Help on Coil Antenna Design

Help on multiturn loop antenna

Hi all, I need some help on a coil antenna design. I have been tasked to design a small low frequency (24Hz) beacon. The design of the electronics is very simple. I am using a square wave generator that drives a low side MOSFET switch, which in turn used to drive the antenna. The MOSFET driver ON time is 0.025s and OFF time is 0.018s. If I understand correctly the coil antenna can be represented as an inductor connected to my MOSFET switch (please correct me if I am wrong). I am using the following equation to compute the peak current: VL = L di/dt, then L = VL dt/Ipeak. Ipeak current has to be around 0.1A and I am driving the coil with 12V square pulse. So, if I am using the correct equation L = 12V 0.025 / 0.1 = 3H. Next I need to determine all the parameters for the antenna. I have found the following web page which describes a very similar design: www.cnktechlabs.com/index_files/CoilAntennaDesign.htm. According to the article presented on the site an antenna radiation depends of the area and the number of turns. I need on how can I determine the number of turn to maximize the radiation efficiency of my antenna and at the same time to keep the peak current under 100mA (to conserve battery life). Can I trust those equations presented on the webpage? They use the following equation to compute the number of turns:
N = \[\sqrt{\frac{L*10^8*Length}{0.4*\pi*Area*\mu} }\]. Is that equation correct?

24 Hz? Are you sure about that?

Thank you for your reply, yes it is a very low frequency beacon 24Hz

The radiated power of a small magnetical "antenna" at 24 Hz into free space (= far field) will be effectively zero. I guess, you are rather interested in the magnetical near field. It's proportional to Ampere-turns multiply coil area.

What will be the distance of the near field from my antenna. Anothe question I have what equation do I use to calculate the number of turns?
Thanks a lot

There are various empirical formulas in use and calculators on the internet for different coil geometries. Usually they give a good estimation, e.g. https://www.qsl.net/in3otd/programs.html

Range of your low frequency beacon will be ruled by transmitter field sterngth, receiver sensitivity and electrical interferences in the enviroment.

I doubt that the current through the air coil at 24 Hz will be primarly set by the air coil inductance. The wire resistance is probably the limiting factor. A core (ferrite rod or laminated steel bar) can improve the efficiency respectively achieved field strength with a specific input power budget.

If I understand right, using a magnetic core will allow me to get my inductance value (the required L value) with a reasonable number of turns. At the same time reducing the number of turns will lower antenna efficiency. I guess my goal is first to select an appropriate core (area, length, permeability), then compute the number of turns it will require to achieve the inductance value. After that I need to select a wire gauge and verify the total resistance of the wire length. If the wire resistance will become the limiting factor of the peak current would it affect my antenna radiation power, as oppose to inductance being the limiting factor of the max current?
Thank you for your help and for the link you have provided.