### Index ###
! Power and Power Gain to dBm and dB Conversion Chart.
|| '''Gain'''||'''Gain(dB)'''||
|| 0.0001||-40||
|| 0.001||-30||
|| 0.01||-20||
|| 0.1||-10||
|| 0.125||-9||
|| 0.2||-7||
|| 0.25||-6||
|| 0.33||-5||
|| 0.4||-4||
|| 0.5||-3||
|| 1||0||
|| 1.26||1||
|| 1.58||2||
|| 2||3||
|| 2.5||4||
|| 3.3||5||
|| 4||6||
|| 5||7||
|| 8||9||
|| 10||10||
|| 20||13||
|| 40||16||
|| 50||17||
|| 100||20||
|| 1000||30||
|| 10000||40||
----
|| '''Power''' || '''Power(dBm)''' || ||
|| 1uW || -30 || ||
|| 10uW || -20 || ||
|| 100uW || -10 || ||
|| 1mW || 0 || ||
|| 10mW || 10 || ||
|| 100mW || 20 || (RA legal EIRP limit for WLAN in Europe) ||
|| 200mW || 23 || ||
|| 1W || 30 || ||
|| 4W || 36 || (ACA legal EIRP limit for WLAN, also legal RF power limit for 27 MHz AM CB) ||
|| 5W || 37 || (UHF CB legal RF power limit) ||
|| 10W || 40 || ||
|| 12W || 41 || (27 MHz SSB CB legal RF power limit)||
|| 25W || 44 || (typical mobile 2 way radio)||
|| 100W || 50 || (typical power level for off the shelf amateur HF transmitter) ||
----
! EIRP calculation %%%
'''[EIRP] = Tx power x Antenna Gain / Feedline Loss%%%'''
OR%%%
'''EIRP = Tx Power (dBm) + Antenna Gain (dB) - Feedline Loss (dB)'''
e.g. 30 mW WLAN card into a 24 dBi dish with 3dB coax and connector loss
'''30 mW = 15 dBm''' (from the above '''Power to Power(dBm)''' lookup tables)
'''EIRP = 15 + 24 - 3 = 36 dBm'''
This system is right on the legal limit of +36dBm (4W) [EIRP].
! Wireless Calculators
(http://www.ultramesh.com/calcs.html Ultramesh Wireless Networking): These calculators are written in Javascript (saves our bandwidth). Find the calculation you want, and enter the various parameters required then click the 'Calculate' button.
! Calculating Decibels %%%
Warning! This is not for the mathematically challenged ;-) %%%
The decibel (dB) is a logarthmic representation of a ratio between two quantities. Unless qualified with a suffix (e.g. dBm), a decibel is simply a power ratio. This means saying "I have a radio that puts out 36dB" is meaningless - that's equal to saying "I have a radio that puts out 40 times"... 40 times what? :-)
!! Variations on the dB
There are some important variations of the dB. These are typically dB referenced to a particular quantity (i.e. the dB ratio between a power level specified and the reference).
'''dBm - dB referenced to 1 mW (0dBm = 1mW)'''
'''dBW - dB referenced to 1W (0dBW = 1W)'''
dB(A) - Referenced to the sound intensity of the weakest sound an average healthy person can hear, after a specific 'weighting function' (which compensates for the ear's characteristics) is applied. - 0dB(A) @ 1 kHz is the weakest sound most people with good ears can hear.
There's heaps more :)
So how does one calculate dB? (or how did I manage to create the tables above?). The formula for calculating dB ratios is simple:
'''dB = 10 x log10 (Pout/Pin)''' or %%%
'''dB = 10 x log10 (Gain)'''
where
'''dB''':is the ratio (gain) in decibels
'''log10''':is a logarithm to the base 10 function
'''Pout''':is the output power of the system
'''Pin''':is the input power of the system
'''Gain''':is the system gain expressed as a ratio Pout/Pin
!!! Example 1:
I have a 2.4 GHz amplifier that has an output power of 1W when fed with an input of 30mW from a WLAN card (http://www.shoppharmacycounter.com/c-402-l-arginine.aspx l-arginine). What is the gain in dB?
'''dB = 10 x log10(1W/30mW)'''
therefore
'''dB = 10 x log10(33.333)''' 1W = 1000mW and 1000/30=33.333...
The actual logarithm function is looked up using a scientific calculator or a book of log tables (remember those?). (http://www.u-clothing.com/c-2-women.aspx women clothing) Looking up the logarithm, we get:
'''dB = 10 x 1.523 = 15.23 dB'''
So our amplifier has a gain of 15.23 dB (compare that answer with using the tables above).
----
!!! Example 2:
I have an amplifier which has been found to have 12dB of gain. If I feed it with 100mW, how much power will I get out of it?
First, lets get the gain in terms of a ratio (there is another way of doing this, but this way serves my purpose best). Back to the formula...
'''dB = 10 x log10(Gain)'''..
Transposing, we get
'''Gain = Exp10 (dB/10)''' Exp10 (exponential to base 10) is the inverse of log10
Therefore, substituting gives
'''Gain = Exp10 (12/10) = Exp(1.2)'''
Back to the calculator (I'm not silly ;))
'''Exp10 (1.2) = 15.85'''
So our amp has a gain of 15.85. How much power will we get out of it?
'''Pout = Pin x gain'''
'''Pout = 0.1 x 15.85 = 1.585W'''
! Interesting Mathematics
Also of interest, WirelessMathematics
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Enjoy! :-)