Random vibration spectra (as in test specifications) usually show intensity as power spectral density (PSD), auto-spectral density, or acceleration spectral density (ASD) in rather strange units of g²/Hz vs. frequency in Hz.

Suppose that your boss asks you to measure the vibration at some location. You gather

• an accelerometer and suitable signal conditioner,
• a band-pass filter (which you temporarily bypass), and
• a true RMS (TRMS) readout voltmeter (Figure 1).

CALIBRATION
First, you calibrate your measurement system. You attach your accelerometer to a small electrody-namic shaker that develops 1g RMS (i.e., 1.414 g peak) at say 500 Hz. You adjust your “set gain” control so that yourtrue RMS readout displays 1 volt RMS (Figure 1).

Figure 1: Vibration Instruments

SENSITIVITY
What is your sensitivity? That is, what is the transfer sensitivity from acceleration in g to volts? 1:1, right? Whenever you see 1 volt on the meter, you know that your accelerometer is experiencing 1 g. Two volts indicates 2 g, etc.

But you only know sensitivity at 500 Hz. How to determine sensitivity at other frequencies? Sweep shaker frequency (maintaining 1 g RMS = 1.414 g peak) over a wide range of frequencies. Plot your voltmeter reading vs. frequency. Hopefully, your graph will be flat at 1 volt/g (Figure 2).

Figure 2: Calibration Results

Now you “unbypass” the filter. You adjust the filter center frequency to 500 Hz and the bandwidth to 160 Hz. Now you repeat the previous sweep and graph. Note the dramatic change in sensitivity vs. frequency (Figure 3). Your sensitivity is still 1 volt/g but only from 420 Hz to 580 Hz. (“Real world” responses are never this flat. The transitions at the “cutoff” frequencies are never vertical. These were drawn with a ruler). Actually, my only reason for Figure 3 is fear that some reader might not be familiar with bandpass filters.