add LPF behav of the cavity

bmarechal
1 parent 07295cdf44
Showing 2 changed files with 157 additions and 1 deletions Side-by-side Diff
tf_cavity/tf_cavity_num.py
tf_cavity/tf_cavity_num_lp.py
@@ -62,7 +62,7 @@
 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))
+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)
+#!/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, int(1e5))
+
+fm = 30e6
+
+ff = linspace(1, 1e6, int(1e5))
+
+#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))
+
+#TF of cavity frequency-to-signal
+def Ff2s(w):
+    s = 1j*w
+    return (1-exp(-2*tau*s))/(2*tau*s)*(1-r**2)/(1-r**2*exp(-2*tau*s))
+
+
+G = Fr(2*pi*f)
+Glsb = Fr(2*pi*(f-fm))
+Gusb = Fr(2*pi*(f+fm))
+
+Gf2s = Ff2s(2*pi*ff)
+
+#plot setup
+fig, axarr = plt.subplots(3, 3, 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()
+
+#plot bode of Ff2s(w)
+axarr[1, 2].set_ylabel('Magnitude')
+#axarr[1, 2].set_xlabel('Frequency (Hz)')
+axarr[1, 2].set_xscale('log')
+axarr[1, 2].plot(ff, 20*log10(abs(Gf2s)))
+axarr[1, 2].grid()
+axarr[2, 2].set_ylabel('Phase (deg)')
+axarr[2, 2].set_xlabel('Frequency (Hz)')
+axarr[2, 2].set_xscale('log')
+axarr[2, 2].xaxis.set_label_coords(0.5, -0.3)
+axarr[2, 2].plot(ff, angle(Gf2s, deg = True))
+axarr[2, 2].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')
+axarr[0, 2].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
+
+'''
...	...	@@ -62,7 +62,7 @@
62	62	tau = L/c
63	63	fsr = 1/(2*tau)
64	64	finesse = pir/(1-r*2)
65		-print('Finesse = %f\n FSR = %f\n FSR/Finesse = %f'%(finesse, fsr, fsr/finesse))
	65	+print(' Finesse = %f\n FSR = %f\n FSR/Finesse = %f'%(finesse, fsr, fsr/finesse))
66	66
67	67	f0 = (193e12//fsr)*fsr
68	68	f = linspace(f0-0.1fsr, f0+0.1fsr, 1e5)
	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_ptinches_per_ptscale # 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 = 0.99998
	59	+L = 140e-3
	60	+c = 299792458
	61	+
	62	+tau = L/c
	63	+fsr = 1/(2*tau)
	64	+finesse = pir/(1-r*2)
	65	+print(' Finesse = %f\n FSR = %f\n FSR/Finesse = %f'%(finesse, fsr, fsr/finesse))
	66	+
	67	+f0 = (193e12//fsr)*fsr
	68	+f = linspace(f0-0.1fsr, f0+0.1fsr, int(1e5))
	69	+
	70	+fm = 30e6
	71	+
	72	+ff = linspace(1, 1e6, int(1e5))
	73	+
	74	+#TF of cavity in reflection
	75	+def Fr(w):
	76	+ s = 1j*w
	77	+ return r(exp(-2taus)-1)/(1-r2exp(-2taus))
	78	+
	79	+#TF of cavity frequency-to-signal
	80	+def Ff2s(w):
	81	+ s = 1j*w
	82	+ return (1-exp(-2taus))/(2taus)(1-r2)/(1-r2exp(-2taus))
	83	+
	84	+
	85	+G = Fr(2pif)
	86	+Glsb = Fr(2pi(f-fm))
	87	+Gusb = Fr(2pi(f+fm))
	88	+
	89	+Gf2s = Ff2s(2piff)
	90	+
	91	+#plot setup
	92	+fig, axarr = plt.subplots(3, 3, sharex='col')
	93	+
	94	+#plot bode of F(w)
	95	+axarr[0, 1].set_ylabel('Magnitude')
	96	+#axarr[0, 1].set_xlabel('Frequency (Hz)')
	97	+axarr[0, 1].plot(f, abs(G))
	98	+axarr[0, 1].grid()
	99	+axarr[1, 1].set_ylabel('Phase (deg)')
	100	+#axarr[1, 1].set_xlabel('Frequency (Hz)')
	101	+axarr[1, 1].plot(f, angle(G, deg = True))
	102	+axarr[1, 1].grid()
	103	+
	104	+#plot bode of Ff2s(w)
	105	+axarr[1, 2].set_ylabel('Magnitude')
	106	+#axarr[1, 2].set_xlabel('Frequency (Hz)')
	107	+axarr[1, 2].set_xscale('log')
	108	+axarr[1, 2].plot(ff, 20*log10(abs(Gf2s)))
	109	+axarr[1, 2].grid()
	110	+axarr[2, 2].set_ylabel('Phase (deg)')
	111	+axarr[2, 2].set_xlabel('Frequency (Hz)')
	112	+axarr[2, 2].set_xscale('log')
	113	+axarr[2, 2].xaxis.set_label_coords(0.5, -0.3)
	114	+axarr[2, 2].plot(ff, angle(Gf2s, deg = True))
	115	+axarr[2, 2].grid()
	116	+
	117	+
	118	+#PDH signal
	119	+iG = (GGusb.conjugate()-G.conjugate()Glsb).imag
	120	+axarr[2, 1].set_ylabel('epsillon normalized')
	121	+axarr[2, 1].set_xlabel('Frequency (Hz)')
	122	+axarr[2, 1].xaxis.set_label_coords(0.5, -0.3)
	123	+axarr[2, 1].plot(f, iG)
	124	+axarr[2, 1].grid()
	125	+
	126	+
	127	+#nyquist
	128	+axarr[2, 0].set_ylabel('$j\omega$')
	129	+axarr[2, 0].set_xlabel('$\sigma$')
	130	+axarr[2, 0].plot(real(G), imag(G))
	131	+axarr[2, 0].grid()
	132	+axarr[2, 0].axis('equal')
	133	+axarr[2, 0].set_xlim([-1.1, 1.1])
	134	+
	135	+#layout
	136	+axarr[0, 0].axis('off')
	137	+axarr[1, 0].axis('off')
	138	+axarr[0, 2].axis('off')
	139	+fig.subplots_adjust(wspace=0.5)
	140	+plt.tight_layout()
	141	+#plt.savefig('fig.pgf')
	142	+plt.show()
	143	+
	144	+'''results
	145	+
	146	+ ⎛ -2.0⋅ⅈ⋅L⋅ω ⎞
	147	+ ⎜ ───────────⎟
	148	+ ⎜ c ⎟
	149	+ r⋅⎝-1 + ℯ ⎠
	150	+F(w) = ─────────────────────
	151	+ -2.0⋅ⅈ⋅L⋅ω
	152	+ ───────────
	153	+ 2 c
	154	+ - r ⋅ℯ + 1
	155	+
	156	+'''