A link budget is the summation of all of the power gains and losses that occur in a communication system. A link budget is a design aid and is one factor used to help ensure the information is received intelligibly. To figure out if a signal can be received at any given location, we need to determine what the received power will be. This article contains some fairly simple math, to help you determine if your signal can be heard. Like most all RF formulas, we use Logarithmic units, centered around the decibel (dB).
Link Budget equations can be complex containing thousands of parameters, so simplifications can be made to speak to generalities, this simplified link budget equation looks like:
$${\displaystyle P_{\text{RX(dBm)}} = P_{\text{TX(dBm)}} + Gains_{\text(dB)} - Losses_{\text(dB)}}$$ More complex link budgets will take into account cross-polarization, multipath, doppler shift, etc.
For line-of-sight radio systems, the main source of losses is the Free Space Loss (Path Loss) which is the decrease of signal power, proportional to the inverse square of the distance between the transmitter and receiver (Antennas) and is frequency dependent.
The propagation loss between the antennaTX and the antennaRX often called the path loss can be written in a dimensionless form, normalizing the distance to wavelength.
$${\displaystyle L_{\text{FS}}{\text{(dB)}}=20\log _{10}\left(4\pi {{\text{distance(m)}} \over {\text{wavelength(m)}}}\right)}$$
It is rare however that the only path loss is that of free space, more often than not, the topography adds further impediments to the transmission, utilizing Empirical propagation models such as Longly-Rice or Egli these topographic impediments can be taken into account. The Coverage plots produced by OCARC utilize Longly-Rice and take these into account.
A practical link budget formula would look more like PRX = PTX + GTX - LTX - LPL - LM + GRX - LRX
Where :
PRX is the Received Power in dBm
PTX is the Transmitter output Power in dBm
GTX is the Transmitter antenna Gain (over isotropic) in dBi
LTX is the Transmitter Losses (coax, connectors...) in dB
LPL is the propagation loss, usually free space loss in dB
LM is the Miscellaneous losses (fading margin, body loss, polarization mismatch, other losses, ...) in dB
GRX is the Receiver antenna Gain (over isotropic) in dBi
LRX is the Receiver Losses (coax, connectors, ...) in dB
In common narrowband FM communications systems, a Signal-to-noise and distortion ratio (SINAD) of 12dB is required to convey an intelligent message, many radio receivers publish their receiver sensitivity at this SINAD in µV.
However, as we've discussed earlier, we'll need to normalize our units into dBm. For a 50-ohm system, the following formula is used.
$$20\log _{10}\left({\text{0.224} \over \text{RX_Sensitivity}}\right)$$
My Kenwood NX-5200K2, according to the spec sheet has a 12 dB SINAD receiver sensitivity of 0.25µV, or
$$20\log _{10}\left({\text{0.224} \over \text{0.25x10e-6}}\right) = -119.05_{dBm}$$
Because this is a portable radio, with a standard rubber ducky antenna (which is shorter than 1/4wave length), its antenna gain is poor, in fact, it is a negative gain in comparison to isotropic, my professional experience tells me that -4dB is fairly typical for this kind of antenna. Again, because this is a portable radio it's safe to assume that the antenna is not going to be out in the clear, there will be obstacles. In the 2meter band for example your body generally causes a 6dB loss and more as the frequency increases.
The VE7HOL (Dilworth Mountain) repeater is a Kenwood TKR-750 with a 50W power output and 0.35µV SINAD, 4 cavity Sinclair Resloc duplexer, with an insertion loss of 1.5dB, coax and connector losses add another 2dB, for a total of 3.5dB in system losses. The Antenna is a 2bay folded dipole, which has a stated gain of 6.6dBi.
What is important for us to figure out is what is the Maximum Allowable Path Loss (MAPL) to allow a communication to be heard. in the downlink (repeater tx, portable rx) direction MAPL = (TX Power - TX attenuation + TX antenna Gain)-(RX Sensitivity - RX body Loss + RX Antenna Gain).
$$Watts \space to \space dBm = 10\log_{10}(W) + 30$$ $$10\log_{10}(50) + 30 = 46.99_{dBm}$$ $${\left({\text{46.99 - 3.5 + 6.6}} \right) - \left({\text{-119.05 - 6 + (-4)}}\right)} = 179.14_{dB}$$ However, the portable is only a 5W transmitter, (and the repeater has a less sensitive receiver) so we need to calculate this in the other direction as well. This would therefore look like in the uplink (portable tx, repeater rx) direction MAPL = (TX Power - TX attenuation + TX antenna Gain)- (RX Sensitivity - RX body Loss + RX Antenna Gain).
$$10\log_{10}(5) + 30 = 36.99_{dBm}$$ $${\left( 36.99 - 6 + (-4)\right)} - {\left( \left(20\log _{10}\left({\text{0.224} \over \text{0.35x10e-6}}\right)\right) -3 + 6.6 \right)} = 139.5_{dB}$$ So, as you can see, for reliable communications, the path loss must be less than 139dB if you want to communicate. If you want full quieting, you'll need to add 8dB of link margin, bringing you to 131dB of allowable path (propagation) loss.
In the case of my mobile radio a Kenwood NX-5700 radio 50W/0.25µV, with a 5/8's wave roof-mounted antenna providing a gain of about 4dBi (this would be closer to 1.5dBi if the antenna is fender mounted) after coax/connector losses, improvements in body losses the downlink MAPL is 9dB better than the portable setup, with the uplink offering 22dB better.
