Antenna Experts - Antenna Formulae

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Antenna Formulae

Wavelength and Frequency
λ = v / f	Where λ = Wavelength in feet v = Velocity of propagation in feet per second f = Frequency in Hz
f = 1 / T	Where f = Frequency in Hz T = Time of one wave period (cycle) in second

Path Loss and Vertical Dipole Isolation
Path Loss (dB) = 10log (λ/4πr)² Isolation (dB) = 28 + 40log (h/λ)	Where λ = Wavelength in metres r = Distance between transmitting and receiving antennas in metres h = Vertical antenna separation

VSWR, Reflection Coefficient (ρ) and Return Loss
VSWR = (1 + ρ)/(1 - ρ)	ρ = (VSWR - 1)/(VSWR + 1)
Return Loss (dB) = -20logρ

Power Received by an Antenna
P = P_tG_tG_rλ² / 16π²d²	Where P = Power received in Watts P_t = Power transmitted in Watts G_t = Gain ratio of transmitting antenna relative to an isotropic radiator G_r = Gain ratio of receiving antenna relative to an isotropic radiator λ = Wavelength in metres d = Distance between transmitting and receiving antennas in metres

Effective Radiated Power
ERP = G x P	Where G = Gain of transmitting antenna relative to an isotropic radiator P = Input Power in Watts

VSWR Vs Return Loss and Effect of VSWR on Transmitted Power
VSWR	Return Loss (dB)	Transmitted Power (%)
1.0	∞	100
1.1	26.4	99.8
1.2	20.8	99.2
1.3	17.7	98.3
1.5	14.0	96.0
2.0	9.50	88.9
3.0	6.00	75.0


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