Handy Formulas

Robert Stedman
2 June 1995

Antennas and Electromagnetic Fields:

P = E^2/(120*pi) = E^2/377 = field power density in watts/meter^2
where E = rms electric field strength in volts/meter
P = Pt*Gt/(4*pi*R^2)
where Pt = transmitter power output in Watts
and Gt = transmitter antenna gain (over isotropic)
and R = distance from the transmitter antenna in meters
W = P*A = available power from a receiving antenna in Watts
where P = field power density in watts/meter^2
and A = effective area of receiving antenna in meter^2
A = [lambda]^2*Gr/(4*pi) = effective area of the receiving antenna in meter^2
where Gr = gain of the receiving antenna (over isotropic) (Gr = 1.64 for a half-wave dipole)

Free Space Path Loss:

L(dB) = 36.6 + 20*log(f(MHz) + 20*log(d(miles))

Gain of a Half-Wave Dipole:

G(dBi) = 10*log(Gr) = 10*log(1.64) = 2.15 dB

Voltage and Power Received by a Half-Wave Dipole:

V(microV) = E(microV/m)*39.46666/f(MHz)
assuming receiver input impedance is 50 Ohms resistive
W(dBm) = -90 + 10*log[V^2(microV)/50}
assuming receiver input impedance is 50 Ohms resistive

Parabolic Dish Antenna Gain:

G(dBi) = 20*log(f(MHz)) + 20*log(D(feet)) - 52.6
for 54% illumnination