FSL = 36.6 + 20Log_{10}(F_{Mc.}) + 20Lopg_{10}(D_{mi})

Where FSL = Free Space Loss in dB

Mc. = Frequency in Mc.

D_{mi} = Distance in miles

PEL = 10Log_{10}[3.45 x 10^{-15}((R_{h} x T_{h})/d^{2})^{2}]

Where PEL = Plane Earth Loss in dB

P_{1} = Transmitted Power in Watts

P_{2} = Received Power in Watts

d = Distance between sites in miles

R_{h} = Height of receive antenna above ground (ft)

T_{h} = Height of transmit antenna above ground (ft)

SL = 10Log10F_{Mc.} + 20Log10D_{mi} – 10Log10H_{ft} – 55.8

Where Mc. = Frequency in Mc.

H_{ft} = Main obstacle height in feet

D_{mi} = Shortest distance
from obstacle to transmitter or receiver in miles

Radio Line-of-Site = SQRT(2H_{1}H_{2}) x 1.15

Where SQRT = Square Root

H_{1} = Height of antenna at site 1 in
feet

H_{2} = Height of antenna at site 2 in feet

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 = 10Log_{10}(P_{1}/P_{2})

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

P_{1} = Transmit power in Watts

P_{2} = .001 (1 mw)

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

Where Watts = ERP in Watts

dBm = ERP in dBm

__Meters __
__Feet__

l_{m} = 300/Mc. l_{ft} = 984/F_{Mc.}

Where l_{m }= Wavelength in meters
Where l_{ft }= Wavelength in feet

Mc. = Frequency in Mc. F_{Mc.} =
Frequency in Mc.

½l = 150/ Mc._{ }½l =
492/ F_{Mc.}

¼l = 75/ Mc._{ }¼l =
246/ F_{Mc.}

__Meters__ __Feet__

l_{m} =
285/Mc. l_{ft} =
936/F_{Mc.}

Where l_{m }= Wavelength in meters
Where l_{ft }= Wavelength in feet

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

½l = 143/ Mc._{ }½l = 468/ F_{Mc.}

¼l = 71/ Mc._{ }¼l = 234/ F_{Mc.}

__Meters__ __Feet__

l_{m} =
(300/F_{Mc.}) x VF l_{ft} = (984/F_{Mc.}) x VF

Where l_{m }= Wavelength in meters Wherel_{ft }= Wavelength in feet

F_{Mc.} = Frequency in Mc. F_{Mc.} =
Frequency in Mc.

VF = Velocity Factor VF = Velocity Factor

½l = (150/ F_{Mc.}) x VF_{ }½l = (492/ F_{Mc.}) x VF

¼l = (75/ F_{Mc. }) x VF
¼l = (246/ F_{Mc.}) x VF

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.

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

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