13.1 Analog and Discrete Signal Types

Why analog versus discrete is a Signals item

The PE Control Systems Signals domain is 11–17 questions. Specification 4.A opens with analog and discrete types because loop voltage budget, HART overlay, analog-input scaling, and discrete diagnostics all assume you can look at a milliamp, a volt, a psi, a millivolt, or a contact and know what a broken wire would do. Those signals usually terminate in a distributed control system (DCS) or programmable logic controller (PLC) analog or discrete input. Picking the wrong family is a failed design, not a unit-conversion slip.

Live zero: 4–20 mA, and why 0 mA is not 0%

A 4–20 mA current loop encodes 0% of calibrated span at 4 mA and 100% at 20 mA. The 4 mA floor is a live zero (elevated zero). Two reasons both show up on the exam:

1. Fault discrimination. An open pair, a dead supply, or a transmitter that has stopped conducting produces about 0 mA. That is a circuit failure, not a process sitting at lower range value. If the span started at 0 mA, a broken wire would look identical to a valid zero reading.
2. Two-wire power. A loop-powered transmitter must take operating current from the same pair that carries the signal. The 4 mA floor is the current the electronics are allowed to consume at 0% process; the remaining 16 mA is the modulation span.

Scale linearly on that 16 mA span. If $I$ is loop current in milliamps, LRV is lower range value, and URV is upper range value:

$\text{fraction of span} = \frac{I - 4}{20 - 4} = \frac{I - 4}{16}$

$\text{PV} = \text{LRV} + \frac{I - 4}{16}\,(\text{URV} - \text{LRV})$

Worked example: 12 mA is 50%

A differential-pressure transmitter is calibrated 4–20 mA = 0–200 inH2O. The analog input reads 12.00 mA.

$\frac{12 - 4}{16} = \frac{8}{16} = 0.50 \quad \Rightarrow \quad \text{PV} = 0 + 0.50 \times 200 = 100\text{ inH2O}$

12 mA is always 50% of a 4–20 mA span, regardless of engineering units. Check a second point: 7.2 mA is $(7.2 - 4)/16 = 0.20$, so the same 0–200 inH2O range reads 40 inH2O. The classic trap is treating 12 mA as $12/20 = 60%$ and reporting 120 inH2O — that ignores live zero.

The 1–5 V signal is the same live-zero idea after Ohm's law. A 250 Ω precision resistor (or analog-input burden) converts 4.00 mA → 1.00 V and 20.00 mA → 5.00 V. Voltage drop in the signal leads then appears as a reading error, which is why current — not voltage — is the long-run analog workhorse.

Other analog families

3–15 psi pneumatic is the live-zero air analog: 3 psig = 0%, 15 psig = 100%, span 12 psi. 9 psi is 50%. A failed air supply or a blown tube heads toward 0 psig, which is not 0% process. Pneumatic still appears on valve actuators, I/P (current-to-pneumatic) transducers, and electrically dead or intrinsically safe areas. Limits are compressibility lag, leaks, freeze-up of wet instrument air, and tubing volume — not induced millivolts.

Thermocouple millivolts are tens of millivolts. They need cold-junction compensation, shielded twisted pair, and usually a local transmitter if the run is long. Ground loops and electromagnetic interference swamp millivolts long before they swamp 4–20 mA.

A resistance temperature detector (RTD) (typically Pt100 = 100 Ω at 0 °C) is a resistance, not a current. Lead-wire resistance is a direct temperature bias on 2-wire connections; 3-wire and 4-wire circuits cancel or measure the leads. An RTD does not “output 12 mA” unless a transmitter is already in the loop.

Pulse / frequency comes from turbine meters, positive-displacement meters, speed probes, and some flow computers. The information is in the count or frequency, not in an analog level. Debounce, pull-up, and the maximum frequency of the high-speed counter card matter. A 4–20 mA analog of the same flow is a different signal with a different error budget.

Discrete: dry contact and NAMUR proximity

A dry contact is a switch with no voltage of its own. The discrete-input card supplies wetting voltage; the field device only closes or opens. Wetting current too low → oxidized contacts and missed closures. Leakage on a wet long cable → false ON. Polarity usually does not matter for a true dry contact, but it does matter if the “contact” is actually a solid-state output.

A NAMUR proximity sensor (IEC 60947-5-6) is a 2-wire current-level discrete, typically powered at about 8.2 V through a switching amplifier. Conventional bands: ≤ about 1.2 mA with the target present (damped), ≥ about 2.1 mA with the target absent. About 0 mA is an open wire; a very high current is a short. That three-way diagnostic (off / on / cable fault) is why NAMUR sensors appear in safety and hazardous-area designs. Do not confuse NAMUR proximity currents with NAMUR NE43 analog-failure currents — different documents, different milliamps.

NAMUR NE43 analog failure currents (practice, not a supplied table)

NAMUR NE43 is a user-association recommendation for how a smart 4–20 mA transmitter should use currents outside 4–20 mA to declare a fault. Typical practice bands:

NCEES does not hand you NE43 as a design-standard table on the Control Systems exam. Treat 3.6 mA / 21 mA as industry practice you should recognize, not as a lookup you can assume is in the electronic handbook. If an item gives the thresholds, use them. If it does not, reason from live zero (0 mA ≠ 0%) rather than inventing a code clause.

Limitations that actually fail loops

• Voltage drop. At 20 mA, every ohm of wire, barrier, isolator, and analog-input burden costs 0.020 V. The transmitter still needs its minimum terminal voltage. Design the loop at 20 mA, not at 4 mA.
• Leakage. Parallel moisture or damaged insulation steals current around a transmitter or holds a dry-contact input ON.
• Polarity. Two-wire transmitters, NAMUR amplifiers, and most analog inputs are polarized. Reverse them and you get 0 mA, a protection-diode drop, or a damaged input — not a negative process value.
• Distance versus noise. Current loops reject induced voltage; millivolt and 1–5 V circuits do not.

[!TIP]

Exam habit

When a stem gives milliamps and a range, convert with $(I-4)/16$. When it gives 0 mA, think open or unpowered, not lower range value.