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calculate number of turns and length for inductor

Discussion in 'Electronics Homework Help' started by ag273n, Nov 25, 2016.

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  1. ag273n


    Nov 24, 2016
    Most circuits has an inductor, and it becomes very hard to create a real working circuit from online circuit diagrams if all the diagram has is the inductance value of the inductor without specific instructions(how many turns, the wire size, length of inductor, the diameter)

    if i have the inductance value (example: 2.2 nH), how do I get the below:
    1. Diameter of core
    2. length of core
    3. number of turns
    4. wire size/ gauge

    I did some reading about this and stumbled on multiple's formula's which derived different values... This concerns me, if we have to use microHenrys and nanohenrys in realworld circuits, then i guess we have to be as accurate and as precise as possible, and finding a variety of formula's with distinct results are confusing..

    On Wheeler's 1925 Long Coil Formula,

    L = ((r^2) X (N^2))/ ((9 X r)+(10 X l))
    L = inductance (unknown yet)
    r = Radius
    N = number of turns
    l = length

    If I use the values below for the above formula
    r = 1.5 cm or 0.59055 inch
    N = 30
    l = 3 cm or 1.18110 inch

    So L= 18.3275 mH

    I understand the above formula is only applicable to a Single layer coil with Air Core - this part doesnt bother me...
    I've come across another formula:

    L=(u X A X (N^2))/ l
    u = Magnetic permeability of core material/medium
    A = Area of Cylinder/Core
    A = pi x (r^2)
    *r = radius
    N = number of turns
    l = length of Core/Cylinder

    so, the formula can be derived:
    L= (u X pi X (r^2) x (N^2)) / l

    using the same values as the first calculation to compare:

    r = 1.5 cm
    N = 30
    l = 3 cm
    u = air core magnetic permeability = 1.256 637 53 X10^-6

    so L = 26.6479 mH

    What confuses me more is how there's a variance between the two formula's...
    Did I calculate these two correctly?
    which one is more accurate?
    I think by changing the number of turns and length and Diameter of Core, we can hit the desired inductance value - is this correct?...

    I'm not enrolled in any school for electronics, I'm self studying...
  2. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

    Jan 21, 2010
    You will note that one is for long coils. This is generally where the length significantly exceeds the diameter.

    I recommend you use the formula that most closely matches the inductor dimensions then measure and trim as required if the absolute value is critical.
  3. Colin Mitchell

    Colin Mitchell

    Aug 31, 2014
    You won't get 26mH out of 30 turns.

    You have to have some idea of what you are doing before you can launch into designing your own inductors.

    It will take about 10 years of circuit designing to get to the stage of starting to design your own inductors.
  4. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

    Jan 21, 2010
    Colin, you are full of bovine excrement.

    I will agree that there is an error in ag's calculation. In the first case, the result is in uH and he mis-stated it as mH. I'm not sure what the error was in the second calculation, but it probably also included a misinterpreted prefix. Perhaps he should confirm his calculations using an on-line calculator?

    I get 18.3uH using the calculators here, here, and here.

    A much more complex calculator here takes into account wire diameter, coating and frequency and yields a slightly different answer (but I made some assumptions).

    There are a gazzilion calculators on the net and many illustrate the formula used.
    chopnhack likes this.
  5. hevans1944

    hevans1944 Hop - AC8NS

    Jun 21, 2012
    It helps to obtain some practical experience measuring the inductance of manufactured inductors to obtain a "gut" feeling for inductance versus size of component, versus core material (if any), versus number of turns of wire. An inexpensive LCR meter will be an invaluable tool.

    Back in the day, a mica capacitor of known value was paralleled with an unknown inductor and the resonant frequency measured with a variable frequency oscillator and a voltmeter. From the known resonant frequency and the known capacitor value the unknown inductance can be calculated. For small inductances in the nanohenry to microhenry range, RF must be used and the capacitor value is in the picofarads range. For this, the grid-dip meter was used to find the resonant frequency. Hams often used grid-dip meters to "prune" (cut to length) commericial air-core coils a few inches in diameter and a few inches long to "load" vertical whip antennas and "tune" parallel-resonant frequency traps in multi-band dipole antennas. They had an idea of what inductance was required for their application, based on available capacitors and the desired operating frequency, and could usually guess after some experimentation, the size of suitable inductors. The actual value of the inductance was not generally of great importance as long as it was "in the ballpark" and the circuit could be tuned to work.

    The important thing is that you obtain some practical experience with actual inductors before deciding whether you want to "wind your own" inductor.
    chopnhack and bushtech like this.
  6. ag273n


    Nov 24, 2016
    thanks a lot for your replies. these matter to me. I'm too new to have enough experience and that "gut feeling". I currently dont have any equipment i can use to physically measure this... Hevans1944, i will look around for any LCR meter i can get

    Steve is right, my calculations were off, I read further about it and eventually made myself an excel version of those online calculators - its still in refinement for all the other formula's i want to add. I see most articles about Wheeler's formula states specifically that the formula can only be more accurate as long as the length divided by the diameter doesnt result to 0.5 - regardles of the units used.
    this one is all clear to me now :)
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