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Reprinted from

VMEbus Systems

/ December 2005

Copyright 2005

What is the meaning of PSD

in

g

2

/Hz units?

By Wayne Tustin

2

TESTING, 1, 2, 3...

Special

Tom’s assignment

Tom is asked to physically measure the vibration existing at some

physically realizable location. Tom gathers vibration-measuring

instruments similar to those in Figure 1. Temporarily, however,

Tom bypasses the filter.

Before taking measurements, Tom calibrates his measurement

system. He temporarily attaches his accelerometer to the table

of a small electrodynamic calibration shaker that develops 1

g

Root Mean Square (RMS); that is, 1.414

g

peak, at the arbitrarily

chosen sine test frequency of 1000 Hz. Tom adjusts his “set gain”

control so that his true RMS readout displays 1 Vrms.

What is the sensitivity of his measurement system? That is, what

is Tom’s transfer sensitivity from acceleration in

g

to volts? 1:1,

right? Whenever Tom sees 1 V on the meter, he knows that his

accelerometer is experiencing 1

g

. Whenever Tom sees 2 V on

the meter, he knows that his accelerometer is experiencing 2

g

and so on.

But Tom has only learned the sensitivity at 1000 Hz. He needs

to determine the sensitivity at other frequencies. Tom sweeps

the frequency of his calibration shaker (maintaining 1-

g

RMS

= 1.414

g

peak) over a wide range of frequencies. Tom plots

his voltmeter reading (which surprisingly remains constant at

1 Vrms) vs. frequency. Figure 2 shows the calibration results.

In the real world, of course, the response will never be this flat.

The graph was drawn with a ruler.

Something motivates Tom to introduce the bandpass filter shown

in Figure 1. He

unbypasses

the filter. He adjusts the filter center

frequency to 1000 Hz and the bandwidth to 160 Hz. Now Tom

repeats the previous sweep and graph.

Note the dramatic change in sensitivity vs. frequency depicted

in Figure 3. Tom’s sensitivity is still 1 V/g but only from 920 Hz

to 1080 Hz.

Real world

responses are never this rectangular. The

transitions at the “cutoff” frequencies are never vertical. These,

too, were drawn with a ruler. The only reason for including Fig-

ure 3 is the remote possibility that some readers might not be

familiar with bandpass filters.

Finally, Tom is prepared to make that measurement. Tom removes

his accelerometer from the calibration shaker and attaches it at the

Editor’s note:

Wayne Tustin is one the electronics industry’s foremost experts on mechanical testing. It this first of a series, Wayne uses a

“Tom, Dick, and Harry” fable to highlight the importance of context in conducting vibration testing.

vibration

input

motion

bypass

set

gain

set

center

frequency

set

bandwidth

“B”

crystal

accelerometer

accelerometer

amplifier

variable

bandpass

filter

TRMS

electronic

voltmeter

Figure 1