Path loss and very small numbers ...

Foundations of Amateur Radio

Sometimes you learn mind boggling things about this hobby, often when you least expect it. Recently I discussed having my 20 mW WSPR or Weak Signal Propagation Reporter beacon heard on the other side of the planet, in Denmark, 13,612 km away. That in and of itself is pretty spectacular, but it gets better if you consider just how weak the signal was by the time it got there.

In radio communications there is a concept called path loss or path attenuation. Until recently I understood this to mean the things that impede a signal getting from transmitter to receiver. That includes coax and connector losses, refraction across the ionosphere, reflection off the surface of the planet and diffraction around objects.

It turns out there is another factor called "Free Space Path Loss" to consider. It's loosely defined as the loss of signal strength between two antennas. The name sort of implies that something happens to the signal in free space, which is odd if you know that in space, radio waves, regardless of frequency, travel without loss and will travel pretty much indefinitely.

So what's going on?

To get started, think about a dome lawn sprinkler, one of those little round discs that sits on the ground with the hose connected to the side. You turn on the tap and the water sprays in all directions. If you're really close to the sprinkler when the tap is turned on you'll get sopping wet almost immediately, since most of the water will hit you directly. This is particularly fun in the heat of summer on New Years Day in Australia, not so much in the middle of winter on the other side of the globe.

If you stand a couple of meters away, you'll still get wet, eventually, but it will take much longer, because most of the water isn't hitting you. If you stand even further away and assuming the water still gets that far, it will take even longer.

A small towel and a big towel will both take the same length of time to get wet if they're held at the same distance from the sprinkler, but if you wring them both out, you'll discover that the big towel captured much more water during the same time.

In radio communications we can combine these two ideas, the distance and the size of the receiver, to describe free space path loss.

The further away from the transmitter you are, the less signal is available to you to capture since much of the signal is not heading in your direction and the bigger your antenna, the more signal you receive. The bigger the antenna, the lower the frequency, which is why you'll discover that free space path loss is dependent on both distance and frequency.

To give you an idea of scale, the free space path loss for 28 MHz over 13000 km is about 144 dB.

While the name "Free Space Path Loss" implies loss of signal across the path in free space, the loss is not due to distance as such, rather it's caused by how much the signal is spread out in space. Similarly, there isn't more loss because the frequency is increased, it's that less signal is captured by the smaller size or aperture of the antenna required for a higher frequency.

So perhaps a better name might be Spherical and Aperture Loss, but then everyone would have to learn how to spell that, so "Free Space Path Loss" it is.

I'll point out that this is the minimum theoretical loss, in reality the loss is higher than this, since it also includes all the other parts of the path loss which are things that we can control, like coax and connector loss, and things we can improve by frequency selection, like ionospheric reflection and refraction which depend on solar conditions.

The one aspect of path loss that we have no control over is the "Free Space Path Loss", so perhaps that's why we don't talk about it very much.

I'll mention that in path loss calculations often antenna gain at the transmitter and receiver are used to reduce any path loss figures. If I have an antenna with 6 dB gain, then that reduces my overall path loss by 6 dB, which is why we spend so much time and effort figuring out what antenna to use when we get on air to make noise.

I mentioned that the free space path loss for my beacon between Australia and Denmark was about 144 dB. This means that my 20 milliwatt signal arrived in Denmark as a -131 dBm signal. That might not mean much, but that's the equivalent of about 80 attowatts. If you're not sure how big that is, 1 milliwatt is 1 quadrillion attowatts, a 1 with 15 zeros. Said another way, 1 watt is 1000 milliwatts, 1 milliwatt is 1000 microwatts. 1 microwatt is 1000 nanowatts, 1 nanowatt is 1000 picowatts, 1 picowatt is 1000 femtowatts, 1 femtowatt is 1000 attowatts.

It might come as a surprise, but these numbers are not unusual. Don't believe me? When your radio shows an S0 signal on HF, it is defined as -127 dBm, so we deal with tiny numbers like this all the time, we're just not quite aware of it on a daily basis.

Remember, my numbers are theoretical only, to give you an idea of scale. In reality everything in the path between the transmitter and receiver affects what ends up at the other end and might make the difference between hearing someone, or not.

I'm Onno VK6FLAB