Summary:

I've been thinking about what we need to do to the de-whitening boards for the ITMs and ETMs, in order to have low noise actuators. Noting down what I have so far, so that people can comment / point out things I've overlooked. 

Attachment #1: Block diagram schematic of the de-whitened signal path on D000183 as it currently exists. I've omitted the unity gain buffer stage at the output, though this is important for noise considerations. 

Some considerations, in rough order of priority:

1. Why do we need de-whitening?
   • Because we want the Johnson noise of the series resistor (4.5 kohm) in the coil driver path to dominate the current noise to the coils at ~200 Hz where we want to measure the squeezing.
2. What should the shape of this de-whitening filter be?
   • The DAC noise was measured to be ~1 uV/rtHz at 200 Hz. 
   • The Johnson noise spectral density of 4.5 kohm at 300 K is ~9 nV/rtHz. 
   • So we need ~60dB of attenuation at 200 Hz relative to DC. Currently, they have ~80dB of attenuation at 200 Hz.
   • However, we also need to consider the control signal multiplied by the inverse of this shape in the digital domain (required for overall flat shape). This should not saturate the DAC range.
   • Furthermore, we'd like for the shape to be such that we don't have a large transient when transitioning between high range and low noise modes. We should use the DARM control signal estimate to inform this choice.
3. What about the electronics noise of the de-whitening filter itself?
   • This shows up at the input of the coil driver stage, and gets transmitted to the coil with unity gain. 
   • So we should aim for < 3nV/rtHz at 200 Hz, such that we are dominated by the Johnson noise of the 4.5 kohm series resistance [the excess will be 5%]. 
   • This can be realized by using the passive network which is the final stage in the de-whitening (there is a unity gain output buffer stage implemented with LT1128, which we also have to account for).   

I will experiment with a few different shapes and investigate noise and de-whitened digital signal levels based on these considerations. At the very least, I guess we should remove the x3 gain on the ETM boards, they have already been bypassed for the ITMs.