Decibel

Warming-up The decibel definition

Decibel is a relative comparison between numbers... A(dB)



10 log10 

whatever the numbers are!

P 1 P 2

Absolute comparison in decibel between betw een numbers... A(dBunity)

A(dBW)



10 log10 

P 



10 log10 

whatever the numbers are! P  P unity

A(dBm)

1 Watt

dBm = dBW + 30



10 log10 

P 

1 milliWatt

The mystic of decibels

Arithmetic operations 3

•



2=

6



 5 dB + 3 dB = 8 dB

8

÷

 9 dB -

4=

Decibel operations dB + dB

 dB

dB - dB

 dB

Multiplying numbers means adding the numbers in decibels

2

  6 dB = 3 dB

Dividing numbers means subtracting the numbers in decibels

The mystic of decibels

Power absolute linear scale 40 mW    B    d    3

20 mW

Power absolute logarithmic scale 16 dBm    B    d    3

13 dBm

Decibel operations 13 dBm + 3 dB = 16 dBm

 dBm + dB  dBm

16 dBm - 3 dB = 13 dBm

 dBm - dB

16 dBm - 13 dBm = 3 dB

 dBm - dBm  dB

13 dBm + 16 dBm = 29 dBm

794 mW

1 mW

 dBm

 dBm + dBm

Undefined!

0 dBm 20 mW + 40 mW = 60 mW

18 dBm

Struggling against decibels

Power - absolute logarithmic scale

+ - 74 dBm - 86 dBm  -(74 dBm + 86 dBm ) - 70 dBm Linear scale

- 74 dBm 10-74/10 0.000000039 mW

Undefined!

+ 10-86/10 0.0000000025 mW

- 80 dBm

0.0000000415 mW - 86 dBm - 90 dBm

-

Logarithm scale

10 • log (0.0000000415) = -73.8 dBm