Strain-Gauge Channel: Is It Resolution or Interference?
A production test rig measures strain with a 350 Ω foil bridge energised from a 5.000 V reference. The bridge is rated 2.00 mV/V, so full-scale differential output is 10.0 mV. An INA333 instrumentation amplifier with Rg = 1.00 kΩ (gain 100) drives a 12-bit SAR ADC whose reference is 2.048 V. With the gauge unloaded and a 0.3 m bridge cable fitted, the ADC code wanders by about ±3 counts. When the cable is replaced by a 2 m unshielded twisted pair routed past a 3-phase motor drive, a 50 Hz component of roughly 20 counts peak-to-peak appears on the same code. The INA333 datasheet quotes 25 µV maximum input offset voltage and 50 nA input bias current; the bridge source resistance seen by each input is 350 Ω nominal but the two arms differ by about 1 Ω because of gauge tolerance. The team proposes two fixes: raise the gain to 200 to 'get more resolution', and solder a 100 nF capacitor directly across the ADC input pins.
1. Express one ADC count in input-referred terms and decide whether the ±3 count wander is adequately explained by the amplifier's DC specifications.
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ADC resolution: LSB = 2.048 V / 4096 = 0.500 mV at the converter input. Referred to the bridge, divide by the gain of 100:
LSB(RTI) = 0.500 mV / 100 = 5.0 µV per count
So the ±3 count wander is ±1.5 mV at the ADC, i.e. ±15 µV referred to the bridge.
Now the budget. The INA333's 25 µV maximum offset is already larger than the observed wander, so a fixed offset alone would show up as a static bias of up to 5 counts - plausible. The wander is smaller than that, which is consistent with an offset that is largely trimmed or with thermal drift over the measurement interval. Add the bias-current term: the two bridge arms differ by about 1 Ω, so the differential source resistance mismatch is ~1 Ω and the offset generated is Ib × ΔRs = 50 nA × 1 Ω = 50 nV - negligible here, though with a 10 kΩ source it would not be. Note also that a 50 nA bias flowing in 350 Ω produces 17.5 µV per input; that is common-mode and is rejected, but any mismatch converts it to differential.
Conclusion: ±3 counts is entirely consistent with device offset and low-frequency drift, needs no exotic explanation, and is small compared with the 2000-count full scale. It is a calibration/auto-zero question, not a fault.
2. Convert the 20 count peak-to-peak hum into input-referred volts and decide whether it is more likely electric-field (common-mode) or magnetic (loop) coupling. What measurement settles it?
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20 counts × 0.500 mV = 10 mV peak-to-peak at the ADC, divided by 100 = 100 µV peak-to-peak referred to the bridge. That is 1% of the 10 mV full scale - a 1% measurement error, entirely unacceptable in a production rig, and it appeared only when the cable was lengthened and rerouted.
Why the discrimination matters: a good instrumentation amplifier has CMRR of order 100 dB at 50 Hz, so a common-mode voltage would have to be about 10 mV at the bridge to leave 100 µV of differential error. A 10 mV common-mode induced capacitively on a 2 m floating cable near a drive is easy to imagine; magnetic pickup, by contrast, induces a voltage around the loop formed by the two signal conductors plus the grounds, and that voltage appears as a genuine differential signal which no CMRR can remove.
The decisive test is to short the two signal leads together at the bridge end (a dummy bridge of 350 Ω, or a short) and observe the residual. If the hum vanishes, it was common-mode and the amplifier was being pushed beyond its CMRR by source-impedance imbalance or by the cable's shield being absent. If it persists, it is magnetic - flux through the loop. Repeat with the cable's shield grounded at one end only: a change implicates electric-field coupling. Winding the pair tightly (fewer loop areas) and rerouting away from the drive should then be tried; if the hum falls, magnetic coupling is confirmed.
3. Evaluate the team's two proposed fixes - gain 200 and a 100 nF capacitor at the ADC - and state what you would do instead.
Read the worked answer
Gain 200. The input-referred LSB halves to 2.5 µV, which sounds attractive. But the hum is a physical 100 µV at the bridge; at gain 200 it becomes 20 mV, i.e. 40 counts instead of 20. Signal-to-noise ratio in input-referred terms is completely unchanged - an amplifier cannot improve SNR by amplifying a disturbance that arrives ahead of it. Worse, full scale becomes 10 mV × 200 = 2.00 V against a 2.048 V reference, leaving 2.3% headroom; any bridge overload, mechanical ringing or offset clips the converter. Reject as a fix for hum; it is only a fix if the limiting factor were quantisation, which at 5 µV LSB and 15 µV of offset it is not.
100 nF at the ADC input. With a series 1 kΩ this forms a single-pole filter at 1/(2π × 1 kΩ × 100 nF) = 1.6 kHz - three decades above 50 Hz, so it does nothing. Without the series resistor it is a capacitive load directly on the INA333 output, which erodes phase margin and can oscillate; and a single capacitor to ground converts common-mode noise into differential current through the two source impedances. Reject.
What to do. Fit shielded twisted pair, shield grounded at one end (the instrument end) to avoid a ground loop; add a differential RC filter at the amplifier input sized for the signal bandwidth - for a 10 Hz strain signal, 1 kΩ with 4.7 µF gives about 34 Hz, suppressing 50 Hz by roughly 3 dB only, so use two poles or a higher-order filter; and check the bridge's cable shield is tied to the excitation return. Then re-run the gain decision against the actual residual noise.