allegro g050208-00-z lsc, livingston 23 march, 2005 1 calibration for the allegro resonant detector...

G050208-00-Z LSC, Livingston 23 March , 2005

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ALLEGRO

Calibration for the ALLEGRO resonant detector -- S2 and S4

Martin McHugh, Loyola University New Orleans

Warren Johnson, Louisiana State University

with the ALLEGRO group, Stochastic Sources Subgroup


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ALLEGRO

Outline

• Motivation, background

• Signal flow diagram, transfer function equations

• Discussion of calibration measurements

• Recent mysteries

• summary


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ALLEGRO

Motivation

• Provide input to stochastic background analysis using ALLEGRO and LLO (John Whelan’s talk earlier this week)

• Unlike an event list based search, a coherent search such as this requires a phase consistent response function for the detector signal path


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ALLEGRO

ALLEGRO schematic


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ALLEGRO

Signal path


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ALLEGRO

€

˜ z v ( f − f r ) = A( f ) ˜ v S ( f ) = aLe i(td 2π ( f − fr ))e−iφ ˜ v S ( f )

€

˜ F ( f ) = J( f ) ˜ h ( f ) = 4MLf 2 ˜ h ( f )

€

˜ x ( f ) = G( f ) ˜ F ( f )

= α1

f p2 − f 2 +

if p f

Qp( )−

1

fm2 − f 2 + ifm f

Qm( )

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟˜ F ( f )

€

˜ I ( f ) = K ⋅ ˜ x ( f ) =IDC

g

⎛

⎝ ⎜

⎞

⎠ ⎟˜ x ( f )

€

˜ v S ( f ) = Z ⋅ ˜ I ( f )

€

˜ z c ( f − f r ) = D ⋅ ˜ z v ( f − f r )

Form of each Transfer Function€

˜ F C ( f ) = H ˜ v e ( f ) =CcVDC

gc

˜ v e ( f )


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ALLEGRO

Need to determine --

• Mode frequencies and Q’s -- fm , fp , Qm , Qp

• overall scale -- in practice we measure is mechanical gain -- includes

‘tuning factor’

• Lock-in amplifier parameters -- gain, filter delay and phase shiftAlso need to know the phase of

the lock-in reference oscillator

€

⋅K ⋅Z

So in practice the calibration amounts to --

€

˜ h ( f − fr ) =˜ z C ( f − f r )

J( f )G( f )KZA( f − f r)D

Inverse fft then gives

€

h H (t) complex heterodyned strain time series


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ALLEGRO

New calibrator installed between S2 and S4 -- known transfer function

• One plate of capacitor is tightly coupled to bar.

• Other plate is weakly coupled to the bar, so acts like a free mass.

• Both plates electrically isolated.

Rest of detector unchanged -Measurements will apply to S2


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ALLEGRO

The calibrator mounted on the bar


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ALLEGRO

Transfer function - white noise excitation to measured output

measurements from 20 March 2004 -- excitation measured through lock-in and A/D plotted here we have

€

TF = H ⋅G( f ) ⋅K ⋅Z

gives us the overall scale -


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ALLEGRO

Band-limited white noise injection -- recorded directly and through lock-in/anti-aliasing filters

Lock-in/ filter measurements


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ALLEGRO

Compare fourier coefficients

Lock-in/filter introduces an 11ms delay and 18 degree phase shift


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ALLEGRO


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ALLEGRO

Calibration lineCalibration line

Detector resonancesDetector resonances

Extra mechanical resonancesExtra mechanical resonances

Raw data


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ALLEGRO

Calibrated strain spectrum from S4


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ALLEGRO

Stability of calibration -- calibration line tracked through S2


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ALLEGRO

• Discrepancy between white noise injection data sets discovered to be due to change in polarity of DC

bias applied to calibrator (?!)

• Two mysteriesNuisance mode at 885 Hz -- relative phase changes

with DC bias polarityApparent offset in DC bias voltage on calibrator

A Problem


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ALLEGRO

Transfer function magnitude, white noise injection --blue curve +3.99VDC nominal biasred curve -3.99VDC nominal bias


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ALLEGRO

… now flip the plate to which the voltage is applied


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ALLEGRO

we can certainly model extra mechanical modes -- but the phase flip is a mystery


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ALLEGRO

837Hz calibration line strength vs. calibrator bias


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ALLEGRO

Summary

• We have calibrated h(t) for S2 data set • Hardware injections done for E12, S4 -- good news

we are able to extract coherent signal between L1 and A1 (see Sukanta’s earlier talk)

• Analyze burst injections done to determine overall sign of the calibration

• Need to investigate calibrator behavior with post S4 measurements -- be sure there is no problem with overall scale determination

allegro g050208-00-z lsc, livingston 23 march, 2005 1 calibration for the allegro resonant detector...

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