py or examples / curved_dielectric_beam_scan. See examples / flat_dielectric_beam_scan. To model a beam through flat dielectric, you must include a flat lens or flat refraction at the front and back surfaces of the dielectric. Refraction components only have an effect on the beam if there is a radius of curvature to the dielectric surface. Trying to connect two spaces together directly will result in an error. You * must * have a component between spaces, even if it is just a flat lens, flat mirror, or flat refraction element. Scan the cavity beam parmater using scan_cavity (). If cavity is stable, find the fundamental eigenmode for the beam ( q - parameter ) Set this q - parameter as q_input beam. User computes the cavity ABCD matrix from the components added using calculate_cavity_ABCD (). org / finesse / pykat # Process User adds in mirrors, lenses, and spaces * in sequential order *. php ? id = geosim : jammt Finesse + pykat : https : // git. com / nicolassmith / alm JAMMT : http : // bham. # Other options MATLAB alamode : https : // github. Just mirrors, lenses, and lengths added in sequence. No fancy optimization like alamode, no nice GUI like jammt. addpath ( 'path/to/this/directory' ) from acer import BeamTrace Docstringįrom beamtrace/tracer.py, the main class BeamTrace docstring Class BeamTrace For very simple beam waist and gouy phase calculations in python. Or if you have LIGO credentials you can git clone the directory at Īnd run import sys sys. Then in a python scipy or ipython terminal, import the BeamTrace class by running import beamtrace from acer import BeamTrace
#ABCD MATRIX INSTALL#
You can install using pip at pip install beamtrace Notch response.Main file in this directory is tracer.py. The classic twin-T filter is a purely RC circuit that can produce a very sharp Things get rather theoreticalĪ little while after publishing the above analysis Hutchins wrote a response published asĭifferent route to the common-RC solution he arrives at the same point, and extends the workīy plotting the root-locus of the filter in the presence of feedback. This far from the cutoff point the attenuation is around 200dB. The time the frequency reaches around 1MHz the phase shift is very close to 360°, although Secondly, the phase shift continues heading towards 360° - by In other words a 2kHz sine wave is inverted,Īlbeit reduced in amplitude by about 26dB (roughly 1/20th of the input level). The phase (dashed line) reaches 180° of phase shift. Some interesting observations can be made from the spice plot. LTSpice confirming the theoretical filter behaviour: To confirm these results an AC simulation was run in We can derive simple expressions for the four terms:Ī = \left.\fracĬ to 100n and sweep over the range 1Hz to 100kHz. Firstįrom here we can write down the expressions for V 1 and I 1:īy setting V 2 or I 2 to zero (short-circuit or open-circuit respectively) The A, B, C and D refer to the names of the four components of the ABCD matrix. Network without tedious sign-changing to worry about. Whereupon the output current of the first network becomes the input current of the second Subtle distinction comes to light when we cascade - or chain - two networks Two-port networks would have spotted the "wrong" sign of I 2 already). One peculiarity of the ABCD matrix as compared to the other two-port networks is theĭirection of the current flow on the second port is reversed (those familiar with The ABCD Matrix (or Chain Matrix or Transmission Matrix) describesĪ two-port network: a box with a two-wire port on the left and a two-wire port on the right. And along the way we'll useĬomputers to do the tedious algebraic crunching. Passive networks using nothing more than 2x2 matrices. The theory of the ABCD matrix, and show how it can be used to solve seemingly-complex While they have been around for decades their power and simplicity is perfect forĭesign and analysis of passive filter networks. A little while back I was reminded of the ABCD matrix during a discussion
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