* [#power_and_power_gain_to_dbm_and_db_conversion_chart_ Power and Power Gain to dBm and dB Conversion Chart.]

* [#eirp_calculation____ EIRP calculation %%%]

* [#wireless_calculators Wireless Calculators]

* [#calculating_decibels____ Calculating Decibels %%%]

** [#variations_on_the_db Variations on the dB]

*** [#example_1_ Example 1:]

*** [#example_2_ Example 2:]

* [#interesting_mathematics Interesting Mathematics]



! 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 {/regexpicons/emoticons/emoticon-face3.png ;)} %%%





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? {/regexpicons/emoticons/emoticon-face7.png :-)}



!! 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 {/regexpicons/emoticons/emoticon-face1.png :)}



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 {/regexpicons/emoticons/emoticon-face3.png ;)})



'''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



----

Enjoy! {/regexpicons/emoticons/emoticon-face7.png :-)}