α

Im

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φ

φ

Im

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R

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Plan\ ℂ\ -\ Impédance\ \underline{Z} = (R + j X)

Plan ℂ - Représentation de Fresnel

EPFL-LAI - P. Germano - 2018

Norme de U = 1 V

x_{offset} = 0 (slider from -5 to 5, step 0.1)
t = 0 (slider from 0 to 2.5, step 0.01)
w = 2.5120000000000005 (slider from -5 to 5, step 1)
α_0 = 0.7330382858376184 rad (slider from 0 to 360°, step 0.5°)
A = Intersect(xAxis, yAxis)
B = Point(yAxis)
C = Point(yAxis)
Axe_{Im_F} = Vector(B, C)
D = Point(xAxis)
E = Point(xAxis)
Axe_{Re_F} = Vector(D, E)
U_1: (cos((w * t) + α_0), sin((w * t) + α_0))
R = 1.201 (slider from 0.001 to 3.5, step 0.1)
X = 0.5 (slider from -3.5 to 3.5, step 0.1)
H: (x_{offset} - 0.25, 0)
I_2: (2 + x_{offset} + 0.25, 0)
Axe_{Re_Z} = Vector(H, I_2)
K: (x_{offset}, 0.8)
J: (x_{offset}, -0.8)
Axe_{Im_Z} = Vector(J, K)
Z_1: R + x_{offset} + (X * ί)
O_Z: (x_{offset}, 0)
Z = Vector(O_Z, Z_1)
F: (R + x_{offset}, 0)
G: (x_{offset}, 0)
L: (R + x_{offset}, X)
φ_Z = Angle(F, G, L)
O_F: (0, 0)
U = Vector(O_F, U_1)
M: (R + x_{offset}, X + 0.25)
N: (R + x_{offset}, -0.25)
f = Segment(M, N)
O: (x_{offset} - 0.25, X)
P: (R + x_{offset} + 0.25, X)
g = Segment(O, P)
I_1: (cos((w * t) + α_0 - φ_Z), sin((w * t) + α_0 - φ_Z)) / sqrt(R^(2) + X^(2))
I = Vector(O_F, I_1)
C_U = Circle(O_F, 1)
C_I = Circle(O_F, 1 / sqrt(R^(2) + X^(2)))
α = Angle(E, O_F, U_1)
β = Angle(E, O_F, I_1)
φ_F = Angle(I_1, O_F, U_1)
Q = (-0.06126135325751214, 1.8745256391021445)
S = (0.365985776064779, 1.7863035180031468)
norme_I: "Norme de I = U/Z = " + (1 / sqrt(R^(2) + X^(2))) + " A"
norme_Z: "Norme\ de\ \underline{Z} : Z = " + (LaTeX[sqrt(R^(2) + X^(2))]) + "\ Ω"