These are plots and notes from last week's PDH adventures. 

For the PDH servo box re-design, we wanted to think a little bit about what we actually wanted out of the box.

* We want the zero of the main transfer function to be at the same frequency as the cavity pole for green, which is about 18kHz.

* We want the boost to suppress noise at a few hundred Hz.  We don't need super-duper low-frequency boost, nor do we want it.  We'd like to leave the boost on all the time.

* Wanted to get rid of 10dB attenuator on PD input, so needed to lower the overall gain.

* We acknowledge that the gain of the raw error signal times the PZT response is very high, so no matter what, we will have to have a low-gain servo, even perhaps have the servo shape be less than unity gain.

---> We reduced the gain of the first amplification stage from a gain of 20 to a gain of 3.

---> Made the boost stage have a DC gain of 1.  Pole at 75 Hz and Zero at 1.6kHz to give suppression at a few hundred Hz.  Boost is *not* a pure integrator, so that we can leave it on.  (If we required triggering anyway, we would have made it a pure integrator).

---> In transfer function stage, put zero at 17.7kHz to match cavity pole.  Pole of servo was going to be at 20 Hz, but we wanted a little more gain, so we lowered it to 2 Hz.

Here is the final measured servo box transfer function for the Yend box (with an arbitrary gain knob setting):

Once installed, I set the gain knob for the Yend at 4.0, which gave an overall UGF of about 10kHz.  Then I measured the loop:

I also measured the error point and the control point, and compared them to Q's measurements in elog 10430.

In order to see what we might expect for a contribution to ALS noise, I looked at the error point spectra and lowpassed it with a pole at 200Hz.  I do this because the PDH error is like sensor noise for the ALS, but the ALS UGF is around 200 Hz, so noise at frequencies higher than that will be suppressed like 1/f.  So, I lowpass the error signal, then look at the RMS, and see that we should be pretty happy with our result. I include also the Xend error spectrum, as measured and reported by Q in elog 10460.