In GSM power level measurements are specified in dBm. In order to understand power measurements it is important to fully understand how the decibel works.
The Bel is not really a measure of power; it is a measure of change from one value to another. It is based on a logarithmic base-10 scale. Here is the formula:
Where P1 is the original value and P2 is the new changed value.
Let's look at an example. Our original value is 10 and our changed value is 20.
So a change from a value of 10 to a value of 20 is equal to 0.3 Bels.
The logarithm can be calculated using any scientific calculator or the calculator provided on any Windows system:
Let's look at another one. Lets say we start with a value of 20 and move to 40.
You will notice that in both of these examples the result is the same, 0.3 Bels. Remember that bels are a unit of change. Every time you double a value there is a change of 0.3 bels.
For most purposes, the Bel is too large of a unit since in most cases it will result in a number below 1.To create a more manageable number we use the decibel (abbreviated dB) which is 1/10 of a bel. For every Bel there are 10 decibels, so:
Decibel = Bel * 10
So is the examples above, a change from 10 to 20 would be 3 dB. Again, a change from 20 to 40 is 3dB.
Let's look at two more examples:
As we can, whenever a value is multiplied by ten we get a change of 10 decibels.
This brings rise to a general rule about calculating decibels; the rule of tens and threes.
- Any time a value is doubled this results in a change of 3dB
- Any time a value is multiplied by ten it is a change of 10dB
- When a value is reduced by half it is a change of -3dB
- When a value is reduced by 1/10 it is a -10dB change.
Since a change of 3dB or 10dB could have any value for the original value, it doesn't do us much good to cite a change in dB unless we know the starting value. For this reason we must standardize the starting value within the industry so that we all know what value we are using as a reference. In radio communications the dBm is used. The m represents milliwatts (1/1000 of a watt.) This tells us that any value given in dB is in relation to a starting value of 1 milliwatt (mW).
Let's look at an example. What is 100 mW equal to in dBm? We know that our standardized reference point (P1) is 1 mW. So the formula will be:
We see that 100mW is equal to 20dBm.
If a power level is below 1 milliwatt then the resulting dBm will be a negative number. For example, how many dBm is 1 microwatt (1 millionth of a watt)
So, whenever we see a positive dBm we know that the power in watts is above 1 mW and if we have a negative dBm we know that the power in watts is below 1dBm.
Now that we know how to convert a power in watts to dBm; we can look at the operation in reverse. What if we are given a value in dBm and we want to translate that to milliwatts? Here is the process:
1. Convert decibels back to bels. (divide by 10)
2. Raise 10 to this power.
3. Multiply it by the reference value (1 milliwatt).
4. The result is the value in milliwatts.
Here is what the formula looks like:
Since our reference value will never change and is equal to 1 (mW) then we don't need to have it in the formula. We can simplify the formula:
Let's look at a few examples:
1. How many milliwatts is a value of 50 dB?
We see that 50 dBm is equal to 100000 mW (which is equal to 100 Watts).
2. How many milliwatts is a value of -60 dBm?
We see that -60 dBm is equal to .000001 mW.
If you don't have a calculator handy you can always use the rule of tens and threes to estimate the value in dBm.
We know that 0 dBm is equal to 1 milliwatt.
Increasing from 0 dBm to 10 dBm is a ten-fold increase to 10 milliwatts.
Increasing from 0 dBm to 3 dBm is doubling power to 2 milliwatts.
Increasing from 0 dBm to 20 dBm is a ten-fold increase twice - from 1 mW to 10 mW and then to 100 mW.
Increasing from 0 dBm to 6 dBm is doubling the power twice - from 1 mW to 2 mW and then to 4 mW.
Example:
How many watts is 26 dbM?
from 0 dBm to 10 dBm - ten times the power - 1 mW to 10 mW
from 10 dBm to 20dBm - ten times the power - 10 mW to 100 mW
from 20 dBm to 23 dBm - twice the power - 100 mW to 200 mW
from 23 dBm to 26 dBm - twice the power - 200 mW to 400 mW
26 dBm is approximately 400 mW.
The same rule can be used to calculate negative dBm values.
-10 dBm divides the power by 10
-3 dBm divides the power in half.
Example:
How many watts is -26 dbM?
from 0 dBm to -10 dBm - 1/10 the power- 1 mW to .1 mW
from -10 dBm to -20dBm - ten times the power - .1 mW to .001 mW (or 10 microwatts)
from -20 dBm to -23 dBm - twice the power - 10 microwatts to 5 microwatts
from -23 dBm to -26 dBm - twice the power - 5 microwatts to 2.5 microwatts
-26 dBm is approximately 2.5 microwatts.