This measurement column addresses frequently asked questions received by our customer support center and provides answers to them. In the previous article, we introduced a method for measuring the frequency response function by outputting a sine sweep signal from a signal output module built into an analysis device such as an FFT analyzer. This time, we will introduce a method for measuring the frequency response function using a sine sweep signal from an external device such as a vibration exciter controller.
In the method described previously, which uses a sine sweep signal from the built-in signal output of the analysis device, the frequency of the sine wave can be changed after the analysis device has completed the FFT calculation for one frequency point, allowing for accurate measurement of the signal's power spectrum and frequency response function.
In methods using sine sweep signals from external devices, the frequency of the sine wave changes independently of the analysis device's FFT calculation. Therefore, if the sine wave sweep speed is too fast, accurate results cannot be obtained, and measurements must be taken under appropriate conditions. Furthermore, this method measures the frequency response function. The power spectrum values for each channel will be smaller than the actual amplitude, so it is not suitable for applications requiring accurate amplitude measurement.
Measurement of frequency response function using signals from external devices
Figure 1 shows an example of a system configuration for measuring the frequency response function using a sine sweep signal from an external device. In this example configuration, a controller with an oscillator outputs a sine sweep signal to vibrate an exciter. Accelerometer are attached to both the exciter and the object under test, and the frequency response function (natural frequency) of the object under test is measured from these signals.
In this configuration example, the channel connected to Accelerometer attached to the vibrator is used as the reference channel for the sine sweep. The analysis device detects the frequency of the currently input vibration from the signal input to the reference channel and measures the frequency response function at that frequency using FFT calculation. Since the controller outputs a sine sweep signal, the frequency response function at each frequency can be measured by repeating the FFT calculation.
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Figure 1: Example of a system configuration for vibration measurement using signals from a vibration exciter controller.
Settings for measuring frequency response function using signals from external devices
The frequency step size (frequency resolution) of the measured power spectrum and frequency response function is determined by the combination of frequency range and sample point count, as shown in the following equation. Select the frequency range that includes the frequency range you want to measure from the combinations of frequency range and sample point count that result in the desired frequency resolution.
Number of lines [points] = Number of sample points [points] ÷ 2.56
Frequency resolution [Hz] = Frequency range [Hz] ÷ Number of lines [points]
Next, the following are the standard settings for measuring frequency response functions using the DS-0321 FFT analysis software of the DS-3000 series. Other FFT analysis software and FFT analyzers have similar settings, although the menus and names may differ.
- Input/Output Settings Menu ⇒ System Settings:
Please ensure that the channel used for measurement is set to "ON".
Please note that you cannot change the channel settings used in graphs or other applications to OFF. - Input/Output Settings Menu ⇒ Cross-Combination Settings:
Please ensure that the channel pair for measuring the frequency response function is registered. - Input/Output Settings Menu ⇒ Frequency Range Settings:
Set the frequency range. - Input/Output Settings Menu ⇒ Input Settings:
Turn the auto-range function "OFF".
The voltage range is adjusted according to the magnitude of the input signal.
If an input overload occurs even once during measurement, increase the voltage range.
The coupling is set to "AC".
When connecting sensors that require a constant current power supply, such as accelerometers and microphones,
Turn CCLD "ON". - Input/Output Settings Menu ⇒ Sample Condition Settings:
The sample condition is set to "internal".
Set the overlap amount to "MAX".
Set the number of sample points. - Input/Output Settings Menu ⇒ Unit and Calibration Settings:
Configure the settings according to the signals and sensors connected to each channel. - Input/Output Settings Menu ⇒ Window Function Settings:
Set it to Hanning. - Input/Output Settings Menu ⇒ Time Axis Preprocessing Settings:
Turn on DC cancellation for each channel.
Leave the other settings as "OFF". - Input/Output Settings Menu ⇒ Averaging Settings:
Set to "Power SP Sweep".
The averaging condition is set to "number of times". The number of times setting will be ignored.
Turn off the signal output-linked sweep.
A channel is set as the reference channel for the sweep channel. - Graph window:
If necessary, graphs of the power spectrum, frequency response function, etc. for each channel are available.
Displayed. Power spectrum and frequency response function graphs show a sine sweep signal.
The results measured by the system are displayed. This includes graphs of time-domain waveforms and Fourier spectra.
The display shows the signal being input at that moment, not the measurement result, so the reference
It can be used to monitor signals and other data being input to a channel.
Examples of frequency response function measurements
Figure 2 shows the results of measuring the frequency response function of the filter circuit using a signal from an external device. The frequency range was 20 kHz, the number of sample points was 2048, and the frequency resolution was 25 Hz.
Function generator with amplitude 0.1 Vrms, frequency range 4 kHz to 14 kHz.
It outputs a sine sweep signal with a sweep time of 16 seconds, and the input signal to the filter circuit (CH.1) and
The power spectrum of the output signal (CH.2) (first and second rows of graphs) and the frequency response function of the filter circuit (third row of graph) were measured. The Fourier spectrum in the fourth row of graph is displayed to confirm the instantaneous spectrum of the input signal to the filter circuit.
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Figure 2 Example of measurement results of frequency response function
Since a 0.1 Vrms signal is input to CH.1, the power spectrum value should be -20 dBVrms. However, in reality, it varies from approximately -20.5 to -21.3 dBVrms depending on the frequency, and the value is also smaller than -20 dBVrms.
In FFT analysis using a Hanning window, the sine wave frequency is accurate when it is an integer multiple of the frequency resolution (25 Hz in this example), but if it deviates from an integer multiple of the resolution, it will yield a value up to 1.42 dB smaller.
The deviation from an integer multiple of the frequency varies depending on when the FFT calculation is performed, so the power spectrum values obtained will vary for each frequency.
Furthermore, although we will provide more details in the next measurement column, the sweep speed of the sine sweep signal is
If the speed is too high, the power spectrum values will be reduced as a result.
The amount by which the power spectrum value decreases due to these causes is the same for both the input signal (CH.1) and the output signal (CH.2). Therefore, these causes cancel each other out when calculating the frequency response function, and the resulting frequency response function is correct.
Measurement of frequency response function and its effect on sweep speed
Figures 3-1 and 3-2 show the measured frequency response function when the sweep speed of a sine sweep signal output from a function generator is varied. The frequency range is 20 kHz, the number of sample points is 4096, and the frequency resolution is 12.5 Hz. The sine sweep signal has an amplitude of 0.1 Vrms, a frequency range of 4 kHz to 14 kHz, and two sweep times: 16 seconds and 64 seconds. The sweep speeds are 625 Hz/second and 156.25 Hz/second, respectively.
In each figure, the first row of the graph shows the power spectrum of the input signal to the filter circuit (CH.1), and the second row shows the frequency response function of the filter circuit.
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Figure 3-1 Example of frequency response function measurement results (sweep time 16 seconds, sweep speed 625 Hz/second)
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Figure 3-2 Example of frequency response function measurement results (sweep time 64 seconds, sweep speed 156.25 Hz/second)
The measurement results in Figure 3-1 show the data as being skewered. In this example, the frequency resolution is 12.5 Hz, but the sweep speed was too fast, causing the sine wave frequency to change by more than 12.5 Hz before one FFT operation was completed. As a result, data for frequency components that could not be measured are missing in the skewered pattern.
In Figure 3-2, the FFT calculation keeps up with the sweep speed, so the phenomenon of data being skipped in a skewer-like fashion does not occur.
Guideline for sweep speed
With a frequency resolution of 12.5 Hz, a time waveform of 0.08 seconds is required for one FFT operation.
Since it is desirable that the frequency changes by only about the same amount as the frequency resolution during one FFT operation (80 ms), the ideal sweep speed is 12.5 Hz ÷ 0.08 seconds = (1.25 Hz)² = 156.25 Hz/second.
If the sweep speed of the sine sweep signal from an external device is faster than this value, accurate measurement results may not be obtained.
The relationship between frequency range, number of samples, FFT time length, and ideal sweep speed is given by the following equation.
Examples of these are shown in Table 1.
Number of lines [points] = Number of sample points [points] ÷ 2.56
Frequency resolution [Hz] = Frequency range [Hz] ÷ Number of lines [points]
FFT time length [seconds] = 1 ÷ frequency resolution [Hz]
Sweep speed [Hz/sec] = Frequency resolution [Hz] ÷ FFT time length [sec]
= (Frequency resolution [Hz]) 2
Table 1: An example of frequency range, number of samples, FFT time length, and ideal sweep speed.
|
Frequency range (Hz) |
Sample score (points) |
Frequency resolution (Hz) |
FFT time length (sec) |
Sweep speed (Hz/second) |
|
40000 |
4096 |
25.0 |
0.04 |
625.0 |
|
20000 |
4096 |
12.5 |
0.08 |
156.3 |
|
10000 |
4096 |
6.25 |
0.16 |
39.1 |
|
5000 |
4096 |
3.13 |
0.32 |
9.77 |
|
2000 |
4096 |
1.25 |
0.80 |
1.56 |
|
1000 |
4096 |
0.63 |
1.60 |
0.39 |
|
20000 |
1024 |
50.0 |
0.02 |
2500.0 |
|
10000 |
1024 |
25.0 |
0.04 |
625.0 |
|
5000 |
1024 |
12.5 |
0.08 |
156.3 |
|
2000 |
1024 |
5.00 |
0.20 |
25.0 |
|
1000 |
1024 |
2.50 |
0.40 |
6.25 |
If you have trouble measuring the frequency response function, check the sweep speed and the ideal values mentioned above.
If the sweep speed seems too fast compared to what you're used to, try slowing it down.
If you cannot change the sweep speed, reduce the number of sample points.
Halving it will make the sweep speed four times faster.
For example, with a frequency range of 2 kHz and 4096 sample points, the frequency resolution is 1.25 Hz, and the ideal sweep speed is 1.56 Hz/second. Sweeping a 1 kHz range at this speed would take 640 seconds (just under 11 minutes). If the number of sample points is reduced to 2048, the frequency resolution becomes 2.5 Hz, the ideal sweep speed becomes 6.25 Hz/second, and sweeping a 1 kHz range takes only 160 seconds.
If the number of sample points is set to 1024, the frequency resolution becomes 5 Hz, and the ideal sweep speed is 25 Hz/second.
Therefore, the time required to sweep within the 1 kHz range is 40 seconds.
summary
This time, we discussed how to measure the frequency response function using a sine sweep signal from an external device, including the phenomena that occur when the sweep speed of the sine sweep signal is too fast, and provided guidelines for the sweep speed. There are other phenomena that can occur when the sweep speed is too fast, which we will cover in the next measurement column.
(Excerpt from the email newsletter issued on February 18, 2016)
