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Entry  Thu Aug 16 13:49:33 2012, Yaakov, Update, PEM, Transfer functions of seismic stacks, differential motion of test mass 8x
    Reply  Thu Aug 16 20:04:46 2012, Yaakov, Update, PEM, Transfer functions of seismic stacks, differential motion of test mass 6x
Message ID: 7204     Entry time: Thu Aug 16 13:49:33 2012     Reply to this: 7209
Author: Yaakov 
Type: Update 
Category: PEM 
Subject: Transfer functions of seismic stacks, differential motion of test mass 

I estimated the transfer function of the seismic stacks using a rough model I made based on the LIGO document LIGO T000058 -00. I used a Q of 3.3 for the viton springs, and resonant frequencies of 2.3, 7.5, 15, and 22 Hz (measured in that document for the horizontal motion). I multiplied the simple mass-spring transfer function four times for each layer of metal/spring, with the respective resonant frequency for each. The pendulum suspending the test masses has a resonant frequency of 0.74 and a Q of 3, according to the same document.

stack_tf.pngstack_tf.fig

When I multiply the net transfer function (pendulum included, the green line above) by the differential motion of the x arm that I measured in eLog 7186, I find the differential motion of the test mass (NOTE: I converted the differential motion to displacement by multiplying by (1/2*pi*f)).

mass_diff_motion.pngmass_diff_motion.fig

It agrees within an order of magnitude to the seismic wall from the displacement noise spectrum hanging above the control room computers.

Finally, I looked at how the geophone and accelerometer noise spectra looked compared to the ground differential motion (any STACIS sensor signal will also be multiplied by the stack/pendulum transfer function, so I'm comparing to the differential motion before it goes through the chamber). Below about 1 Hz, it is clear from the plot below that the STACIS could never be of any benefit, even with accelerometers rather than geophones as the feedback sensors.

noise_v_diff_motion.pngnoise_v_diff_motion.fig

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stack_tf.png
Attachment 5: stack_tf.fig  2.005 MB
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