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Basics: What is a decibel (dB) anyway? Why is it used?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

 Background

The decibel (abbreviated as ‘dB’) seems to be everywhere in the world of NVH measurements.  It may seem like a unit of measurement (as it is typically shown on the Y-axis) but really it’s not, it is unit-less.  We see it used in acoustics, vibration, electronics, telephony, audio engineering & design…. But what is this unitless-unit, why is it used, and how do we use it correctly?

 

The decibel was originally developed and used by the telephone industry to quantify power loss in telegraph and telephone signals when sent through long cables.  It is named in honor of Alexander Graham Bell, a pioneer in the field of telecommunication.  While a decibel is defined as one tenth of a Bel, the Bel unit is rarely used.

 

Formulation

The decibel is really nothing more than a logarithmic ratio between two numbers – a measured value and a reference value.  It is shown in two forms below: Equation 1 for POWER quantities , and Equation 2 for field AMPLITUDE quantities.

 

dB Formulations.JPG

Examples of POWER quantities:  Sound Power (Watts), Sound Intensity (Watt/m2), electrical Power, electrical Intensity, etc. 

Examples of AMPLITUDE quantities:  Pressure (Pa), Voltage (V), Acceleration (m/s2), temperature, etc.  The amplitude of the field quantities should be in RMS.

 

As the decibel value depends entirely on the ratio between a measured value and the reference value, it is therefore critical to select the proper reference for the calculation.  This is particularly important when comparing values between tests or measurements.  

 

In acoustics, dB are often used to report sound pressure level (SPL).  The reference for pressure in Pascals has been established as 20 micro Pascals (20e-6 Pa).  This value represents the average human hearing threshold at 1000 Hz, or the smallest pressure fluctuation perceivable to the average human ear at 1000 Hz.

 

Let’s take a look at a sample calculation to see how it works.

 

Example

Using your LMS SCADAS hardware and LMS Test.Lab software, suppose you set up a microphone to record an orchestra.  While they are tuning their instruments you make a quick recording.  The RMS amplitude of the sound reads 1.084 Pascals.  What is the dB amplitude of the sound?

Frequency spectrum shown in Amplitude formatFrequency spectrum shown in Amplitude format

Since sound pressure is an AMPLITUDE quantity, we will use the formulation below

 

dB calc formulation.JPG

Remember our dB Reference for Sound Pressure Level is 20 micro Pascals.  Filling in our equation we get the following:

 

dB calc formulation2.JPG

 

You can check your work by having Test.Lab display your recording in decibel format.

Right-click on the Y-axis, select “Format” 

 

format update.png

 

Then select “dB/Level”

 

dB_level_update.png

 

 

Spectrum in dB.JPG

 

Looks like we got the correct answer!  Of course this is ONLY because we chose the same reference value as Test.Lab used. 

 

Double Check - LMS Units Editor

You can always check to see what the default reference value that Test.Lab will use by looking in the LMS Configuration & Units System editor and finding your particular quantity. 

 

UnitSystem.JPG

 

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