Calculate number of coil turns for a given inductance?

Discussion in 'Radio Circuits, Repair & Performance' started by KF5YDR, Jul 11, 2018.

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  1. KF5YDR

    KF5YDR Ham Member QRZ Page

    There are a bunch of online calculators that will give you the inductance for a given coil, but I need to design a coil for a given inductance.
    I’m wanting to build an air-core coil antenna for HF reception only, essentially a continuously-loaded electrically short monopole. I’m using length of two feet, diameter of 1 inch, and estimated capacitance of 12 pF to make things easy (I’d have to dig through Evernote to find the site that gives 6pF/ft as a reasonable estimate for reactance of electrically-short monopoles). An online calculator for loaded monopoles gives me an inductance of 424uH for a 2ft monopole at 3.9MHz. I’m not sure if it’s reasonable to assume for the sake of that calculation that a continuously-loaded antenna will behave like an electrically-short monopole of similar height, so I’m not considering the inductance to be a known variable.

    Is there an online calculator for such a thing, or at least a formula? The variables I have are:
    - resonant frequency
    - length of coil
    - diameter of coil
    - diameter of wire
    - spacing/pitch (insulated wire makes this easy :p)

    I don’t think I need super precision—this is going to be a strictly receive-only antenna, and all it has to do is out-perform a 9ft whip!
  2. KD8DEY

    KD8DEY Ham Member QRZ Page

    Professor Coyle....(Also available as a downloadable spreadsheet)
  3. WB2WIK

    WB2WIK Premium Subscriber QRZ Page

    Interesting, but why would a two foot long monopole outperform a nine foot long one?:)

    You can make it perfectly resonant at any frequency you choose, but it will be very narrowband and may be better to tune out most of the reactance of the 9' whip and do the same thing with a broader curve and better performance.
    KF5YDR likes this.
  4. G3YRO

    G3YRO Ham Member QRZ Page

    What exactly are you trying to achieve here?

    If it's a small receiving antenna, then you'd be much better making a small loop. You then have the added advantage that it's balance (so low noise) . . . and directional (so you can null out the noise).

    I recently made one for 160m, and it works fantastically well . . . a square loop on a 6ft cross, with 4 turns on the tuned part, resonated using varicap diodes (as its up in my loft). You could scale that down, and just make it 3ft across for 80m.

    Roger G3YRO
    KF5YDR likes this.
  5. SM0AOM

    SM0AOM Ham Member QRZ Page

    What you are trying to do is calculate a "normal mode helix", which is a 1/4-wave self-resonant
    coil with a physical length of a few percent of the wavelength at the design center frequency.

    This is a notoriously difficult electromagnetic problem, and most "ordinary"
    coil design software provide quite incorrect results.

    However, some quite recent research aimed
    at Tesla coils and high-voltage problem has provided more useful approximations. One such calculator can be found at, and if reasonable values are "plugged into" the software, it can be calculated that
    a space-wound coil of 25 mm diameter , 700 turns of 1 mm diameter wire and a length of 900 mm becomes self-resonant at 3.79 MHz.

    You should however be advised that such an helix would have an intrinsic Q in the order of 1500, which makes it extremely narrow-band
    and also extremely sensitive to its surroundings and of the dielectric properties of any insulating materials.

    KF5YDR likes this.
  6. KF5YDR

    KF5YDR Ham Member QRZ Page

    Thanks for the helpful responses, everyone. This antenna would be for receiving indoors with a military-surplus manpack radio (a PRC-2200, in case anyone is interested), so it sounds like a loop is probably a better option.

    That’s a good point. Obviously I have demonstrated that I’m not the most knowledgeable when it comes to antenna design. :p

    The advantage of the 2-foot antenna over the 9-foot antenna is not electrical: sometimes I’m in places where a 9ft antenna won’t fit!
  7. KB4QAA

    KB4QAA XML Subscriber QRZ Page

    Experienced Short Wave Listeners know that for receiving only, you don't need a resonant antenna. Simply having a sufficiently long piece of wire is generally adequate. Something like 25-50 feet of wire is usually adequate.

    Arrange it in whatever way is convenient. Best performance would be to lead it out the window and to a tree or roof peak, but draping it around the room will work. Thumb tack it to the ceiling. Winding it in a loose coil around a cardboard box will work better than some tight tubular coil, IMO. I believe your performance results for your antenna design will be disappointing, especially for the effort required.

    There are dozens of websites with ideas for very good performing and cheap loop antennas for shortwave and AM broadcast (which can be modified for shortwave).

    Shortwave milk crate antenna

    AM Shortwave Tuned Loop
  8. AA7QQ

    AA7QQ Ham Member QRZ Page

    MFj has a preselector amplifer unit 1020c. You can use it fine with the telescoping antenna, or the jack on the back for other antennas. Works great for my SDRs. It also helps wipe out the urban noise of Las Vegas.


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