Technical Information

Free Space Loss

FSL = 36.6 + 20Log₁₀(F_MHz) + 20Log₁₀(D_mi)

Where FSL = Free Space Loss in dB

F_MHz = Frequency in MHz

D_mi = Distance in miles

Plane Earth Loss

PEL = 10Log₁₀[3.45 x 10^-15((R_h x T_h)/d²)²]

Where PEL = Plane Earth Loss in dB

d = Distance between sites in miles

R_h = Height of receive antenna above ground (ft)

T_h = Height of transmit antenna above ground (ft)

Shadow Loss

SL = 10Log₁₀F_MHz + 20Log₁₀D_mi – 10Log₁₀H_ft – 55.8

Where F_MHz = Frequency in MHz

H_ft = Main obstacle height in feet

D_mi = 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 = Gains_dB + Losses_dB

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

Loss_dB = 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

l_m = 300/F_MHz l_ft = 984/F_MHz

Where l_m= Wavelength in meters Where l_ft= Wavelength in feet

F_MHz = Frequency in MHz F_MHz = Frequency in MHz

½l = 150/ F_MHz½l = 492/ F_MHz

¼l = 75/ F_MHz ¼l = 246/ F_MHz

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

Meters Feet

l_m = 285/F_MHz l_ft = 936/F_MHz

Where l_m= Wavelength in meters Where l_ft= Wavelength in feet

F_MHz = Frequency in MHz F_MHz = Frequency in MHz

½l = 143/ F_MHz½l = 468/ F_MHz

¼l = 71/ F_MHz ¼l = 234/ F_MHz

Wavelength in Transmission Line

Meters Feet

l_m = (300/F_MHz) x VF l_ft = (984/F_MHz) x VF

Where l_m= Wavelength in meters Where l_ft= Wavelength in feet

F_MHz = Frequency in MHz F_MHz = Frequency in MHz

VF = Velocity Factor VF = Velocity Factor

½l = (150/ F_MHz) x VF½l = (492/ F_MHz) x VF

¼l = (75/ F_MHz) x VF ¼l = (246/ F_MHz) 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.

P_r = P_t – L_w1 – L_f1 + G_a1 – L_fs + G_a2 – L_w2 – L_f2

Where: P_r = Received power level in dBm

P_t = Transmit power level in dBm

L_w1 = Transmit site transmission line loss in dB

L_w2 = Receive site transmission line loss in dB

L_f1 = Transmit site filter/miscellaneous losses in dB

L_f2 = Receive site filter/miscellaneous losses in dB

L_fs = Free Space Path Loss in dB

G_a1 = Transmit antenna gain in dBd

G_a2 = Receive antenna gain in dBd

SAL Electronics LLC

Algonquin, IL 60102

Phone: (815) 669-6567