NFC: Calculating the coupling coefficient using a specific formula

Thread Starter


Joined Jan 15, 2017
The past three days I've been busy with finding out how a specific formula works. Right now, I am really down to my luck. The formula in question is the one in the attachments.
The reason that I wanted to use this specific formula is because it lets me calculate the coupling coefficient using theoretical input (such as the distance). The problem I am constantly facing is that the output value isn't between 0 and 1 (as it should be).

Right now I am using the following values for mu formula:

0.999994 * (10 ** 2 / (2 * ((((10 ** 2) + (20 ** 2)) ** (3 / 2))))) * (2778.5 / sqrt(3 * 3)) = 4.141 (no between 0 or 1, as it should be)

Clearly I am doing something wrong, but right now I already spent a lot of time on it that I cannot spot the error anymore. I am not asking for a complete solution for my problem, a push towards the right direction would already be such a great help. More information on this formula can be found at:
  1. (page 11)
  2. (page 12)


Thread Starter


Joined Jan 15, 2017

You have taken μr in stead of μ0.

Thank you for your reaction. I already tried that by calculation μ0 = 4π * 10 ** −7; somebody told be that I should use the value of μr to try to get the formula to work. Apparently, that was not the solution. When I change my formula to this:
(4 * π * 10 ** (−7)) * (10 ** 2 / (2 * ((((10 ** 2) + (20 ** 2)) ** (3 / 2))))) * (2778.5 / sqrt(3 * 3)) = 0.00000520492 (which is also not within the range to 1).

I also played around with the input values to get a value which is close to 1, but up until now I only get values with 6 zeroes behind the comma.


Joined Jun 17, 2014

Are you working in the right units?
Many formulas are written with distance units of meters or centimeters, but that may or may not help and you should check the other units too like for the inductances which are sometimes given in micorhenries instead of Henries.
Just a thought.

It is rather strange for them to state the relative permeability as u0 too when that is usually quoted as ur and u0 is reserved for the magnetic space constant. Most authors know that u0 usually means the latter so they would not use it for the relative permeability. It's not a super strict convention, but it is more the norm.


Joined Mar 24, 2008
You really should start you own thread instead a the TS thread starter may never see your post, this one time only I have approved your post but future necroposts will simply be deleted.