home 
wiki
wiki
Spelling: WirelessMathematics
INTERESTING MATHEMATICS
DECIBELS (DBM) AND MILLI-WATTS (MW) RELATIONSHIP:
dBm = 10 log (mW)
TYPICAL LOSS PER CONNECTOR AT 2.4GHZ:
0.25 - 0.5 dBm
ANTENNA GAIN:
Gain(dBi) = 10 log (n * ( (4*PI)/lambda^2 ) * A)
Where, A = Area of antenna
n = ?
APPROXIMATE ANTENNA GAIN (YAGI AND OMNI ANTENNAS):
Gain(dBi) = 10 log (#elements)
WAVE LENGTH:
lambda(mm) = 300 / freq(Ghz)
(eg for 2.4Ghz, lambda = 123mm)
WAVE LENGTH (IN COAX):
lambda(mm) = 300 / velocity(%) / freq(Ghz)
(eg LMR400 has velocity factor of 0.85, lambda = 123 * 0.85 =
104.5mm)
Note: For brass tubing (4/16") use a velocity factor of 0.95
PATH LOSS, ATTENUATION DUE TO AIR (SIGNAL LOSS IN AIR):
Loss (dB) = 10 log ( ( (4*PI*d) / lambda ) ^ 2 )
Where, d = distance (in meters)
lambda = wave length (in meters)
or for 2.4Ghz use
Loss (dB) = 40 + 20 log (d)
Note: Fade margin, usually an additional loss of 10dB is added to
take into account things like frensal zones, multipath and other real
world stuff
EIRP (EFFECTIVE ISOTROPIC RADIATED POWER) CALCULATING:
(Transmitter Gain:)
EIRP(dB) = Card Output(dBm) + Antenna Gain(dBi)
- Cable Loss(dBm) - Connector Losses(dBm)
Note: EIRP for 2.4 to 2.462Ghz ISM band must be 84)
OVER-THE-AIR DATA RATE:
RF Data Rate = (Dpl + Dao + Dro) * (1 + rt) / time
Where, Dpl = payload data in bits
Dao = application overhead in bits/payload transmission
Dro = radio data overhead in bits
rt = retry percentage
RECEIVE SENSITIVITY (JUST READ DATA SHEET):
Rx Sensitivity = Thermal Noise Floor + System Noise + 10 log
(SymbolRate) + SNR
-------------------------
See also: PowerAndGainToDecibels [1]
Links:
------
[1] http://melbournewireless.org.au/?PowerAndGainToDecibels
[EditText] [Spelling] [Current] [Raw] [Code] [Diff] [Subscribe] [VersionHistory] [Revert] [Delete] [RecentChanges]