There is no Loss in Free Space Path Loss. And it doesn’t change with frequency

Whether a professional or amateur, one of the first things we learn about propagation is that lower frequencies propagate better. Or propagation loss increases with frequency. In this post I will make the case that Free Space Path Loss really does not exist, and that the real effect we see is independent of frequency.

How can this be so you say. I know my HF HAM radio can transmit for hundreds of miles, yet I can’t receive my WiFi at the bottom of the garden. Ignoring the fact that WiFi data rates are vastly larger than FM voice that our friend Claude Shannon will tell you requires more energy, trust me, WiFi would have shorter range than HF voice even if the data rates were the same.

So let’s square away my statement that true Pathloss does not depend on frequency with our lived experience.

Our sun is a ball of light that shines in all directions. It emits electromagnetic waves(light) that illuminate all the planets in our solar system. The further a planet is from the sun, the dimmer the light that reaches it. Why is this so? It’s clearly not because of dust in space that is absorbing this light and turning it into heat, such an effect would cause the dust to emit black body radiation(probably IR light) and the sky would glow(at least in IR) which it doesn’t. No, the light gets dimmer because it spreads out as it travels. If we placed a huge sphere around our solar system (Dyson sphere) pretty much all the light emitted from the sun would be hit the inside surface of that sphere. Note, that I haven’t had to discuss the colour or frequency of this light. It does not matter.

The same is true for a radio signal. Within the air of our atmosphere and within the frequencies we normally deal with for radio signals, air is pretty much a lossless medium. We will ignore some effects like hydrogen lines and water absorption that happen in specific bands. Regardless, my argument here is about Freespace Pathloss, so let’s assume we are in a vacuum. There is no Loss in a vacuum, if there were we would not be able to see the stars. Hence Freespace Pathloss does not depend upon frequency.

Fig1 – Freespace Pathloss Formula

But above is the Freespace pathlos formula Mr HexAndFlex, it clearly has a frequency term! What is going on? Well I will try and avoid too much math here, but unfortunately some is essential.

Fig2 – Power Intensity as a function of distance from an isotropic antenna

Let us first understand that the freespace pathloss formula is derived from this basic principle. In the formula above(fig2), we show the transmitted power in the numerator(above the line). In the denominator, we see what is clearly recognisable as the formula for the surface area of a sphere. The intensity of the signal decreases as the surface area of a sphere of radius d(yes, I know radius is normally r, but for some reason RF people use d to equal distance). There is no loss, but the power density, which would have units like Watts per Meter Squared, decreases according to the size of the sphere. This in my opinion really is the fundamental formula we should understand. Its not complicated, and very easy to intuitively understand.

So, why does our FSPL formula differ from this. Well its because of the way we specify antenna gain. For good reasons, we do this in a way that similar similar antennas provide the same gain when scaled for frequency. A standard half-wave dipole will have a gain of 2.15dBi regardless of frequency. Our dipole is tuned to a specific frequency that we can change by making it shorter or longer. If we want to make our antenna work at a higher frequency we make it shorter. The power intensity we calculated in fig2 is in units of W/m^2, ie. Watts per Unit Area, it stands to reason that if the Area is smaller(because our antenna is shorter) there will be less received power.

Formulas in fig1 and fig2 are different because the FSPL formula has the assumption of an isotropic antenna built in.

This brings me to what I think is the real understanding of the link between FSPL and frequency. Freespace Pathloss increase with frequency because our antennas get smaller. In fact to call it a ‘loss’ is somewhat confusing. Nothing is lost, we are just using a smaller bucket to catch the signal with.

If we can design an antenna such that its size remains the same with increasing frequency, we can compensate for this loss. This is true for a type of antenna called an ‘aperture antenna’. A common example of which would be a satellite dish. So long as the wavelength is smaller than the area of the dish, these antennas work to capture all the energy that hits the dish. It has a constant aperture, dictated by the diameter of the dish. Assuming its 100% efficient(dishes are normally at least 70% efficient). We can calculate this aperture(area of the dish) and multiply if by the power intensity(fig2), we can work out the received power.

For my Palmtree Vivaldi antenna, I did a similar calculation. As a planar antenna, its hard to easily see what the aperture is, but given a bit of experimentation I was able to derive a suitable area that worked for my needs. In the diagram below I have drawn a cyan rectangle to represent the assumed aperture for my antenna(45cm^2). Assuming this was fixed, I calculated the calculated the expected gain that this would result in.

Effective Aperture(Average)
Gain plotted with expected gain for given effective area

In the above plot, we can see that the blue gain(dBi) and red fixed aperture gain plots show very good correlation. There would be very little point in trying to optimise this antenna any further to enhance gain, unless we are willing to try and increase the aperture(and hence size).

Summing up

Firstly, to get it out of the way. The standard FSPL formula is correct and within the system we tend to work with where we calculate our antenna gains with respect to a isotropic antenna, it is a useful way to calculate link budgets etc. Please don’t read this post and think that antenna theory is really built on a lie and you need to throw away your books. However hopefully this post provides another viewpoint that may give you greater insight into why things work the way they do.

The terminology of FSPL somewhat misleading in my opinion. We do not loose energy because the there is some ‘loss’ along a path. The energy is lost, because some of it has traveled down a different path that no longer leads to our antenna. It is still there should we place more antenna in its way to receive it.

I have been careful in this post to only discuss things in freespace(i.e. a vacuum). when we start to add real world materials into the mix, things definitely diverge from this. House bricks definitely do increase the loss of signals that pass through them and this loss is very much dependent upon frequency, although not necessarily in a way that can be easily inserted into such a simple mathematical formula. However, when we start to think about propagation in environments that contain significant other materials, FSPL is probably not the way we want to estimate pathloss.

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Impedance Matching with QUCS Studio and VNA


In my last blog post I alluded to the fact that you could take s1p touchstone files generated by nanoVNAsaver and use this to automatically calculate/simulate a matching network in QUCSstudio. This could be used to quickly design antenna matching networks for instance. I was asked in the comments about exactly to do this. Of course, I had totally forgotten!!! But lets go through it again.

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Getting Started with the NanoVNA -Part 3 – PC Software

VNA Saver – PC Software

There is now a variety of PC based software that is available to use with your nanoVNA. In this post, I will be demonstrating NanoVNASaver(version 0.0.9). This is developed by Rune Broberg and is fully open source. Rune originally developed the software as a way to save Touchstone files from the NanoVNA to use in other programs, but couldn’t resist expanding it’s functionality into what is now a fairly complete PC app to run the NanoVNA. If you want to participate in conversations with Rune, He is active on the nanoVNA group which is an excellent place to find all the latest tips and experimental firmware builds etc.

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Getting Started with the NanoVNA -part 2

In the previous post, we got up to speed with the basics of what a VNA is and how to run a basic calibration. In this post we will look at configuring the traces and formats.

Note on Charging – One note, before we go deeper. My NanoVNA doesno like to charge from my PC USB type C port or my Samsung Quick charger. Use a regular USB-Type-A from an less intelligent charger and it’s fine.

Configuring Traces, Channels and Formats.

Throughout this guide, I will assume you are using a stylus(or your finger) to control the NanoVNA via the touchscreen. You can of course use the rocker control to perform all these applications. Read more ›

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Getting Started with the NanoVNA -part 1

This post now includes some edits based on user feedback[in green italic]

What is a VNA?

The Vector Network Analyser is an essential piece of test equipment that no RF engineer should be without. If you have previously worked with Electronics at low frequencies, you may consider a good DMM or Oscilloscope your best friend. RF Engineers would gladly trade both a scope for a good VNA!

A good VNA is an expensive bit of kit. Many years ago, a good one would probably cost you as much as a fairly nice house. Nowadays, you can pickup something really good for the price of a nice car. Note, High-end VNAs can still sell for between $100K and $1M. I will use the term ‘professional┬áVNA’.


“What’s it’s dynamic range again?”

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Spiral Antenna – Part 3 – Results and Suckers

In the chamber

Antenna in Test Lab

The original aim for this antenna was to be a general purpose antenna that worked down to 400MHz. The results are now in and I am really pleased with them. The antenna was tested by AntennaTestLab in a full anechoic chamber with a 3D positioning system to automatically rotate the antenna. ATL use a dual polarized (horizonal and vertical) Vivaldi antenna to measure the radiation pattern. By recording both the amplitude and phase of each antenna they can use clever math to calculate the circular polarized gain. Clever stuff eh?! Take a look at ATL’s writeup here

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Spiral Antenna – Part 2 – Modelling and Simulation with OpenEMS

Now tested by AntennaTestLab. For now see results here

Electromagnetic simulation software can be very expensive. While some software is cheaper, it often comes with either technical or artificial limitations. There are however a couple of free alternatives.

NEC2 – Originally written by Lawrence Livermore National Labs, NEC2 was open sourced many years ago. Since then a couple of users have created good free or low cost front ends for it. 4NEC2 is my personal favourite. The best feature is it’s speed, especially if you can find a copy of NEC2/MP that makes good use of multiple core moderns processors. The big limitation is with dielectrics. Everything in NEC2 is either wire, free-space or earth.

OpenEMS – A Finite Difference Time Domain (FDTD) tool that uses MATLAB or the excellent free Octave as a front end. It was created by Thortsten Liebig at the General and Theoretical Engineering University in Germany. As suggested in FDTD, OpenEMS uses a time-domain approximation of Maxwells equations to calculate the results. The big advantage of OpenEMS over NEC2 is that it can handle bulk dielectric materials with different EM properties, I will need this to simulate an antenna on FR4 with an Er~=4. While it may not seem it at first, being able to generate geometry mathematically in is another advantage. This is especially true for a spiral antenna. Hence this is the package I decided to learn and use for this project.

Dont Panic!!!

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Spiral Antenna – Part 1


My original Palm Tree Vivaldi Antenna has proved amazingly popular. Much more so than I originally intended. The design aim for this was primarily for it to be small and portable.

When deciding what to do next I decided to create a survey and see what other people were interested in.


R&D Survey Results

The overwhelming response was that people wanted a bigger version that would cover lower frequencies. I can understand this, there are loads of interesting signals below 800MHz.

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Reconfigurable Ultra-Wideband Antenna Array Kit – part 2 (Spacing)

Why Spacing Matters

Firstly, the antenna array I am designing is a fixed in-phase array. Hence we assume that the total path length from each antenna to the single input/output connection are the same length. This makes the design and analysis much simpler, especially for an ultra-wide-band design.

In my design signals that arrive at right angle to the antenna will add up co-herently (in-phase)

spacing boresight

Signals arriving from boresight add up in phase

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Ultra-Wideband Antenna Lab Measurements


Antenna being tested in anechoic chamber

My Vivaldi Antenna was recently tested by Antenna Test Lab who offer an excellent professional antenna testing facility. Antenna Test Lab are able to provide customers with full 2D/3D antenna measurement using their anechoic antenna testing chamber. Read more ›

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