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Technical Information - Helpful calculations for VHF/UHF systems
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Free Space Loss


FSL = 36.6 + 20Log10(FMc.) + 20Lopg10(Dmi)


Where FSL = Free Space Loss in dB

Mc. = Frequency in Mc.

                         Dmi = Distance in miles


Plane Earth Loss


PEL = 10Log10[3.45 x 10-15((Rh x Th)/d2)2]


Where PEL = Plane Earth Loss in dB

            P1 = Transmitted Power in Watts

             P2 = Received Power in Watts

             d = Distance between sites in miles

Rh = Height of receive antenna above ground (ft)

Th = Height of transmit antenna above ground (ft)

Shadow Loss


SL = 10Log10FMc. + 20Log10Dmi 10Log10Hft 55.8


Where Mc. = Frequency in Mc.

              Hft = Main obstacle height in feet

             Dmi = Shortest distance from obstacle to transmitter or receiver in miles

Radio Line-of-Site for VHF/UHF


Radio Line-of-Site = SQRT(2H1H2) x 1.15


Where SQRT = Square Root

H1 = Height of antenna at site 1 in feet

                        H2 = Height of antenna at site 2 in feet

 Effective Radiated Power (ERP)


ERP = GainsdB + LossesdB


Where GainsdB = all system gains in dB (i.e., Tx Power & Antenna Gain)

             LossdB = all system losses in dB (i.e., Line Loss, Jumper Cables,Protective Devices, & Lightning Arrestor)

To convert Tx Power to dBm, dBm = 10Log10(P1/P2)

Where dBm = Power in dB reference to 1 milliwatt (mw)

              P1 = Transmit power in Watts

              P2 = .001 (1 mw)


To convert dBm to Watts, Watts = 10((dBm-30)/10)


Where Watts = ERP in Watts

            dBm = ERP in dBm

Wavelength in Free Space


Meters                                                              Feet

lm = 300/Mc.                                                    lft = 984/FMc.


Where lm = Wavelength in meters                        Where lft = Wavelength in feet

       Mc. = Frequency in Mc.                                     FMc. = Frequency in Mc.


          l = 150/ Mc.                                                                  l = 492/ FMc.

          l = 75/ Mc.                                                                     l = 246/ FMc.

 Wavelength in Wire (Where Velocity Factor of wire = 95%)

Meters                                                                 Feet
lm = 285/Mc.                                                     lft = 936/FMc.


Where lm = Wavelength in meters                          Where lft = Wavelength in feet

        Mc. = Frequency in Mc.                                Mc. = Frequency in Mc.

l = 143/ Mc.                                                                       l = 468/ FMc.

l = 71/ Mc.                                                                           l = 234/ FMc.

 
 Wavelength in Transmission Line

Meters                                                                 Feet

lm = (300/FMc.) x VF                                            lft = (984/FMc.) x VF

Where lm = Wavelength in meters                          Wherelft = Wavelength in feet

       FMc. = Frequency in Mc.                                       FMc. = Frequency in Mc.

          VF = Velocity Factor                                              VF = Velocity Factor

l = (150/ FMc.) x VF                                                         l = (492/ FMc.) x VF

l = (75/ FMc. ) x VF                                             l = (246/ FMc.) x VF

VSWR Calculations

RL = -20Log10(|G|)

Where RL = Return Loss in dB

         |G| = Reflection Coefficient



|G| = [ (VSWR-1) / (VSWR+1) ] x 100

         Where |G| = Reflection Coefficient

               VSWR = Voltage Standing Wave Ratio


VSWR = (1+|G|)/(1+|G|)

          Where VSWR = Voltage Standing Wave Ratio

                         |G| = Reflection Coefficient


VSWR = [SQRT(Fwd) + SQRT(Ref)]/ [SQRT(Fwd) - SQRT(Ref)]

           Where VSWR = Voltage Standing Wave Ratio

                         Fwd = Measured forward transmitter power

                          Ref = Measured reflected transmitter power

Calculating Received Signal in Free Space


Convert transmit power and receiver sensitivity into dBm; Then have all other units in dB.


Pr = Pt Lw1 Lf1 + Ga1 + Lfs + Ga2 Lw2 Lf2

Where: Pr = Received power level in dBm

            Pt = Transmit power level in dBm

          Lw1 = Transmit site transmission line loss in dB

          Lw2 = Receive site transmission line loss in dB

           Lf1 = Transmit site filter/miscellaneous losses in dB

           Lf2 = Receive site filter/miscellaneous losses in dB

           Lfs = Free Space Path Loss in dB

          Ga1 = Transmit antenna gain in dBd

          Ga2 = Receive antenna gain in dBd

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