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4-20 mA scaling

A physical quantity to a 4-20 mA loop current and back, reversed scale included, with faults flagged.

Parameters

The sensor’s measuring range, in its unit: 0-10 bar, −50-150 °C…

Result

Loop current

12 mA

Calculation
mA = 4 + 16 × (5 − 0) / (10 − 0) = 12
12 mA0 – 4 mA: outside the range (live zero)048121620mA02.557.510value
Loop current
12 mA
Physical value
5
Position in the range
50 %
Notes (2)

A single vertical marker links both rulers: the computed value is in copper, the entered value in ink.

The sensor outputs 12 mA, that is 50% of the range.

Calculation, assumptions and sources

OverviewTwo-way conversion between a physical quantity (pressure, level, temperature, in the chosen unit) and the current of a 4-20 mA loop, for any range, reversed scale included.

Two-way conversion between a physical quantity (pressure, level, temperature, in the chosen unit) and the current of a 4-20 mA loop, for any range, reversed scale included. Currents below 4 mA (probable loop fault) and above 20 mA (saturation or alarm) are flagged.

Method & formulasmA = 4 + 16 × (value − min) / (max − min)
mA = 4 + 16 × (value − min) / (max − min)value = min + (max − min) × (mA − 4) / 160% ↔ 4 mA, 50% ↔ 12 mA, 100% ↔ 20 mA

Sixteen milliamps cover the whole range: 1% of range is 0.16 mA. Mid-range, 12 mA, is the quickest checkpoint with a multimeter.

Span
the sensor’s physical range, from low (4 mA) to high (20 mA).
Live zero
low end set at 4 mA. A current of 0 mA signals a fault (cut wire, dead sensor); the 4 mA at rest power the sensor through the loop.
Reversed scale
4 mA at the physical maximum. Common in ullage-based level measurement, and when safety logic must read a fault (0 mA) as the high value.
NAMUR alarms
usual fault thresholds: ≤ 3.6 mA low, ≥ 21 mA high (NE 43).
Validity domainThe transmitter is assumed linear between its calibration bounds.

The transmitter is assumed linear between its calibration bounds. Square-root transmitters (flow by differential pressure) or characterised ones fall outside this model. The same current reading error weighs more on a wide range: a 0-100 bar sensor read at ±0.01 mA gives ±0.06 bar.

Reading the resultOutside [4; 20] mA, the result is extrapolated along the line and marked as such; it serves diagnosis.

Outside [4; 20] mA, the result is extrapolated along the line and marked as such; it serves diagnosis. The range percentage is the figure to compare between transmitter and PLC.