We've seen that CBC hardware injections in ER8 have caused ETMY saturations - see this alog for the injection, and my comment about the overflows. These are often called 'ETMY saturations' but what is happening is that the DAC is being driven beyond its maximum range of 2^17 counts. This is occurring much more often now that the driver has much more analog lowpassing.

Peter Fritschel wrote this DCC document tabulating the available actuation amplitude before overflowing the DAC, which allows us to check whether a hardware injection of a binary neutron star coalescence would overflow the DAC.

The summary is that a BNS hardware injection at a typical SNR would saturate the digital actuation at H1 as soon as it gets into the 500 to 800 Hz range. And a BNS typically goes up to 1.5 kHz. This has nothing to do with the inverse actuation or notches, it's just the limits of how much the digital system can push on the mirrors using the ESD, which has a lot of low-passing to reduce noise. At these frequencies, the DARM loop has almost no feedback so I'm assuming that the injection just moves the mirrors freely.

I made a simple fit of Peter's tables, and plotted it along with the amplitude of a BNS signal as a function of frequency. My Python code is attached below and should be well commented. There's no interface, but you can edit the distance or masses in the file. The output plot is also attached.

The waveform is from Duncan Brown's thesis, because that's where it's given most clearly in the time domain with the amplitude fully specified. I chose a system with masses 1.4,1.4 Msolar and a distance 120 Mpc and optimal orientation. The waveform, over a short period of time, looks like

h(t) = A f^(2/3) cos (2 pi f t)

where f is the gravitational wave frequency. Since this is strain, I plot A f^(2/3) times the arm length (4000 meters).

I tried to avoid the limit by changing the distance to 180 Mpc, and multiplying Peter's limit by 3.3. He assumed we've got 30,000 counts to work with, but we can manage 100,000 counts if we're lucky. It's still not enough and hits the DAC limit at 800 Hz. 

As soon as the DAC overflows (hits 2^17 counts), there's a huge glitch produced so the injection becomes pretty much useless. The likely path forward, in the short term, is to push the masses up into the NSBH range, like to make one object 10 solar masses. We also might need to roll off the high frequencies artificially.