I have tried various online calculators and get inconsistent results. Maybe because the values are too high. Could someone please tell me the correct way determine how many turns are required on a coil with the following specs to obtain a resonant frequency of 8 (eight) Hz? 30 awg enamel coated copper wire Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm wide by 16mm deep rectangular PVC trunk conduit. From this I can calculate the length and weight of wire required. Kevin Foster
Calculate Resonant Frequency Large Loop Coil
Started by ●January 13, 2017
Reply by ●January 13, 20172017-01-13
Kevin Foster wrote...> > Could someone please tell me the correct way determine how > many turns are required on a coil with the following specs > to obtain a resonant frequency of 8 (eight) Hz?For coils that aren't too thick, you simply use Wheeler's equation, Here's a discussion I found in Google's files from 20 years ago. -------------------------------------------------------------------- From: Winfield Hill (hill@rowland.org) Subject: Re: multi-layer solenoid inductor design equations Newsgroups: sci.electronics.design Date: 1997/12/28 Jack Niewoehner, <ne1r@mwci.net> said...> > Could someone please post formulas relating to the design of multi-layer > air-core inductors? I am specifically looking for equations relating > impedance to length and diameter of coil, as well as # of turns and # > or layers. Thanks in advance for any help.There are several types of multilayer air-core inductors, but I assume you're referring to solenoidal inductors? As some will recall, I've written frequently about various aspects of different types of air-core inductors before here on sci.electronics.design, and thought this might be a good time to sum up one aspect of my studies: various inductance formulas for multi-layer solenoids. I'm sorry, if you learn more than you wanted to know! In that event, just use formula (1). Throughout this discussion, we'll use the same dimensional system, based on the drawing below. Here and in the 14 formulas below, N = turns, a = mean radius, b = length, and c = winding thickness, and all are in inches, unless otherwise stated. length |------ b --------| --- ,-----------------, c | cross section | ------------ a = winding mean radius --- '-----------------' a | __________________________ | axis D = 2a ,-----------------, | | cross section | -------- '------------\----' \ solenoid coil layout N turns * To start, there is a venerable equation, related by Wheeler in his 1928 paper and credited to Prof L.A. Hazeltine (note: Wheeler worked for Hazeltine Corporation in Hoboken, N.J.): (1) L = 0.8 a^2 N^2 / (6a + 9b + 10c) uH/inch, Wheeler said this equation is good to 1% when "the three terms in the denominator are about equal." In a few attempts to accurately determine multilayer solenoid winding parameters, I haven't found this equation accurate as claimed. For various practical coils, it often seems 5 to 15% or even more in error, so better formulas seem necessary. Also I've noticed that many authorities don't bother to repeat this equation. Note, when one says, the "Wheeler equation" this generally isn't the one referred to (see below). * There are very accurate inductance equations derived from the basic physics of current sheets, etc. These are complex infinite-series equations, and hard to use (especially if you need to solve for N). As a result, many forms of simplification have been developed. * In Grover's famous book "Inductance Calculations" (Van Nostrand 1946, reprinted Dover 1962), page 95, we find an exact formula for solenoids wound with square cross-sections, (2) L = 0.001 a N^2 Po uH/cm. Po is a function of c/2a and is given in a lengthy table, varying from 60 for very short coils to a maximum of 7. For small cross-sections he shows a hairy formula credited to Stefan in 1884. * Relevant to this is the Brooks coil, a square-cross-section solenoid that is an air-core-inductor champion: requiring minimum wire for a given inductance. The cross-section below shows the Brooks coil's easy-to-remember "four-squares" geometry: Two wire squares, spaced two squares apart. | ##### | ##### ##### | ##### ##### | ##### |-- a --| | coil axis The coil's mean diameter is 3.00 times its length and the winding height equals its length. Grover (pages 94 and 98) provides a simple, precise formula for the theoretical inductance. Rearranged, we have (3) L = 1.35234 mu_o a N^2 where mu_o is the permeability of free space = 4 pi 10^-7 H/m and a is the coil's mean radius. (4) L = k1 Do N^2 N = sqrt ( L / k1 Do) where Do is the outer diameter (twice the coil-form diameter), and k1 = 0.006373 uH/cm or 0.016187 uH/inch. * For non-square cross-sections, we can first consider _single-layer_ solenoid inductance calculations. An accurate and accepted solution is Nagaoka's equation (Grover p 143), (5) L = 0.002 pi^2 a (2a/b) N^2 K uH/cm where K is a factor which is a function of 2a/b, ranges from 0 to 1.00, and is determined from lookup tables and interpolation. For very short coils, a series like this can be used, K_x = (ln x - 1/2) + 2/x^2 (ln x + 1/8) - 4/x^4 (ln x -2/3) + ... where x = 8 a / b, and K = ( 2 b / pi d ) K_x. Although one of the more simple series formulas, this does give the flavor of calculations of K. Clearly most of the exact physics formulas are very painful to use. * In an actual coil design, tables or complex formulas are hard to use. Consider for example, the difficulty in calculating the number of turns, N, from either. To simplify our lives, Wheeler empirically derived his popular single-layer solenoid equation, using Nagaoka's equation and tables. Wheeler's equation is shown below in two different ways. a N^2 a^2 N^2 / 10 b (6) L = ---------- = -------------- uH / inch 9 + 10 b/a 1 + 0.9 a/b Wheeler says this equation is accurate to about 1% for long coils, or any coils with (b/a > 0.8). It's easy to solve this equation for N. A simple re-arrangement adds the concept of winding pitch. This can be very useful, because a low-winding-height multilayer coil can be treated as a single-layer coil with a higher winding pitch. a^2 p N 1 (7) L = -------- * ---------------- uH / inch 10 1 + 0.9 a p / N Here p is my turn-density pitch parameter, in turns/inch. Incidentally, this makes clear that for long coils, once you pick a coil-winding pitch, the inductance scales by N, rather than by N^2. Of course, the length scales as well. Now solving for N isn't as easy. I get, 10 b (8) N =~ ----- ( 1 + 9 a^3 p^2 / 100 L ) turns p a^2 Alan Fowler pointed out a version of Wheeler's equation, claimed more accurate, in F. Langford-Smith's "The Radiotron Designer's Handbook," 1942. In the 3rd edition only, the work of Esnault-Pelterie is detailed, a Frenchman who followed the "des savants japonais" (i.e. Nagaoaka) for his derivation of a simple Wheeler-like formula with a claimed accuracy of 0.1% for values of diameter/length between 0.2 and 1.5. Rearranging, a^2 N^2 / 9.972 b (9) L = -------------------- uH / inch 0.9949 + 0.9144 (a/b) But, excuse me for these digressions, back to multi-layer coils. * Grover has two formulas for multilayer coils, one for "thin coils" and another for thick (pancake) coils. (10) L = 0.05014 a (2a/b) N^2 K' uH/in. Here K' = K - k, or basically K (Nagaoka's constant) adjusted by a new k to account for the radial turns. k is a function of c/2a and c/b, and ranges from 0.00 fro very thin coils, to 0.82 for thick coils, as shown in Grover's lookup tables. For thick pancake coils, Grover has equation (2) above, but with a different P, ranging from 69.0 to 13.9 as a function of (c/2a). We're back to the accurate but painful tables. * Terman's "Radio Engineer's Handbook" has a simplified approach using a formula with a factor F, which is provided in a lookup table or plotted in a curve (p. 55). (11) L = N^2 (F d - 0.03193 a c / b) uH/in The factor d is the diagonal distance of the winding cross section, or d^2 = b^2 + c^2. Terman claims 0.5% accuracy and even includes an additional winding insulation-thickness correction formula (see p. 60). I think there may be ways we can avoid using the tables with Terman's formula: For long coils, say 2a/b < 0.3, we can use F = a/20 b, but for short coils F is less than this, approaching F = 0.09 for a length = 1% of the diameter. Wheeler's equation implies that F = 1 / (18 + 20 b/a) may be a tempting correction possibity that might work over Wheeler's valid range (where the length is at least 40% or more of the diameter). I haven't tested this idea. * I'll close with some interesting formulas from Welsby's fabulous book "The Theory and Design of Inductance Coils" 2nd ed (1960) MacDonald. I haven't come across these formulas in other publications, and he doesn't reference them, so they may be his own derivations. He does say Kn is the "equivalent of the Nagaoka constant" ... (12) L = 4 pi^2 (a^2 / b) N^2 Kn nH/cm For closely-wound single-layer solenoids (p. 42) he says, (13) Kn = 1 / ( 1 + 0.9 a/b - 0.02 (a/b)^2 ) and he also provides a hairy correction formula for spaced turns. For multi-layer solenoids he has a different formula, invoking the thickness c in the "Nagaoka constant" (p. 44). (14) Kn = 1 / ( 1 + 0.9 a/b + 0.32 c/a + 0.84 c/b ) I haven't tested these interesting Welsby's formulas, but they do look very useful if correct. OK, that's it gang, I'm going to bed! -- Winfield Hill hill@rowland.org _/_/_/ _/_/_/_/ The Rowland Institute for Science _/ _/ _/_/ _/ Cambridge, MA USA 02142-1297 _/_/_/_/ _/ _/ _/_/_/ _/ _/ _/ _/ _/ http://www.artofelectronics.net _/ _/ _/_/ _/_/_/_/ -- Thanks, - Win
Reply by ●January 13, 20172017-01-13
On Fri, 13 Jan 2017 18:27:54 +1100, Kevin Foster <kfoster@internode.com> wrote:>I have tried various online calculators and get inconsistent results. >Maybe because the values are too high. > >Could someone please tell me the correct way determine how many turns >are required on a coil with the following specs to obtain a resonant >frequency of 8 (eight) Hz? > >30 awg enamel coated copper wire > >Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >wide by 16mm deep rectangular PVC trunk conduit. > > From this I can calculate the length and weight of wire required. > >Kevin FosterI don't think you can make a coil like that that resonates at 8 Hz. Why do you want it to be resonant? What are you trying to do? -- John Larkin Highland Technology, Inc lunatic fringe electronics
Reply by ●January 13, 20172017-01-13
On 13/01/2017 07:27, Kevin Foster wrote:> I have tried various online calculators and get inconsistent results. > Maybe because the values are too high. > > Could someone please tell me the correct way determine how many turns > are required on a coil with the following specs to obtain a resonant > frequency of 8 (eight) Hz?In the ballpark of at least 1000x more turns than would be needed to make a coil that self resonates at a much more reasonable 8MHz.> 30 awg enamel coated copper wire > > Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm > wide by 16mm deep rectangular PVC trunk conduit. > > From this I can calculate the length and weight of wire required.Several truck loads at a rough guess. You would be a lot better off adding an external capacitor to it. Back of envelope mental arithmetic suggests for 8Hz : eg. 400uF & 1H 400nF & 1kH 400pF & 1MH * this might be around the self resonant regime (give or take an order of magnitude either way) I have a sense of deja vu about this thread. -- Regards, Martin Brown
Reply by ●January 13, 20172017-01-13
On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:>On 13/01/2017 07:27, Kevin Foster wrote: >> I have tried various online calculators and get inconsistent results. >> Maybe because the values are too high. >> >> Could someone please tell me the correct way determine how many turns >> are required on a coil with the following specs to obtain a resonant >> frequency of 8 (eight) Hz? > >In the ballpark of at least 1000x more turns than would be needed to >make a coil that self resonates at a much more reasonable 8MHz. > >> 30 awg enamel coated copper wire >> >> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >> wide by 16mm deep rectangular PVC trunk conduit. >> >> From this I can calculate the length and weight of wire required. > >Several truck loads at a rough guess. > >You would be a lot better off adding an external capacitor to it. >Back of envelope mental arithmetic suggests for 8Hz : > >eg. > >400uF & 1H >400nF & 1kH >400pF & 1MH * this might be around the self resonant regime >(give or take an order of magnitude either way)I suspect that the q would be so low that the resonance is undetectable.> >I have a sense of deja vu about this thread.Yup. -- John Larkin Highland Technology, Inc lunatic fringe electronics
Reply by ●January 13, 20172017-01-13
On 13.1.17 18:26, John Larkin wrote:> On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown > <|||newspam|||@nezumi.demon.co.uk> wrote: > >> On 13/01/2017 07:27, Kevin Foster wrote: >>> I have tried various online calculators and get inconsistent results. >>> Maybe because the values are too high. >>> >>> Could someone please tell me the correct way determine how many turns >>> are required on a coil with the following specs to obtain a resonant >>> frequency of 8 (eight) Hz? >> >> In the ballpark of at least 1000x more turns than would be needed to >> make a coil that self resonates at a much more reasonable 8MHz. >> >>> 30 awg enamel coated copper wire >>> >>> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >>> wide by 16mm deep rectangular PVC trunk conduit. >>> >>> From this I can calculate the length and weight of wire required. >> >> Several truck loads at a rough guess. >> >> You would be a lot better off adding an external capacitor to it. >> Back of envelope mental arithmetic suggests for 8Hz : >> >> eg. >> >> 400uF & 1H >> 400nF & 1kH >> 400pF & 1MH * this might be around the self resonant regime >> (give or take an order of magnitude either way) > > I suspect that the q would be so low that the resonance is > undetectable. > >> >> I have a sense of deja vu about this thread. > > Yup.You're all wasting your gunpowder to crows ... The OP is attempting to listen plants growing. -- -TV
Reply by ●January 13, 20172017-01-13
On Fri, 13 Jan 2017 18:37:36 +0200, Tauno Voipio <tauno.voipio@notused.fi.invalid> wrote:>On 13.1.17 18:26, John Larkin wrote: >> On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown >> <|||newspam|||@nezumi.demon.co.uk> wrote: >> >>> On 13/01/2017 07:27, Kevin Foster wrote: >>>> I have tried various online calculators and get inconsistent results. >>>> Maybe because the values are too high. >>>> >>>> Could someone please tell me the correct way determine how many turns >>>> are required on a coil with the following specs to obtain a resonant >>>> frequency of 8 (eight) Hz? >>> >>> In the ballpark of at least 1000x more turns than would be needed to >>> make a coil that self resonates at a much more reasonable 8MHz. >>> >>>> 30 awg enamel coated copper wire >>>> >>>> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >>>> wide by 16mm deep rectangular PVC trunk conduit. >>>> >>>> From this I can calculate the length and weight of wire required. >>> >>> Several truck loads at a rough guess. >>> >>> You would be a lot better off adding an external capacitor to it. >>> Back of envelope mental arithmetic suggests for 8Hz : >>> >>> eg. >>> >>> 400uF & 1H >>> 400nF & 1kH >>> 400pF & 1MH * this might be around the self resonant regime >>> (give or take an order of magnitude either way) >> >> I suspect that the q would be so low that the resonance is >> undetectable. >> >>> >>> I have a sense of deja vu about this thread. >> >> Yup. > > >You're all wasting your gunpowder to crows ... > >The OP is attempting to listen plants growing.Why not stick electrodes on them? That has a chance of detecting something. I'd expect the signal frequencies will be more like 12 uHz. Tree EKG. -- John Larkin Highland Technology, Inc lunatic fringe electronics
Reply by ●January 13, 20172017-01-13
On 1/13/2017 11:26 AM, John Larkin wrote:> On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown > <|||newspam|||@nezumi.demon.co.uk> wrote: >> On 13/01/2017 07:27, Kevin Foster wrote: >>> I have tried various online calculators and get inconsistent results. >>> Maybe because the values are too high. >>> >>> Could someone please tell me the correct way determine how many turns >>> are required on a coil with the following specs to obtain a resonant >>> frequency of 8 (eight) Hz? >> >> In the ballpark of at least 1000x more turns than would be needed to >> make a coil that self resonates at a much more reasonable 8MHz. >> >>> 30 awg enamel coated copper wire >>> >>> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >>> wide by 16mm deep rectangular PVC trunk conduit. >>> >>> From this I can calculate the length and weight of wire required. >> >> Several truck loads at a rough guess. >> >> You would be a lot better off adding an external capacitor to it. >> Back of envelope mental arithmetic suggests for 8Hz : >> >> eg. >> >> 400uF & 1H >> 400nF & 1kH >> 400pF & 1MH * this might be around the self resonant regime >> (give or take an order of magnitude either way) > > I suspect that the q would be so low that the resonance is > undetectable.He could use superconducting wire and soak it in liquid helium. Then it will be terrific. You won't believe how great it will be. I seen a picture of something like that hanging from a helicopter and got a good close look at the G10 dewar they put it in. http://library.seg.org/doi/abs/10.1190/1.2035912?journalCode=gpysa7 -- Grizzly H.
Reply by ●January 13, 20172017-01-13
"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message news:3o0i7c99sojfuukdn3aoq7druilg6qaq9m@4ax.com...> On Fri, 13 Jan 2017 18:37:36 +0200, Tauno Voipio > <tauno.voipio@notused.fi.invalid> wrote: > >>On 13.1.17 18:26, John Larkin wrote: >>> On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown >>> <|||newspam|||@nezumi.demon.co.uk> wrote: >>> >>>> On 13/01/2017 07:27, Kevin Foster wrote: >>>>> I have tried various online calculators and get inconsistent results. >>>>> Maybe because the values are too high. >>>>> >>>>> Could someone please tell me the correct way determine how many turns >>>>> are required on a coil with the following specs to obtain a resonant >>>>> frequency of 8 (eight) Hz? >>>> >>>> In the ballpark of at least 1000x more turns than would be needed to >>>> make a coil that self resonates at a much more reasonable 8MHz. >>>> >>>>> 30 awg enamel coated copper wire >>>>> >>>>> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >>>>> wide by 16mm deep rectangular PVC trunk conduit. >>>>> >>>>> From this I can calculate the length and weight of wire required. >>>> >>>> Several truck loads at a rough guess. >>>> >>>> You would be a lot better off adding an external capacitor to it. >>>> Back of envelope mental arithmetic suggests for 8Hz : >>>> >>>> eg. >>>> >>>> 400uF & 1H >>>> 400nF & 1kH >>>> 400pF & 1MH * this might be around the self resonant regime >>>> (give or take an order of magnitude either way) >>> >>> I suspect that the q would be so low that the resonance is >>> undetectable. >>> >>>> >>>> I have a sense of deja vu about this thread. >>> >>> Yup. >> >> >>You're all wasting your gunpowder to crows ... >> >>The OP is attempting to listen plants growing. > > Why not stick electrodes on them? That has a chance of detecting > something. I'd expect the signal frequencies will be more like 12 uHz. > > Tree EKG. > > > --Is this like measuring brain waves in democrats?
Reply by ●January 13, 20172017-01-13
On 01/13/2017 11:37 AM, Tauno Voipio wrote:> On 13.1.17 18:26, John Larkin wrote: >> On Fri, 13 Jan 2017 16:19:32 +0000, Martin Brown >> <|||newspam|||@nezumi.demon.co.uk> wrote: >> >>> On 13/01/2017 07:27, Kevin Foster wrote: >>>> I have tried various online calculators and get inconsistent results. >>>> Maybe because the values are too high. >>>> >>>> Could someone please tell me the correct way determine how many turns >>>> are required on a coil with the following specs to obtain a resonant >>>> frequency of 8 (eight) Hz? >>> >>> In the ballpark of at least 1000x more turns than would be needed to >>> make a coil that self resonates at a much more reasonable 8MHz. >>> >>>> 30 awg enamel coated copper wire >>>> >>>> Laid multi-row, multi-layer into a 1 metre diameter hoop made of 25mm >>>> wide by 16mm deep rectangular PVC trunk conduit. >>>> >>>> From this I can calculate the length and weight of wire required. >>> >>> Several truck loads at a rough guess. >>> >>> You would be a lot better off adding an external capacitor to it. >>> Back of envelope mental arithmetic suggests for 8Hz : >>> >>> eg. >>> >>> 400uF & 1H >>> 400nF & 1kH >>> 400pF & 1MH * this might be around the self resonant regime >>> (give or take an order of magnitude either way) >> >> I suspect that the q would be so low that the resonance is >> undetectable. >> >>> >>> I have a sense of deja vu about this thread. >> >> Yup. > > > You're all wasting your gunpowder to crows ... > > The OP is attempting to listen plants growing. >Maybe try strontium titanate insulation. ;) Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
