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# How to Read dB and dBm and to Convert Back and Forth !

Date:2019/10/8 17:26:53 Hits:

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

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.

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

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

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