Fourieranalyse einer einweggleichgerichteten Phasenanschnittssteuerung
Author: Johannes Kiesel

Fourierreihe

Cosinus-Glieder

Sinus-Glieder

Spektrum

Originalfunktion

Einzelne Wellen

A

A = 1.5 (slider from 1 to 4, step 0.1)
α = 0.6 (slider from 0 to 3.141592653589793, step 0.1)
max_n = 3 (slider from 1 to 10, step 1)
a_0: A / 3.142 * (1.0 + cos(α))
b = 0.03 (slider from 0 to 1, step 0.01)
a_1: -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 A sin(α)^(2.0) / (2.0 * 3.14)
b_1: A * (3.14 - α + 1.0 / 2.0 sin(2.0 α)) / (2.0 * 3.14)
b_n = Sequence(A / 3.142 * (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 n sin(α) cos(n α) + cos(α) sin(n α)) / (1.0 - n^(2.0)), n, 2.0, max_n)
a_n = Sequence(A / 3.14 * ((-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0)^(n) + cos(α) cos(α n) + n sin(α) sin(α n)) / (1.0 - n^(2.0)), n, 2.0, max_n)
funcs_a = Sequence(If[k > 1.0, Element[a_n, k - 1.0] cos(k x), a_1 cos(x)], k, 1.0, max_n)
funcs_b = Sequence(If[k > 1.0, Element[b_n, k - 1.0] sin(k x), b_1 sin(x)], k, 1.0, max_n)
sum_a = Sum(funcs_a)
sum_b = Sum(funcs_b)
f(x) = a_0 / 2.0 + sum_a(x) + sum_b(x)
g = If(x > -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 0.3, If[x < 10.3, f(x)])
i = false
spektrum_a = Sequence(Segment[(k - b, 0.0), (k - b, If[k > 1.0, Element[a_n, k - 1.0], If[k > 0.0, a_1, a_0]])], k, 0.0, max_n)
spektrum_b = Sequence(Segment[(k + b, 0.0), (k + b, If[k > 1.0, Element[b_n, k - 1.0], b_1])], k, 1.0, max_n)
orig_1 = Sequence(If[x > -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.14159 + 2.0 k 3.14159, If[x < 3.14159 + 2.0 k 3.14159, If[x > α + 2.0 k 3.14159, A sin(x), 0.0]]], k, 0.0, 3.0)
orig_2 = Sequence(Segment[(α + 2.0 k 3.14159, 0.0), (α + 2.0 k 3.14159, A sin(α))], k, 0.0, 3.0)
a = false
c = true
d = false
e: 1.0 * 1.0 * 1.0 y = A
gleich_a: 1.0 * 1.0 y = a_0 / 2.0