tf_cavity_num.py
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#!/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
'''