Analog Scaling: Raw Counts to Engineering Units

What the card gives you

An analog input module converts the current on the loop into a number using an analog-to-digital converter. The number itself is arbitrary and depends entirely on the module. A 16-bit card configured for 4-20 mA might present 0 to 32767, or 6242 to 31208, or engineering units directly if the card supports it. There is no universal value; read the module documentation and, better, verify it by injecting a known current.

The linear scaling formula

Worked example: a card producing 0 to 32767 counts across 4-20 mA, a radar transmitter calibrated 0 to 25.0 feet, and a present reading of 13107 counts.

EU = (13107 - 0) / (32767 - 0) * (25.0 - 0.0) + 0.0
   = 0.4000 * 25.0
   = 10.0 feet

Sanity check: 13107 of 32767 counts is 40% of span.
40% of a 0-25 ft range is 10 ft, and 40% of 4-20 mA is 10.4 mA.
All three agree, so the scaling is right.

The three ranges that must agree

Nearly every scaling problem is a mismatch between three separate places where a range is recorded.

1. 01The transmitter calibrated range: what 4 mA and 20 mA actually mean at the device. A radar might be set 0-25 ft, or 0-30 ft, or 2-27 ft.
2. 02The analog card range configuration: whether the module is set for 4-20 mA or 0-20 mA, and what count range it reports.
3. 03The scaling constants in the PLC program: the numbers a programmer typed, often from a drawing rather than from the device.

When a level reads 20% high across the whole range and nobody can find a wiring fault, the usual answer is that someone re-ranged the transmitter in the field and did not update the program. This is why the calibrated range belongs on the loop sheet and in the instrument list, not only in code.

Clamping and validity

Raw scaling arithmetic will happily produce a level of negative four feet or a pressure of 340 psi on a 100 psi transmitter. Do not let those values into control logic.

• Clamp the scaled result to the calibrated range so downstream logic never sees a physically impossible number.
• Test the raw value against the NAMUR thresholds and set a separate fault bit when it is below 3.6 mA or above 21 mA equivalent counts.
• Hold the last good value when the input is faulted, and make the held state visible on the HMI so an operator knows they are looking at stale data.
• Alarm the fault. A silently held value is more dangerous than an obviously wrong one.

Square root extraction

Differential pressure flow measurement produces a signal proportional to the square of flow. Getting flow requires taking the square root of the normalized signal before applying the flow range.

The trap is applying it twice. Many transmitters can perform square root extraction internally. If the transmitter is set to linear output and the PLC extracts, that is correct. If the transmitter extracts and the PLC also extracts, the reading is wrong everywhere except at zero and full scale, which is exactly where people check. Decide where extraction happens, write it on the loop sheet, and verify at 50%.

Analog outputs scale the same way, backwards

An analog output takes an engineering value and produces counts. The arithmetic is the inverse of the input case. The thing people forget is the output range at the far end: a valve positioner calibrated 4-20 mA for 0-100% open behaves very differently from one calibrated for a split range of 4-12 mA. Confirm what the receiving device expects before assuming 20 mA means fully open.