# Single circular loop inductor

Inductance realized in the form of a single circular loop, in other words in the form of a single turn, most often used in the UHF band. Due to the lack of proximity effect, has a fairly high Q-factor, depending on wire diameter and a small self-capacitance. Also such inductors we can see as magnetic detectors.

**The single-turn loop** can be calculated by numerical methods using **J.C. Maxwell** equation:

is the complete elliptic integral of the first kind**E(k)**is the complete elliptic integral of the second kind**K(k)**is the radius of the loop (m)**r = D/2**is the radius of the wire cross-section, half of the wire diameter (m)**a = d/2**

and the parameter * k* is calculated as follows:

However, in the Coil32 calculation of the loop inductance is carried by a simple empirical formula, which was first brought by **F. W. Grover** in 1946. In this case, there is no sense to apply more complicated algorithm of calculation, because the accuracy is quite sufficient for practical purposes, when * D/d > 5* to about

*1%*. The numerical algorithm of the program is based on the method of successive approximations to reach a required inductance. The maximum possible diameter of the loop is taken as 10 m. If the calculation is obtained by a larger diameter value, the program displays the message: "Coil cannot be realized". In this case, you must choose another form of coils, for example, singlelayer.

One loop inductance formula:

- inductance (µH)**L**- diameter of loop (mm)**D**- diameter of the wire (mm)**d**

The diameter of the loop is from center to center of the wire as on a figure above.