One turn loop coil
The inductance in the form of an isosceles triangle loop is calculated by the formula:
where:
- L - inductance [H];
- a, b - the sides of the triangle [m];
- r - radius of the wire (d/2) [m];
- μ0 = 4π·10-7 permeability of free space;
- μ - relative magnetic permeability of the conductor;
The inductance in the form of a rectangle loop is calculated by the formula:
where:
- L - inductance [H];
- a, b - the sides of the rectangle [m];
- r - radius of the wire (d/2) [m];
- μ0 = 4π·10-7 permeability of free space;
- μ - relative magnetic permeability of the conductor;
The inductance in the form of a round loop is calculated by the formula:
where:
- L - inductance [H];
- D - diameter of the loop [m];
- d - diameter of the wire [m];
- μ0 = 4π·10-7 permeability of free space;
- μ - relative magnetic permeability of the conductor;
You can often find the last formula in which the last member of the equation is 1.75 instead 2. That variant uses Coil32. In this case, the inductance of the round loop is calculated at low frequency. If the last term is 2, then the inductance is calculated at a high frequency. The low frequency means that the condition is met when the skin depth is greater than the wire radius. At the high frequency, the skin depth is much less than the wire radius.
References:
- Inductance Calculations: Working Formulas and Tables: © F W Grover, 1946, 1962, 2004;
- On the self-inductance of circles: E. B. Rosa, L. Cohen, Bureau of Standards, 1908;
I am not an important person, just one of many who benefit from using COIL64. I know you would want to know about any errors.
https://coil32.net/one-turn-loop-coil.html
This is an old web page article published in 2019, but it has an error. In the last paragraph, "If the last term is 2, then the inductance is calculated at a low frequency."
This is backwards from the usage reported by Grover and Rosa. The original derivation for a loop with circular conductor cross section was done by Kirchhoff. Where frequency is low, and there is no skin effect, the constant is 7/4. With high frequency the current is restricted in a smaller cross-sectional area, so there is less inductance. For the high frequency case, the constant to subtract is 2.
I appreciate your work, and hope you remain well in these crazy times.
Bill Triplett
Thank you very much for your comment. The error has been corrected.