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I need to know one thing about making a small loop antenna using the LC and coil inductance formula.

The solenoid inductance formula is:

Inductance formula

Where, l is the length of the coil and N is the number of turns. So, does that mean that the turns of a loop can't be overlapped?

If I need to use 20 meter long wire to wrap around a square plastic frame of 20 cm each side with a width of 2 cm, and if the wire is 1 mm thick and doesn't fit after a few turns then can I wrap the wire over the previous turns?

I need one more clarification:

A perfect resonant antenna is the one that has 1/4 of the wavelength. So, if I need to receive the 850 kHz using a loop antenna, then as per the formula, I will need a (300/0.85 = 356/4 = 88 meter) long wire.

Instead of using it as a long wire antenna, if I wrap it around a plastic square frame of any size, then will it work as a loop antenna?

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    $\begingroup$ Please state your actual goal here so we can help... this is a bit of a rambling question with various misconceptions, some stated as fact, some with a question mark at the end. Is this an antenna theory question about small loops, or are you trying to build an antenna to improve your MW reception at 850 kHz? What's wrong with the current signal quality? Is this on a small portable radio, or one with an antenna connector? Have you tried walking outside? What type of connector? How much room do you have for the antenna? Thanks! $\endgroup$
    – tomnexus
    Commented Sep 23 at 17:23
  • $\begingroup$ No I need to improve the reception of overall MW bands. That's why I need to build a broadband loop antenna using a variable capacitor. $\endgroup$
    – user29605
    Commented Sep 25 at 12:01

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If I need to use 20 meter long wire to wrap around a square plastic frame of 20 cm each side with a width of 2 cm, and if the wire is 1 mm thick and doesn't fit after a few turns then can I wrap the wire over the previous turns?

Yes, that's normally done for this kind of loop (what else are you going to do?). It means that the inductance will be lower than what you get from the solenoid formula, but that's life. Since it's difficult to model exactly what you would get from hand-winding in this fashion, you would probably want to measure rather than model.

A perfect resonant antenna is the one that has 1/4 of the wavelength. So, if I need to receive the 850 kHz using a loop antenna, then as per the formula, I will need a (300/0.85 = 356/4 = 88 meter) long wire.

No, this is completely irrelevant. 1/4 wavelength is the resonant length for a monopole. 1/2 wavelength is resonant for a dipole. 1 wavelength is resonant for a large loop. You don't have any of those, you have a small multi-turn loop. A small loop is never "resonant by construction". If you want it to be resonant, you do so with a tuning capacitor that cancels out the inductance of the loop.

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  • $\begingroup$ I'd agree that a single-turn "small loop" is not resonant by construction. If you wind with multiple turns, it is possible to have enough inter-turn capacitance to hit its self-resonant frequency. Some multi-turn loops try to spread out turns to minimize inter-turn capacitance so as to allow more turns before reaching self-resonance. So many turns might require a lot of copper, resulting in lowish-Q resonance due to too-thin wire. With only self-capacitance, it is a single-frequency antenna. $\endgroup$
    – glen_geek
    Commented Sep 24 at 2:11
  • $\begingroup$ So, what's going to be the length of the wire for a small loop? How do I calculate the length of the wire for 850 kHz? $\endgroup$
    – user29605
    Commented Sep 25 at 12:04

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