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Technical Information - Helpful calculations for VHF/UHF systems

# 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)

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.

½l = 150/ Mc.                                                                  ½l = 492/ FMc.

¼l = 75/ Mc.                                                                     ¼l = 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.

½l = 143/ Mc.                                                                       ½l = 468/ FMc.

¼l = 71/ Mc.                                                                           ¼l = 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

½l = (150/ FMc.) x VF                                                         ½l = (492/ FMc.) x VF

¼l = (75/ FMc. ) x VF                                             ¼l = (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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