bmarechal / sicav_sim

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Commit 2ae5099ce4f9fc7e6ea0edff2924ea1d040acda8

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File was created 1 from sympy import *
2 from sympy.simplify.fu import *
3
4 init_printing()
5
6 #constants
7 E0, E1, W, t, dphi, kphi = symbols('E0, E1, Omega, t, Delta_phi, k_phi', real=True, imaginary=False)
8
9 #define LO and RF
10 LO_I = E0*cos(W*t)
11 LO_Q = E0*cos(W*t+pi/2)
12 RF = E1*cos(W*t+dphi)
13
14 #mixer
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''Pound-Drever-Hall setup
5
6 ----- ---
7 ------------|EOM|------|/|-----( )
8 w_laser ----- --- cavity
9 ^ |
10 | U
11 | |
12 | v
13 |------->(X) π/2
14 (w_pdh) |
15 -----
16 |LPF|
17 -----
18 |
19 v eps_pdh
20
21 '''
22
23 from time import time
24 tic = time()
25
26 from sympy import *
27 from sympy.simplify.fu import *
28
29 init_printing()
30
31 #constants
32 E0, J0, J1, w_laser, w_pdh, t, c = symbols('E0, J0, J1, omega_laser, Omega_pdh, t, c', imaginary=False, real=True)
33
34 '''laser and phase-mod laser
35 E_laser = E0*exp(I*(w_laser*t))
36
37 E_inc = \
38 E0*( \
39 J0*exp(I*((w_laser )*t)) \
40 + J1*exp(I*((w_laser+w_pdh)*t)) \
41 - J1*exp(I*((w_laser-w_pdh)*t)) \
42 )'''
43
44 #reflection near resonance
45 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
46 def F(phi):
47 dw = phi.diff(t) - w_cav
48 return -(I/pi)*(dw/dnu)
49
50 #reflected phase-mod laser
51 v_x, d_x = symbols('v_x, delta_x', imaginary=False, real=True)
52 dx = v_x*t + d_x
53 E_ref = \
54 E0*( \
55 F( (w_laser )*t - w_laser*dx/c ) \
56 *J0*exp(I*( (w_laser )*t - 2*w_laser*dx/c ) ) \
57 + -1*J1*exp(I*( (w_laser+w_pdh)*t - 2*w_laser*dx/c ) ) \
58 - -1*J1*exp(I*( (w_laser-w_pdh)*t - 2*w_laser*dx/c ) ) \
59 )
60
61 #intensity of reflected phase-mod laser
62 I_pdh = abs(E_ref)**2
63 I_pdh = expand(TR8(expand(expand_complex(I_pdh))))
64
65 #demodulation of I_pdh at Omega_pdh
PDH_doppler_mach-zender/PDH_doppler_mach-zender_eom_amont.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''Pound-Drever-Hall setup
5 Mach-Zender with one photodiode
6
7 ----- --- ---
8 ---------|EOM|-|\|------------|/|-----------( )
9 w_laser ----- --- --- cavity
10 | |
11 | |
12 | ----- ---
13 \-|AOM|-------|\|
14 ----- ---
15 ^ |
16 | U
17 | |
18 | V
19 |-------->(X)
20 | | -----
21 (W_aom) |---|LPF|--> eps_dop
22 V -----
23 (W_pdh)---------->(X)
24 |
25 |
26 V eps_pdh
27
28
29
30 '''
31
32 from time import time
33 tic = time()
34
35 from sympy import *
36 from sympy.simplify.fu import *
37
38 init_printing()
39
40 #constants
41 E0, J0, J1, w_laser, w_pdh, w_aom, t = symbols('E0, J0, J1, omega_laser, Omega_pdh, Omega_aom, t', imaginary=False, real=True)
42 v_x, d_x = symbols('v_x, delta_x', imaginary=False, real=True)
43 c = symbols('c', imaginary=False, real=True)
44
45 #laser and phase-mod laser
46 E_laser = E0*exp(I*(w_laser*t))
47
48 E_aom_eom = \
49 E0*( \
50 J0*exp(I*( ( w_laser+w_aom )*t) ) \
51 + J1*exp(I*( ( w_laser+w_aom+w_pdh )*t) ) \
52 - J1*exp(I*( ( w_laser+w_aom-w_pdh )*t) ) )
53
54
55 E_eom = \
56 E0*( \
57 J0*exp(I*( ( w_laser )*t ) ) \
58 + J1*exp(I*( ( w_laser+w_pdh )*t ) ) \
59 - J1*exp(I*( ( w_laser-w_pdh )*t ) ) )
60
61 #approximation of F(w) near a resonance
62 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
63 def F(phi):
64 dw = phi.diff(t) - w_cav
65 return -(I/pi)*(dw/dnu)
66
67 #reflected phase-mod laser and dephased by doppler effect and by actuator
68 dx = v_x*t + d_x
69 E_ref = \
70 E0*( \
71 F( w_laser*t - w_laser*(dx)/(2*pi*c) ) \
72 *J0*exp( I*( (w_laser )*t - 2*w_laser*dx/c ) ) \
73 + -1*J1*exp( I*( (w_laser+w_pdh)*t - 2*w_laser*dx/c ) ) \
74 - -1*J1*exp( I*( (w_laser-w_pdh)*t - 2*w_laser*dx/c ) ) \
75 )
76
77 #optical mixer
78 E_mz = sqrt(2)/2 * E_aom_eom + sqrt(2)/2 * E_ref
79
80 #intensity of mixed wave
81 I_mz = abs(E_mz)**2
82 I_mz = expand(TR8(expand(expand_complex(I_mz))))
83
84
85 #Q demodulation of I_mz at Omega_aom for doppler error signal obtention
86 kphidop = symbols('k_phi_doppler', real=True)
87 eps_dop = 2 * kphidop * I_mz * cos(w_aom*t-pi/2)
88 eps_dop = expand(TR8(TR7(expand(eps_dop))))
89
PDH_doppler_mach-zender/PDH_doppler_mach-zender_eom_arm.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''Pound-Drever-Hall setup
5 Mach-Zender with one photodiode
6
7 --- ----- ---
8 ----------|\|---|EOM|---------|/|-----------( )
9 w_laser --- ----- --- cavity
10 | |
11 | |
12 | ----- ---
13 \----|AOM|---------|\|
14 ----- ---
15 ^ |
16 | U
17 | |
18 | V
19 |---------->(X)
20 | | -----
21 (W_aom) |---|LPF|--> eps_dop
22 V -----
23 (W_pdh)---------->(X)
24 |
25 |
26 V eps_pdh
27
28
29
30 '''
31
32 from time import time
33 tic = time()
34
35 from sympy import *
36 from sympy.simplify.fu import *
37
38 init_printing()
39
40 #constants
41 E0, J0, J1, w_laser, w_pdh, w_aom, t = symbols('E0, J0, J1, omega_laser, Omega_pdh, Omega_aom, t', imaginary=False, real=True)
42 v_x, d_x = symbols('v_x, delta_x', imaginary=False, real=True)
43 c = symbols('c', imaginary=False, real=True)
44
45 #laser and phase-mod laser
46 E_laser = E0*exp(I*(w_laser*t))
47
48 E_aom = E0*exp(I*((w_laser+w_aom)*t))
49
50 E_eom = \
51 E0*( \
52 J0*exp(I*( ( w_laser )*t ) ) \
53 + J1*exp(I*( ( w_laser+w_pdh)*t ) ) \
54 - J1*exp(I*( ( w_laser-w_pdh)*t ) ) )
55
56 #approximation of F(w) near a resonance
57 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
58 def F(phi):
59 dw = phi.diff(t) - w_cav
60 return -(I/pi)*(dw/dnu)
61
62 #reflected phase-mod laser and dephased by doppler effect and by actuator
63 dx = v_x*t + d_x
64 E_ref = \
65 E0*( \
66 F( w_laser *t - w_laser*dx/c ) \
67 *J0*exp( I*( w_laser *t - 2*w_laser*dx/c ) ) \
68 + -1*J1*exp( I*( (w_laser+w_pdh)*t - 2*w_laser*dx/c ) ) \
69 - -1*J1*exp( I*( (w_laser-w_pdh)*t - 2*w_laser*dx/c ) ) \
70 )
71
72 #optical mixer
73 E_mz = sqrt(2)/2 * E_aom + sqrt(2)/2 * E_ref
74
75 #intensity of mixed wave
76 I_mz = abs(E_mz)**2
77 I_mz = expand(TR8(expand(expand_complex(I_mz))))
78
79
80 #Q demodulation of I_mz at Omega_aom for doppler error signal obtention
81 kphidop = symbols('k_phi_doppler', real=True)
82 eps_dop = 2 * kphidop * I_mz * cos(w_aom*t-pi/2)
PDH_doppler_michelson/PDH_doppler_michelson_with_pzt.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''Pound-Drever-Hall setup
5 Michelson with piezo actuator in cavity arm and AOM in reference arm
6
7 -----
8 (2*W_aom)-->(X)---|LPF|--->
9 | ----- eps_dop
10 O
11 |
12 ----- --- ---
13 ------------|EOM|---|\|---|/|-----------( )
14 w_laser ----- --- --- cavity
15 ^ | |
16 | ----- U
17 | |AOM| |
18 | ----- |
19 | _|_ |
20 | //// |
21 | v
22 |---------->(X)
23 (W_pdh) |
24 -----
25 |LPF|
26 -----
27 |
28 v eps_pdh
29
30 '''
31
32 from time import time
33 tic = time()
34
35 from sympy import *
36 from sympy.simplify.fu import *
37
38 init_printing()
39
40 #constants
41 E0, J0, J1, w_laser, w_pdh, w_aom, t, c = symbols('E0, J0, J1, omega_laser, Omega_pdh, Omega_aom, t, c', imaginary=False, real=True)
42
43 '''#laser and phase-mod laser
44 E_laser = E0*exp(I*(w_laser*t))
45
46 E_eom = \
47 E0*( \
48 J0*exp(I*(w_laser*t)) \
49 + J1*exp(I*((w_laser+w_pdh)*t)) \
50 - J1*exp(I*((w_laser-w_pdh)*t)) \
51 )'''
52
53 #aom double shifted phase-mod wave in reference arm
54 E_aom = \
55 E0*( \
56 J0*exp(I*((w_laser +2*w_aom)*t)) \
57 + J1*exp(I*((w_laser+w_pdh+2*w_aom)*t)) \
58 - J1*exp(I*((w_laser-w_pdh+2*w_aom)*t)) \
59 )
60
61 #approximation of F(w) near a resonance
62 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
63 def F(phi):
64 dw = phi.diff(t) - w_cav
65 return -(I/pi)*(dw/dnu)
66
67 #reflected phase-mod laser and dephased by doppler effect
68 v_x, d_x, v_u, d_u = symbols('v_x, delta_x, v_u, delta_u', imaginary=False, real=True)
69 dx = v_x*t + d_x
70 du = v_u*t + d_u
71 E_ref = \
72 E0*( \
73 F( w_laser *t - (dx+du)*(w_laser)/c ) \
74 *J0*exp( I*( w_laser *t - 2*(dx+du)*(w_laser)/c ) ) \
75 + -1*J1*exp( I*( (w_laser+w_pdh)*t - 2*(dx+du)*(w_laser)/c ) ) \
76 - -1*J1*exp( I*( (w_laser-w_pdh)*t - 2*(dx+du)*(w_laser)/c ) ) \
77 )
78
79 #intensity of reflected wave
80 I_pdh = abs(E_ref)**2
81 I_pdh = expand(TR8(expand(expand_complex(I_pdh))))
82
83 #optical mixer
84 E_mich = sqrt(2)/2 * E_aom + sqrt(2)/2 * E_ref
85
86 #intensity of mixed wave
87 I_mich = abs(E_mich)**2
88 I_mich = expand(TR8(expand(expand_complex(I_mich))))
89
90 #Q demodulation of I_pdh at Omega_pdh for PDH error signal obtention
91 kphipdh = symbols('k_phi_pdh', real=True)
92 eps_pdh = 2 * kphipdh * I_pdh * cos(w_pdh*t-pi/2)
93 eps_pdh = expand(TR8(TR7(expand(eps_pdh))))
94
95 #Q demodulation of I_mich at 2*Omega_aom for doppler error signal obtention
96 kphidop = symbols('k_phi_doppler', real=True)
97 eps_dop = 2 * kphidop * I_mich * cos(2*w_aom*t-pi/2)
98 eps_dop = expand(TR8(TR7(expand(eps_dop))))
99
100 toc = time()
PDH_doppler_michelson/PDH_doppler_michelson_without_pzt.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''Pound-Drever-Hall setup
5 Michelson with piezo actuator and AOM in cavity arm
6
7 -----
8 (2*W_aom)-->(X)---|LPF|--->
9 | ----- eps_dop
10 O
11 |
12 ----- --- --- -----
13 ------------|EOM|---|\|---|/|---|AOM|---( )
14 w_laser ----- --- --- ----- cavity
15 ^ | |
16 | | U
17 | | |
18 | | |
19 | _|_ |
20 | //// |
21 | v
22 |---------->(X)
23 (W_pdh) |
24 -----
25 |LPF|
26 -----
27 |
28 v eps_pdh
29
30 '''
31
32 from time import time
33 tic = time()
34
35 from sympy import *
36 from sympy.simplify.fu import *
37
38 init_printing()
39
40 #constants
41 E0, J0, J1, w_laser, w_pdh, t = symbols('E0, J0, J1, omega_laser, Omega_pdh, t', imaginary=False, real=True)
42 v_x, d_x, c = symbols('v_x, delta_x, c', imaginary=False, real=True)
43 w_aom, dw, dphi = symbols('Omega_aom, delta_Omega, delta_phi', imaginary=False, real=True)
44
45 phi_u = dw*t #+ dphi
46 phi = w_aom*t + phi_u
47
48 '''#
49 #laser
50 E_laser = E0*exp(I*(w_laser*t))
51 '''
52
53 #phase-mod laser
54 E_eom = \
55 E0*( \
56 J0*exp(I*((w_laser )*t)) \
57 + J1*exp(I*((w_laser+w_pdh)*t)) \
58 - J1*exp(I*((w_laser-w_pdh)*t)) \
59 )
60
61 #approximation of F(w) near a resonance
62 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
63 def F(phi):
64 dw = phi.diff(t) - w_cav
65 return -(I/pi)*(dw/dnu)
66
67 #reflected phase-mod laser and dephased by doppler effect with double aom shift
68 dx = v_x*t + d_x
69 E_ref = \
70 E0*( \
71 F( (w_laser )*t - dx*(w_laser+phi.diff(t))/c + phi ) \
72 * J0*exp( I*( (w_laser )*t - 2*dx*(w_laser+phi.diff(t))/c + 2*phi ) ) \
73 + -1*J1*exp( I*( (w_laser+w_pdh)*t - 2*dx*(w_laser+phi.diff(t))/c + 2*phi ) ) \
74 - -1*J1*exp( I*( (w_laser-w_pdh)*t - 2*dx*(w_laser+phi.diff(t))/c + 2*phi ) ) \
75 )
76
77 #intensity of reflected wave
78 I_pdh = abs(E_ref)**2
79 I_pdh = expand(TR8(expand(expand_complex(I_pdh))))
80
81 #optical mixer
82 E_mich = sqrt(2)/2 * E_eom + sqrt(2)/2 * E_ref
83
84 #intensity of mixed wave
85 I_mich = abs(E_mich)**2
86 I_mich = expand(TR8(expand(expand_complex(I_mich))))
87
88 #Q demodulation of I_pdh at Omega_pdh for PDH error signal obtention
89 kphipdh = symbols('k_phi_pdh', real=True)
90 eps_pdh = 2 * kphipdh * I_pdh * cos(w_pdh*t-pi/2)
91 eps_pdh = expand(TR8(TR7(expand(eps_pdh))))
92
93 #Q demodulation of I_mich at 2*Omega_aom for doppler error signal obtention
94 kphidop = symbols('k_phi_doppler', real=True)
95 eps_dop = 2 * kphidop * I_mich * cos(2*w_aom*t-pi/2)
96 #eps_dop = 2 * kphidop * I_mich * cos(2*phi.diff(t)*t-pi/2)
97 eps_dop = expand(TR8(TR7(expand(eps_dop))))
98
99 toc = time()
PDH_doppler_michelson/PDH_doppler_michelson_without_pzt_eom.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''pseudo Pound-Drever-Hall setup
5
6 -----
7 (2*W_aom)-->(X)---|LPF|--->
8 | ----- eps
9 O
10 |
11 ---
12 --------------------|\|-----------------( )
13 w_laser --- cavity
14 |
15 -----
16 |AOM|
17 -----
18 _|_
19 ////
20
21 '''
22
23 from time import time
24 tic = time()
25
26 from sympy import *
27 from sympy.simplify.fu import *
28
29 init_printing()
30
31 #constants
32 E0, J0, J1, w_laser, w_pdh, t = symbols('E0, J0, J1, omega_laser, Omega_pdh, t', imaginary=False, real=True)
33 v_x, d_x, c = symbols('v_x, delta_x, c', imaginary=False, real=True)
34 w_aom = symbols('Omega_aom', imaginary=False, real=True)
35
36 #laser and phase-mod laser
37 E_laser = E0*exp(I*(w_laser*t))
38
39 #aom shifted phase-mod wave
40 E_aom = \
41 E0*exp(I*((w_laser+2*w_aom)*t))
42
43 #approximation of F(w) near a resonance
44 dnu, w_cav = symbols('delta_nu, omega_cav', imaginary=False, real=True)
45 def F(phi):
46 dw = phi.diff(t) - w_cav
47 return -(I/pi)*(dw/dnu)
48
49 #reflected phase-mod laser and dephased by doppler effect with double aom shift
50 dx = v_x*t + d_x
51 E_ref = \
52 F( (w_laser)*t - (w_laser)*(dx)/(2*pi*c) ) * E0*exp( I*( (w_laser)*t - (w_laser)*(2*dx)/c ) )
53
54 #optical mixer
55 E_mich = sqrt(2)/2 * E_aom + sqrt(2)/2 * E_ref
56
57 #intensity of mixed wave
58 I_mich = abs(E_mich)**2
59 I_mich = expand(TR8(expand(expand_complex(I_mich))))
60
compensated_link/compensated_link.py
Diff comments   View file @ 2ae5099
File was created 1 from sympy import *
2 from sympy.simplify.fu import *
3
4 init_printing()
5
6 #constants
7 E0, w_laser, W_aom, t = symbols('E0, omega_laser, Omega_aom, t', real=True, imaginary=False)
8 dphi, dW = symbols('Delta_phi, Delta_Omega', real=True, imaginary=False)
9 c, dx = symbols('c, Delta_x', real=True, imaginary=False)
10
11 phi_u = dW*t + dphi
12 phi = W_aom*t + phi_u
13
14 #laser
15 E_laser = E0*exp(I*(w_laser*t))
16
17 #reflected wave and dephased by doppler and noise and double shifted
18 E_aom_ref = E0*exp(I*( w_laser*t + 2*dx*(w_laser+phi.diff(t))/c + 2*phi ))
19
20 #reflected wave on the reference arm of michelson
21 E_ref = E_laser
22
23 #optical mixer
24 E_mix = sqrt(2)/2*E_ref + sqrt(2)/2*E_aom_ref
25
File was created 1 from sympy import *
2 from sympy.simplify.fu import *
3
4 init_printing()
5
6 #constants
7 A, B, w, t, kphi, c = symbols('A, B, omega, t, k_phi, c', imaginary=False, real=True)
8 dx = symbols('delta_x', cls=Function)
9 #wave vector
10 k = w/c
11
12 #reflected wave
13 E1 = A*cos(w*t-2*k*dx(t))
14
15 #demodulation of E1 at omega in quadrature
mich_psd_calculations/calc.py
Diff comments   View file @ 2ae5099
File was created 1 from numpy import log, log10, pi
2
3 #constants
4 c = 3E8
5 nu = c/1542E-9
6 f = 1
7
8 #allan deviation aimed
9 sigma_y = 1E-17
10
11 #PSD of frequency fluctuations (frequency flicker) in dB.Hz^-1
12 Sy = 10*log10(sigma_y**2/(2*log(2)))
13
14 #PSD of phase fluctuations in dB.rad^2.Hz^-1
15 Sphi = Sy + 20*log10(nu) - 20*log10(f)
michelson_w_AOM/michelson_w_AOM.py
Diff comments   View file @ 2ae5099
File was created 1 from sympy import *
2 from sympy.simplify.fu import *
3
4 init_printing()
5
6 #constants
7 E0, E1, w, W, t, dphi, kphi = symbols('E0, E1, omega, Omega, t, Delta_phi, k_phi', real=True, imaginary=False)
8 dx, du, c = symbols('Delta_x, Delta_u, c', real=True, imaginary=False)
9
10 #reference wave
11 Eb0 = E0*exp(I*(w*t))
12
13 #double Omega shifted and dphi dephased wave
14 Eb1 = E1*exp(I*((w+2*W)*t -2*w*(dx+2*du)/c))
15
16 #optical mixer
17 Emix = sqrt(2)/2 * Eb0 + sqrt(2)/2 * Eb1
18
File was created 1 from sympy import *
2 from sympy.simplify.fu import *
3
4 init_printing()
5
6 A, B, w, t, dphi = symbols('A, B, omega, t, Delta_phi', real=True, imaginary=False)
7
8 #polynimial approach of RF mixer
9 k1, k2, k3 = symbols('k1, k2, k3', real=True, imaginary=False)
10 e = A*cos(w*t) + B*cos(w*t+dphi-pi/2)
11 Vmix_poly = k1*e + k2*e**2
12 Vmix_poly = expand(TR8(TR7(expand(Vmix_poly))))
13
14 print('Polynomial result :\n' + pretty(Vmix_poly) + '\n')
15
tf_cavity/tf_cavity.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''TF of FP cavity in reflection
5
6 ----------
7 X(s) ----- | -tau⋅s |
8 -------------->|1-R|----->(X)----->|e |------
9 | ----- ^ ---------- |
10 | | |
11 | | V
12 ---- ---- ----
13 |-R| |-R| |-R|
14 ---- ---- ----
15 | ^ |
16 | | ---------- |
17 Y(s) V ----- | | -tau⋅s | |
18 <-----(X)<-----|1-R|<--------------|e |<-----
19 ----- ----------
20
21 '''
22
23 from sympy import *
24
25 init_printing()
26
27 w, r, L, c = symbols('omega, r, L, c', imaginary=False, real=True)
28
29 tau = L/c
30 fsr = 1/(2*tau)
31
32 #TF of cavity in reflection
33 def Fr(w):
34 s = 1j*w
35 return r*(exp(-2*tau*s)-1)/(1-r**2*exp(-2*tau*s))
36
37 dw = symbols('dw', imaginary=False, real=True)
38 Fr_dw_0 = simplify(simplify(Fr(2*pi*fsr+dw).series(dw, 0, 2).expand().coeff(dw))*dw)
39
40 '''results
tf_cavity/tf_cavity_num.py
Diff comments   View file @ 2ae5099
File was created 1 #!/usr/bin/python
2 # -*- coding: utf-8 -*-
3
4 '''TF of FP cavity in reflection
5
6 ----------
7 X(s) ----- | -tau⋅s |
8 -------------->|1-R|----->(X)----->|e |------
9 | ----- ^ ---------- |
10 | | |
11 | | V
12 ---- ---- ----
13 |-R| |-R| |-R|
14 ---- ---- ----
15 | ^ |
16 | | ---------- |
17 Y(s) V ----- | | -tau⋅s | |
18 <-----(X)<-----|1-R|<--------------|e |<-----
19 ----- ----------
20
21 '''
22
23 '''import matplotlib as mpl
24 mpl.use('pgf')
25
26 def figsize(scale):
27 fig_width_pt = 469.755 # Get this from LaTeX using \the\textwidth
28 inches_per_pt = 1.0/72.27 # Convert pt to inch
29 golden_mean = (5.0**0.5-1.0)/2.0 # Aesthetic ratio (you could change this)
30 fig_width = fig_width_pt*inches_per_pt*scale # width in inches
31 fig_height = fig_width*golden_mean # height in inches
32 fig_size = [fig_width,fig_height]
33 return fig_size
34
35 pgf_with_latex = { # setup matplotlib to use latex for output
36 "pgf.texsystem": "pdflatex", # change this if using xetex or lautex
37 "text.usetex": True, # use LaTeX to write all text
38 "font.family": "serif",
39 "font.serif": [], # blank entries should cause plots to inherit fonts from the document
40 "font.sans-serif": [],
41 "font.monospace": [],
42 "axes.labelsize": 10, # LaTeX default is 10pt font.
43 "text.fontsize": 10,
44 "legend.fontsize": 8, # Make the legend/label fonts a little smaller
45 "xtick.labelsize": 8,
46 "ytick.labelsize": 8,
47 "figure.figsize": figsize(0.9), # default fig size of 0.9 textwidth
48 "pgf.preamble": [
49 r"\usepackage[utf8x]{inputenc}", # use utf8 fonts becasue your computer can handle it :)
50 r"\usepackage[T1]{fontenc}", # plots will be generated using this preamble
51 ]
52 }
53 mpl.rcParams.update(pgf_with_latex)
54 '''
55 from numpy import *
56 import matplotlib.pyplot as plt
57
58 r = 0.99
59 L = 140e-3
60 c = 299792458
61
62 tau = L/c
63 fsr = 1/(2*tau)
64
65 f0 = (193e12//fsr)*fsr
66 f = linspace(f0-0.1*fsr, f0+0.1*fsr, 1e5)
67
68 #TF of cavity in reflection
69 def Fr(w):
70 s = 1j*w
71 return r*(exp(-2*tau*s)-1)/(1-r**2*exp(-2*tau*s))
72
73 G = Fr(2*pi*f)
74
75 #plot bode of F(w)
76 ax1 = plt.subplot(3, 1, 1)
77 ax1.set_ylabel('Magnitude')
78 ax1.plot(f, abs(G))
79 ax1.grid()
80
81 ax2 = plt.subplot(3, 1, 2, sharex = ax1)
82 ax2.set_ylabel('Phase (deg)')
83 ax2.set_xlabel('omega (rad.s$^{-1}$)')
84 ax2.plot(f, angle(G, deg = True))
85 ax2.grid()
86
87
88 #nyquist
89 ax3 = plt.subplot(3, 1, 3)
90 ax3.set_ylabel('$j\omega$')
91 ax3.set_xlabel('$\sigma$')
92 ax3.plot(real(G), imag(G))