Radio Frequency (RF) & Wireless Design

A deci (1/10) of a Bel is a dB,

but the equation for dB = 10 * Log (Po/Pi)

where Po is power out and Pi is power in.

Since the Log (base 10) math function is to extract the exponent,

a decibel uses the Log math function to find the exponent and that is what is called out.

e.g.  10 dB = 10^1 = 10x power gain       whereas 30 dB = 10^3 = 1,000x power gain

from there, you just multiple by 10 and so for

10 dB = 10x power gain

20 dB = 100x power gain

30 dB = 1,000x power gain

40 dB = 10,000x power gain

below 10 dB these are the power gains

0 dB = 1.000x power gain = 1.0x

1 dB = 1.259x power gain = ~ 1.3x

2 dB = 1.585x power gain = ~ 1.6x

3 dB = 1.995x power gain = ~ 2.0x

4 dB = 2.512x power gain = ~ 2.5x

5 dB = 3.162x power gain = ~ 3.2x

6 dB = 3.901x power gain = ~ 4.0x

7 dB = 5.012x power gain = ~ 5.0x

8 dB = 6.310x power gain = ~ 6.3x

9 dB = 7.943x power gain = ~ 8.0x

(the ones in bold are the ones you need to remember)

Since all decibels ADD but the power is MULTIPLIED you only need to know the factor of one to get the others.

And since 3 is a factor of 6 and 9 you only need to know 3.

Notice that 6dB and 9dB are multiples of 3dB so you only need to remember that 3dB is 2x and

therefore :

6dB = 3dB + 3dB = 2 * 2 = 4x power 

and

9dB = 3dB + 3db + 3dB = 2 * 2 * 2 = 8x power

Notice that 4dB and 8dB are multiples of 2dB so you only need to remember that 2dB is 1.6x and

therefore :

4dB = 2dB + 2dB = 1.6 * 1.6 = ~2.5x power 

and

8dB = 2dB + 2db + 2dB = 1.6 * 1.6 * 1.6 = ~4.0x power

Even 10dB = 5dB + 5dB = 3.2 * 3.2 = 10x power ; so in essence 5dB is really the square root of 10.

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milliWatts are used many times for Power and the dB term is expressed as milli-deciBels or dBm

10 milliWatts = 10 dBm

10 dBm = 10x power gain (in milliWatts)

20 dBm = 100x power gain(in milliWatts)

30 dBm = 1,000x power gain(in milliWatts)

40 dBm = 10,000x power gain(in milliWatts)

However 1,000 mW = 1 Watt

so 30 dBm = 0 dB

and 0 dB is 1x power

since milli means 1/1,000

and 1,000 is 10^3

where 10^3 is the ratio of the power (Po/Pi)

so 0 dBm = 10 * Log (Po/Pi)

10 * 3 = 30x power

the other expressions are the same but expressed in milliWatts not Watts :

0 dBm = 1.000x power gain = 1.0x

1 dBm = 1.259x power gain = ~ 1.3x

2 dBm = 1.585x power gain = ~ 1.6x

3 dBm = 1.995x power gain = ~ 2.0x

4 dBm = 2.512x power gain = ~ 2.5x

5 dBm = 3.162x power gain = ~ 3.2x

6 dBm = 3.901x power gain = ~ 4.0x

7 dBm = 5.012x power gain = ~ 5.0x

8 dBm = 6.310x power gain = ~ 6.3x

9 dBm = 7.943x power gain = ~ 8.0x

(the ones in bold are the ones you need to remember)

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To convert milliWatts to Watts just subtract 30 (since 30 dBm = 1,000 mW = 1W)

55dBm = 25 dB

35 dBm = 5 dB

25 dBm = -5dB

To convert Watts to milliWatts just add 30 (since 30 dBm = 1,000 mW = 1W)

35 dB = 65 dBm

15 dB = 45 dBm

3 dB = 33 dBm