# Calculating receive wattage given transmit power, antennae dBi and path loss

I would like to understand how to calculate receive wattage given the following (excluding feeder loss and SWR):

Transmit 50 dBm (100W) => 24 dBi directional antenna => 30 dB path loss => 24 dBi directional antenna (receive) => wattage?

On the one hand: just add the numbers. 50 dBm + 24 dB - 30 dB + 24 dB = 68 dBm.

On the other hand: that's more power out than in! What that's telling you is that you will never have path loss as low as 30 dB and a pair of 24 dB gain antennas at the same time.

For instance, say we're working at a wavelength of 2 meters. The Friis formula tells us that the path loss will be $$20 \log \left( \frac{4\pi d}{2 m} \right)$$. Setting that equal to 30, we get $$d$$ = 5.03 meters. But a gain of 24 dB for a 2 meter wavelength requires a parabolic dish at least 10 meters in diameter, for which the far field begins (and the Friis equation is valid) only at a distance of at least 100 meters! No matter how you slice it, the laws of physics won't let you do that. So your example numbers don't represent a physically possible system.

• Thank you, great answer! I'm using this path loss calculator: pasternack.com/t-calculator-fspl.aspx . With 50dBm transmit @ 2.4GHz, 24dBi gain on each side (readily available) and 100 meter distance it gives 32dB loss, thus received power is 66 dBm. Certainly we can't receive more than was transmitted, is their path loss calculator wrong? What am I missing here? – KJ7LNW Jan 18 at 23:21
• @user16278 They're giving you the total loss including antenna gain, so the received power in this case is 50dBm - 32dB = 18dBm. To get what I would call the path loss, you have to enter 0 for both antenna gains in their calculator. – hobbs - KC2G Jan 18 at 23:45
• An equation for the path loss between two antennas in free space is A = 96.6 + 20(logF) + 20(logD); where A = path loss in dB, F = frequency in GHz, and D = path distance in miles. Logarithms are referred to base 10. – Richard Fry Jan 19 at 8:37