February 2003
Table of Contents

Low-Pass Filtering for
Vibration Sensors

Vibratory signals can reveal a great deal about a machine’s health, but not when extraneous noise corrupts the data. Adding the right filter to your accelerometer can clean that signal right up.

Ed Ramsden and Christopher Dix
Lattice Semiconductor


Vibration and acoustic sensors are often used to monitor the health of various types of mechanical systems. By listening for the presence and magnitude of signals at certain frequencies, it is often possible to detect abnormal operation, component wear, or minor faults in time to take preventive measures against catastrophic failure. One of the principal types of sensor used for this type of monitoring is the piezoelectric accelerometer. While capacitive and electrodynamic accelerometers are well established, piezoelectric devices are gaining in popularity because they are rugged, straightforward to operate, and capable of providing useful signal bandwidths into the tens of kilohertz, covering much of the audio signal range.

High bandwidth can be a useful feature, but it can also become a liability in that a high-bandwidth sensor will often detect many unwanted signals (noise) in addition to the one we’re looking for. A low-frequency vibration signal, such as that representing the balance of a rotating shaft, can often be masked in high-frequency noise. One solution to the problem is an electronic filter that attenuates unwanted signals while retaining those of interest.

Piezoelectric Accelerometers
Materials that experience a change in their internal electric fields in response to applied mechanical force are said to be piezoelectric. If electrodes are attached to opposite sides of a specimen of a piezoelectric material, a voltage will be developed when the material is squeezed or stretched (see Figure 1).

Figure 1. A piezoelectric material develops an internal electric field when compressed (A) or stretched (B). If electrical contacts are attached to the material, a quantity of electrical charge proportional to the applied force can be measured.

Conversely, a voltage applied to a piezoelectric material will cause it to mechanically deform. While many familiar materials such as quartz and sugar exhibit the piezoelectric effect to a measurable degree, specialized ceramic and plastic materials such as PZT (lead zirconate titanate) and PVdF (polyvinylidene fluoride) are extremely effective at converting a mechanical stimulus to an electrical response.

Figure 2. Practical piezoelectric accelerometers use a seismic mass to convert acceleration to force on the piezoelectric element.
In the time since the piezoelectric effect was discovered by Jacques and Pierre Curie in 1880, it has been put to many uses, ranging from submarine sonar systems to barbecue starters. One of its most significant applications is the detection of mechanical vibration. Figure 2 shows a simplified diagram of a piezoelectric vibration sensor. In addition to the piezoelectric transducer element, the sensor contains a seismic, or proof, mass that provides a force against the piezoelectric element in response to applied acceleration. This has the effect of greatly increasing the device’s response over that which would be obtained using just the raw piezoelectric element.

The seismic mass is held in contact with the piezoelectric element by a spring force (in this case, the screw). The combination of a mass constrained by a spring can cause the system to mechanically resonate at a particular frequency. The vibration sensor will exhibit a much higher sensitivity when stimulated at this frequency (see Figure 3).

Figure 3. The accelerometer's seismic mass and its support structure form a mechanical resonant system that can result in pronounced increases in sensitivity to signals at the sensor's resonant frequency.

For many general-purpose piezoelectric vibration sensors, resonant frequencies range from 10 to 50 kHz. A particular accelerometer’s resonant frequency usually sets a practical upper limit on the maximum frequency at which it can be used effectively.

In addition to posing problems when measuring signals near the resonant frequency, resonance can also interfere with measuring signals of lower frequencies. One reason is that many signals contain harmonics, which are higher frequency components at some multiple of the fundamental frequency. If these harmonics occur at frequencies near the accelerometer’s resonance, they may be disproportionately magnified and distort the output signal. A transducer’s resonances may be excited also through nonlinear distortion. Nonlinearities in a material’s mechanical response can often create harmonics where none had previously existed. These harmonics then are disproportionately reported by the transducer.

Filtering Out Unwanted Signals
While the mechanical resonance of an accelerometer can be attenuated by mechanical means, such as by interposing a damper (e.g., a thin sheet of rubber) between the sensor and the object being monitored, it can be difficult to precisely control the degree to which resonant effects may be reduced. Depending on the properties of the damper, this addition can also add resonant modes to the system.

Another option is to electrically filter the electric signal output from the accelerometer. By passing the accelerometer’s output signal through a low-pass filter with a cutoff frequency below that of the accelerometer’s mechanical resonance (see Figure 4), it is possible to reduce the magnitude of any resonant signals.

Figure 4. A low-pass filter can be used to effectively reduce the effects of resonance by attenuating signals at the accelerometer's resonant frequency.

The principal advantage of electronic filters is that they are straightforward to construct with very precise and well-defined characteristics. Another positive note is that these filters don’t change the mechanical properties of the sensor or of the system being measured.

To illustrate the effectiveness of electrically filtering an accelerometer’s output, we took a PCB Piezotronics Model 308B accelerometer and attached it to a steel plate with a magnetic base coupling. We then used a digital sampling oscilloscope to monitor
Click for larger image
Click for larger image Figure 5. For our test, we struck a piece of steel to cause it to ring, and monitored both filtered and unfiltered versions of the accelerometer's output.
both the accelerometer’s direct output and a filtered version of it. For the filter, we used a Lattice Semiconductor ispPAC81 continuous-time, fifth-order, low-pass programmable filter IC, which we programmed to a 10.8 kHz Butterworth configuration. Figure 5 shows our experimental setup.

For a stimulus source we struck the plate with a screwdriver blade, producing an audible ring that provided a signal rich in harmonics from the plate’s resonances as well as transient higher frequency components caused by the metal-on-metal impact. Figure 6 shows the oscilloscope’s representation of the time-domain responses, both directly from the accelerometer (upper trace) and after filtering (lower trace).

Figure 6. The top trace shows the unfiltered output of the accelerometer, while the bottom trace shows the effect of filtering with a 10.8 kHz fifth-order Butterworth filter.

Note that the unfiltered signal is buried in a significant amount of high-frequency “noise,” while the filtered signal shows only slight traces of the obscuring noise of the original.

Although the cleaned-up version of the signal may look “better” than the raw one, an eyeball comparison of the two does not provide much insight into exactly how the signal is being transformed. Specifically, how can we be sure that the filter isn’t thrüwing out useful information along with the noise? Another way of looking at signals is in the frequency domain. A filter’s performance is typically specified in the frequency domain, where its response is characterized in terms of gain (magnitude) and delay (phase) as functions of frequency. It is also possible to characterize a signal in a similar way—by its power spectrum, which describes the amount of energy a signal contains as a function of frequency. A sinusoidal waveform, for example, will have a power spectrum consisting of a single spike at the sinusoid’s frequency. Because a signal’s power spectrum can be directly compared to a filter’s magnitude response, it is a useful tool for predicting a given filter’s effects on a class of signals.

Figure 7A shows the power spectrum of the accelerometer’s unfiltered response; Figure 7B shows the spectrum after being passed through the ispPAC81.

Figure 7. Spectral analysis provides another view of the signals in Figure 6. The spectrum of the unfiltered signal (A) clearly shows a large 14 kHz component; the filtered version (B) shows significant attenuation of this peak.

These spectra were obtained from the time-domain data by invoking the oscilloscope’s FFT function. In both plots, the vertical scale is 5 dB/ division and the horizontal scale is 2.5 kHz/ division. In the unfiltered signal, we can clearly see a series of low-frequency peaks ranging from 2 to 5 kHz, as well as a single large peak at ~14 kHz. This 14 kHz component contributes much of the noise present in the unfiltered time-domain signal (the upper trace in Figure 6). Passing the signal through the filter attenuates this 14 kHz peak
Company Information

PCB Piezotronics Inc.
Depew, NY
by ~12 dB, as can be seen in Figure 7B. Note that the filter doesn’t eliminate this peak, but rather attenuates it. Real filters can’t completely get rid of unwanted signals, but they can reduce their magnitude to an arbitrary degree. (One measure of a filter’s usefulness is the degree to which it can reduce an unwanted signal.)

Just as significant as the filter’s attenuation of the unwanted signal is that it does not significantly attenuate signals within its pass band, those with a frequency of <10 kHz. A comparison of Figures 7A and 7B shows that the magnitudes of peaks at frequencies of <10 kHz are substantially the same. The ability to selectively attenuate nearby interfering signals without affecting those of interest is one desirable feature of a high-order filter, such as the ispPAC81 (fifth order).

Although the ruggedness and high bandwidth of modern piezoelectric accelerometers makes them a preferred choice for measuring vibration, these attributes can also result in measuring unwanted high-frequency noise. While mechanical filters and proper mounting techniques can reduce the effects of this noise, electronic filters can accomplish the task as well, as demonstrated by the ispPAC81.

A Continuous-Time Programmable Low-Pass Filter
One example of a modern analog filter IC is the Lattice ispPAC81. This device can be used to implement fifth-order low-pass filters with corner frequencies ranging from 10 to 75 kHz, with a choice of Butterworth, Chebyshev, or elliptical characteristics. Figure 8, showing how this device looks to the designer, consists of an input amplifier (offering gains of 1, 2, 5, and 10); a filter engine; nonvolatile memory for storing configuration data; and a fixed-gain output driver amplifier. All these functions are implemented on a monolithic silicon die and require no external components to adjust filter parameters.

Figure 8. The ispPAC81 provides both a programmable-gain preamplifier and a flexible fifth-order low-pass filter engine that can be programmed with corner frequencies spanning a 10-75 kHz range.

The primary advantage of using a high-order, rather than a simpler RC first-order, filter is that the higher the filter order, the faster the response rolls off above the corner frequency. In the case of a first-order filter, every 10 3 increase in frequency above the corner results in 20 dB of attenuation, a factor of 10. For a fifth-order filter such as the ispPAC81 (see Figure 9), the same increase results in 100 dB of attenuation, a factor of 100,000.

Figure 9. PAC-Designer's built-in simulator allows designers to quickly evaluate the performance of a candidate filter design. The magnitude and phase responses of three different 12 kHz filters are shown superimposed in this plot.

By storing filter parameters in nonvolatile memory on chip as opposed to setting parameters with discrete resistors and capacitors, the ispPAC81 can be used to implement thousands of different filters using the same hardware. A library of ~2000 predesigned and tested configurations is supplied with PAC-Designer, but the software also allows low-level access to individual capacitive elements on the chip so that designers can tailor a response to their requirements.

Ed Ramsden, a member of the Sensors Editorial Advisory Board, and Christopher Dix are Senior Applications Engineers, Lattice Semiconductor, Hillsboro, OR; 503-268-8648, ed.ramsden@latticesemi.com (Ramsden), 503-268-8671, chris.dix@latticesemi.com (Dix).

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