Frequently Asked Questions about Measurement - Part 46: "The Lower Limit of Acceleration Values Measurable by Accelerometers"

This measurement column addresses frequently asked questions received by our customer support center and provides answers to those questions.

The specifications for acceleration detectors do not specify a lower limit for the acceleration values that can be measured by the detector. The actual lower limit depends on the self-noise of the acceleration detector and analysis equipment, the measurement method, and the required level of accuracy in the measurement results.

Accelerometer detector noise

Accelerometers with built-in preamplifiers (voltage output type) have a specification called detector noise. Even in the absence of any vibration, the accelerometer outputs a voltage signal (noise) corresponding to this value. Table 1 shows the sensitivity and detector noise of some of our preamplifier-equipped accelerometers. Generally, detectors with higher sensitivity have lower detector noise when converted to acceleration values.

Table 1 Detector noise of a preamplifier-integrated accelerometer (example)

If an acceleration of 40 mm/ ^s² is input to an acceleration detector with a detector noise of 0.004 m/ ^s² rms, or 4 mm/ ^s² rms, the output will vary in a distribution with an average value of 40 mm/ ^s² and a standard deviation of 4 mm/ ^s². Simply put, the accuracy can be said to be 10%, but the actual accuracy depends on the number of averages and the measurement method.

Charge-type accelerometers do not have a specification called "detector noise." The magnitude of the noise is determined by the input-referred noise level of the charge amplifier to which the detector is connected. The input-referred noise level of our charge amplifier CH-1200A is 0.05 pC rms or less. The detector noise, converted from this value to acceleration based on the charge sensitivity of the accelerometer, is determined. Table 2 shows the sensitivity and the resulting detector noise for some of our charge-output type accelerometers.

Table 2 Detector noise of charge-output type accelerometer (example)

Power spectral density of detector noise in an accelerometer

Power spectrum of the detector noise measured for the NP-3574 3-axis accelerometer with built-in preamplifier.
The torque density (PSD) is shown in Figure 1. CH.1 (blue) is the X-axis of the NP-3574, and CH.3 (red) is the Z-axis of the NP-3574. CH.4 (green) is the self-noise of the DS-3000, measured by short-circuiting the input terminal with a 50 Ω resistor. The same voltage sensitivity as the NP-3574 was set and converted to an acceleration value.

Equipment used
NP-3574 Preamplifier-integrated 3-axis accelerometer
DS-3000 Series Data Station

Measurement conditions
Frequency range: 800 Hz
Sample score: 2048 points
Voltage range: 10 mV rms
Average time 10 seconds DC cancellation: ON

The purpose was to measure detector noise, but the measurement location is a typical office, so it is affected by background vibrations. Vibrations that appear to be background vibrations were observed between 5 Hz and 80 Hz. The overall noise level for CH.1 (NP-3574 X-axis) is 3.229 mm/ ^s², which meets the detector noise specification (4 mm/ ^s² or less). Background vibrations larger than the detector noise were observed in CH.3 (NP-3574 Z-axis). CH.4 (DS-3000 self-noise) is about 1/100th of the detector noise, so it does not affect the measurement of the detector noise.

For this measurement, we set the DS-3000's voltage range to the smallest setting, 10 mV rms. At this voltage range, the DS-3000's self-noise is sufficiently low. If the voltage range is left at its default value (1 V rms) or at a larger voltage range, the DS-3000 data station's self-noise also increases, making it impossible to measure detector noise, background vibrations, and minute vibrations. The voltage range must be set appropriately according to the magnitude of the vibration being measured.

Furthermore, DC cancellation was turned ON. When 0 V is input to the analysis device, the device should display it as 0 V, but in reality, there is a slight deviation. This deviation is called residual offset. The residual offset specification under these measurement conditions is 0.14 mV (equivalent to 14 mm/ ^s²) or less. Since the impact on the measurement cannot be ignored, DC cancellation was used to eliminate it before measurement.

Time-domain waveform of accelerometer detector noise

Figure 2 shows the time-domain waveform of the X-axis detector noise measured for the NP-3574 3-axis accelerometer with built-in preamplifier.

Equipment used
NP-3574 Preamplifier-integrated 3-axis accelerometer
DS-300 Series Data Station

Measurement conditions
Frequency range: 8 kHz
Recording time: 10 seconds
Voltage range: 10 mV rms

The time-domain waveform being shifted positively by approximately 14 mm/ ^s² (0.14 mV) is likely due to the residual offset (DC offset) of the DS-3000 data station. The residual offset specification under these measurement conditions is less than 0.14 mV (equivalent to 14 mm/ ^s²), and this value is in close agreement with that specification.

The slow, undulating waveform on the time axis is likely due to low-frequency dark oscillations.

Reading acceleration values from time-domain waveforms (Part 1)

The time-domain waveform data of a 10-second detector noise was divided into 10 1-second time-domain waveforms, and a sine wave with a frequency of 160 Hz and an amplitude of 40 m/ ^s² was added to each of these divisions. This results in data that simulates the situation of performing a total of 10 measurements of a 160 Hz frequency, 40 m/ ^s² amplitude, 1-second length sine wave under the presence of detector noise.

Table 3 shows the results of measuring the single-ended amplitude by reading the maximum and minimum values of the time-domain waveform during the first sinusoidal period (62.5 ms) of a 1-second measurement data, and then dividing the difference by 2.

Table 3: Acceleration amplitude readings (from the time-domain waveform over one period of a sine wave)

The average of 10 measurements was 40.88 mm/ ^s², and the standard deviation (variability) was 0.71 m/ ^s². The results are generally accurate.

The average value during the first sinusoidal period (62.5 ms) of the 1-second measurement data varied within the range of -3.92 to 23.22 mm/ ^s², as shown in Table 3. This is due to the residual offset of the analysis instrument and the influence of background vibrations. Evaluating the amplitude using only the maximum or minimum value would be affected by the deviation of the average value from zero; therefore, in this case, the single amplitude was calculated from the difference between the maximum and minimum values.

Reading acceleration values from time-domain waveforms (Part 2)

Table 4 shows the results of measuring the single-ended amplitude values by reading the maximum and minimum values of the entire time-domain waveform over a length of 1 second using the same data as in the previous section and dividing the difference by 2.

Table 4. Acceleration single amplitude readings (from the maximum value of the time-domain waveform over a 1-second period)

The average of 10 measurements was 49.65 mm/s², and the standard deviation (variability) was 1.76 m/s². Since it is a 160 Hz sine wave, the maximum and minimum values (the maximum value on the negative side) occur 160 times per second, and these values vary due to detector noise. Because the maximum value was captured 160 times under these conditions, the result obtained is more than 20% larger than the actual value (40 mm/s²).

When evaluating using RMS values

Table 5 shows the results of obtaining the power spectrum from the same data as in the previous section using FFT analysis, and then calculating the single amplitude values from the overall values. For a frequency range of 8 kHz and a frame length of 1024 points, the length of the time-domain waveform required for one FFT operation is 50 ms. Since the length of one time-domain waveform data is 1 second, analyzing with a 50% overlap allows us to extract time-domain waveforms equivalent to 39 FFT operations. The single amplitude values shown for each measurement count are the average results of these 39 measurements.

Analysis conditions
Frequency range: 8 kHz
Frame length: 1024 points
Frame duration: 50 ms
Overlap amount: 50%
DC Cancellation: ON

Table 5 Calculation results of the overall power spectrum value

The average of 10 measurements was 40.146 mm/ ^s², and the standard deviation (variability) was 0.044 m/ ^s². Since the overall power spectrum is calculated using the square of the acceleration, it is less susceptible to detector noise. When calculated using the square, the overall value of the combined signal when the signal amplitude is 40 mm/ ^s² and the noise amplitude is 4 mm/ ^s² is only √(^40² + ^4²) = 40.2. Sufficiently good accuracy can be obtained if the signal is about 10 times larger than the noise.

summary

This time, we presented the results of measuring the detector noise of an accelerometer. We confirmed that the measured detector noise included dark vibrations and residual offset.

We determined the amplitude of the sine wave from data obtained by adding a sine wave to the measured detector noise using three different methods. The influence of the detector noise varies depending on the method used to determine the amplitude.

(Excerpt from the email newsletter issued on May 19, 2021)