# How to compute the required length and turns for an air-cored antenna

I'm experimenting with RF reception in the 433MHz band and have made the most simple "whip" monopole antenna with 17.6 centimeters of wire.

Out of curiosity, I tried various designs for the antenna among which the one described in the step by step instructions created by Ben Schueler in 2013 and republished a large number of times since then, such as here

This design also works quite well for my application and using online calculators such as this one and this one, I can compute the inductor value.
But why is 0.220µH right?
And what about the size of the two straight parts? They are given as 17 and 53 millimeters but how does one gets these values?

I'm asking because I would like to replicate this design, but tuned for 868MHz reception.

Would you have the link to a reference document so that I can compute the values for 868MHz myself? Or should I just go ahead and divide every value by two as 868 is roughly 433 multiplied by two?

Thanks for any pointers.

• Hello and welcome to ham.stackexchange.com! Commented Mar 24, 2021 at 15:26
• What is your actual goal? Why not just use a simple 8 cm monopole? Your linked site implies the loaded antenna works better, which may be true in his case but is not true in general. Commented Mar 24, 2021 at 17:07
• Well, one of the goal would be to use smaller antennas that less prone to being bent, especially with the 433MHz one. But it's also a matter of curiosity. Commented Mar 24, 2021 at 17:11

## 1 Answer

A quick simulation with NEC2 indicates that scaling the wire lengths and the inductance by a factor of 0.5 will give the results you seek.

As for why a smaller, loaded monopole gives better results than a full-sized monopole, that is a mystery.

• I did not know about NEC2, it's a very interesting software! I'll experiment with it, it's much easier to compare antennas this way. Commented Mar 24, 2021 at 17:09
• Antenna modeling software will take you into a new world of experimentation. Good luck! Commented Mar 25, 2021 at 4:22
• Thanks. I'm struggling a bit with the loaded monopole design. Would you care to share the model that you have been using? Commented Mar 26, 2021 at 8:33
• @OBones Modeling indicates that, to achieve resonance, the antenna must be operated against an RF ground which is large compared to the antenna. Since we don't have the details of that part of the system, modeling can only provide qualitative guidance, not quantitative information. Commented Mar 26, 2021 at 12:05