Diff: WirelessMathematics

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+!! 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 <= 4W 

+ 

+'''Receiver Gain:''' 

+ Gr = Antenna Gain(dBi) - Connector Losses(dBm) - Cable Loss(dBm) 

+ 

+'''Link Budget:''' 

+ Link Budget = Path Loss + Rx Sensitivity + Gt + Gr 

+ Adjusted Link Budget = Link Budget - 10dB (ie fade margin) 

+ Note: Use -ve of Rx Sensitivity (ie value is positive, --84 => 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