In this measurement column, we will address frequently asked questions received by our customer support center.
We are presenting the answers. This time, we will again discuss the measurement of frequency response functions using sweep signals, etc.
We will cover the following topics.
To measure the natural vibration frequency, the object is excited with a vibrator, the vibration is measured, and the frequency response function is obtained.
It is common to measure this. Also, when measuring the frequency response of a filter circuit, the circuit
A signal is input, and the output signal is measured to determine the frequency response function.
This time, we'll use a sine sweep from a signal output module built into an analysis device such as an FFT analyzer.
This section describes a method for outputting a signal and measuring its frequency response function.
There are two methods: FFT and FRA. This time, we will introduce the FFT method.
Overview of frequency response function measurement using a sine sweep signal
Figure 1 shows an example of a system configuration in which a sine sweep signal is output from a signal output module built into an FFT analyzer, etc., and the frequency response function is measured. The DS-3000 series outputs a sine wave (pure sine wave) of a specific frequency from its built-in signal output module, and the response of that signal (CH.1) and the CR circuit (CH.2) are analyzed using FFT to obtain the frequency response function at that frequency. This calculation is automatically repeated while changing the frequency to measure the frequency response function of the required bandwidth.
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Figure 1: Example of a system configuration for measuring the low-pass filter characteristics of a CR circuit.
Time required to measure the frequency response function using a sine sweep signal.
When measuring the frequency response function using a sine sweep signal, to measure one frequency
The FFT operation is performed once or an average number of times set. Each FFT operation consists of the FFT
Data equivalent to the time duration is required, and the FFT time duration can be calculated from the frequency range and the number of sample points using the following formula.
It is possible.
- 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]
For example, if the frequency range is 1 kHz and the number of sample points is 1024, the number of lines will be 400 and the frequency resolution will be 2.5 Hz, so the length of data required for one FFT calculation (FFT time) will be 0.4 seconds.
The theoretical measurement time required for measuring the frequency response function is determined by the following formula: When the average count is 1, the measurement time is the FFT calculation time multiplied by the number of counts. When the average count is 1, the measurement time will be longer because multiple FFT calculations are performed for a single frequency.
- FFT calculation count = (end frequency [Hz] - start frequency [Hz]) ÷ frequency resolution + 1
- Measurement time (average 1 time) = FFT duration [seconds] × Number of FFT operations
- Measurement time (multiple times) = Measurement time (average per measurement) × { 1 + (1 - overlap amount [%] ÷ 100)
× (average number of times - 1)
The measurement time calculated using the above formula is a theoretical value. In reality, there is a slight time delay between the completion of the FFT calculation at one frequency and the switching of the sine wave frequency, so the actual measurement time will be 10-20 % longer than calculated using this formula.
To determine the frequency response function from 100 Hz to 500 Hz, the frequency resolution is 2.5 Hz, so (500 - 100) / 2.5 + 1 = 161 FFT operations are required. Since one FFT operation takes 0.4 seconds, the measurement time when the average is performed once is 161 × 0.4 seconds = 64.4 seconds. If the overlap is 66.7% and the average is performed four times, the measurement time will be twice that of when the average was performed once, so it will be 128.8 seconds.
In frequency response function measurement using a sine sweep signal, increasing the frequency step size (frequency resolution) increases the measurement time. Halving the frequency step size doubles the FFT time and doubles the number of FFT operations, so the measurement time quadruples.
If you perform measurements using the default settings of the FFT analyzer for frequency range, number of samples, and number of averaging cycles, the measurement time may become extremely long. Check the measurement time using the formula above, and if it is too long, reduce the number of samples or increase the frequency range to coarseen the frequency resolution before performing the measurement.
Sine wave frequency switching and frequency response function measurement
In measuring the frequency response function using a sine sweep signal, the frequency of the sine wave is switched, and an FFT calculation is performed each time. In the FFT calculation for a single frequency, the data is reused for a percentage specified by the overlap amount.
Figure 2-1 shows an example of the timing of sine wave frequency switching and FFT calculation when the average number of cycles is 1. In this example, the frequency step (frequency resolution) is 1 Hz, so 1 second of data is required for one FFT calculation. First, a 1 Hz sine wave is output for 1 second, and the data is subjected to an FFT calculation to obtain the spectrum and frequency response function of the 1 Hz component. Then, the frequency is changed to 2 Hz, 3 Hz, and so on, and the FFT calculation is repeated.
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Figure 2-1 Timing of FFT calculations (average number of calculations: 1)
Figure 2-2 shows an example of the timing of sine wave frequency switching and FFT calculation with an average of 4 cycles and an overlap of 66.7%. After outputting a 2 Hz sine wave for 1 second, the first FFT calculation for 2 Hz is performed. Since the overlap is 66.7%, the latter 66.7% of the data from the first FFT calculation is reused, and the second FFT calculation is performed when a new 33.3% (0.33 seconds) of data arrives. Since an FFT calculation is performed every time 0.33 seconds of data arrives, the measurement at 2 Hz is completed in a total of 2 seconds.
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Figure 2-2 Timing of FFT calculations (average number of calculations: 4, overlap: 66.7%)
Settings for measuring frequency response function using a sine sweep signal
The following are 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.
The frequency step size (frequency resolution) of a sine sweep is determined by the combination of frequency range and sample point count. Select a frequency range that includes the frequency range you want to measure from among the frequency range and sample point count combinations that will achieve your desired frequency resolution.
- Input/Output Settings Menu ⇒ System Settings:
Please ensure that the channel to be used for measurement is set to "ON".
Please note that you cannot change the channel settings used in graphs or other elements. - 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.
Set the coupling 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".
Additionally, you can set the number of sample points and the amount of overlap. - 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 rectangular. - Input/Output Settings Menu ⇒ Averaging Process Settings
Set it to “Power SP Sweep”.
Set the averaging process condition to "Number of times" and set the number of times.
Turn on the signal output linked sweep. - Input/Output Settings Menu ⇒ Signal Output Settings
Set the output mode to "Sweep Averaging Signal Output".
Sets the start and end frequencies of the sine sweep signal.
Set the unit to "V" and set the amplitude of the sine sweep signal and the DC offset in V units. - Graph window
If necessary, the time-domain waveform, power spectrum, and frequency response function of each channel.
This displays graphs of coherence functions and other similar functions. It also allows you to set the X and Y axis scales as appropriate.
summary
In this article, we introduced a method for measuring frequency response functions using a sine sweep signal, specifically by outputting a sine sweep signal from the signal output module built into the FFT analyzer.
Next time, we'll introduce measurements using a sine sweep signal output from an external device.
(Excerpt from the email newsletter issued on December 17, 2015)
