Analogue signal processing: counts to engineering units, NE43 and filtering

What arrives is not a value

An analogue input does not hand you "52.3%". It hands you counts: an integer from an ADC. And every vendor counts differently:

27648 is not arbitrary: it is 1.25 × 22118, and the headroom up to 32511 exists because a transmitter can legitimately send more than 20 mA.

The 4-20 mA loop

Field zero is 4 mA, not zero. That is the live zero, and the reason is diagnostic: if the wire breaks the current is zero, zero is not a valid reading, so you know you have a fault. With 0-10 V you cannot tell "zero" from "cut".

mA  := 4.0 + Counts * 16.0 / 27648.0;
Eng := (mA - 4.0) * 100.0 / 16.0;

Or straight to a general form for any range:

Eng := EngMin + (Counts - CntMin) * (EngMax - EngMin) / (CntMax - CntMin);

Write the constants with a decimal point (16.0, not 16) or you do integer division and throw the fraction away.

NAMUR NE43: the current tells you its own health

NAMUR NE43 splits the loop into bands, and it is now general industrial practice:

So do not test "is this value plausible?". Test the current, before scaling. And put a short on-delay on the fault, because an electrical transient is not a failed sensor.

The EMA filter

An exponential moving average is one line, and its memory is one variable:

Filt := Filt + Alpha * (Eng - Filt);

Alpha is between 0 and 1. One means no filter, 0.05 is heavy. The relation to a time constant:

Alpha ≈ Ts / (Tau + Ts)

At a 50 ms scan, Alpha = 0.15 gives roughly a 280 ms time constant. Rule of thumb: light filtering on level and pressure, heavier on flow, and almost none on anything feeding safety logic, because a filter delays.

The rate-of-change limit

This is the strongest way to catch a sensor failing inside its valid band. Ask what the process can physically do. In this lab the pump moves the level 6% per second, so a 40%-per-second jump is not process, it is a wire or a loose terminal.

Slope := ABS(Eng - Prev) / Ts;
IF Slope > 40.0 THEN
  (* do not feed the filter; hold the last good value *)
END_IF;

Order matters

Counts, NE43 check, engineering units, rate limit, filter, logic. Never filter before you validate: the filter hides the fault and makes a broken wire look like a dignified slow decline.