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Technical Information
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Free Space Loss

 

FSL = 36.6 + 20Log10(FMHz) + 20Log10(Dmi)

 

          Where FSL = Free Space Loss in dB

FMHz = Frequency in MHz

                   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

    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 = 10Log10FMHz + 20Log10Dmi 10Log10Hft 55.8

 

         Where FMHz = Frequency in MHz

                   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(2H1 + 2H2) 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 = Transmit ERP in Watts

                    dBm = ERP in dBm

 

Wavelength in Free Space

 

Meters                                                         Feet

 

lm = 300/FMHz                                                         lft = 984/FMHz

 

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

        FMHz = Frequency in MHz                               FMHz = Frequency in MHz

 

l = 150/ FMHz                                                         l = 492/ FMHz

l = 75/ FMHz                                                l = 246/ FMHz

 

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

 

Meters                                                         Feet

 

lm = 285/FMHz                                               lft = 936/FMHz

 

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

       FMHz = Frequency in MHz                               FMHz = Frequency in MHz

 

l = 143/ FMHz                                                          l = 468/ FMHz

l = 71/ FMHz                                                l = 234/ FMHz

 

Wavelength in Transmission Line

 

Meters                                                         Feet

 

lm = (300/FMHz) x VF                                               lft = (984/FMHz) x VF

 

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

       FMHz = Frequency in MHz                               FMHz = Frequency in MHz

          VF = Velocity Factor                                       VF = Velocity Factor

 

l = (150/ FMHz) x VF                                                       l = (492/ FMHz) x VF

l = (75/ FMHz ) x VF                                             l = (246/ FMHz) 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

 

Below are some helpful formulas for radio path calculations:

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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