Doing a basic link budget for RF transmission

Tina Z, June 23, 2016

To ensure we have the right range and right power to transmit and receive RF, we usually do a RF link budget to make sure it’s feasible. Instead of multiplying gains and such, this is usually done by adding the logs of the gain ratios, which usually makes this process a bit easier. For instance, we do

10log(init power/some unit) + 10log(gain A) - 10log(loss B)=10log(out power/some unit)

instead of

(initial power in some unit)*(gain A)*(1/loss B) = output power in some unit

Anyway, if you divide out the 10 in the first formula, and convert the logs back into exponents by setting the output power = 10^(log10s of the gains/losses), you can tell pretty clearly it’s exactly the same thing. Doing it the former way is the convention though, and it’s much easier to just add numbers anyway.

The above is all we need to compute a basic RF link budget. You start off with your initial signal, which for instance could be 500mW, which would be 10*log(500mW/1mW) or 27dBm, or dB relative to milliWatts.

Your gains in a RF link budget are usually amplifiers and antennas, so if your transmitted signal passes through an amplifier with a gain of 10, that’s now 10*log(10) or 10dB. Your transmitting antenna could have a rating of something like 12dB at the frequency you want to transmit at, and your receiving antenna could have a rating of 10dB for that frequency as well. Let’s say our receiving amplifier has a gain of 100 or 10*log(100), so 20dB.

Your losses would be attenuation as the signal travels through the atmosphere. There’s a pretty good model for how much a signal will attenuate in air called the Free Space Path Model, and the formula to find it is this:

The basis for this formula is that our antennas are radiating spherically, which is great for some approximations and in some cases isn’t completely true. A regular half-dipole antenna doesn’t have directed radiation patterns and is pretty omnidirectional, so we’re ignoring antenna directivity in this case. Higher frequencies attenuate more in the atmosphere, and of course, distance away increases path loss. For our case, if we assume we’re 14 meters away and we’re transmitting 1GHz, we have a path loss of -55dB.

After we add all these things together, we can calculate the received power.

27dBm + 12dB - 55dB + 10dB + 20dB = 14dBm. 10^(1.4) mW is something like 25mW. If the resistance of your antenna is 50ohms, then the voltage you should expect is V=sqrt(R*P)=sqrt(50ohms*.025W).

Unfortunately, even though that’s what you hope for, the above is probably not what you’d get. This is only the mean received power you can expect. There’s standard deviations for both losses and gains along your link budget, so you won’t reliably get the output you expect 50% of the time. The amplifiers have pretty small standard deviations though, they pretty much always give you the right gain no matter what. Antennas are finnicky though, so your actual antenna gain is +/-3dB from the reported value, for both your transmitting and receiving antenna. You will definitely want to have enough “room” in your link budget so that a 6dB loss won’t ruin everything.

If you’re careful, especially when you want to design commercial equipment, you might want to account for even more loss so your product will work +98% of the time. However, this also means on a particularly good day, you’ll have incredible range and received power many times what you expect (i.e. 100 meters for something rated for 10 meters), which could be a nice bonus.

There’s even more issues though - FSPL isn’t the best approximation at times due to weather, environment, or if there’s other RF sources in your area. When your RF signal bounces off of water, earth, scatters off metal fences, etc., you can experience even more loss. When it does so, it can even deconstructively interfere with itself (multipath interference). This is why those who design RF systems for a living place antennas on tall buildings, long poles, etc., since it decreases the chances of that happening.

Another thing - choosing your wires for most RF systems is something you also need to consider. Wires can act as antennas at high frequencies, so any wire that carries HF should be well shielded coaxial cable. At extremely high frequencies, even coaxial cable can slightly attenuate your signal, and this needs to be taken into consideration when making exact measurements.