def Angle_calibration(plot1=False, plot2=False, printA=False):
plt.close('all')
angle_data = np.load(nppath + "angle_cal.npy")
X = angle_data[:, 0] # sec
Y = angle_data[:, 1] # mRad
x_minima = [62, 178, 293, 407] # sec
x_maxima = [120, 235, 350] # sec
minima, maxima = dg.extrema(X, Y, 10, x_minima, x_maxima)
ext = minima + maxima
ext = dg.sort(np.array(ext), 0)
if plot1 == True: # '0_1_Angles_cal', angles for angle calibration
# plots: X , Y , style , label
p1 = dp.data(X, Y, '-', 'b', '$\\theta_{comp}$')
p2 = dp.data(ext[:, 0], ext[:, 1], 'r*', 'r', 'Extrema')
ax = dp.ax([p1, p2], 111, 'time [sec]', "$\\theta_{comp}$ [mRad]",
"$\\theta_{comp}$ for Angle Calibration")
dp.plot([ax], name=gp + '0_1_Angles_cal')
X_data, Y_data = AuxOne(L.val, S.val, ext[:, 1])
m, m_err = df.m_exp(X_data, Y_data), df.sig_m(X_data, Y_data)
b, b_err = df.b_exp(X_data, Y_data), df.sig_b(X_data, Y_data)
m_err_p, b_err_p = m_err * 100 / m, b_err * 100 / b
r2 = df.R2(X_data, Y_data)
X_lin = np.linspace(0, max(X_data) + 10, 1000)
Y_lin = df.lin_fit(X_data, Y_data, X_lin)
if plot2 == True:
p1 = dp.data(X_data, Y_data, 'bs', 'b', 'Laser vs Comp')
p2 = dp.data(X_lin, Y_lin, 'r-', 'r', 'Linear Fit')
n2 = dp.note(
"Y = C x + B\nm = %s $\pm$ %s\nb = %s $\pm$ %s\nR$^2$ = %s" %
(round(m, 2), round(m_err, 2), round(b, 1), round(
b_err, 1), round(r2, 5)), 20, 7, p2.color)
ax = dp.ax([p1, p2], 111, '$\\theta_{comp}$ [mRad]',
'$\\theta_{laser}$ [mRad]',
'$\\theta_{laser}$ vs. $\\theta_{comp}$')
ax.notes = [n2]
dp.plot([ax], name=gp + '0_2_laser_vs_comp')
if printA == True:
print("")
print("Calibrtion:")
print("theta_comp = %s" % X_data)
print("theta_laser = %s" % Y_data)
print("calibration constant = %s +/- %s (%s)" % (m, m_err, m_err_p))
print("intercept = %s +/- %s (%s)" % (b, b_err, b_err_p))
print("R2 = %s" % r2)
print("")
return m, m_err
def fig07(saveA=True):
data = pd.read_table(three_d['txt'])
B = data['MagField'].values * C['T'] # T
I = data['MagCurr'].values # A
X = B # T
Y = I * C['L'] / C['A'] # T
X_fit = np.linspace(min(X), max(X), 1000)
FIT = df.lin_fit(X, Y, X_fit)
Y_fit = FIT['Y_fit']
m = FIT['m']
b = FIT['b']
R2 = FIT['R2']
mu_rval = m.val
mu_rerr = m.err
mu_r = dg.var(mu_rval, mu_rerr)
fig = plt.figure(figsize=pp['figsize'])
plt.title('Finding $\mu_r$', fontsize=pp['fs'] + 2)
plt.xlabel('B [ T ]', fontsize=pp['fs'])
plt.ylabel('I L / A [ T ]', fontsize=pp['fs'])
plt.xlim([min(X), max(X)])
plt.plot(X, Y, color='c', lw=pp['lw'], label='p-Ge')
plt.plot(X_fit, Y_fit, pp['fit_style'], lw=pp['lw'], label='fit')
plt.legend(loc='best', fontsize=pp['fs'])
note = 'y = m x + b\n\
m = $\mu_r$ = %s $\pm$ %s [ H/m ]\n\
b = %s $\pm$ %s [ T ]\n\
R$^2$ = %s'\
% (m.pval,m.perr,b.pval,b.perr,"{0:.4f}".format(R2) )
plt.annotate(note, xy=(.097, 24500), color='r', fontsize=pp['fs'])
if saveA:
fig.savefig('png/fig07.png')
plt.close()
else:
plt.show()
dic = {'mu_val': mu_r.val, 'mu_err': mu_r.err, 'mu_r': mu_r}
return pd.Series(dic)
def part3(printA=True,saveA=True,figsize=(15,15), fs=20, lw=2):
print("")
print("Part III")
# compare
G2 = 1*10*100
R = 10e3 # Ohm
delta_f = 110961 # Hz
vout = .94 # V
vrms_conv = out2rms(G2,vout) # V
vrms_calc = v_rms(delta_f,k_default,R_default)
vrms, perr = err(vrms_conv,vrms_calc)
if printA == True:
print("compare")
print("v_out = ", vout)
print("v_rms_conv = ", vrms_conv)
print("v_rms_calc = ", vrms_calc)
print("v_rms = %s +/- %s V (%s percent)" % (vrms.pval,vrms.perr,perr) )
print("")
# amplifier noise
R = np.array([ 1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6 ])
G2 = np.array([ 10*10*20, 10*10*20, 10*10*20, 10*10*20, 10*10*10, 1*10*40, 1*10*30 ])
VOUT = np.array([ .9727, .9722, .9715, .9718, .9743, .9773, .9747, .9755, 1.0005, 1.0025, .9998, 1.0010,
1.2441, 1.2492, 1.2468, 1.2435, .9323, .9319, .9355, .9337, .8912, .8882, .8863, .8877,
.9585, .9550, .9595, .9650 ]).reshape([7,4])
VOUT = np.array([ np.average(VOUT[i]) for i in range(7) ])
Y_data = ( VOUT * (1e6)**2 ) / ( gain(G2)**2) # micro V^2
X_fit = np.linspace(0, 2e4, 1000) # Ohm
cutoff = 2 # num
Y_fit, m, b = df.lin_fit( R[:-cutoff] , Y_data[:-cutoff] , X_fit ) # micro V^2
R2 = df.R2(R[:-cutoff],Y_data[:-cutoff]) # num
amp = np.sqrt(b.val)
amp_err = b.err/(2*np.sqrt(b.val))
ampN = dg.var( amp,amp_err ) # micro V
fig = plt.figure(figsize=figsize)
plt.title('Part III: Amplifier Noise', fontsize=fs+2)
plt.xlabel('R [$\\Omega$]', fontsize=fs)
plt.ylabel('<Vj$^2$> [$\\mu$ V$^2$]', fontsize=fs)
plt.xlim(min(X_fit),max(X_fit))
plt.plot(R[:-cutoff],Y_data[:-cutoff], 'bo', markersize=15, label='data')
plt.plot(X_fit,Y_fit, color='r', lw=lw, label='fit')
note = '$Vj^2 = mR + b$\n$m = %s \pm %s\ \\mu\ V^2/\\Omega$\n$b = %s \pm %s\ \\mu\ V^2$\n$R^2 = %s$' % (m.pval,m.perr,b.pval,b.perr,round(R2,6) )
plt.annotate(note, xy=(1e3,35), color='r', fontsize=fs)
note2 = 'Pre-Amp Noise = $\sqrt{b} \pm \\Delta b/(2 \sqrt{b})$\n $= %s \pm %s\ \\mu V$' % (ampN.pval,ampN.perr)
plt.annotate(note2, xy=(1e3,30), color='m', fontsize=fs+2)
plt.legend(loc='best', fontsize=fs)
if saveA == True:
fig.savefig('../graphs/fig02.png')
plt.close(fig)
else:
plt.show(fig)
if printA == True:
print('amplifier noise')
print('R = %s Ohm' % R)
print('Vj^2 = %s micro V^2' % Y_data )
print("The best fit was found by not considering the last %s data points" % cutoff )
print("n = %s +/- %s micro V^2/Ohm" % (m.pval,m.perr) )
print("b = %s +/- %s micro V^2/Ohm")
print('amplifer noise = %s +/- %s micro V^2' % (ampN.pval,ampN.perr) )
print('')
# experimental k
DELTA_f = np.array([ 355, 1077, 3554, 10774, 35543, 107740 ]) # Hz
G2 = np.array([ 10*10*60, 10*10*40, 10*10*20, 10*10*10, 1*10*60, 1*10*40 ])
VOUT = np.array([ .8, 1.0, .9, .7, .8, .9 ]) # V
R = 100e3 # Ohm
Y_data = ( VOUT * (1e9)**2 ) / ( gain(G2)**2 * 4 * R * T_room ) # nV^2/Ohm/K
X_fit = np.linspace(0,120000,1000) # Hz
Y_fit, m, b = df.lin_fit( DELTA_f , Y_data , X_fit )
R2 = df.R2(DELTA_f,Y_data)
kval = m.val/(1e9)**2 # J/K
kval_err = m.err/(1e9)**2
k = dg.var( kval,kval_err )
fig = plt.figure(figsize=figsize)
plt.title('Part III: Bolzmann Constant', fontsize=fs+2)
plt.xlabel('$\\Delta$ f [Hz]', fontsize=fs)
plt.ylabel('<Vj$^2$>/R/T [nV$^2$/$\\Omega$/K]', fontsize=fs)
plt.xlim(min(X_fit),max(X_fit))
plt.plot(DELTA_f,Y_data, 'bo', markersize=15, label='data')
plt.plot(X_fit,Y_fit, color='r', lw=lw, label='fit')
note = '$V^2 = m f + b$\n$m = %s \pm %s\ nV^2/ \\Omega/ K / Hz$\n$b = %s \pm %s\ nV^2/ \\Omega/ K$\n$R^2 = %s$' % (m.pval,m.perr,b.pval,b.perr,round(R2,3) )
plt.annotate(note, xy=(1.5e3,1.2), color='r', fontsize=fs)
note2 = '$k = (m \pm \\Delta m)/(1_{+9})^2$\n $= %s \pm %s\ J/K$' % (k.pval,k.perr)
plt.annotate(note2, xy=(1.5e3,1), color='m', fontsize=fs+2)
plt.legend(loc='best', fontsize=fs)
if saveA == True:
fig.savefig('../graphs/fig03.png')
plt.close(fig)
else:
plt.show(fig)
if printA == True:
print("Bolzmann constant")
print("m = %s +/- %s 1e18 J/K" % (m.pval,m.perr) )
print("k = %s +/- %s J/K" % (k.pval,k.perr) )
return
def part4(printA=True,saveA=True,figsize=(15,15),fs=20,lw=2):
print("")
print("Part IV:")
R = np.array([ 10, 10e3 ]) # Ohm
G2 = np.array([ 10*10*20, 10*10*10 ])
# JOHNSON NOISE AT T_room with A_ext and B_ext
VOUT = np.array([ np.average([.9831, .9843, .9841, .9820]), np.average([.7650, .7653, .7669, .7662]) ]) # V^2
Y_data = ( VOUT * (1e6)**2 ) / (gain(G2)**2) # (micro V)^2
X_fit = np.linspace(0, 11e3, 1000) # Ohm
Y_fit, m, b = df.lin_fit( R , Y_data , X_fit )
R2 = df.R2(R,Y_data)
mval = round(m.val,4)
merr = 5e-4
bval = round(b.val,1)
berr = .5
noise = round(np.sqrt(b.val),1) # micro V^2
noise_err = round(berr/(2*np.sqrt(b.val)),1)
# ampN = dg.var( noise,noise_err )
fig = plt.figure(figsize=figsize)
plt.title('Part IV: Amplifier Noise from A$_{ext}$ and B$_{ext}$', fontsize=fs+2)
plt.xlabel('R [$\\Omega$]', fontsize=fs)
plt.ylabel('<Vj$^2$> [$\\mu$V$^2$]', fontsize=fs)
plt.xlim(min(X_fit),max(X_fit))
plt.plot(R,Y_data, 'bo', markersize=15, label='data')
plt.plot(X_fit,Y_fit, color='r', lw=lw, label='fit')
note = '$Vj^2 = mR + b$\n$m = %s \pm %s\ \\mu V^2/\\Omega$\n$b = %s \pm %s\ \\mu V^2$\n$R^2 = %s$' % (mval,merr,bval,berr,round(R2,4) )
plt.annotate(note, xy=(1e2,19), color='r', fontsize=fs)
note2 = 'Pre-Amp Noise = $\sqrt{b} \pm \\Delta b/(2 \sqrt{b})$\n $= %s \pm %s\ \\mu V$' % (noise,noise_err)
plt.annotate(note2, xy=(1e2,17), color='m', fontsize=fs+2 )
plt.legend(loc='best', fontsize=fs)
if saveA == True:
fig.savefig('../graphs/fig04.png')
plt.close()
else:
plt.show()
if printA == True:
print('amplifier noise from Aext and Bext')
print('it was found that Cext did not measure at an correct value and was discarded.')
print('m = %s +/- %s micro V^2/Hz' % (mval,merr) )
print('b = %s +/- %s micro V^2' % (bval,berr) )
print('amplifer noise = %s +/- %s micro V' % (noise,noise_err) )
print('')
# experimental k at T = 77 K
VOUT2 = np.array([ np.average([.9825, .9832, .9804, .9827]), np.average([.3909, .3905, .3905, .3911]) ]) # V^2
Y_data2 = ( VOUT2 * (1e9)**2 ) / (gain(G2)**2 * 4 * 77 * 110961 ) # nV^2 / K / Hz
Y_fit2, m, b = df.lin_fit( R , Y_data2 , X_fit )
R22 = df.R2(R,Y_data2)
bval = round(b.val,2)
berr = .05
mval = round(m.val,6)
merr = 5e-6
kval = round(m.val/(1e9)**2,24) # J/K
kerr = round(merr/(1e9)**2,24)
# k = dg.var( kval,kval_err )
fig = plt.figure(figsize=figsize)
plt.title('Part IV: Boltzmann Constant at 77 K', fontsize=fs+2)
plt.xlabel('R [$\\Omega$]', fontsize=fs)
plt.ylabel('[nVj$^2$/K/Hz]', fontsize=fs)
plt.xlim(min(X_fit),max(X_fit))
plt.plot(R,Y_data2, 'bo', markersize=15, label='data')
plt.plot(X_fit,Y_fit2, color='r', lw=lw, label='fit')
note = '$nVj^2/T/\\Delta f = mR + b$\n$m = %s \pm %s\ nV^2/K/Hz/\\Omega$\n$b = %s \pm %s\ nV^2/K/Hz$\n$R^2 = %s$' % (mval,merr,bval,berr,round(R22,4) )
plt.annotate(note, xy=(1e2,3e-1), color='r', fontsize=fs)
note2 = '$k = (m \pm \\Delta m)/(1_{+9})^2$\n $= %s \pm %s\ J/K$' % (kval,kerr)
plt.annotate(note2, xy=(1e2, 2.8e-1), color='m', fontsize=fs+2)
plt.legend(loc='best', fontsize=fs)
if saveA == True:
fig.savefig('../graphs/fig05.png')
plt.close()
else:
plt.show()
if printA == True:
print('Bolzmann Constant at 77 K')
print('it was found that Cext did not measure at an correct value and was discarded.')
print('experimental k = %s +/- %s J/m' % (kval,kerr) )
print('')
def fig08(saveA=True):
# raw data
data = pd.read_table(three_c['txt'])
T = data['Temp'].values + C['K'] # temperature [K]
Vs = data['SampVolt'].values # sample voltage [V]
Is = data['SampCurr'].values / 1000 # sample current [A]
# form data into axis
X = 1000 / T # [K]
Y = (C['l_samp'] * Vs) / (C['a_samp'] * Is) # [ohm-cm]
Y = np.log(Y)
# start of semi-conductor phase (increase temperature -> lower resistance)
semi0 = 2.95
i_semi0 = dg.nearest(X, semi0)
# fit semi-conductor phase to line
X_fit = np.linspace(2.7, 3.4, 1000)
FIT = df.lin_fit(X[X > semi0], Y[X > semi0], X_fit)
Y_fit = FIT['Y_fit']
m = FIT['m']
b = FIT['b']
R2 = FIT['R2']
fig = plt.figure(figsize=pp['figsize'])
plt.title('Resistivity of p-Ge', fontsize=pp['fs'] + 2)
plt.xlabel('1000/T [ 1/K ]', fontsize=pp['fs'])
plt.ylabel('ln( $\\rho$ [ $\Omega$ cm ] )', fontsize=pp['fs'])
plt.xlim([min(X), max(X_fit)])
plt.ylim([min(Y), max(Y_fit)])
plt.plot(X[i_semi0:],
Y[i_semi0:],
color='b',
lw=pp['lw'],
label='p-Ge data')
plt.plot(X_fit,
Y_fit,
pp['fit_style'],
lw=pp['lw'],
label='semi-phase fit')
plt.vlines(x=semi0, ymin=6.5, ymax=8, color='r', linewidth=1)
plt.legend(loc='best', fontsize=pp['fs'])
note = 'semi-conductor phase fit cut off = %.0f K' % (1000 / semi0)
plt.annotate(note,
xy=(semi0 + .005, 6.9),
color='r',
fontsize=pp['fs'] - 4,
rotation=-90)
note1 = 'y = m x + b\n\
m = %s $\pm$ %s [ $\Omega$ cm K ]\n\
b = %s $\pm$ %s [ $\Omega$ cm ]\n\
R$^2$ = %.4f'\
% (m.pval,m.perr,b.pval,b.perr,R2)
plt.annotate(note1, xy=(3, 6.99), color='r', fontsize=pp['fs'] - 4)
T_interest = 300 # K
x_interest = 1000 / T_interest
i_interest = dg.nearest(X_fit, x_interest)
rho_val = np.exp(Y_fit[i_interest])
rho = equation5(rho_val, m, x_interest, b)
note2 = '$\\rho$ ( T = %.0f K ) = %s $\pm$ %s $\Omega$ cm' % (
T_interest, rho.pval, rho.perr)
plt.annotate(note2,
xy=(3.17, 6.85),
color='g',
fontsize=pp['fs'] - 4,
rotation=-41)
plt.plot(X_fit[i_interest], Y_fit[i_interest], 'og', ms=pp['ms'])
if saveA:
fig.savefig('png/fig08.png')
plt.close()
else:
plt.show()
dic = {
'mval': m.val,
'merr': m.err,
'm': m,
'bval': b.val,
'berr': b.err,
'b': b,
'R2': R2
}
return pd.Series(dic)
def fig05(saveA=True):
data = pd.read_table(five_c['txt'])
T = data['Temp'].values # K
Vs = data['SampVolt'].values # V
Is = data['SampCurr'].values / 1000 # A
l = 20e-3 # m
A = 10 / (1000)**2 # m^2
sigma = l * Is / A / Vs # 1/(Ohm m)
# linearize
X = 1 / (T + 273.15) # 1/K
Y = np.log(Vs)
X_fit = np.linspace(min(X), max(X), 1000)
FIT = df.lin_fit(X, Y, X_fit)
Y_fit = FIT['Y_fit']
m = FIT['m']
b = FIT['b']
R2 = FIT['R2']
E_gval = 2 * C['k'] * m.val
E_gerr = 2 * C['k'] * m.err
E_g = dg.var(E_gval, E_gerr)
fig = plt.figure(figsize=pp['figsize'])
plt.title('i-Ge Band Gap', fontsize=pp['fs'] + 2)
plt.xlabel("1/T [ 1/K ]", fontsize=pp['fs'])
plt.ylabel("ln ( V$_s$ [ V ] )", fontsize=pp['fs'])
plt.xlim(min(X_fit), max(X_fit))
plt.plot(X, Y, 'b', lw=pp['lw'], label='data')
plt.plot(X_fit, Y_fit, 'r', lw=pp['lw'], label='fit')
note = ' Y=m x + b\n\
ln( V$_s$ ) = ( -E$_g$/2k ) ( 1/T ) + ln( A )\n\
m = %s $\pm$ %s\n\
b = %s $\pm$ %s\n\
R$^2$ = %.4f\n\
E$_g$ = 2 k m $\pm$ 2 k $\Delta$ m\n\
= %s $\pm$ %s eV'\
% (m.pval,m.perr,b.pval,b.perr,R2,E_g.pval,E_g.perr)
plt.annotate(note, xy=(.00255, .9), color='r', fontsize=pp['fs'])
plt.legend(loc='best', numpoints=1)
if saveA:
fig.savefig('png/fig05.png')
plt.close()
else:
plt.show()
dic = {
'm_val': m.val,
'm_err': m.err,
'm': m,
'E_g_val': E_g.val,
'E_gerr': E_g.err,
'E_g': E_g
}
return dic
def fig02(saveA=True):
# data
X = one_d['g']
Y1 = one_d['B']
Y = Y1 * X**2
# fit and theory
X_fit = np.linspace(.2, 2.5, 1000)
Y_T = equation1(1, X_fit) * X_fit**2
# find flux leak
Y_T1 = equation1(1, X) * X**2
Y_L = (Y_T1 - Y) / Y_T1
yl_av = np.average(Y_L)
yl_std = np.std(Y_L)
yl = dg.var(yl_av, yl_std)
FIT = df.lin_fit(X, Y, X_fit)
Y_fit = FIT['Y_fit']
m = FIT['m']
b = FIT['b']
R2 = FIT['R2']
fig = plt.figure(figsize=pp['figsize'])
plt.title('Magnetic Field Strength vs. Magnet Gap', fontsize=pp['fs'] + 2)
plt.xlabel('Gap [cm]', fontsize=pp['fs'])
plt.ylabel('B Gap$^2$ [%s cm$^2$]' % units['MagField'], fontsize=pp['fs'])
plt.xlim([min(X_fit), max(X_fit)])
plt.plot(X, Y, pp['data_style'], markersize=pp['ms'], label='data')
plt.plot(X_fit, Y_fit, pp['fit_style'], lw=pp['lw'], label='data fit')
plt.plot(X_fit, Y_T, 'g', lw=pp['lw'], label='theory')
plt.legend(loc='best', fontsize=pp['fs'], numpoints=1)
note = 'y = m x + b\n\
m = %s $\pm$ %s [kG cm]\n\
b = %s $\pm$ %s [kG cm$^2$]\n\
R$^2$ = %s'\
% (m.pval,m.perr,b.pval,b.perr,"{0:.4f}".format(R2) )
plt.annotate(note, xy=(.3, 1.1), color='r', fontsize=pp['fs'])
note1 = '100 (B$_T$ - B$_L$) / B$_T$ = %s $\pm$ %s percent' % (yl.pval,
yl.perr)
plt.annotate(note1, xy=(.3, 1), color='g', fontsize=pp['fs'])
if saveA:
fig.savefig('png/fig02.png')
plt.close()
else:
plt.show()
dic = {
'X': X,
'Y': Y,
'fit': FIT,
'theory': Y_T,
'leak': yl.val,
'leak_error': yl.err
}
return pd.Series(dic)