Simply type in the antenna gain in dBi, and total feeder loss in dB, the calculator does the rest. You can use zero, positive or negative numbers and up to 2 decimal places. It’s free to use but you do so entirely at your own risk and the author accepts no responsibility for the results.

Select ERP required
Enter antenna gain in dBi (from your EMF Assessment)
Enter feeder loss in -dB (from your EMF Assessment)
Antenna system gain referenced to a dipole
Gain linear ratio
Maximum transmitter power (PEP)
RMS voltage in 50 Ohms matched (1:1 SWR)
Peak voltage in 50 Ohms matched
Required attenuation for a 5W PEP transmitter

The voltages are provided for those who may wish to measure them at the transmitter end of the feeder, but note they are theoretical, and do not take account of losses in connectors etc. They also assume a 50 Ohm system, for example a dummy load.

The attenuation value is theoretical and assumes a constant 50 Ohm system, with a 5W PEP transmitter. It is not provided for 25W ERP.

The maths

The calculation steps are:

  1. Net system gain in dBd, Nsg = antenna gain in dBi – 2.15 – feeder losses in dB.
  2. Divide result by 10 to get Bels, B = Nsg/10
  3. Linear gain multiplier M by using antilog of B, M = 10 (B)
  4. Maximum transmitter power, Tm = ERP/M
  5. RMS voltage in 50 Ohms, Vrms = √(Tm/50)
  6. Peak voltage, Vpk = Vrms x √(2) or Vpk = Vrms x 1.414
  7. Required attenuation for a 5W PEP transmitter, dBatten = 10 x log10(Tm/5)

Calculation notes:

  • ERP is calculated from the net gain of antenna and feeder in dBd so we change dBi to dBd by subtracting 2.15 then obtain net system gain (Nsg) in dBd by subtraction of feeder and other losses
  • To find the maximum transmitter power we need Nsg expressed as a linear not logarithmic value. Convert Nsg to a linear gain multiplier (M) by finding the antilog of the Nsg dBd value:
    • For a pure logarithmic value this is normally 10 raised to the power of the dB value, but in this case the standard formula for finding a dB power ratio includes a multiplier of 10 (eg see equation 6) to convert from Bels to deciBels, or dB, so to reverse it the linear gain formula becomes 10 to the power of system net gain divided by 10
    • This is confirmed by the detailed explanation of dB given at Wikipedia (under Examples) ignoring their term x 1 as it makes no arithmetic difference
  • Maximum transmitter power (Tp) is then given by dividing the required ERP by the calculated linear multiplier M
    • For a Tp of less than 1W PEP the result is given in milliwatts
  • RMS voltage (Vrms), Peak voltage (Vpk), and the required dB attenuation (dBatten) are given by standard equations
  • All results are rounded

Use with WSPR and a 5W PEP transmitter

WSPR is a beacon mode under the 2024 licence so if necessary the simplest way to reduce power for WSPR usage is to vary the audio drive, as the system is based on upper sideband, a form of amplitude modulation.  The attenuation number can be added on top of any drive reduction already in use to avoid over driving the transmitter. Note it is a theoretical approximate value, because soundcards are not calibrated, so to keep within your licence terms you may consider it prudent to increase it. 

Why build this calculator?

My home antenna system has some gain on various bands, and I also like to experiment with WSPR with experimental antennas of varying gain.

With a minimum 5W PEP output from my main transceiver my ERP could easily be more than the permitted 5W so I built a simple spreadsheet to calculate the maximum transmitter power for 5W ERP with a given set of antenna gain and feeder loss.

I expect others are in a similar position so I decided to write my calculator into Javascript for everyone to use, and also as a learning project for myself. I added an option for 25W ERP for Full licensees.

The Javascript is licensed for use elsewhere if wished under a Creative Commons CC-BY-SA licence v4.0

As a learning resource for both HTML and Javascript my thanks are due to MDN Web Docs and their contributors at https://developer.mozilla.org/en-US/

I hope you find it useful!