While attempting to develop a somewhat accurate noise budget for the 40m, I reasoned that while the shape of the transfer function for the ISS is important, the degree to which we can 'tune' it to a particular experiment/application is limited.

• Since we're using a DC-coupled servo, the TF magnitude will go like f^k with k < 0 for low frequency.
• The UGF will be somewhere around 10 kHz to 1 MHz (most likely right around 100 kHz) as beyond 1 MHz, the gain of our servo is limited by the GBWP of the op-amps.
• We need around 3 or 4 orders of magnitude of gain in the 1-100 Hz range based on this, with gain > 10 for f < 10 kHz

Beyond that, we're sort of limited by the desired high and low frequency behavior as well as the general principle that more electronics = more noise so we probably don't want more than 3 or 4 filter stages, if that. Additionally, the ISS can be over-engineered so that it suppresses the laser noise to levels well below other fundamental noise sources over the important regime ~10 - 10^3 Hz without particular regard to a noise budget.

The design I propose is very similar to a previous design, with a few adjustments. It consists of 3 filter stages that easily be modified to increase gain for higher frequencies if it is known/determined that the laser being stabilized has a lot of high frequency noise.

Stage 1: Basic LP Filter + Establish UGF (each stage 'turning on' will not change the UGF),  Stage 2: Integrator with zero @ 10 kHz,  Stage 3: Optional extra gain if necessary

With the full TF given by,

As usual we consider the noise caused by the servo itself. Noise analysis in LISO is done with a 1 V input excitation.

This servo should function sufficiently for the 40m.