# Aufgabe 3a
w_3a = npfarray([0, 30, 60, 90])
w_3a_dsys = npfarray([2.5, 2.5, 2.5, 2.5])
Vss_3a = npfarray([1.48, 1.29, 0.73, 0.03])
Vss_3a_dsys = npfarray([0.03, 0.02, 0.01, 0.02])
Uind_3a = Vss_3a / 2
Uind_3a_dsys = Vss_3a_dsys / 2
def fitfunc_3a(w, B):
return B * A_i * N_i * 2 * pi * 100 * cos(w * deg_to_rad)
w_array = nplinspace(-10, 100)
popt_3a, pcov_3a = curve_fit(fitfunc_3a, w_3a, Uind_3a, sigma=Uind_3a_dsys)
B_3a = popt_3a[0]
B_3a_dsys = sqrt(pcov_3a[0][0])
pltext.initplot(
num=3,
title='Abbildung : Induktionsspannung als Funktion des Winkels',
xlabel='Winkel in deg',
ylabel='Induktionsspannung in V')
plt.plot(w_array, fitfunc_3a(w_array, *popt_3a), label=' Fit')
pltext.plotdata(w_3a, Uind_3a, Uind_3a_dsys, w_3a_dsys, label=' Measurements')
pltext.set_layout(legend=True, xlim=(-10, 100), ylim=(0, 0.8))
print('\nAufgabe 3a:\n')
print(val(B_3a, B_3a_dsys, 'B'))
U_top.append(abs(kl_U[n]))
lastmax = abs(kl_U[n])
t_top.append(kl_t[n])
lastn = n + 1
for n in range(lastn, len(kl_U)):
if abs(kl_U[n]) >= np.max([abs(kl_U[j]) for j in range(n, len(kl_U))]):
U_top.append(abs(kl_U[n]))
t_top.append(kl_t[n])
def gauss(x, A, mu, sigma):
return A * exp(-(x - mu)**2 / (2. * sigma**2))
popt, pcov = curve_fit(gauss, t_top, U_top)
sigma = popt[2]
sigma_dtot = sqrt(pcov[2][2])
t_int = npfarray([0.1e-2 * n for n in range(-30, 91)])
pltext.initplot(num=2,
title='Signalverlauf LED',
xlabel='Zeit in s',
ylabel='Spannung in V')
plt.plot(kl_t, kl_U, label='Messwerte')
plt.plot(t_int, gauss(t_int, popt[0], popt[1], popt[2]), label='Gaußfit')
L = 2. * kl_v * sigma * 2. * sqrt(2. * ln(2.))
L_dtot = 2. * kl_v * sigma_dtot * 2. * sqrt(2. * ln(2.))
print()
title=r'$\sqrt{E_\alpha}$ als Funktion von $Z$',
xlabel=r'$Z$',
ylabel=r'$\sqrt{E_\alpha}$ in $\sqrt{keV}$')
pltext.plotdata(x=Z, y=sqrt_K_alpha, dy=Delta_sqrt_K_alpha)
n1 = 1
n2 = 2
def fit_func_alpha(x, sqrt_Er, sig12):
return sqrt_Er * (x - sig12) * sqrt(1 / n1**2 - 1 / n2**2)
popt, pcov = curve_fit(fit_func_alpha,
Z,
sqrt_K_alpha,
sigma=Delta_sqrt_K_alpha,
p0=p0)
sqrt_Er_alpha = popt[0]
Delta_sqrt_Er_alpha = sqrt(pcov[0, 0])
sig12_alpha = popt[1]
Delta_sig12_alpha = sqrt(pcov[1, 1])
plt.plot(Z, fit_func_alpha(Z, *popt))
print()
print('K_alpha:')
print(val('sqrt(Er)', sqrt_Er_alpha, Delta_sqrt_Er_alpha))
print(
sig('Abweichung',
plt.xlim(-3, 3)
plt.ylim(0, 0.6)
plt.hist(d_all, density=True)
plt.plot(points, gauss)
plt.text(-2.41, 0.504, 'σ = ' + val('', sigma) + '\nμ = ' + val('', mu))
plt.savefig('fig2.pdf', format='pdf')
# Kumulative Verteilung der Verschiebungsquadrate
r_kum = np.cumsum(r_sqr)
def lin(x, a, b):
return a * x + b
popt, pcov = curve_fit(lin, t[:-1], r_kum)
slope = popt[0]
yitc = popt[1]
slope_dtot = sqrt(pcov[0][0])
yitc_dtot = sqrt(pcov[1][1])
vert_D = slope / 4.
vert_D_dtot = slope_dtot / 4.
vert_kB = 6. * pi * nu * r_k * vert_D / T_mv
vert_kB_dtot = 6. * pi / T_mv * sqrt((nu_dsys * r_k * vert_D)**2 +
(nu * r_k_dsys * vert_D)**2 +
(nu * r_k * vert_D_dtot)**2 +
(nu * r_k * vert_D * T_dtot / T_mv)**2)
pltext.initplot(num=3,
title='Kumulative Verteilung der Verschiebungsquadrate',
pltext.set_layout(xlim=(1e2, 1e6), ylim=(3e0, 2e3))
def fitfunc(f, V, W1, W2, n1, n2):
return V / (np.sqrt(1 + 1 /
(f / W1)**(2 * n1)) * np.sqrt(1 + (f / W2)**(2 * n2)))
V = 1000
W1 = 1000
W2 = 50000
n1 = 5
n2 = 5
p0 = (V, W1, W2, n1, n2)
popt, pcov = curve_fit(fitfunc, f[15:-43], g[15:-43], p0)
print()
print(val(popt[0], sqrt(pcov[0][0]), 'V'))
print(val(popt[1], sqrt(pcov[1][1]), 'W1'))
print(val(popt[2], sqrt(pcov[2][2]), 'W2'))
print(val(popt[3], sqrt(pcov[3][3]), 'n1'))
print(val(popt[4], sqrt(pcov[4][4]), 'n2'))
pltext.initplot(num=2,
title='Abbildung : Frequenzgang (Fit)',
xlabel='Frequenz in Hz',
ylabel='g(f)',
scale='loglog')
pltext.plotdata(f[17:-45], g[17:-45], label='Messwerte')
f_array = nplinspace(4e2, 1.2e5)