Okay, kicking an old topic as you nerd-sniped the shit out of me when you started this topic. I knew for a fact that your antenna configuration probably wouldn't perform well as any antenna designs currently in use, because of the logic that your antenna is so dead simple: if it really was that easy to get optimal performance, everyone else would have stumbled on the idea and we'd all use the antenna.
The issue is that that is only circumstancial evidence, though: perhaps humanity ignored the trivial solution all this time? To prove that the meandered printed F-antenna we have on our current designs works better, I'd either have to be able to analytically explain why or to simulate or measure one. I'm decently sure learning why antenna designs work is not something I can pull off in a few days, so I spent the time instead learning a simulation package, in this case OpenEMS.
As a reference, here's our mPIFA antenna as seen on the WROOM modules.
![ant-mpifa.png](./download/file.php?id=11933&sid=98eff5d9fbad400920d0c8f9cab87075)
- ant-mpifa.png (202.37 KiB) Viewed 5966 times
I needed to convert the ever-loving shit out of the thing (Gerber -> PDF -> Inkscape SVG -> png -> Inkscape SVG -> Freecad -> STL -> OpenEMS) to get it to import in OpenEMS, and I think some error creeped in the scaling, as seen in the results:
![ant-mpifa-res.png](./download/file.php?id=11934&sid=98eff5d9fbad400920d0c8f9cab87075)
- ant-mpifa-res.png (139.42 KiB) Viewed 5966 times
Of major interest is the large S11 graph on the right. As described
here, the S11 ratio is the amount of signal *NOT* radiated by the antenna. If this is very low at your target frequency, you have a good antenna. In this case, there's a really nice low -20dB minimum around 2.7GHz. This should be at 2.4GHz obviously, but as I said it's likely the antenna got scaled down somewhere along the line, increasing its frequency.
Now your antenna design. As your specs aren't much more than 'meander a line for about 12CM', that is what I did. I took a fairly random trace width, trying to keep your drawing in mind but also the size it occupies on a module. For the substrate, I use the same 0.8mm FR4 as I did for the mPIFA.
![ant-sven.png](./download/file.php?id=11935&sid=98eff5d9fbad400920d0c8f9cab87075)
- ant-sven.png (204.96 KiB) Viewed 5966 times
And here's the result:
![ant-sven-res.png](./download/file.php?id=11936&sid=98eff5d9fbad400920d0c8f9cab87075)
- ant-sven-res.png (77.43 KiB) Viewed 5966 times
Note the antenna does actually work: there's a minimum nicely around 2.4GHz in the S11-graph. Unfortunately, this is only at -5dB, meaning that for WiFi, this antenna will emit about 32x less energy than the mPIFA we use right now (ignoring the scaling error in the previous simulation, in other words assuming the actual minimum is at 2.4GHz).
All in all, it looks like the 'meandered whip' you made is actually functional, but it has a very low Q-factor; it trades a high gain for a high bandwidth. Unfortunately, that is not very efficient for WiFi which uses a narrow range around 2.4GHz and doesn't need the rest of the band where this thing works well. If this were for e.g. an UWB signal, it would be the other way around: the mPIFA would not be ideal as it has a narrow bandwitdh and your meandered whip would work a lot better. (But also note that UWB modules tend not to use either of these designs: they likely use something that given the bandwidth they do need has the highest gain possible.)
I'll include the OpenEMS scripts I used/wrote for this as an attachment as well; I'm done playing with this but if you think I did something wrong or you want to mess around to get a better result, feel free to use those as a starting point.