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tf_cavity/tf_cavity.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 |<-----
----- ----------
'''
from sympy import *
init_printing()
w, r, L, c = symbols('omega, r, L, c', imaginary=False, real=True)
tau = L/c
fsr = 1/(2*tau)
#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))
dw = symbols('dw', imaginary=False, real=True)
Fr_dw_0 = simplify(simplify(Fr(2*pi*fsr+dw).series(dw, 0, 2).expand().coeff(dw))*dw)
'''results
⎛ -2.0⋅ⅈ⋅L⋅ω ⎞
⎜ ───────────⎟
⎜ c ⎟
r⋅⎝-1 + ℯ ⎠
F(w) = ─────────────────────
-2.0⋅ⅈ⋅L⋅ω
───────────
2 c
- r ⋅ℯ + 1
'''
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