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Chapter 11 Introduction to Measurement Analysis in LabVIEW

into a logarithmic scale. We will now see why this transformation is necessary.

Suppose that you want to display a signal with very large as well as very small amplitudes. Let us assume you have a display of height 10 cm, and will utilize the entire height of the display for the largest amplitude. So, if the largest amplitude in the signal is 100 V, a height of 1 cm of the

display corresponds to 10 V. If the smallest amplitude of the signal is 0.1 V, this corresponds to a height of only 0.1 mm. This will barely be visible on the display.

To see all the amplitudes, from the largest to the smallest, you need to change the amplitude scale. Alexander Graham Bell invented a unit, the Bell, which is logarithmic, compressing large amplitudes and expanding the small amplitudes. However, the Bell was too big of a unit, so commonly the decibel (1/10th of a Bell) is used. The decibel (dB) is defined as

one dB = 10 log10 (Power Ratio) = 20 log10 (Voltage Ratio)

The Table 11-1 shows the relationship between the decibel and the Power and Voltage Ratios.

Table 11-1. Decibels and Power and Voltage Ratio Relationship

dB

Power Ratio

Voltage Ratio

 

 

 

 

 

 

+40

10000

100

 

 

 

+20

100

10

 

 

 

+6

4

2

 

 

 

+3

2

1.4

 

 

 

0

1

1

 

 

 

–3

1/2

1/1.4

 

 

 

–6

1/4

1/2

 

 

 

–20

1/100

1/10

 

 

 

–40

1/10000

1/100

 

 

 

Thus, you see that the dB scale is useful in compressing a wide range of amplitudes into a small set of numbers.

LabVIEW Measurements Manual

11-8

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