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PowerAndGainToDecibels


Power and Power Gain to dBm and dB Conversion Chart.

GainGain(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
10
1.261
1.582
23
2.54
3.35
46
57
89
1010
2013
4016
5017
10020
100030
1000040


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

External linkUltramesh 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 External linkl-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?). External linkwomen 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


Enjoy! :-)


Version 8 (current) modified Thu, 24 Feb 2011 09:20:37 +1100 by Fendy
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