Chapter 3: Path Loss and Free-Space Path Loss (FSPL)

This chapter discusses two topics that will come up time and again while planning your WISP: path loss (how far can my signal go?), and link budget (what devices can I use for this link?).

Radio signals lose power as they pass through the air. The rate at which they lose power is a function of frequency, which can be derived into a formula for calculating “free space path loss”. This is a fundamental calculation: knowing how much power your radio signals lose over a given distance in ideal conditions permits you to:

Warning: Mathematical Theory Ahead!

Radio signal degrades in proportion to the distance covered. It can be modeled at the most basic level with the “inverse square law”: that is, signal degrades in direct proportion to one divided by distance squared (d represents distance):

signal = 1 / d 2
The inverse square law

This is a very simplified model, and while useful for understanding the basic concept of radio signal strength propagation, it doesn't take frequency into account. It also ignores terrain (as a rule of thumb, you can replace the power of two with a power of four for areas with obstacles such as trees or stadia; you might replace it with a power of 1.5 or less when transmitting through a tunnel!).

Inverse Square Law

As you can see, the inverse-square law shows signal dropping off rapidly over distance. This is a law of physics, and cannot be avoided – but it can be mitigated by having a very strong signal to begin with (both in terms of transmission power and antenna gain).

Free Space Path Loss (FSPL, sometimes abbreviated to just “path loss”) is calculated with the following formula:

FSPL = ( 4πdf / c ) 2
d is the distance from the receiver to the transmitter in meters.
f is the frequency in hertz.
c is the speed of light in a vacuum, in meters per second (2.99792458 * 108)
Free Space Path Loss (FSPL)

This is more useful, and models the effects of different frequencies on distance propagation.

Free Space Path Loss by Distance and Frequency

The higher the frequency, the more quickly signal-strength drops off over distance. This is why Verizon like to use 700 Mhz for their cell-phones: the frequency penetrates very well, and can cover a large distance. Sprint's WiMAX service, in the 2.5 ghz frequency band loses power more quickly over distance. Point-to-point services in 5.8 ghz and above lose power even more dramatically over distance – but this is mitigated by permission to use higher power levels and large, high-gain, antennas. Also, these figures are not yet in decibels; decibels (signal strength as seen by your radio) are a logarithmic scale. This has the effect of dampening the exponential signal decay over distance into a straighter graph.

In radio modeling, it is common to measure Free Space Path Loss in decibels, for easy inclusion in link-budgets. The formula for this is as follows:

FSPL (dB)=32.44+20 log10⁡f+20 log10⁡d
d is the distance of the receiver to the transmitter in kilometers (km).
f is the signal frequency in Megahertz (Mhz).

This is a very useful graph, and one to which you will frequently refer. It shows that path-loss increases over distance, with lower frequencies dropping off more slowly than higher frequencies – but thanks to the logarithmic nature of the decibel, the increase in path-loss over distance is relatively slow over long distances. It also shows that you only need a relatively modest antenna and transmission strength to make use of these frequencies; as discussed below (in “Link-Budgets”), you need your transmit gain plus receive gain plus transmission power to exceed these path-loss numbers by around 75 dB. With a pair of 30 inch dishes, you can achieve a usable link at 100 km!

Tip: There are a number of freely available Free Space Path Loss calculators available online. In my experience, it helps to understand the concepts before relying on a calculator, which is why I didn't just include a link!

Now that we know that a 10 kilometer (6.2 mile) link at 5800 Mhz provides a path loss of 127.72 dB, the obvious question is what do we do with that number? The answer is: we plug it into a link-budget!

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