## Formulas for Calculating DB Gain and Loss.

Monday, 23. March 2020

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