Abstract:

I calculated the input equivalent noise of CARM CMS from the several DAQ channels when locking IRX, and compared them.
There are discrepancy between the channels, so some noisy components might exist in CARM CMS.

Detail:

One of the evaluations of characteristics of IRX LSC, I calculated the input equivalent noise of the CARM CMS from several .
Figure 1 shows the CARM medm screens when locking IRX.

1. K1:LSC-CARM_SERVO_MIXER_DAQ_OUT_DQ

K1:LSC-CARM_SERVO_MIXER_DAQ_OUT_DQ is calibrated to the voltage before the GENERIC FILTER (overall gain of 100).
So, calibration from K1:LSC-CARM_SERVO_MIXER_DAQ_OUT_DQ to CARM CMS input is just a gain of -10dB = 0.3162.

2. K1:LSC-CARM_SERVO_FAST_DAQ_OUT_DQ

K1:LSC-CARM_SERVO_FAST_DAQ_OUT_DQ is also calibrated to the voltage before the GENERIC filter (poles:100,100, zeros:10,10, DC gain:1), thanks to the filter modification today (klog30103).
So, calibration from K1:LSC-CARM_SERVO_FAST_DAQ_OUT_DQ to CARM CMS input is as follows:
poles: 0, 0, 1000, 1000
zeros: 5.3, 5.3, 10, 10
DC gain: 5.3**2 for compasating 5.3 Hz high pass filter, -11dB for FAST gain, 0.01**2 for compensating two BOOST filters, and -10dB for IN1 gain = 2.503e-4

3. K1:LSC-CARM_SERVO_SLOW_DAQ_OUT_DQ

K1:LSC-CARM_SERVO_SLOW_DAQ_OUT is also calibrated to the voltage before GENERIC filter (poles:100,100, zeros:10,10, DC gain:1).
So, calibration from K1:LSC-CARM_SERVO_SLOW_DAQ_OUT to CARM CMS input is as follows:
poles: 1000, 1000
zeros: 10, 10
DC gain: 0.01**2 for compensating two COM BOOST filters and -10dB for IN1 gain = 3.162e-5

4. K1:LSC-REFL_PDA1_RF45_I_ERR_DQ

K1:LSC-REFL_PDA1_RF45_I_ERR_DQ is calibrated to the input equivalent signals of analog whitening filters in the unit of DGS counts.
In addition, differential signals from I/Q demodulator to analog whitening filter is double of the signals sent to CARM CMS according to the circuit diagram (JGW-D1402413-v1).
So, calibration from K1:LSC-REFL_PDA1_RF45_I_ERR_DQ to CARM CMS input is as follows:
DC gain: 0.5 for differential to single end and 6.104e-4 for DGS counts to voltage = 3.052e-4

Figure 2 shows the CARM CMS input equivalent noise from each signal.
During the measurement, I engaged three dewhitening stages and 30dB overall gains not to be limited by ADC noise.

Discussion:

K1:LSC-CARM_SERVO_MIXER_DAQ_OUT_DQ is limited by ADC noise below several hundreds Hz but the other signals should not be limited by ADC noise.
At high frequency, all signals except for K1:LSC-REFL_PDA1_RF45_I_ERR_DQ are consistent, so they seems residual frequency noise.
Since K1:LSC-REFL_PDA1_RF45_I_ERR_DQ is roughly 2 times smaller than the others, I might miss a factor of 2 somewhere.

The spectrum of K1:LSC-REFL_PDA1_RF45_I_ERR_DQ is much higher than the others below 1kHz.
This implies that noise is induced after dividing error signals into two: the signals to CMS and the signal to analog whitening.
However, noise level seems too large if the noise comes from analog circuits, so something might happen in the I/Q demodulator or analog whitening filter.

The spectra of K1:LSC-CARM_SERVO_FAST_DAQ_OUT_DQ and K1:LSC-CARM_SERVO_SLOW_DAQ_OUT are similar but coherence between 20 Hz -to 1kHz is not close to 1.
ADC noise should be enough small, so some noisy component might exist after splitting feedback signals to fast and slow pathes.
Since FAST path signals are higher around several tens of Hz and lower than several hundreds of Hz, both FAST and SLOW pathes might have noise components.

Further investigation is necessary to characterize CARM CMS noise (noise budget of signle arm lock might be effective).

Note:

It would be better to do the same analysis for GRX and GRY PDH CMS.