tf_cavity_num.py
4.01 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
#!/usr/bin/python
# -*- coding: utf-8 -*-
'''TF of FP cavity in reflection
----------
X(s) ----- | -tau⋅s |
-------------->|1-R|----->(X)----->|e |------
| ----- ^ ---------- |
| | |
| | V
---- ---- ----
|-R| |-R| |-R|
---- ---- ----
| ^ |
| | ---------- |
Y(s) V ----- | | -tau⋅s | |
<-----(X)<-----|1-R|<--------------|e |<-----
----- ----------
'''
'''import matplotlib as mpl
mpl.use('pgf')
def figsize(scale):
fig_width_pt = 469.755 # Get this from LaTeX using \the\textwidth
inches_per_pt = 1.0/72.27 # Convert pt to inch
golden_mean = (5.0**0.5-1.0)/2.0 # Aesthetic ratio (you could change this)
fig_width = fig_width_pt*inches_per_pt*scale # width in inches
fig_height = fig_width*golden_mean # height in inches
fig_size = [fig_width,fig_height]
return fig_size
pgf_with_latex = { # setup matplotlib to use latex for output
"pgf.texsystem": "pdflatex", # change this if using xetex or lautex
"text.usetex": True, # use LaTeX to write all text
"font.family": "serif",
"font.serif": [], # blank entries should cause plots to inherit fonts from the document
"font.sans-serif": [],
"font.monospace": [],
"axes.labelsize": 10, # LaTeX default is 10pt font.
"text.fontsize": 10,
"legend.fontsize": 8, # Make the legend/label fonts a little smaller
"xtick.labelsize": 8,
"ytick.labelsize": 8,
"figure.figsize": figsize(0.9), # default fig size of 0.9 textwidth
"pgf.preamble": [
r"\usepackage[utf8x]{inputenc}", # use utf8 fonts becasue your computer can handle it :)
r"\usepackage[T1]{fontenc}", # plots will be generated using this preamble
]
}
mpl.rcParams.update(pgf_with_latex)
'''
from numpy import *
import matplotlib.pyplot as plt
r = 0.99998
L = 140e-3
c = 299792458
tau = L/c
fsr = 1/(2*tau)
finesse = pi*r/(1-r**2)
print(' Finesse = %f\n FSR = %f\n FSR/Finesse = %f'%(finesse, fsr, fsr/finesse))
f0 = (193e12//fsr)*fsr
f = linspace(f0-0.1*fsr, f0+0.1*fsr, 1e5)
fm = 30e6
#TF of cavity in reflection
def Fr(w):
s = 1j*w
return r*(exp(-2*tau*s)-1)/(1-r**2*exp(-2*tau*s))
G = Fr(2*pi*f)
Glsb = Fr(2*pi*(f-fm))
Gusb = Fr(2*pi*(f+fm))
#plot setup
fig, axarr = plt.subplots(3, 2, sharex='col')
#plot bode of F(w)
axarr[0, 1].set_ylabel('Magnitude')
#axarr[0, 1].set_xlabel('Frequency (Hz)')
axarr[0, 1].plot(f, abs(G))
axarr[0, 1].grid()
axarr[1, 1].set_ylabel('Phase (deg)')
#axarr[1, 1].set_xlabel('Frequency (Hz)')
axarr[1, 1].plot(f, angle(G, deg = True))
axarr[1, 1].grid()
#PDH signal
iG = (G*Gusb.conjugate()-G.conjugate()*Glsb).imag
axarr[2, 1].set_ylabel('epsillon normalized')
axarr[2, 1].set_xlabel('Frequency (Hz)')
axarr[2, 1].xaxis.set_label_coords(0.5, -0.3)
axarr[2, 1].plot(f, iG)
axarr[2, 1].grid()
#nyquist
axarr[2, 0].set_ylabel('$j\omega$')
axarr[2, 0].set_xlabel('$\sigma$')
axarr[2, 0].plot(real(G), imag(G))
axarr[2, 0].grid()
axarr[2, 0].axis('equal')
axarr[2, 0].set_xlim([-1.1, 1.1])
#layout
axarr[0, 0].axis('off')
axarr[1, 0].axis('off')
fig.subplots_adjust(wspace=0.5)
plt.tight_layout()
#plt.savefig('fig.pgf')
plt.show()
'''results
⎛ -2.0⋅ⅈ⋅L⋅ω ⎞
⎜ ───────────⎟
⎜ c ⎟
r⋅⎝-1 + ℯ ⎠
F(w) = ─────────────────────
-2.0⋅ⅈ⋅L⋅ω
───────────
2 c
- r ⋅ℯ + 1
'''