### 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 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.  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?).  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

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Enjoy! :-)