## Friday, 4 January 2013

### What's All This dBm Stuff Anyhow ? - With suitable homage to Bob Pease :-)

dBm is a logarithmic measurement of power that is used in telecommunications as a more convenient form of power measurement than the linear Watt (W) that most people are familiar with.

dB is a measurement value that represents the ratio of two powers :
dBm is the power ratio in decibels (dB) between the measured power and the reference power of one milliwatt (mW).

In a telecoms systems the transmit power is driving the channel impedence, which in audio telephony is typically 600 ohm, while in wireless applications 50 ohms is the most common.
Note that while dB is a relative measurement between the two powers (e.g. input and output), dBm is absolute because it is measured relative (if that makes sense) to a fixed reference power of 1 mW.

Being a logarithmic scale, dBm is really handy for calculating powers through a network so for example in audio telephony, a -13 dBm Tx power would be seen as -55 dBm at the receiver if the channel attenuation were 42 dB.

The following table shows some typical dBm / mW values used in mobile comms.

dBm mW
36 4000 (i.e. 4W) Typical macrocell basestation Tx power
30 1000
26 400 Typical mobile phone or indoor office basestation Tx power
20 100
16 40 Typical residential small basestation Tx power
10 10
6 4
3 2
1 1
-3 0.5
-10 0.1 Typical maximum received signal power
-60 10^-6 Typical minimum receive power to be able to detect a signal (in mobile comms, without a front end AGC)

The key things to learn from the table are the following :
The absolute power doubles for a 3 dB increase and halves for a 3 dB drop.
The absolute power is multiplied by 10 for a 10 dB increase. So a 20 dB increase is equivalent to absolute power being multiplied by 100.
Given that Power = (V^2 / R) then the voltage increases by sqrt(2) for a 3 dB increase. Hence a 6 dB increase is required in order for the voltage (or current for which power = I^2.R) to double.

If you would like to read more on the subject Rohde And Schwartz have written a very good applications note called dB or not dB? Everything you ever wanted to know about decibels but were afraid to ask.

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Numerix-DSP Libraries : http://www.numerix-dsp.com/eval/