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* Power and Power Gain to dBm and dB Conversion Chart. [1]
* EIRP calculation
* Wireless Calculators [2]
* Calculating Decibels
* Variations on the dB [3]
* Example 1: [4]
* Example 2: [5]
* Interesting Mathematics [6]
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 [7] = 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 [8].
WIRELESS CALCULATORS
Ultramesh Wireless Networking [9]: 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 l-arginine [10]. 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?). women clothing
[11] 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 [12]
-------------------------
Enjoy!
Links:
------
[1]
http://melbournewireless.org.au/#power_and_power_gain_to_dbm_and_db_conversion_chart_
[2] http://melbournewireless.org.au/#wireless_calculators
[3] http://melbournewireless.org.au/#variations_on_the_db
[4] http://melbournewireless.org.au/#example_1_
[5] http://melbournewireless.org.au/#example_2_
[6] http://melbournewireless.org.au/#interesting_mathematics
[7] http://melbournewireless.org.au/?EIRP
[8] http://melbournewireless.org.au/?EIRP
[9] http://www.ultramesh.com/calcs.html
[10] http://www.shoppharmacycounter.com/c-402-l-arginine.aspx
[11] http://www.u-clothing.com/c-2-women.aspx
[12] http://melbournewireless.org.au/?WirelessMathematics
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