In radio communications, having a good estimate of the possible range of communications between two stations is very useful. The general approach to this calculation is to analyze the transmitter signal, the receiver sensitivity, and the expected path loss due to signal propagation. This article will look closely at all three elements. In general the values for the transmitted signal and receiver sensitivity are chosen to provide good communication, based on the expected value for propagation loss at the distance between stations.
Transmitted Signal
The signal level emitted by the transmitter consists of three factors: the transmitter power output, any power lost in the transmission line between transmitter and antenna, and any gain (or) loss in the antenna. The power is generally calculated using the unit dBm, which is a power level referenced to one-milliwatt (0.001-Watt). The transmitter power output in Watts is converted to a value of dBm. The transmission line loss in decibels is subtracted from the transmitter power to obtain the power at the antenna input. Any antenna gain is then added to the antenna input power to become the Effective Radiated Power in dBm.
Example of ERP Calculation
Transmitter power = 25 Watts
Convert to dBM = 44 dBm
Subtract transmission line loss of 1 dB = 43 dBM
Add antenna gain of 3 dB = 46 dBm Effective Radiated Power
Path Loss
During propagation of the signal, considerable loss occurs, varying with the distance between transmit and receive antennas, the frequency of the signal, and the nature of the intervening space. These losses typically are assessed in decibel proportions to make calculations easier. See the Wikepedia article Friis Equation, for more details on the basis for the calculation of propagation loss with distance and frequency.
The most simplistic assumption for path loss assumes the best case: propagation in a free space vacuum where there are no objects of any kind in the region between antennas or near to the antennas. The effect of distance is expressed as a logarithmic factor of the distance (using the same distance unit as used for the speed of wave propagation, generally meters or miles), subject to multiplication by a linear factor the varies with terrain. For Free Space calculations the distance's influence of signal loss is consider to be a factor of 20*log(d), which is a way to express the expected relationship that intensity decreases with the square of the distance. For real-world propagation over terrain, a more realistic estimate is to use a distance factor of 40*log(d), resulting in the distance having a much greater influence on communication range.
The frequency is also a logarithmic influence, again with a factor of 20(log)f.
For units of Miles and Megahertz, the Friis Equation in decibel form becomes
FreeSpacePathLoss_db = -36.58 - [DistanceFactor]log(f) - 20log(d)
For more on the derivation of the expression of path loss in decibels, miles, and Megahertz, see a prior article at:
Marine VHF Radio Communications
https://continuouswave.com/whaler/reference/VHF.html
and see the Addendum at the article's end:
Converting Path Loss to Decibel Equation
Power At Receiver Input
The power available at the receiver input is the result of the the reception of the transmitted signal ERP by the receiver antenna and possible improvement by antenna gain (or reduction by loss), then reduced by any transmission line loss between antenna and receiver input. Input power at the receiver is calculated by taking the ERP of the transmitter, adding receiver antenna gain, and subtracting any transmission line loss. If the receiver has a 3 dB gain antenna and a 1 dB loss in the transmission line, the net received signal power in increased 2 dB, or in or example, an ERP+RxGain signal level of 48 dBm.
Receiver Sensitivity
All receivers exhibit a particular lowest possible received signal level at which they can effectively receive and demodulation a signal. Often the sensitivity is stated in terms of an input voltage (typically in microVolts) that is needed to produce a particular signal-to-noise ratio in the demodulated output of the signal. To convert to power in dBm, the impedance must be known, which typically is 50-Ohms. For a receiver sensitivity of 1-microVolt at 50-Ohms, the equivalent power is -107 dBm. Also see previous article
Conversion of Receiver Sensitivity
From Microvolts to dBm
https://continuouswave.com/whaler/reference/dBm.html
Rather than use the ultimate best sensitivity of the receiver, most calculations introduce a factor called "fade margin" to account for variations in propagation that will cause the received signal to decrease periodically. Using a fade margin of 20 dB is a good practice, as it tends to produce conservative estimates of communication ranges that will be more likely to be reliable paths.
To account for the fade margin we just derate the receiver sensitivity by 20 dB, so a typical sensitivity changes to -87 dBm from the minimum -107 dBm.
Maximum Path Loss Tolerated
Once the anticipated minimum signal at the receiver is determined, we then calculate the difference in signal levels between the ERP (with receiver antenna gain) and the minimum desired signal power. This is the last factor in the communication range calculation, and it will be the difference in the signal power at the receiver input (without any propagation loss or 48 dBm in our example) compared to the required minimum detectable signal (with fade margin) that can be tolerated (-87 dBm in the example) resulting in a maximum path loss the can be tolerated (which in our example is a 135 dB loss).
Finding Distance for the Maximum Path Loss
To find the distance at which the path loss increases to the maximum tolerated value, the Friis Equation is again used, but in this case we solve for the distance, not the path loss. The result is:
d(miles) = 10^[(FreeSpacePathLoss) - 20log(f) - 36.3] / DistanceFactor
Again the influence of the space or intervening terrain involved is very influential, so the choice of an appropriate distance factor has enormous influence on the calculated distance. For the power levels and path loss used in the example, using a real world distance factor of 40 results in a calculated communication range of 23-miles. If the free space distance factor were used, that distance would increase to 530-miles. But such a path would required the two stations to be in line-of-sight and literally in space.
An RF Spreadsheet
To facilitate making these calculations, a computer spreadsheet is a very useful tool. I have created my own spreadsheet for solving this RF calculation, along with many other useful RF related calculations. The spreadsheet makes tedious and error-prone calculations much simpler and reduces errors. Because it is a spreadsheet working on a local computer, you do not need to be on-line to use it.