I've written an Open Office (3.1.0) spreadsheet that is aimed at hobbyists who want to calculate the low frequency inductance of various common configurations of wire. You can get the spreadsheet and an explanatory document. Since the file will likely evolve over time, I haven't uploaded it to AAC so that I only have to maintain it in one place. Remember, I'm an electrical hobbyist, so go easy on the EE bashing in case I've messed up technically.
Air Coil Inductance Calculation Formula
If you do find errors or places where things could be improved, please send me email and I'll fix the tools. Warning: messing with inductance calculations can be hazardous to your free time. You'll soon be knee-deep in elliptic functions, Kelvin functions, power series, etc. And saying to yourself, 'Oh, just one more function.' I finally caught myself and realized all I wanted was something that would give me a 10% or so estimate of the inductance, as I'm not designing inductance standards. Thus, a spreadsheet with simple formulas is an entirely adequate tool.
Since I don't use MS Office, writing it in Open Office was my only choice. I perfectly understand not wanting to download a huge amount of stuff just to use one program. SgtWookie, I'd be interested in knowing whether these add-ons allow people to use the spreadsheet in Excel. It's likely some things won't come through. For example, I put the equations used next to every inductance calculation and OO's equation language feels similar to TeX/LaTeX, but MS Office had the most gawd-awful implementation for equations.
I'd be surprised if MS wrote the code to convert things. More importantly, the BASIC macro environments of MS Office and Open Office are different (at least they were a decade ago). Since I haven't used MS Office in about a decade, I won't state absolutely that OO's macros will work in MS Office, but, again, I'd be quite surprised if they do. I fiddled a bit more with the spreadsheet today and just uploaded a third version. It now includes the ability to calculate the resistance of a chunk of wire at different temperatures. It performs the calculations for:.
Single layer air-core solenoid. Multiple layer air-core solenoid. Straight round wire. Loop of round wire. Rectangle of round wire. Regular polygons (sides 3, 4, 5, 6, 8).
General planar loop of round wire. Planar spiral. Two parallel wires. Wire parallel to ground plane. Parallel rectangular traces. Wide trace over ground plane.
Coplanar traces. Isosceles triangle loop of round wire. Coaxial cable. Toroidal inductor If you find errors or omissions, please let me know via the email in the documentation and I'll get things fixed.
Grover's book is definitely something you should have if you're interested in making inductance calculations. By the way, you can buy a Dover reprint of the book from Amazon for $10. There's an errata; also make sure to take a look around that website from David Knight, as there's lots of material on inductance calculations and some useful papers, such as Nakaoka's 1909 paper (a formulation still used today) and a useful compendium by Rosa and Grover from the mid 1940's; both are in PDF form.
Grover was interesting - he was born 3 years before Maxwell died and lived to be almost 100 years old. One of the problems with Grover's book, however, is it was written in 1946 before the times of cheap computation. Much of the book is focused on practical work that avoids lots of calculation; this is done by giving shortened formulas with table look-ups.
It made eminent sense 60 years ago, but not today. In a few cases, people have derived empirical formulas for some of the tables; otherwise, one would need to go back to the original literature, which is not easy for someone without access to a big research library. For those who don't have OpenOffice and don't want to install it on their computer.
Have a look here: All you need is a USB flash 'stick' memory and a PC that will access it. You can get a 4GB USB flash stick for around $10 nowadays.
Make a directory on your USB stick called PortableApps. Download the Portable Apps suite to your memory stick, and run it to expand the suite. Suite: Choose just the Portable Apps Platform only, or the Suite Light (2mb and 50mb respectively) Then go here: Scroll down to Office, and download OpenOffice portable (33mB) Install that to your USB stick. Drag and drop the OpenOfficePortable directory into the PortableApps PortableApps directory. To launch the apps menu, click on PortableApps StartPortableApps.exe This is a really cool tool, you can get some really handy applications, and it's all free.
Formulas for the Calculation of Common Inductances.) (unless otherwise noted use SI-units in all presented formulas).) Planar geometries which are not very common in pulsed power systems are not covered in this table. Readers are refered to references 1, 6 and especially 8.
More information on rectangular loops can be found here: Of course no guarantee is given for the accuracy of the listed formulaes or the calculators although I tried my best to select the formulas carefully from the literature. Please let me know when you find any mistakes.
Low frequency inductance formula example long, thin wire (as segment of closed circuit) (reference 1) r = mm l = cm nH conductor from parallel wires (currents in same direction) r 0.8 R) N: number of turns (reference 1) R = mm l = cm N = μH single layer very long (ideal) solenoid ( l 2R ) N: number of turns (reference 3) R = mm l = cm N = μH multi layer solenoid N: number of turns and are computed automatically correction factor dL for insulation thickness. D: distance between wire centers d: diameter of bare wire (reference 9) R = mm l = cm w = mm N = μH R = mm N = D = mm d = mm μH multi layer thin wall solenoid N: number of turns (reference 4) N = 1000 d = 10 mm l = 5 cm m r = 1 L = 1.645 mH toroid N: number of turns (reference 4) N = R = mm D = cm m r = μH spiral (flat coil) N: number of turns (Wheeler formula) (reference 1) N = 20 R = 5 cm w = 2 cm L = 63.501 μH windings cover entire area (Schieber formula) (reference 1) N = 20 R = 5 cm L = 1.380 nH Both formulas can also be used for printed flat coils.
For the Wheeler formulas errors up to 20% have been reported. A more accurate calculation takes the ratio between coil radius, R, and winding-thickness, w, into account (Grover method). See reference 1 for details.
Conical coils.