13.3 Signal Conversion, I/P, Splitters, and Bit Precision
Key Takeaways
- Analog-to-digital and digital-to-analog converters map 4–20 mA (or 1–5 V) to integer codes; quantization is commonly bounded by ±½ LSB and isolation does not remove it.
- An I/P converts 4–20 mA to 3–15 psi; a P/I reverses that; an I/I repeats or isolates current and may steal loop voltage if it is a passive series device.
- Splitters duplicate a 4–20 mA signal for a second consumer; each series burden is a voltage tax that must be checked at 20 mA.
- Engineering-unit resolution over a 4–20 mA span is approximately (URV − LRV)/2^n, so 16-bit is 16 times finer than 12-bit on the same span.
- Stacking a series splitter and a series isolator on a 24 V loop is a classic brown-out: the transmitter can be left below its minimum terminal voltage at 20 mA.
Why conversion is its own spec item (4.B)
Specification 4.B is the hardware that sits between signal types: analog-to-digital (A/D), digital-to-analog (D/A), I/P, P/I, I/I, splitters, filters, and the bit precision of the converter. The exam loves two mistakes: treating bit depth as decoration instead of engineering-unit resolution, and stacking isolators and splitters until a 24 V loop cannot power the transmitter at 20 mA.
A/D, D/A, quantization, and isolation
An analog-input card samples a 4–20 mA (or 1–5 V) signal, usually after a burden resistor and an anti-aliasing filter, and maps it to an integer. That is A/D. An analog-output card does the reverse: integer to current — D/A. Quantization error is inherent: the true analog value is replaced by the nearest code. A common bound is ±½ LSB (least significant bit).
Galvanic isolation on the card or in a field isolator breaks ground loops and common-mode voltage. Isolation does not remove quantization, and a series isolator in the field adds voltage drop and its own transfer error. If two systems must share a 4–20 mA without tying commons, isolate on purpose — then pay for that isolation in the voltage budget, not as an afterthought.
If the converter’s electrical range is 0–20 mA or 0–24 mA but the process span is only 4–20 mA, some codes sit below live zero. Effective counts on the process span shrink:
Always ask whether $n$ bits cover 4–20 mA or a wider card range. A “12-bit input” that actually digitizes 0–24 mA is coarser on the live-zero span than a 12-bit converter mapped only across 16 mA.
I/P, P/I, and I/I
An I/P (current-to-pneumatic) transducer converts 4–20 mA → 3–15 psi (sometimes 6–30 psi). That is how an electronic loop still drives a pneumatic actuator or positioner. Live zero maps to live zero: 4 mA → 3 psi, 12 mA → 9 psi, 20 mA → 15 psi. A P/I is the reverse, used when a pneumatic process variable must enter a distributed control system.
An I/I is a current isolator/repeater: 4–20 mA in, isolated 4–20 mA out. Use it to break a ground loop, to re-power a long run, or to feed a second system without tying commons. It is not free: a passive I/I sits in series and consumes loop voltage; an active (powered) I/I can source the output loop from a separate supply so the input loop only sees a modest burden.
Splitters and filters
A splitter takes one 4–20 mA and produces two (or more) isolated 4–20 mA outputs — for example the basic process control system and a local recorder, or a control analog input and a safety analog voter, with isolation between them. Passive splitters add series voltage drop on the input loop. Powered splitters need 24 V and still have input compliance limits.
Filters (RC, instrumentation-amplifier low-pass, 50/60 Hz rejection) sit before the A/D. They reduce aliasing and noise but add lag. Do not put a one-second filter on a loop that must trip in 200 ms, and do not skip anti-aliasing on a high-speed sampled input. Filtering is signal conditioning; it is not a substitute for shielding and a current loop.
Worked numeric: 12-bit versus 16-bit over a 4–20 mA span
A level transmitter is 4–20 mA = 0–80.00 in. The analog input maps that 16 mA span onto the converter (live zero aligned to 0% counts).
12-bit: $2^{12} = 4096$ codes.
Half-LSB quantization ≈ ±0.0098 in.
16-bit: $2^{16} = 65536$ codes.
Half-LSB ≈ ±0.00061 in.
The ratio is exact: $65536/4096 = 16 = 2^{4}$. Sixteen-bit is 16 times finer than 12-bit over the same span. If the process only needs 0.1 in resolution, both converters are finer than the requirement — and the analog transmitter accuracy, not the bit depth, will dominate. If the item asks which converter can resolve 0.002 in, only 16-bit gets there ($0.00122 < 0.002 < 0.0195$).
Using $2^{n}-1$ instead of $2^{n}$ changes the 12-bit step from 0.0195 to $80/4095 \approx 0.0195$ in — immaterial at PE precision. The traps are using 20 mA as the span instead of 16 mA, treating the card as 8-bit leftover from an old analog-output stereotype, or ignoring that a 0–24 mA card wastes codes below 4 mA.
Exam trap: splitter plus isolator kills the voltage budget
Loop voltage is checked at 20 mA (worst IR drop, worst burden).
Given: 24.0 VDC supply. Transmitter minimum 12.0 V at 20 mA. Cable loop resistance 100 Ω. Analog-input burden 250 Ω. A technician then series-inserts a passive isolator (5.0 V drop at 20 mA) and a passive splitter (another 5.0 V at 20 mA).
Drops at 20 mA:
- Cable: $0.020 \times 100 = 2.0$ V
- Analog-input burden: $0.020 \times 250 = 5.0$ V
- Isolator: 5.0 V
- Splitter: 5.0 V
- Sum of drops = 17.0 V
- Voltage left for the transmitter: $24.0 - 17.0 = 7.0$ V
7.0 V < 12.0 V required. The transmitter browns out as current rises: the process variable may peg, drop toward a fail-low current, or chatter. The fix is not a bigger splitter. Use a powered splitter/isolator that does not steal 10 V from the input loop, raise the supply if the transmitter allows, shorten or thicken the cable, or take the second copy from a control-system analog output or HART instead of another series burden.
Without the two add-ons, remaining voltage would be $24.0 - 2.0 - 5.0 = 17.0$ V — comfortably above 12 V. The stack, not the original loop, is what dies.
[!CAUTION]
Stacking burdens
Every series device is a voltage tax at 20 mA. Isolator + splitter + barrier + 250 Ω card is how a healthy 24 V design fails on paper while each device “only drops 5 V.”
A 4–20 mA level transmitter is calibrated 0–80.00 in. A 12-bit analog input maps that 16 mA span onto the converter. What is the approximate engineering-unit resolution?
A 24.0 VDC two-wire loop supplies a transmitter that needs 12.0 V at 20 mA. Loop cable is 100 Ω, the analog-input burden is 250 Ω, a passive isolator drops 5.0 V at 20 mA, and a passive splitter drops another 5.0 V at 20 mA. What voltage remains at the transmitter terminals at 20 mA?
In a standard electronic-to-pneumatic analog loop, what does an I/P transducer convert?