away.
Calculator assumptions
- The quantizer is ideal and uniform: every one of the 2^N steps is exactly the same width, and the converter rounds to the nearest code.
- Quantization error is treated as uniformly distributed across one LSB, which is the standard basis of the 6.02N + 1.76 dB figure.
- The SNR figure assumes a full-scale sine wave; the derated figure assumes a sine wave of the stated amplitude.
- The full-scale range is the reference voltage for a unipolar input, or twice it for a bipolar one.
References
- Standard uniform-quantisation relations: step size FSR/2^N, worst-case error ±½ LSB, and the ideal full-scale-sine SNR of 6.02·N + 1.76 dB, where 1.76 dB is 10·log₁₀(3/2).
- Walt Kester (ed.), The Data Conversion Handbook, Analog Devices.
- IEEE Std 1241, Standard for Terminology and Test Methods for Analog-to-Digital Converters, cited by identity for the definitions of SNR, SINAD and effective number of bits.

Why these steps, in this order

Why the span is 16 mA and not 20 mA

A 4–20 mA loop has a live zero: the signal starts at 4 mA so that no current at all is distinguishable from a genuine reading of zero, which is a broken conductor or a dead transmitter rather than a measurement. The consequence is that the fraction of span is (I − 4) / 16. Dividing by 20 is the most common error with these loops and gives an answer that looks right at every point except the two endpoints.

Why a current and then a voltage

Current is used to carry the signal because the voltage dropped along a long cable run subtracts from a voltage signal and does nothing at all to a current one. Converters, on the other hand, read voltage. The sense resistor is the whole of the conversion between the two, and the resistance chosen is what sets the voltage span the converter sees — 250 Ω turns 4–20 mA into 1–5 V, which is why that value is so common.

Why the resolution and the reading are separate steps

They answer different questions from the same reference. The resolution step describes the ruler: how many codes there are, how large one step is, and how much dynamic range the bit depth buys. It takes no signal at all. The conversion step describes this particular reading on that ruler — which code it lands on, the error at that point, and how much of the converter's range the signal occupies.

Why range utilisation is the number to read

Quantization noise is fixed by the step size and does not shrink when the signal does. Every part of the converter's range a signal leaves unused is signal-to-noise ratio given away: a converter driven to a tenth of its range behaves like one with about three fewer bits. Matching the sense resistance and the reference voltage so the signal fills the range is one of the highest-value decisions in a measurement chain, and this study reports the cost of not doing it.

What the study does not model

Every stage here is an ideal one. The transmitter is exactly linear between its calibrated endpoints, the resistor is exact, and the converter's only imperfection is its finite step size. Sensor accuracy, transmitter linearity and drift, resistor tolerance and temperature coefficient, amplifier offset and noise, reference drift, and converter non-linearity are all outside these models — and in a real chain the sensor's own accuracy usually dominates everything else here. Each calculator states its own limitations, and the study carries them through rather than summarising them away.

What this study reports, and what it leaves to you

The study runs each calculation and reports the numbers with the assumptions, model boundaries and references the calculators state for themselves. It draws no conclusion about your installation. Comparing a derated ampacity against a load current, or a voltage drop against a design limit, is engineering judgement — the study puts the numbers in front of you and stops there.

Results are preliminary and educational. They are not verified for any specific installation and must be reviewed by a licensed Professional Engineer before they inform construction, equipment selection or protection settings.

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Frequently asked questions

What is a measurement chain?

The sequence of stages a measurement travels through between the process and the number an operator reads: the sensor and transmitter, the wiring that carries the signal, whatever conditioning turns it into the form the converter wants, and the analogue-to-digital conversion itself. Each stage has its own arithmetic and its own error sources, and the total is what determines what the reading means.

What process value does 12 mA represent?

Exactly mid-span. The span of a 4–20 mA loop is 16 mA, so 12 mA is (12 − 4) / 16 = 50 % of span. On a transmitter ranged 0–200 that is 100, not 120 — dividing by 20 mA rather than the 16 mA span is the most common mistake with these loops.

Why is the sense resistor usually 250 Ω?

Because 4 mA through 250 Ω is 1 V and 20 mA through 250 Ω is 5 V, so it turns the standard current span into the standard 1–5 V voltage span that converter inputs were built around. Any resistance works arithmetically; 250 Ω is the one that lands on the conventional voltage range.

What do I have to enter?

Five values, each entered once: the process value, the transmitter's lower and upper range values, the sense resistance, and the converter's reference voltage — plus the bit depth and input range on the two converter steps. The loop current and the sense voltage are derived rather than entered.

Does the study choose components or settings for me?

No. It reports a calculated current, voltage, step size, code and percentage with the assumptions, model boundaries and references each calculator states for itself. It reaches no conclusion about component selection, converter choice, or whether any value is appropriate for your installation. Every result is preliminary and educational and needs a licensed Professional Engineer's review before it informs construction, equipment selection or instrument configuration.

Can I use this to design a temperature trip or a protective function?

No. A measurement chain study is for measurement analysis and education only. It is not a design tool for a temperature trip, over-temperature protection, or any safety-instrumented function. A process transmitter very often does feed a protective system, which is exactly why this boundary is stated rather than assumed: designing that protection is a separate engineering activity with its own requirements for redundancy, response time, failure modes and independent verification, none of which a scaling and conversion calculation addresses.

Can I change one input and run it again?

Yes. Changing a shared input marks every step it reaches, and running the study again recomputes only those steps — in dependency order, so the conversion step never reads a sense voltage that is about to change in the same run.

What do I get at the end?

A professional PDF report with every step's worked solution, the inputs each one used and where each value came from, the measurement-chain diagram annotated with the run's own values, the calculators' own assumptions and limitations, the collected references, and the standing engineering disclaimer.

Is this study clear?

Tell us if a step, an input or a worked solution needs explaining better — or which study you'd like next. Reports go straight to our team.