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I am trying to find a formula (if one exists, and this is the right place) to try and calculate how far a radio station can transmit, under ideal conditions. I have searched Google, and I can not find a solid answer.

  • Broadcast Frequency: 89.7 MHz
  • Effective Radiated Power: 910 Watts
  • Transmission Power: 936 Watts
  • Transmitter Height: ~39m
  • Terrain: Flat

Thanks for the help.

Colum
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2 Answers2

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You can make some assumptions like a typical FM receiver needs -110 dBm to work. Then assume you have an isotropic antenna in both cases because you didn't say anything about the antennas so we'll ignore the gain.

Next take a look at the path loss based on the 910 W (+59.6 dBm) power.

Your path loss can not exceed 59.6 + 110 = 169.6 dB (with loss dB and dBm are the same, but dB and dBm to watts is different).

The free space loss model is $L_{fs}=32.45 + 20*log(d_{km}) + 20*log(f_{MHz})$

You'll need to solve this for $D_{km}$ and set $L_{fs}=169.6$ and $f_{MHz}=89.7$.

There are many other path loss models. NIST suggests several

  • Free Space Model (shown above...least accurate)
  • CCIR
  • Hata
  • Walfisch-Ikegami (WIM)

Having the antenna height will reduce your path loss some. In the popular WIM model in a line of sight (LOS) situation like yours where the base antenna is >30m high with no obstructions in the direct path then you can use a more realistic estimate:

$L_{wim-los}=42.64+26*log(d_{km})+20*Log(f_{MHz})$

Also the ITU has a specification ITU 1546 Method for point-to-area predictions for terrestrial propagation (pdf here). You can also find MatLab solutions and a lot of literature on their technique and field test results for broadcast FM. (FYI the models are all very similar in structure to NIST's models).

user6972
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  • Thanks! This was exactly what I was looking for, and the added information is a bonus! – Colum Nov 02 '13 at 20:03
  • Where can you find an isotropic antenna? The cheapest, non-direction FM broadcast antenna is going to be vertical dipole with a gain of around 3dB over isotropic. A vertical colinear dipole array will have higher gain, and still have no directional pattern on the map. The gain is due to the antennas sending more energy parallel to the ground, and less energy up into the sky. – Solomon Slow Dec 23 '15 at 02:03
  • @jameslarge an isotropic antenna is a mathematical tool and doesn't exist in real life. – user6972 Jan 29 '16 at 18:15
  • @user6972, my point exactly! The choice of transmitting and receiving antennas has a significant impact on the value that you are trying to estimate (i.e., on the max distance from which the station can be heard), and yet you are assuming that both are isotropic, when a cheap, practical antenna performs better by a factor of 3dB. You are handicapping your estimate by at least 6dB, right out of the gate. – Solomon Slow Jan 29 '16 at 18:39
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Would very well depend on the sensitivity of the receiver. Perhaps you want to know by how many dB the signal is attenuated over distance?

See: Determining a radio signal's range

Community
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lionelbrits
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  • Yes, although I think the surveys referred to in that answer are not only needed to find out whether the proposed radio link will work, but a great deal also to check that your link won't interfere with other communications - this latter problem turns out to be the main work of the survey. – Selene Routley Nov 02 '13 at 02:07