SOME TYPICAL RF FORMULAS

PROPAGATION

Free space propagation loss: FSPL (dB) = 32,4 + 20*log R(km) + 20*log f(MHz)

where:
R = distance in km
f = frequency in MHz
 
CONVERSIONS

Conversion from P(dBm) to P(W): P (W) = 10E((P(dBm) / 10) - 3)
Conversion from P(W) to P(dBm): P(dBm) = 10 * log (P(W) / 10E-3)
Conversion from P(dBm) to E(V) at 50 ohms: E(V) = 0.2236 * 10E(P(dBm)/20)


 

TRANSMISSION LINE FORMULAS

Phase constant: B = 6.28/LAMBDA
Input impedance of line length L: Zl = Zo * (Zb + jZo * tan(B * L))/ (Zo + jZb * tan(B * L))

where:
Zb = load impedance
Zo = characteristic impedance of line

Impedance of short circuited line length L: Zsc = jZo * tan(B * L)
Impedance of open circuited line length L: Zoc = -jZo * cotg(B * L)
Impedance of line an odd number of quarter wavelengths long: Z = (Zo * Zo) / Zb
Impedance of line an integral number of half wavelengths long: Z = Zb
Voltage Standing Wave Ratio: SWR = Zr / Zo or Zo / Zr; Zr = R (Imaginary part is 0)
Voltage Standing Wave Ratio: SWR = (1 + SQRT(Pref / Pfor))/(1 - SQRT(Pref / Pfor))

where:
Pfor = forward power
Pref = reflected power


Voltage Reflection Coefficient: /r/ = (SWR - 1)/(SWR + 1) = SQRT(Pref / Pfor)
Return Loss: RL (dB) = -20 * log(/r/