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I'm reading the instructions on preparing the ferrite rod antenna. If I understand it correctly it is matter of building an LC circuit.

My question is: Can the ferrite rod antenna be built using a small vertical choke instead of winding coil around the ferrite rod manually? Or the size matter in this case?

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    $\begingroup$ Maybe, but it depends on the LC circuit in question. Maybe show a schematic and tell us what target frequencies and bandwidth you are going for? Remember that the qualities of the ferrite matter. $\endgroup$
    – user21417
    Mar 15 at 18:21

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A ferrite rod antenna is a small loop antenna, just with more than one turn (usually lots more), and wrapped around something with a relative permeability of greater than one (usually much greater). The Q, radiation resistance, sensitivity, and inductance increase with increasing permeability (linear or square). So an air core inductor would need a larger diameter, and/or more turns, and/or lower resistance windings to approach similar antenna performance.

Here's an example of how to make one: https://www.instructables.com/Spider-Web-Coil/ for a crystal radio.

As for whether to mount your loop antenna or coil vertically or horizontally, that depends on the polarization of the signals you wish to receive.

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A ferrite rod antenna isn't just an inductor. It's designed to have the magnetic field component of an electromagnetic wave (the transmitted signal) to pass through many turns of wire. Each turn multiplies the signal. Because current handling isn't a concern the wire can be very fine, and the smaller the diameter of the wire the less copper is needed for a given number of turns.

Most ferrites used for chokes are donut-shaped (like a torus) rather than rod-shaped. This is useful for inductors because more of the lines of flux can pass through the ferrite rather than air, which means that the inductor radiates less of a magnetic field. By the reciprocity principle, if it transmits less of a field, it also receives less of a field. So a choke based on a donut-shaped ferrite core would be a bad choice.

A choke based on a rod-shaped ferrite might work, but the designers of chokes are concerned about current-handling capability, so the wire is thicker than the wire of a ferrite rod antenna, with less turns, perhaps a few dozen turns rather than hundreds or thousands of turns. Such a choke might work as a ferrite rod antenna, but probably not as well as a purpose-built ferrite rod antenna.

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One more nugget of information for you:

The effective permeability $\mu_{r_\text{effective}}$ of the ferrite rod is strongly related to its length to diameter ratio, as well as the $\mu_r$ of the material. Short fat ferrite rods have very low effective permeability. This applies for both antennas and inductors.

In the case of an inductor, there is a another problem - core saturation. For example in the case of a high current inductor, it may be useful to add a small slug of ferrite, 2:1 ratio, and gain a few times inductance increase from this. A longer ferrite wouldn't be useful, keeping everything else constant, because it would simply saturate.

For antennas the field strengths and currents are small, so there is real benefit to having a longer ferrite rod. You can be sure the ~20:1 ratio seen in a small transistor ratio is a reasonable use of the expensive ferrite material (limited by the size of the case, and possible risk of breaking a longer thinner rod).

A search for "Effective permeability of a ferrite rod length diameter" yields many useful results, including this paper from NIWC, May 2020 and this calculator from Fair-Rite. The NIWC document includes this graph:
enter image description here

You can see that for high permeability materials (say 100 for a medium wave ferrite?) there is real benefit in making the rod 20 times its diameter. Of course making it fatter also increases the inductance, so there is an optimum ratio for a given mass of ferrite.

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