Technical Note · Sine Vibration Control
Tracking Filters in Sine Vibration Control
Why the signal on a sine test is never a pure sine, how peak, average, rms and tracking-filter measurements disagree about it, and how to choose a filter bandwidth that is both clean and fast enough.
Key takeaways
- A sine test specifies the amplitude of one frequency, but the control accelerometer also sees harmonics, noise and other vibration. How the controller measures amplitude decides whether the test article gets the specified level.
- Peak, average and rms detectors measure the whole signal, so harmonics and noise make them read high. The controller then reduces the drive and the article is under-tested.
- A tracking filter follows the drive frequency and measures only the component at that frequency, so it reads the true fundamental even on a heavily distorted signal.
- Narrow filters reject more noise but respond more slowly. A filter that is too narrow for the sweep rate under-reports resonance peaks and shifts them in frequency.
- Settling time is roughly 3 / bandwidth seconds: about 3 s for a 1 Hz filter, 0.3 s for 10 Hz.
The sine test signal is never a pure sine
A sine profile asks for, say, 1 g at each frequency of a sweep. The controller generates a clean sine drive, but by the time the motion reaches the control accelerometer it has picked up several unwanted components:
- Harmonics at 2×, 3× and higher multiples of the drive frequency, from nonlinearity in the shaker armature and suspension, the power amplifier, rattling or preloaded fixture joints, and nonlinear test articles.
- Broadband noise from the amplifier, cooling blowers, the facility and the measurement chain.
- Other tonal content such as fixture or test-article resonances excited by harmonics, and in combined environments, vibration from other sources.
None of this is unusual. Harmonic distortion of a few percent to several tens of percent is common, particularly at low frequencies, where shakers run at large displacement, and at control points near anti-resonances, as shown below.
Four ways to measure sine amplitude
Sine controllers have traditionally offered four measurement methods. All four agree on a pure sine. They disagree as soon as anything else is present, because three of them measure the whole signal and one measures only the drive frequency.
| Method | How it works | Effect of harmonics and noise |
|---|---|---|
| Peak | Largest instantaneous value in each cycle | Reads high. Harmonics that add in phase with the fundamental peak inflate it directly; noise adds random spikes. |
| Average | Mean of the rectified signal, scaled by π/2 to equal the peak of a pure sine | Reads high, though less than peak. The scale factor is only correct for a pure sine. |
| RMS | Root mean square of the whole signal, scaled by √2 | Reads high. Every component adds its power, so the reading is √(fundamental² + harmonics² + noise²). |
| Tracking filter | Narrow band-pass filter whose center follows the drive frequency | Reads the fundamental only. Harmonics fall outside the passband; noise is reduced in proportion to the filter bandwidth. |
Why it matters: the anti-resonance case
The errors become serious where the fundamental at the control point is small but the distortion is not. That happens at an anti-resonance: a frequency where the fixture or test article moves very little at the control location, for example near a node of a fixture mode. The drive must rise to hold the control level, and the harmonics and noise rise or stay put while the fundamental is weak.
A controller adjusts the drive until its measurement equals the reference. If the measurement reads high, the controller cuts the drive, and the real fundamental ends up below the specification.
| Detector | Case A reading (true 1.0 g) | Case B reading (true 0.2 g) | Case B: fundamental actually delivered |
|---|---|---|---|
| Peak | 1.44 g | 0.79 g (×3.96) | 25% of reference (−12.0 dB) |
| Average | 1.06 g | 0.41 g (×2.06) | 49% of reference (−6.3 dB) |
| RMS | 1.08 g | 0.46 g (×2.31) | 43% of reference (−7.3 dB) |
| Tracking filter | 1.00 g | 0.20 g (×0.99) | ≈ 100% of reference |
The last column assumes the distortion stays the same as the drive changes, which is a simplification, but the direction of the error is always the same: whole-signal detectors under-test the fundamental when distortion is present. There are cases where measuring the whole signal is intended, for example when a specification defines the level as peak acceleration including harmonics, or when protecting a fragile article from its total peak response. That should be a deliberate choice written into the test procedure, not a default.
How a tracking filter works
The controller always knows its own drive frequency exactly, because it generates it. A tracking filter uses that knowledge. Conceptually it multiplies the measured signal by a sine and a cosine at the drive frequency, then low-pass filters the products. Everything at the drive frequency becomes a steady (DC) value that passes through; everything at other frequencies becomes an oscillation that the low-pass filter removes. The result is the amplitude and phase of the fundamental, updated continuously as the sweep moves.
The result behaves like a narrow band-pass filter that slides along with the sweep. Two settings define it:
- Bandwidth: how wide the passband is. Narrower means more rejection of noise and nearby tones, but a slower response.
- Fixed or proportional: whether the bandwidth stays constant in hertz or scales with the drive frequency.
Fixed versus proportional bandwidth
| Fixed bandwidth (Hz) | Proportional bandwidth (% of frequency) | |
|---|---|---|
| Noise rejection | Constant across the sweep; best at high frequency | Excellent at low frequency, poorer at high frequency |
| Harmonic rejection | Weakens at low frequency, where harmonics are only a few hertz away | Constant across the sweep, because harmonic spacing also scales with frequency |
| Response speed | Constant settling time in seconds | Slow at low frequency, fast at high frequency |
| Best suited to | Sweeps starting above roughly 20 Hz; high-frequency work in noisy environments | Wide sweeps that start at low frequency, where distortion is highest |
The bandwidth trade-off: clean versus fast
A narrow filter needs time to respond. As a practical rule, a tracking filter settles to within 2% of a new amplitude in about 3 / B seconds, where B is its bandwidth in hertz.
| Bandwidth B | Settling time (to 2%) | Noise reduction vs. 2 kHz band |
|---|---|---|
| 50 Hz | 0.06 s | 16 dB |
| 20 Hz | 0.16 s | 20 dB |
| 10 Hz | 0.31 s | 23 dB |
| 5 Hz | 0.63 s | 26 dB |
| 2 Hz | 1.6 s | 30 dB |
| 1 Hz | 3.1 s | 33 dB |
| 0.5 Hz | 6.3 s | 36 dB |
Noise reduction follows 10·log10(2000 / B): each tenfold narrowing gains 10 dB, but costs ten times the settling time. During a sweep, settling time becomes a measurement error, and resonances are where it shows.
The reason is the same build-up behavior described in our Resonance note, applied to the filter instead of the structure. At this sweep rate the drive crosses the resonance's 2 Hz half-power band in under two seconds. A filter that needs three seconds or more to settle cannot keep up, so it averages the peak with the lower response on either side and reports it late.
A practical check. The filter should settle well within the time the sweep spends crossing a resonance's half-power bandwidth. For a resonance of frequency fn and quality factor Q on a logarithmic sweep of R octaves per minute, that crossing time is about 86.6 / (Q·R) seconds. Choose B so that 3/B is a small fraction of it. For the example above (Q = 25, R = 2) the crossing takes 1.7 s, so B of 5–10 Hz is appropriate and 1 Hz is already marginal.
Choosing settings in practice
| Situation | Suggested approach |
|---|---|
| General swept sine qualification test | Tracking filter on, moderate bandwidth that settles quickly relative to the sweep rate |
| Low-frequency start (below about 20 Hz) or large-displacement tests | Proportional bandwidth, which keeps harmonics rejected where distortion is worst |
| Noisy facility, high-frequency sweeps, low test levels | Narrower fixed bandwidth, with a slower sweep if the specification allows |
| Resonance search with lightly damped (high-Q) articles | Bandwidth wide enough to settle within the half-power crossing time; slow the sweep instead of narrowing the filter |
| Resonance dwell at fixed or tracked frequency | Narrow bandwidth is fine once the frequency is stable; it gives the cleanest amplitude and phase |
| Specification defines level as total peak including harmonics | Peak detection, by deliberate choice and documented in the test procedure |
Common misconceptions
| Misconception | Reality |
|---|---|
| "Peak, average and rms are just different units for the same sine level." | They are equivalent only for a pure sine. With distortion they give different numbers and lead the controller to different drive levels. |
| "Reading high is the safe direction." | A detector that reads high makes the controller lower the drive, so the test article receives less than specified. That is an under-test, not a margin. |
| "The narrowest filter is always the most accurate." | Only when the frequency is steady. During a sweep, a filter that is too narrow lags and attenuates resonance peaks (Figure 5). |
| "Tracking filters are only for noisy labs." | Harmonic distortion from the shaker and fixture is present in every lab, and is largest at low frequencies and anti-resonances. |
| "If the control signal looks clean on a scope, distortion doesn't matter." | Distortion of 10–20% is hard to see on a time trace but changes peak and rms readings substantially. Look at the spectrum, as in Figure 2. |
Quick reference
| Quantity | Formula | Rule of thumb |
|---|---|---|
| RMS detector reading | √2 · √(a1²/2 + a2²/2 + … + noise²) | Every component adds power |
| Settling time | ≈ 3 / B | 1 Hz filter → about 3 s |
| Noise reduction | 10·log10(band / B) | 2 kHz band, 2 Hz filter → 30 dB |
| Sweep rate at frequency f (log sweep) | f · ln2 · R / 60 Hz/s | 2 oct/min at 50 Hz → 1.16 Hz/s |
| Half-power crossing time | ≈ 86.6 / (Q·R) s | Independent of frequency on a log sweep |
| Bandwidth check | 3/B ≪ crossing time | Slow the sweep rather than narrowing the filter |
| Proportional bandwidth | B = p · f | 10% at 20 Hz = 2 Hz; at 2000 Hz = 200 Hz |
How Panther helps
- Tracking filters built in: Panther Sine measures control and response channels through tracking filters that follow the drive frequency, so control acts on the fundamental rather than on harmonics and noise.
- Precise frequency tracking: High Precision Frequency Tracking keeps the filter locked to changing frequencies, including during resonance-tracked dwells and rotating-machinery measurements.
- Clean amplitude and phase: 24-bit acquisition with more than 110 dB of dynamic range and channel-to-channel phase match on the order of 0.01° keeps small fundamentals at anti-resonances measurable, and keeps transmissibility phase trustworthy for resonance identification.
- Configurable measurement: filter bandwidth and measurement method can be set to suit the sweep rate, frequency range and specification.
References and further reading
- C. M. Harris and A. G. Piersol (eds.), Harris' Shock and Vibration Handbook, 5th ed., McGraw-Hill.
- R. B. Randall, Frequency Analysis, 3rd ed., Brüel & Kjær (synchronous detection and tracking analysis).
- MIL-STD-810H, Method 514.8, Vibration.
- Spectral Dynamics Technical Library: Understanding Sine Test Methodologies; Resonance; FFT Fundamentals: Resolution, Windowing and Leakage.
