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PowerAndGainToDecibels
- Power and Power Gain to dBm and dB Conversion Chart.
- EIRP calculation
- Wireless Calculators
- Calculating Decibels
- 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 LossOR
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
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
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?).
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
Enjoy!
Version 8 (current) modified Mon, 26 Jul 2021 12:49:29 +0000 by Fendy
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