A VFD Interferer That Aliases Straight Into the Measurement Band

Where it lands. Sampling folds every component to |f − n·fs|. With fs = 8 kS/s:

6.4 kHz − 8 kHz = −1.6 kHz → aliases to 1.6 kHz

1.6 kHz sits squarely inside the 20 Hz–2 kHz band of interest. This is not a filter-quality problem, it is an aliasing problem: once folded, the interferer is indistinguishable from real machine vibration, and it explains both the stable unexplained tone and the ±15 % RMS swing.

What the existing filter does. Single pole at 2 kHz, evaluated at 6.4 kHz:

|H| = 1 / sqrt(1 + (6.4/2.0)²) = 1 / 3.35 = 0.298 → −10.5 dB

So 2 Vpp arrives at the ADC as roughly 0.6 Vpp of fold-down energy in-band - about 740 LSBs peak, i.e. 186 LSB rms. Against a signal band that wants sub-LSB resolution, the interferer dominates completely.

Why the notch idea fails. A firmware notch at 6.4 kHz removes nothing: the energy is no longer at 6.4 kHz, it is at 1.6 kHz. A notch at 1.6 kHz would delete genuine vibration content. A notch at 6.4 kHz in a system with adequate fs would work only while the carrier is exactly 6.4 kHz - VFD carriers are configured and drift with load, and a carrier that moves by a few hundred hertz walks into the signal band. Reject it.

Target. Require the folded component to fall below the converter's noise floor. Taking 1 LSB = 3.3/4096 = 0.806 mV as a demanding target, and using the 2 Vpp (1 V peak) interferer:

required attenuation = 0.806 mV / 1000 mV = 8.1×10⁻⁴ → −62 dB

(If you target 1 LSB peak-to-peak rather than peak, it is −68 dB; the conclusion is identical.)

Order at fc = 2 kHz. You cannot push the corner lower - 2 kHz is the top of the signal band - so the ratio 6.4/2.0 = 3.2 is fixed and each pole contributes 10.5 dB at 6.4 kHz:

n = 62 / 10.5 ≈ 6 poles (7 for a Butterworth with the −3 dB corner at 2 kHz, since the asymptotic slope is reached only well above the corner)

A 6–7 pole active filter with a corner that must stay within a few percent across temperature and component tolerance, in the space of two op-amp stages, is not realistic. Worse, a sharp 2 kHz corner introduces group-delay distortion right at the edge of the band you care about, and its component tolerance eats the margin you just computed.

Change fs instead - this is the correct decision. The ADC is capable of 1 MS/s; the system has CPU headroom. Move to fs = 32 kS/s:

• Nyquist becomes 16 kHz, so 6.4 kHz is not folded. It appears at its true frequency, above the 20 Hz–2 kHz band, and a digital low-pass removes it with no analog cost.
• Harmonics of the carrier (12.8 kHz, 19.2 kHz) fold to 19.2 kHz → 12.8 kHz and 12.8 kHz → 12.8 kHz - all far above the signal band, all removable digitally.
• The analog filter's job changes: it now only has to control what folds around 32 kHz and above. A 2-pole Sallen-Key at fc ≈ 10 kHz gives roughly 1/(1+(3.2)²) ≈ −21 dB at 32 kHz, which is a far easier requirement than 62 dB at 6.4 kHz.

Trade-offs to acknowledge: 4× data rate (still trivial - 32 kS/s × 2 bytes = 64 kB/s), 4× digital filter work, and a strict new requirement to know what spectral content exists above 16 kHz on this machine, especially the VFD's higher harmonics and any switching transients. Verify that with a spectrum sweep before committing.

Analog front end.

• Two-pole Sallen-Key low-pass, Butterworth, fc = 10 kHz, in front of the ADC. Enough to keep carrier harmonics and switching edges above Nyquist from folding into the 0–2 kHz band.
• Add a series resistor at the ADC input with a small differential capacitor to absorb charge-injection spikes from the SAR input, and keep the source impedance low enough for the chosen sampling time.
• Keep the RC that already exists at 2 kHz only if it does not compromise the 2 kHz signal edge; otherwise replace it. Do not stack filters whose tolerances push the corner below the band.
• Confirm with a network analyser sweep from 10 Hz to 200 kHz that the composite response is −3 dB at the intended corner and monotonic in the stopband, across at least three boards and over temperature.

Digital side.

• A linear-phase FIR low-pass with passband to 2 kHz and stopband from 4 kHz, decimating 32 kS/s → 8 kS/s (or → 4 kS/s) so downstream processing cost stays where it is today. Passband ripple under 0.1 dB.
• Keep a diagnostic spectrum capture over the full 0–16 kHz band; the 6.4 kHz carrier should now be visible at its true frequency and be ignorable, which is a strong sanity check that the fold-down is gone.
• Add a saturation flag: if the front end clips on the carrier before the filter, no amount of DSP recovers it.

Validation.

1. Bench: inject a 6.4 kHz, 2 Vpp tone and confirm it appears at 6.4 kHz in the diagnostic spectrum and that the reported 1.6 kHz band RMS does not move by more than 0.5 %.
2. Floor: run with the VFD at minimum, nominal and maximum carrier settings and with the motor loaded and unloaded. Record the RMS and the full spectrum for each.
3. Compare against a reference accelerometer or a tachometer-derived vibration level to confirm the ±15 % swing is gone rather than merely moved.
4. Sweep the VFD carrier deliberately across 4–8 kHz and confirm no setting produces an in-band artefact - this is the check that would have caught the original problem.