Therm

Analog 4–20 mA Thermistor Temperature Transmitter

A fully analog (no microcontroller) 2-wire 4–20 mA temperature transmitter built from standard, multi-sourced parts — and a worked tutorial in the instrumentation theory behind it.

It does two jobs:

1. A teaching reference. If you've ever wanted to understand how a 4–20 mA transmitter actually works — loop power, sensor excitation, linearization, zero/span calibration — this is a complete, honest, end-to-end example with the math shown and a calculator you can run.
2. A real instrument. It was designed for chocolate temperature control (the 20–40 °C tempering/working range), as a more accurate and more robust replacement for thermocouples. But it is parameterized: point the included calculator at your thermistor and your temperature band and it tells you which resistors to fit.

Why analog? You can absolutely bolt a microcontroller and a 12-bit ADC on top of this for fine digital adjustment — see Optional digital upgrade. In practice, for "hold a setpoint in a known band" process control, that layer is rarely worth the complexity. This project deliberately stays in the analog domain so the whole signal path is visible and every part is replaceable.

Not a safety device. This is a process measurement instrument, not a safety-rated (SIL) one. Don't use it as a protective function.

Specifications (default build)

Outside the chosen band the output saturates near 4 mA (cold) or 20 mA (hot) — intentional. Accuracy is only specified inside the band.

How a 4–20 mA transmitter works (the theory)

The current loop. A 2-wire transmitter sits in series with a DC supply and a receiver. The transmitter's job is to draw a controlled current from the loop — 4 mA represents the bottom of the range, 20 mA the top — regardless of loop voltage or wiring resistance (within limits). Because the current is the signal, voltage drops in long cable runs don't corrupt the reading, and a broken wire reads 0 mA (a detectable fault, distinct from a valid 4 mA "low"). That noise immunity and fault detection is why 4–20 mA has survived for decades in industry.

Loop-powered ("2-wire"). The same two wires that carry the signal also power the transmitter. The catch: the entire circuit must run on less than 4 mA, because that floor is the lowest the loop ever provides. Every microamp the electronics draw is part of the loop current, so the design budgets quiescent current carefully and lets an output ("dump") transistor make up the difference to hit the commanded 4–20 mA.

Why a thermistor? An NTC thermistor is cheap, has a large signal (thousands of ohms change over our band), is available with tight interchangeability (±0.1–0.2 °C for the Omega 44000 series), and needs no cold-junction compensation like a thermocouple. Its one drawback is that it is very nonlinear — which is the interesting part of this design.

The nonlinearity problem (and the one-resistor fix)

An NTC's resistance is approximately

R(T) = R25 · exp( β · (1/T − 1/298.15) )      [T in kelvin]

For our 10 kΩ part that's ~57 kΩ at −10 °C falling to ~3.6 kΩ at +50 °C — about 15:1, and badly curved. Fed straight into a linear amplifier you'd get large errors away from one calibration point.

The fix is a single resistor in parallel with the thermistor. The parallel combination Rt ∥ Rlin has an S-shaped curve with an inflection point; placing that inflection at the center of your band makes the network resistance very nearly linear in temperature there. The value for maximum linearity at center temperature Tc (kelvin) is:

Rlin = Rt(Tc) · (β − 2·Tc) / (β + 2·Tc)

For the chocolate build (center 30 °C) the closed-form (unloaded) value is ~5.9 kΩ; the build uses 6.04 kΩ, re-optimized for the gain-stage loading (see below). Either way the residual nonlinearity across 20–40 °C is only ~±0.06 °C — comfortably inside the ±0.1 °C system spec, so the linearization is never the limiting term.

Why one resistor and not two

A second resistor can add a curvature-shaping term (by exciting through a divider instead of a constant current), so we checked whether it's worth it. For an NTC it essentially isn't — the optimizer drives the second resistor back toward "constant current," and the conformity barely moves:

~5% improvement for an extra precision part and an extra calibration interaction. We dropped it. The real lever is band width, not resistor count (see the table — the wider the band, the worse the conformity). Pick the narrowest band that covers where your process actually operates.

Don't let the gain stage load the sensor

There's a subtle trap the ideal math hides. The single-op-amp difference amp (next stage) presents its input network — R9 + R12 from the sensor node to ground — as a load on node X. The sensor's source impedance there is the linearized network (a few kΩ), so a low input impedance bleeds a temperature-dependent current out of the node and bows V(X), adding nonlinearity the zero/span trims cannot remove.

We only caught this with the device-level SPICE model (the ideal netlist and the first cut of design.py both assumed an infinite-impedance gain input). With the original 10 k / 24.9 k divider (R9+R12 ≈ 35 kΩ) loading a ~4 kΩ source, the in-band conformity blew out to ±0.18 °C — past the spec. Two fixes, both verified:

1. Raise the gain-stage input impedance so it stops loading the node — this build uses R9=R10=100 kΩ, R11=R12=249 kΩ (R9+R12 ≈ 349 kΩ, ~1 % loading).
2. Re-optimize R1 for whatever loading remains — design.py now models the load (--rload) and searches for the best linearization resistor rather than trusting the unloaded closed form (hence 6.04 kΩ, not 5.9 kΩ).

With both, conformity is back to ±0.058 °C, confirmed in the device-level sim. Lesson: a difference amp driven from a non-trivial source impedance must have an input impedance well above it, or you pay for it in linearity.

You can reproduce all of this — and design for your own sensor/range — with tools/design.py.

Circuit overview

Two views: the signal chain (what computes the current) and the power/output loop (how a 2-wire device powers itself and sets loop current).

Signal chain

 Vref(2.5V) ──[ NTC ∥ Rlin ]──● X ─────────────►┌────────────┐
                              │                 │   A2       │
              A1 sinks Iexc ──┘                 │ gain/zero  │─ Vcmd ─►┌──────────┐
              (0.25 mA, constant)               │  (2 pots)  │         │ A3 servo │─► loop
                                                └────────────┘         │  + Q2    │   current
   V(X) = Vref − Iexc·(NTC ∥ Rlin)                                     └──────────┘
        (rises with temperature)        Vcmd = SPAN·(V(X) − ZERO)   Iloop = Vcmd / Rsense

A constant current is pulled through the linearized network, so the node voltage V(X) is a clean, near-linear function of temperature. The gain/zero amplifier scales and offsets it; the output stage turns that command voltage into loop current.

Power / output loop

 LOOP+ ──▷|──┬───────────────────────────────┬──────────► IN (raw 7..30 V)
   (24 V) D1 │                               │
           TVS         pre-reg: Q1 + TL431 ───┤────────► VL (+5 V) ─► Vref, A1, A2, A3
            │          (series NPN follower)  │
            │                                 └────────► Q2 collector (dump)
            │                                                  │ emitter
 LOOP- ─────┴────────────────[ Rsense 50Ω ]──────  AGND ───────┘
                                    ▲
                A3 drives Q2 so that  Iloop · Rsense = Vcmd

Everything returns to AGND and flows out through Rsense, so the sense resistor sees the total loop current — the electronics' own ~2.6 mA quiescent draw plus whatever the dump transistor Q2 adds. A3 servos Q2 until that total equals Vcmd / Rsense. Because quiescent draw (~2.6 mA) is below the 4 mA floor, Q2 always has something to add.

Stage-by-stage

The three knobs are orthogonal, which makes calibration sane: Rlin depends only on the band center, span on the band width, and zero on the band position. Move the band up/down → re-zero only. Widen it → re-span only. Re-center it → change Rlin.

Selecting components for your own range

Run the calculator with your sensor and the two temperatures you want at 4 mA and 20 mA:

python3 tools/design.py --r25 10000 --beta 3892 --tlow 20 --thigh 40

It prints the linearization resistor, the excitation resistor, the span (gain) and zero (offset) targets, the conformity error you'll get, the self-heating estimate, and a transfer table. Defaults are the chocolate build. Output for the default:

--- Linearization ---
Rlin (E96)      : 6.040 kohm   <- re-optimized for gain-stage loading
Conformity      : +/- 0.059 C
--- Excitation ---
Rexc (E96)      : 10.000 kohm  -> Iexc = 0.2500 mA
--- Amplifier / output stage ---
SPAN  (gain)    : 2.5706 V/V   <- set by span pot
ZERO  (Vzero)   : 1.3872 V     <- set by zero pot

Manual recipe (what the script does):

1. Center → Rlin. Tc = (Tlow+Thigh)/2; Rlin = Rt(Tc)·(β−2Tc)/(β+2Tc), rounded to the nearest E96 value.
2. Excitation. Pick Iexc (~0.25 mA is a good balance of signal size vs. self-heating); set Rexc = Vref / Iexc.
3. Edge voltages. V(X) = Vref − Iexc·(Rt ∥ Rlin) at Tlow and Thigh.
4. Span (gain). SPAN = (20mA−4mA)·Rsense / (V(X)@Thigh − V(X)@Tlow).
5. Zero (offset). Choose ZERO so the output is 4 mA at Tlow.

Then check the printed conformity. If it exceeds your target, your band is too wide — narrow it (see the table above).

Calibration

You need a way to present two known temperatures (a stirred ice/water-and-warm bath, a dry-block calibrator, or — easiest for bench bring-up — two precision resistors substituted for the probe equal to Rt(Tlow) and Rt(Thigh), which the calculator prints).

1. Apply the low point (Tlow, e.g. 20 °C → Rt = 12.49 kΩ). Adjust the ZERO pot for 4.00 mA.
2. Apply the high point (Thigh, e.g. 40 °C → Rt = 5.35 kΩ). Adjust the SPAN pot for 20.00 mA.
3. Repeat once. Zero and span interact only slightly (the gain term scales the zero point a little), so a second pass nails both to within a microamp.

Use a loop calibrator or a 250 Ω precision resistor + DMM (1.000–5.000 V = 4–20 mA) to read the current.

Bill of materials (multi-sourced)

Every active part below is available from multiple manufacturers, or in a footprint with many drop-in alternatives. That is a design goal: this instrument should be repairable for decades without a single-source IC.

Thermal note (Q2). A 2-wire transmitter must drop the loop voltage somewhere; that's Q2. Worst case ≈ (instrument voltage) × (loop current) ≈ 20 V × 20 mA ≈ 0.4 W. Use a SOT-223 (or larger) device with adequate copper, or split the drop with a series resistor ahead of Q2's collector.

Op-amp footprint. Standardizing A1–A3 on SOT-23-5 singles is deliberate: precision op-amps are mostly single-source by part number, but the SOT-23-5 single-op-amp pinout is a de-facto industry standard with many footprint- compatible options, so a substitute is always a re-qualification away, never a redesign.

Simulation

sim/transmitter.cir models the ideal signal chain (reference + op-amps as behavioral sources, NTC as a temperature-dependent resistor) and DC-sweeps temperature to confirm the 4–20 mA transfer and in-band linearity.

ngspice -b sim/transmitter.cir   # DC-sweeps temperature; prints Iloop vs T

(LTspice: change the behavioral-resistor r='...' syntax to R=....)

It has been run with ngspice 46; the full output is saved in sim/SIM_RESULTS.txt. Key points (Iloop = Vcmd / 50 Ω):

The node voltages match tools/design.py to the millivolt, and the in-/out-of- band clamping behaves as designed.

Verification status (be honest about it):

• ✅ Signal-chain transfer and linearization conformity (~±0.06 °C, well inside the ±0.1 °C system spec) — verified in tools/design.py and confirmed in ngspice (table above).
• ⬜ Discrete output stage (the Q1 pre-regulator and the Q2/A3 servo loop, including loop stability and Q2 thermals) — designed but not yet device-level simulated or bench-verified. The netlist above models the op-amps as ideal behavioral sources, so it validates the transfer math, not the real parts. Simulate with device models and prototype before trusting it.

Optional digital upgrade

If you later want digital trim, datalogging, or a nonlinear curve over a wide range, you can add an MCU with a ≥12-bit ADC reading V(X) and driving the loop via a current-output DAC (or by replacing the A3/Q2 stage). For a "hold a setpoint in a known band" application this is usually unnecessary complexity — the analog path here already beats thermocouple accuracy in-band — but the sensor front-end and linearization theory carry over unchanged.

Working with KiCad — notes and gotchas

Taking this from netlist to schematic to PCB surfaced a few KiCad limitations worth recording — both for anyone reproducing the board and for anyone doing a careful (or AI-assisted) review of a .kicad_sch:

• Connectivity can't be read reliably from the .kicad_sch text. Symbol mirror/rotation transforms and overlapping wire segments defeat any attempt to infer "what's connected to what" from pin coordinates. Let KiCad compute it instead — kicad-cli sch export netlist --format kicadsexpr -o net.net therm.kicad_sch — and read the nets. Every net-by-net review of this board was done that way, not by eyeballing the schematic file.

• ERC does not catch wrong values or wrong roles. Several real errors here passed connectivity checks clean: a 49.9 kΩ loop-sense resistor that should have been 49.9 Ω; a bypass cap with both pins on the same net (a no-op); an op-amp powered from the 2.5 V reference instead of the 5 V rail; and the LM4040 reference wired across the loop input as if it were the TVS. None of these trip ERC — they need an explicit value-and-node audit against intent.

• Symbol variants have different pin numbering. The OPA333 in SOIC-8 (OPA333xxD) uses pins 2/3/4/6/7; in SOT-23-5 (OPA333xxDBV) it's 1–5. Grab the wrong variant and the schematic looks right while the netlist is wrong — always confirm the symbol's package/pinout matches the footprint you intend.

• Not every jellybean part is in the stock library. The TL431 is (Reference_Voltage:TL431DBZ); the TLV431 is not, which had forced a custom symbol — one reason we standardized on the TL431. Preferring stock-library parts avoids custom-symbol upkeep.

• Footprints aren't auto-assigned. Symbols sit with an empty footprint until you assign one, and nothing warns you until you try to lay out the board — the two trimpots were caught this way. Sweep for missing footprints before routing.

• File hygiene. KiCad scatters *-backups/ zips, ~*.lck locks, #auto_saved_files#, and per-user *.kicad_prl state through the project; the .gitignore excludes them so only the real design files track.

Takeaway: a parameterized calculator proves the design intent, and ERC proves the nets are connected — but neither flags a wrong value, a wrong package variant, or a node that's electrically valid yet functionally pointless. A net-by-net netlist review plus a device-level SPICE pass are what actually prove the instrument.

Repository layout

Therm_temp_4_20_xmtr/
├── README.md                    # this file
├── LICENSE                      # MIT
├── docs/
│   └── DESIGN_CONVERSATION.md   # the prompts that drove the design + decisions
├── hardware/
│   └── BOM.md                   # bill of materials (consolidated values, tempco notes)
├── tools/
│   └── design.py                # parameterized design calculator (models gain-stage load)
├── sim/
│   ├── transmitter.cir          # ideal transfer-function verification
│   ├── device_level.cir         # discrete model (real BJTs + IC macromodels)
│   └── SIM_RESULTS.txt          # captured ngspice 46 output
└── therm_kicad/                 # KiCad project: schematic + rough PCB
    └── therm/                   # therm.kicad_sch / .kicad_pcb / .kicad_pro

For how this design came to be — the design conversation and the reasoning behind each choice — see docs/DESIGN_CONVERSATION.md.

Status: schematic + a rough PCB are in therm_kicad/; the device-level SPICE model verifies the discrete signal chain. Still open: output-stage loop stability (AC/transient) and bench bring-up.

License

MIT. Use it, build it, sell it — just keep the copyright notice.