Merge pull request #9 from Patarimi/lumped_l_matching

adding function to make a L lumped matching.

hades/equation/matching.py

@@ -0,0 +1,26 @@
+from math import sqrt
+
+
+def lumped_l(
+ z_load: complex, r_0: float
+) -> tuple[tuple[float, float], tuple[float, float]]:
+ """
+ return the two solutions to match a complex load to a line.
+ :param z_load: impedance of the load.
+ :param r_0: impedance of the line.
+ :return:
+ """
+ r_l = z_load.real
+ x_l = z_load.imag
+
+ if r_l > r_0:
+ b_n = sqrt(r_l / r_0) * sqrt(r_l**2 + x_l**2 - r_0 * r_l)
+ b_1 = (x_l + b_n) / (r_l**2 + x_l**2)
+ b_2 = (x_l - b_n) / (r_l**2 + x_l**2)
+ x_1 = 1 / b_1 + x_l * r_0 / r_l - r_0 / (b_1 * r_l)
+ x_2 = 1 / b_2 + x_l * r_0 / r_l - r_0 / (b_2 * r_l)
+ return (b_1, x_1), (b_2, x_2)
+ else:
+ x_n = sqrt(r_l * (r_0 - r_l))
+ b = sqrt((r_0 - r_l) / r_l) / r_0
+ return (b, x_n - x_l), (-b, -x_n - x_l)