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Entry  Tue Dec 2 02:44:45 2014, Jenne, Update, LSC, Tried cav pole compensation trick - fail 
    Reply  Wed Dec 3 01:46:12 2014, Koji, Update, LSC, Tried cav pole compensation trick - fail 
Message ID: 10748     Entry time: Wed Dec 3 01:46:12 2014     In reply to: 10746
Author: Koji 
Type: Update 
Category: LSC 
Subject: Tried cav pole compensation trick - fail 

Where did these 200Hz, 6kHz come from?


I wonder what are the correct filters to be incorporated in the filter banks for the cav pole compensarion.

Facts:

1. ALS Common and Diff have the cavity pole for the green (fcav_GR)

2. IR DARM has the cavity pole of the arms for IR (fcav_IR_DARM)

3. IR CARM (REFL, POP, POX, or POY) has the double cavity pole (fcav_IR_CARM)

Calculations:

1. T(ITM_GR) = 1.094%, T(ETM_GR) = 4.579% => F=108.6 (cf. https://wiki-40m.ligo.caltech.edu/Core_Optics)
L = 37.8 m (cf. http://nodus.ligo.caltech.edu:8080/40m/9804)
=> fcav_GR = c /( 4 L F) = 18.3 kHz ... ignore

2. T(ITM_IR) = 1.384%, T(ETM_IR) = 13.7ppm => F=450.4
=> fcav_IR_DARM = 4.40 kHz

3. The common cavity pole is lower than fcav_IR by factor of power recycling gain.
=> fcav_IR_CARM = fcav_IR / (P_TR * T_PRM)
P_TR is normalized for the locked arm cavity with the PRM misaligned.
T_PRM is 5.637%

e.g. for the TR of 100, fcav_IR_CARM = 4.40/(100*0.05637) = 780Hz

                         (IR CARM) o--|
                                      +--[CARM 780Hz zero / ??? pole]
(ALSX) o--|   |-[ALS C 780Hz pole]----|
          | M |
(ALSY) o--|   |-[ALS D 4.40kHz pole]--|
                                      +--[DARM 4.40kHz zero / ??? pole]
                         (IR DARM) o--|

???Hz pole is to ensure the servo filters does not have infinite gain at f=infinite, but in practice we probably can ignore it as long as it is provided by a roll-off filter

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