Building The Net

Every time I have to figure out ERP or dB gain I always have to search the Internet to find the formulas. Well, I figured I could just look them up here if I posted them, so here they are!

Calculate dB gain based on actual output change. This is good for working out how much gain and amplifier gives you:

10 X log(power/refpower) = dBm Gain / loss

Example using 65 Watt output from radio into an amp and seeing that the output power is 500 Watts.

10 X log(500/65) = 8.86 dBm gain

Calculate dBm from output power:

10 X log(1000 X output watts) = Total DB Output

Example using a 100 Watt output.

10 X log(1000 X 100) = 50 dBm Output

Calculate output power from dBm

10^(dBm/ 10) / 1000

Calculate ERP based on radio output and Antenna gain:

Radio Power * 10^(dBm gain/10) = ERP

Example using 100 Watts radio output and a dB gain of 9 dBm from the antenna system:

100 * 10^(9/10) = 794 Watts

Calculate percentage of gain or loss based on dB

1 - (10^((-(dBm Loss/10)))) = Percentage of Loss

10^(dBm Gain/10) = Percentage of Gain

Example using a 3 dBm loss and gain:

Loss:
1 - (10^((-(3/10)))) = 50%

Gain:
10^(3/10) = 200%

Calculate SWR Power Loss Percentage:
(SWR -1 )² / (SWR + 1)² = Percentage of Loss

Power and Attenuation Calculations:
(all voltages are RMS)

Drop in dBm = 20 x log(R1 / R2)
Example: 50dBm = 20 x log(8000 / 25)

R1 = 10^(dBm / 20) x R2
V = √(Watts x 50Ω)
Watts = V² / 50Ω
Watts Required = V² / R1

Bulletin 65 Formulas:

Power Density:
S = PG / 4πR²
Where:
S = power density as mW/cm2
P = power at input of antenna
G = power gain of antenna in the direction of interest
R = distance to the center of the radiation of antenna

Max Power for Distance:
Max Power Density X (4π X (Distance²) = Max Power

Minimum Distance:
Square Of((Power / Max PD) / (4π))

Adding for Reflection:
ERP X (1.6)²

There are the two I use all the time. These two also serve as a really good platform for all sorts of calculations. One note, if you are looking for Voltage Gain, change the base 10 to base 20.

— Stu