Optimal coupled array of three coils

Optimal coupled array of three coils

This script computes optimal array composed of air core coils in terms of minimal coupling between the array elements. The considered array is composed of three air-core, circular coils, with their centers set at edges of a triangle. At pitch values smaller than the diameter of the coil, there is a partial overlap between them. For such situation, vertical separation is set as one of the input parameters. The coil 1 is assumed to be on the top of the stack, coil 2, in the middle, and coil 3 at the bottom. The vertical separation between the coil 1 and 2 is identical to the vertical separation of coil 2 and 3.
The script accepts upper limits of number of turns per layer and number of layers, as well as the required self inductance of each element. The script returns the optimal number of turns per layer and number of layers, axes pitch separation, and resultant inductance.
The script is based on the paper:
N. Tal, Y. Morag, and Y. Levron, “Magnetic Induction Antenna Arrays for MIMO and Multiple-Frequency Communication Systems,” Progress In Electromagnetics Research C, vol. 75, pp. 155–167, 2017.
Available online at: http://www.jpier.org/PIERC/pierc75/16.17030703.pdf
The input parameters are given along with units:
h_s: vertical spacing between coils - the distance between the bottom conductor of the top coil to the top conductor of the bottom coil [m]
R_inner: inner radius of the coil [m]
n_x_max: maximum number of layers
n_y_max: maximum number of turns in each layer
b: wire radius [m]
Kw: coil filling factor - turn-to-turn pitch divided by wire diameter (Kw>1)
L_self_required: required self inductance

The output parameters are:
n_x: number of layers
n_y: number of turns per layer
d12: axes pitch between coil 1 and 2
d13: axes pitch between coil 1 an 3
L_self_coil: resulted inductance
k12: coupling coefficient between coil 1 and 2
k13: coupling coefficient between coil 1 and 3

The main function name is: optimal_coupled_array_of_three_main_func.m