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Why are antenna PCB traces square instead of rounded?

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While doing some reading on RF designs I ran across this paragraph: Image alt text

I have never designed an RF circuit, but all the PCB trace antennas I have seen on development boards are square. For example, ESP32: Image alt text

More examples can be found online. If the important thing is the length of the antenna for the corresponding frequency, wouldn't it be better to have round corners for the trace antenna for the reasons mentioned in the paragraph above?

Edit: Lundin has expressed doubts regarding the design of the ESP32. So I feel compelled adding more examples to emphasize that this is not a one-off design. And it would be interesting if a bunch of people decided it to do one particular way without a good reason. So another antenna: Image alt text

And yet another one: Image alt text

To be fair, after more searching I did find one that has round edges: Image alt text

This does not seem to be the standard approach from what I can find.

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Corners and chambers that are a small fraction of a wavelength are not significant in the <4Ghz band. More significant is the tolerance and loss tangent on the substrate. They would hardly be measureable even with a 2 ps TDR. Emissions are not significantly different.

WHAT COUNTS is the RL and loss tangent.

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PCB antennas are not designed by electrical engineers, but guys with pointy hats and wands They use trial and error after starting with the result of some mystic ritual including lots of mumbling and waving of the afore-mentioned wand.

OK, that's not completely fair, but there is still a high component of trial and error to tweak the final radiation pattern and impedance. Simulation software can go a long way these days, but the good stuff is still quite expensive, and out of reach of many engineers that don't specialize in RF. Not everything can be accurately modeled, so the result of a simulation is only a starting point. Testing needs to be done with real hardware.

It is easier to model antennas as a series of straight elements. Not all simulation programs handle curved segments, or handle them well. Straight segments are also easier to lay down. Sure, any competent modern PCB layout software allows curved segments, but these are all more work. Tracks with straight segments are just easier.

You have shown some examples with angled corners, but without an analysis of how well the result works, those examples are meaningless. How do you know the curved ones are optimal and the cornered ones not?

Note also that your main point is about impedance discontinuities, but that's quite different from "bad antenna". What matters is the overall impedance presented to the transmitter (or receiver), the radiation pattern, and sometimes the polarization in each direction. If an antenna achieves the desired result, why does it matter that this is done with some impedance discontinuities along the way? You haven't provided any reason we should care about impedance discontinuities by themselves.

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