Summary:

Using the Wiener Filter estimate of the DARM disturbance we will have to cancel, I computed how the control signal would look like for a few scenarios. Our DACs are 16-bit, +/-10V (i.e. +/-32,768cts-pk, or ~23,000cts RMS). We need to consider the shape of the de-whitening filter to conclude whether it is feasible to increase the series resistance by x10 or not.

Some details:

Note that in this first computation, I have not considered

• Actuation range required by other loops (e.g. local damping, Oplev etc).
• At some point, I need to add the 2P/c radiation pressure disturbance as well.
• The control signal is calculated assuming we are actuating equally on both ETMs (but with opposite phase).
• RMS computation is done from 30 Hz downwards, as above 30 Hz, I think the estimate from the previous elog is not true seismic displacement. 
• De-whitening filters (or digital whitening), which will be required to suppress DAC noise at 100Hz.
• DARM loop shape, specifically low-pass to avoid sensing noise injection. In this calculation, I just used the pendulum transfer function.

While doing this calculation, I have accounted for the fact that right now, the analog de-whitening filters in the ETM drive chain have a x3 gain which we will remove. Actually this is an assumption, I have not yet measured a transfer function, maybe I'll do one channel at EY to confirm. Also, the actuator gains themselves need to be confirmed.

As I was looking at the coil driver schematic more closely, I realized that there are actually two separate series resistances, one for the fast controls path, and another for the DC bias voltage from the slow ADCs. So I think we have been underestimating the Johnson noise of the coil drivers by sqrt(2). I've also attached screenshots of the IFOalign and MCalign screens. The two  ITMs and ETMX have pitch DC bias values that are compatible with a x10 increase of the series resistance. But even so, we will have ~3pA/rtHz per coil from the two resistances.

gautam 8pm May8: Seems like I had confirmed the x3 gain in the EX de-whitening board when Johannes and I were investigating the AI board offset.