Hall sensor noise, its zero, and the filter for Ip

A second, narrower look at the plasma current channel Ip in the 2026-09-15 files, done on 2026-09-19 to choose a frequency filter. The September 15 page (plasma run and noise) found the two lines on Ip; this page finds where they come from in time, why the zero is always negative, and which filter removes the most for the least delay. The 2026-09-18 run was meant to be analysed too, but its files had not reached data/rig/ when this was written; everything here is September 15.

Files analysed

Read-only, from the git-ignored data/rig/2026-09-15/; checksums are in the September 15 page.

• cu_20260915_170626.csv, 17:07–18:24: 78 minutes of Ip with no gas and no plasma (a filament conditioning), the long quiet record the spectra are taken from.
• cu_20260915_184419.csv: 18:45–18:52 before the gas, 18:55–19:10 the settled discharge, and the ignition at 18:54:14.
• cu_20260915_161413.csv and cu_20260915_192533.csv for the zero.

The ADC's real cadence in these files is 9.995 Hz (mean interval 0.10005 s), and that is the rate every frequency below is computed with.

What the noise is made of

Raw Ip scatters by 23 mA (standard deviation after removing drifts slower than two minutes). Most of that is two regular patterns, not randomness.

Every third sample. Folding the 78-minute record on the sample number modulo 3 gives −2.49, +0.21 and +2.29 mV at the ADC, about ±12 mA. The line sits at 3.3317 Hz, which is a third of the real 9.995 Hz cadence and not a third of 10 Hz: it follows the sample count, not the clock. The ADC worker hands its rows to the main thread in batches of three (STEP = 3 in controlunit/devices/device.py), so the main thread's work comes around every third sample. The same fold on every other channel gives at most 37 µV and mostly under 7 µV: the pattern is on Ip alone.

Every 7.5 seconds. The line measures 0.13334 Hz with 0.00022 Hz resolution, which is 7.500 s of clock time, and carries harmonics at 0.267 Hz (8.0 mA) and 0.400 Hz (5.3 mA) beside its 15.7 mA fundamental. Folded on clock time it is a stepped pattern, 39 mA peak to peak (7.8 mV at the ADC): about 1.5 s low, 3 s high, 2 s near the middle (middle panel above). The first and second halves of the 78 minutes give the same profile (correlation 0.998), so it is stable for over an hour. The other channels carry faint copies of 10 to 390 µV, twenty to eight hundred times smaller. Nothing in ControlUnit runs on a 7.5 s timer that this search found.

The rest is broadband, about 8 mA once both patterns are removed, with small lines of its own (2.0 Hz, 2.7 mA, among them).

Why the zero is always negative

The conversion is 5 * (v - 2.52): 5 A per volt about a fixed 2.52 V. The sensor's output with no current is lower than that every time:

Stretch	Ip_c	Raw voltage	Twice the raw voltage
16:14 file	−0.3305 A	2.4539 V	4.908 V
17:06 file, start	−0.3473 A	2.4505 V	4.901 V
17:06 file, end	−0.3420 A	2.4516 V	4.903 V
18:45 before the gas	−0.3305 A	2.4539 V	4.908 V
19:15 after the run	−0.3343 A	2.4531 V	4.906 V
19:26 vacuum only	−0.3223 A	2.4555 V	4.911 V

Both Hall sensors the lab documents (the ACS712 and the WCS1800 in the explainers' docs/hardware/sensors/) are ratiometric: with no current the output is half the sensor's own supply, and the sensitivity scales with the supply too. The sensor is powered from the Raspberry Pi's 5 V pin, and a Pi's 5 V pin under load commonly reads about 4.9 V. Half of 4.90–4.91 V is exactly the zero measured. The fixed 2.52 V would be right for a 5.04 V supply.

The same mechanism explains why the two patterns are on Ip alone: it is the only channel whose instrument runs from the Pi's own supply. Whatever makes the Pi draw more current — the main thread waking for a batch every third sample, and something on a 7.5 s cycle — sags that supply, and the sensor's zero moves with half of it. The ±2.4 mV and 7.8 mV peak-to-peak patterns correspond to ±5 mV and 16 mV on the supply. This is a hypothesis the files are consistent with, not a measurement; the supply itself was not recorded. (The 2026-09-09 finding that "Pi's own power was clean" was about the Pi's undervoltage flags; 4.9 V is well above that threshold and still moves the Hall zero by millivolts.)

The negative zero does not affect the zeroed reading, which subtracts it. It does make the zero wander: 30 mA across the evening here, which is 6 mV at the sensor, 12 mV of supply.

The zero button's two seconds

The baseline behind "Zero now" and the Scales dock's zero button averages the last BASELINE_SECONDS = 2.0 (controlunit/main.py). Two seconds land at a random point of the 7.5 s pattern. Measured over the 78 minutes, a two-second zero is off by 10.9 mA (standard deviation), 31 mA at worst. A 7.5 s zero is off by 1.8 mA, 9 mA at worst; 15 s, by 1.5 mA and 6 mA.

The absolute value

The zeroed current is 5 A/V × (v − zero), so its scale rests entirely on the 5 A per volt, which is 200 mV/A. That matches none of the documented sensors: the ACS712-05B is 185 mV/A (the 20 A part 100, the 30 A part 66) and the WCS1800 72 mV/A. If the sensor is an ACS712-05B, every current ControlUnit shows is 8 % low, and the 0.78 A plasma of September 15 was 0.84 A; on a 4.91 V supply the sensor's own sensitivity is a further 2 % lower. Neither closes the gap to the 1 A queezz read on the discharge supply's panel. Only a calibration with a known current settles it (below).

Filters

Each filter was run causally, on past samples only, as it would run live. Noise is the standard deviation after removing drifts slower than two minutes; delay is the time for the filtered value to cover half of a step. The discharge was 0.79 A.

Filter on Ip	No plasma, 78 min	No plasma, 18:45	Plasma, 18:55	Delay
none	22.9 mA	22.7 mA	23.6 mA	—
3-sample mean	15.8	12.6	18.3	0.1 s
0.5 Hz low-pass, Butterworth, 2nd order	13.9	11.0	16.3	0.5 s
3-sample mean, then a 1 s mean	10.7	8.6	12.2	1.1 s
3-sample mean and notches at 7.5, 3.75 and 2.5 s	9.0	7.9	10.0	0.1 s
the same, then a 1 s mean	3.6	4.0	4.3	1.1 s
7.5 s mean	1.8	1.3	2.2	3.7 s

A low-pass is the wrong tool here: the largest component is at 0.133 Hz, inside the band the plasma current itself moves in, and a low-pass that removed it would cost seconds. The 3-sample mean puts an exact zero on the every-third-sample pattern. The notches are second-order IIR notches (a band-stop a few thousandths of a hertz wide) at 1/7.5 s and its second and third harmonics, with Q = 100. The 7.5 s mean is one period of the pattern and nulls it and every harmonic outright, the every-third-sample pattern included, since 75 is a multiple of 3.

The notches' cost is a small ring after a step: a 0.4 A step leaves 10 mA, 6 mA of it still there after 60 s, below the noise that remains. The choice of Q and of the number of harmonics:

Notches	Noise, no plasma	Noise, plasma	Ring after a 0.4 A step
1 harmonic, Q 100	11.5 mA	13.8 mA	4 mA
2 harmonics, Q 100	10.0	11.8	7
3 harmonics, Q 100	9.0	10.1	10
6 harmonics, Q 100	8.6	9.6	17
10 harmonics, Q 100	8.4	9.3	26
3 harmonics, Q 30	8.7	9.5	31
3 harmonics, Q 300	9.5	11.9	3

Past three harmonics the noise hardly falls and the ring keeps growing, because what remains is the broadband part. A running template of the 7.5 s pattern, subtracted phase by phase, did no better (8.5 mA) than three notches. The ignition in the bottom panel stays a two-sample jump through the 3-sample mean and notches.

For the three uses:

• Live value and PID: the 3-sample mean and three notches. 23 to 9 mA, 0.1 s.
• Display: the same and a 1 s mean. About 4 mA, 1.1 s.
• A settled number, a report, a zero: a 7.5 s mean. About 2 mA, 3.7 s.

The notches are designed for the actual sampling period, and must be redesigned whenever it changes; the file keeps the raw readings.

What the hardware can change

The two patterns are the Pi's load reaching the sensor, through its supply or its ground, if the hypothesis holds, and no filter on the signal wire removes that. Amended the same day with the boards' own files and queezz's corrections: the ADC board has pads for the RC and the surge diodes, the breakout has a ground, and the sensor should take its ground from the ADC side, star-like.

Where things are, from the two boards' own files. The ADC board is the Y2 Corporation AIO-32/0RA-IRC (schematic in the explainers, docs/assets/y-corp-adc-schematic.pdf); the panel between it and the rig is the lab's own breakout, panel-bncs in queezz/controlunig-pcb.

• Every ADC input passes a 39 kΩ / 10 kΩ divider on the ADC board (the 4.9 in the code's volts) and is read against the board's analogue ground AG, which joins the Pi's ground through one ferrite (L2). AG reaches the breakout on ribbon pins 33–34: the breakout's ground is AG.
• At each divider's midpoint the ADC board has an unfitted capacitor pad to AG and an unfitted dual clamp diode to AG and 3.3 V. Channel 0, Ip: R1 (39 kΩ), R33 (10 kΩ), C1, D1. Channel 1: R3, R35, C3, D3. Do not fit the pads after the multiplexers (C41, C42): those are shared by sixteen channels each and would carry one channel's voltage into the next.
• On the breakout, the lower terminal block carries channels 0–7, the upper 8–15, and the BNCs the even channels 16–30 (channel 18 free) with pads for a ferrite, a capacitor and a surge diode. The ferrite pad sits in series between the BNC's centre pin and the channel; queezz fitted resistors there, the ferrites not being to hand, and capacitors on the capacitor pads ("I have caps and resistors in my breakout panel PCB"), so every BNC channel already has an RC and the terminal channels, Ip among them, have none. A ferrite bead in place of a resistor would filter only radio frequencies and drop that RC. The ADC board's own pads are empty ("Those pads are pads, not populated"). The odd channels 17–31 are not brought out.

1. Record the sensor's supply. One wire from the sensor's own 5 V pin to channel 1, the lower terminal block's "1", beside Ip's "0" (owner's choice of channel 2026-09-19). The input takes 0–10 V, so it goes straight in. If that channel shows the two patterns, the Pi's load reaches the sensor, and the reading can be made ratiometric in software: current from v_out / v_supply, which cancels the supply's movement and the negative zero with it.
2. Ground the sensor on the ADC side. The sensor's ground now comes from the Pi. Take it from the breakout's ground instead, which is AG, the node every channel is measured against, so that none of the Pi's own return current flows between the sensor's ground and the ADC's. That is the second route by which the Pi's load can reach Ip, besides the supply sagging, and the ratio in step 1 cancels only half of a ground shift. The ADC board already joins AG to the Pi at one point (L2); nothing on the sensor's side should make a second joint.
3. Power the sensor from its own supply. Powering it from the Mean Well directly, on its own pair of wires, removes the drop in the Pi's cable and fuse that moves with the Pi's load; the Mean Well's own output still moves somewhat with everything else it feeds, and carries switching ripple. A small linear regulator of its own (a 7805 or a low-noise LDO, fed from a 12 or 24 V rail if the rack has one) is quieter still. Its minus joins at the breakout's ground and nowhere else.
4. The RC is on the ADC board already, less the capacitor. The 39 kΩ series resistor and the 10 kΩ to ground look like 7.96 kΩ to a capacitor at the midpoint, so C1 alone makes the RC: 2.2 µF gives a 9 Hz corner and 17.5 ms, a step settled to 0.3 % within one 100 ms sample (1 µF: 20 Hz, 8 ms). Ceramic, X7R, 6.3 V or more; the midpoint never sees more than about 2 V. It stops noise between 5 Hz and a few hundred hertz from folding down into the samples, which is what most of the remaining broadband 8 mA probably is, and adds no error, since there is no extra resistor. Fit the same value on C3, so the supply channel is filtered exactly like Ip and the ratio stays exact.
5. Clamp diodes, if fitted, silicon. D1's pads take a SOT-23 series pair. A BAV99 (silicon) fits; a BAT54S (Schottky) fits too but leaks more, and a leak through the 8 kΩ midpoint is an offset, of millivolts at the input once warm. For the sensor inside the rack the clamp is optional; the gauges' long BNC cables are where it matters.
6. Ferrites and decoupling. Keep the resistors in the breakout's FB1–FB8 pads, which make the gauges' RC; a clip-on ferrite on the sensor cable, and 100 nF with 10 µF across the sensor's supply pins at the sensor. These treat radio-frequency pickup from the discharge, arcs and switching supplies, not the two slow patterns.

In that order, with ten quiet minutes at 10 Hz after step 1 so the cause is seen before it is removed; then:

1. Calibrate with a known current. With the discharge off, a bench supply in constant-current mode (or any supply, a power resistor and a multimeter in series as the reference) through the sensor, at 0, ±0.5, ±1 and ±2 A, 30 s each at 10 Hz, with the zero taken again at the end. With the supply recorded, fit v_out / v_supply against the current: the slope is the sensitivity and the intercept the zero, the two numbers the conversion needs. A sensor with a through hole (the WCS1800) can take N turns of wire to multiply a small current.

After the hardware change, ten quiet minutes at 10 Hz show which patterns survive; the filter is then built for what is left.

What the data cannot answer

Whether the supply is the cause, until it is recorded; what runs every 7.5 s; which sensor is fitted and its true sensitivity; and whether the 2026-09-18 run shows the same patterns, until its files arrive.