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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 <= 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


Version 1 (current) modified Tue, 03 Jul 2007 23:12:23 +1000
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