Two temperature sensors,
measured properly.

The brief, as it actually arrived

Nine requests over the day. Most arrived mid-task, which is why the shape of the tool kept changing.

One loop, two instruments

The host both drives the chip and listens to it. GR07 free-runs, so listening is enough; GR06 emits nothing until its reset is toggled, so the host has to close the loop.

Same physics, two ways of reading it out

Both sensors are a PTAT current charging a capacitor into a comparator. The current rises with absolute temperature, so the time to reach the threshold falls with it:

t = V_ref·C / I(T),   I(T) = k·T·ln(N) / (q·R)

So t ∝ 1/T, and the rate r = 1/t is proportional to absolute temperature. The app works in the rate domain and fits r = a·TK + b — with one calibration point it fits the ideal PTAT line through the origin, which is the only honest model from a single observation.

Two bottlenecks stood between “works” and “usable”

GR06 needs a reset pulse every few hundred microseconds. Naively that is impossible from a host; both fixes were about finding where the time was going.

The result: one asynchronous burst of ~4500 reset pulses runs during a capture, so a single 0.5 s window yields thousands of independent GR06 measurements instead of the handful that host round-trips would allow.

GR07's period only takes four values

A 1-second capture holds — periods. They land on — distinct values, in two clusters one 64 MHz clock period apart.

This slide used to call the retiming "accidentally a first-order sigma-delta", whose quantisation noise would rise toward Nyquist. It does not. Keeping every edge of a 1 s capture gives — individual periods — a — record reaching —, about — the bandwidth the demo board can reach — and the period noise is flat across all of it, varying — in total. First-order shaping would climb four decades over that span. Three things agree it is white: the flat spectrum integrates to — against — measured directly, so it holds all the variance; a two-level dither at the measured fraction predicts —; and the accumulated phase falls as exactly 1/f, which is integrated white noise. The earlier chamber fit already implied this — it matched a model assuming independent quantisation per period at r = 0.997 — and I did not notice the contradiction. Nothing downstream changes: every noise budget here already assumed the white case. Only the explanation was wrong.

The comparator trip is re-timed by the project clock, so each period is either N or N+1 clock cycles. One whole step is —. All the resolution therefore comes from the ratio between the two levels — the circuit dithers, and averaging ~900 000 periods reads that ratio to a few millikelvin.

This is also why outlier rejection had to be rebuilt — see slide 11.

Both sensors, —, same time base

Captured simultaneously on two channels — identical thermal environment, identical clock. Each is calibrated at a single point, 23.00 °C, on its first reading; everything after that is the silicon talking.

—

A blast of freeze spray, then a fingertip

Quiet-room data only shows a sensor's noise. To see what it does with a real thermal input: a can of freeze spray at —, then a finger held on the package from 88 s to 122 s. Both sensors, one capture, 1 ms points.

—

A caveat on the absolute numbers. Both sensors are calibrated at a single point, 23 °C, against the ideal PTAT line through the origin — there is no offset term to absorb comparator delay or reset time. At 8 °C that model is extrapolating 15 K beyond its only anchor, so the depth carries a systematic uncertainty we cannot bound without a second calibration temperature. The rates and the timing are on much firmer ground: they depend on the slope of the trace, not on where the zero sits.

And what is measured is the die, not the spray. The can is rated −55 °C, but the sensor only ever sees its own silicon, reached through the package: what the −37 K/s describes is how fast the die followed, not how cold the propellant was.

A real event moves both sensors. Noise doesn't.

Slide 07 found the two sensors uncorrelated in a quiet room and concluded the wander was sensor-local rather than ambient. This run is the control that decides it.

When the die genuinely changes temperature the two sensors agree almost perfectly, despite different circuits, different readout schemes and a 200× difference in events per point. When nothing is happening to the die they drift apart. That is exactly the signature that the quiet-run wander was not temperature — and it means these sensors are far better at telling you that something changed than at telling you what the temperature is.

The cost of re-timing: GR07 has dead zones

The stimulus run swept GR07 across 15 K, and its noise turned out to depend strongly on where it sat. The period is re-timed by the 64 MHz clock, so what matters is where it falls between two clock edges:

The noise collapses exactly where the period lands on a whole number of clock cycles, and peaks half-way between. That is a dead zone, not precision: when the ramp always crosses in the same clock interval every period gives the same answer, the dither that carried the resolution switches off, and the sensor stops responding to small changes while looking ten times quieter. It is the same mechanism that makes a sigma-delta idle — and it explains slide 07's rising Allan curve, since idle-tone plateaus read as drift.

Practical consequence: a quiet-looking GR07 reading is not evidence of a good one. GR06, having no clock in its path, has no equivalent failure.

Breathing on the chip, GR06 swings 2.4× further

Four breaths over —. Each moves both sensors, but not by the same amount: GR06 reads about —× the excursion GR07 does. The obvious reading is that the two circuits have different gains. They don't.

The same two sensors agree to within — over the 15 K freeze-spray run. A real difference in calibrated gain would show up more strongly over a wider excursion, not vanish. So this is a property of small, fast signals, not of the circuits' sensitivity.

It is GR07 sitting on a clock edge

Slide 09 showed GR07's period lands on a staircase of whole 64 MHz clock cycles, and that its dither — and with it its resolution — collapses wherever the period sits close to a whole cycle. This run happened to sit exactly there, and stayed there: a 1 K breath moves GR07 by about a quarter of a clock cycle, nowhere near enough to escape.

GR07's noise falls to 9 mK — not because it got better, but because it stopped responding. GR06, with no clock anywhere in its path, sits at a flat ~110 mK throughout. The sensor that looks ten times quieter is the one compressing the signal.

The simulations agree the gains should match

Worth checking against what the students designed, because a real 2.4× mismatch would be a design finding rather than a measurement artefact. Fitting each simulated transfer to t = K/T + td — a PTAT ramp plus whatever fixed time does not scale with temperature — gives a fixed term of only −2 % of the period for GR06 and −5 % for GR07. Both are near-ideal, so their gains should differ by a few per cent, not a factor of two. GR07's simulated PTAT current is proportional to absolute temperature within 2 % across corners (13.8 / 18.2 / 24.9 µA cold / typical / hot).

Measurement, simulation and the 15 K run all say the same thing: the factor of two is an artefact of reading a quantized sensor over an excursion smaller than its quantum.

What to do about it. For small excursions, trust GR06. For GR07, either move it off the edge — the project clock sets where the staircase falls, so changing the clock frequency shifts the dead zones — or accept that excursions of a few kelvin are compressed by an unknown factor between one and about three.

A climate chamber, —, and the first honest transfer curve

Everything up to here calibrated each sensor against itself at one room-temperature point, so it could measure change but never accuracy. A Vötsch chamber stepping through — set points, logging its own probe beside both sensors, finally supplies an outside opinion. Each point below is the mean of the last — s of a dwell, after the oven and the die have both stopped moving.

One point, two points, three points

The question a product asks is not "how linear is it" but "how many oven visits must I pay for". Nothing here fits more than three points: fitting all fourteen chamber set points measures how well a polynomial can chase this part, which is not a calibration anybody performs and flatters the sensor.

GR06 behaves the way a sensor should — each extra trim point buys accuracy, down to — over 5–70 °C. GR07 gets worse from one point to two. A two-point fit only corrects a slope, and GR07's error is not a slope: its residual changes sign across the range, so anchoring the line at 20 and 60 °C tilts it to satisfy two points that happen to sit on opposite excursions and throws the middle further out. More trim points only help a curve they can actually follow.

An earlier version of this deck blamed GR07's floor on its quantiser. That was wrong. Its period is re-timed onto whole — clock cycles, but it sits at some fraction between two codes and alternates between them — so the quantiser is dithered, and a dithered quantiser's mean survives averaging. The model for that (σ = √(p(1−p))·LSB⁄√N) predicts the measured per-bin noise with r = — across all 14 setpoints, and what is left in a dwell mean is — — some three orders of magnitude below the error it was supposed to explain. Quantisation sets GR07's single-shot noise, not its accuracy. A faster clock would give a quieter live trace and nothing else.

GR06 does not drift — it switches

Ninety seconds of GR06 at a fixed —, with the dwell drift removed. If this were thermal noise it would be a fuzzy band around zero. Instead it sits flat, drops — to a second flat level, stays there for a second or two, and comes back. That is random telegraph noise: one charge trap in the silicon capturing and emitting a single carrier.

What is left when nothing is happening

Half an hour per sensor at a fixed temperature, measured by the demo board alone. The logic analyser is the wrong instrument for this: its capture–arm–export cycle leaves dead time between blocks, and dead time is poison for a spectrum. The RP2350 counts continuously — — duty, the rest being the USB transfer — so the record spans — in one piece.

What the logic analyser adds, and where it runs out

The demo board reduces as it measures — one value per 907 periods — so its spectrum stops at 500 Hz. Keeping every edge of a one-second capture gives — individual periods, a — record reaching —: about — the bandwidth, and the only view of what the retiming does between one period and the next.

Scripts, data, instruments

Five days, 31 July to 4 August, from "can we see the period of output 0" to a pair of sensors characterised against an external reference and down to their own noise floor. What follows is the inventory, so the next person knows what exists and what it cost to make.

Four corrections worth recording

Three were mine. The measurement one mattered most, because it was silently producing plausible numbers.

What exists now

From a bare board to a live trace

Two USB cables, three probe clips and one calibration press. The whole thing takes about five minutes, and most of the ways it goes wrong are listed at the bottom.

cd meas
pip install -r requirements.txt
python3 main.py

First run

Reading the trace

The temperature pane is cicwave's waveform plot, so its keys work here too. Click the plot first, then:

Cursors A and B print their values and the delta between them under the plot, alongside min / max / mean / σ / rms / peak-to-peak per series. The view stops auto-fitting the moment you zoom, so it will not re-frame itself while you are reading a value off; f hands it back.

Three settings that matter

After a power cycle

The demo board keeps its project selection across a reset but not its clock: tt.auto_clocking_freq comes back 0, and GR07 — whose comparator output is re-timed by that clock — simply stops toggling. GR06 is unaffected, which makes it look like a wiring fault on one channel. Pressing Connect fixes it; the app sets the clock as part of configuring the chip, and warns in the log if it fails to start.

Logic 2 is the other half: an application update resets the Enable automation server preference, so it has to be ticked again. The two failures look identical from the outside — nothing works — which is why the app now connects the two instruments independently and reports each one separately rather than giving up at the first.

If it misbehaves