After we improved the performance of the PMC locking -- that was degraded because of excessive RF getting past the demodulation stage, see PSL:2228) -- I though I'd have a look at the TTFSS boxes. It turns out that the FSS has a elliptical LP with a notch tuned to 21 MHz. This had not been modified since the box was made, meaning that for the period of 14.75 MHz modulation it was sub-optimal.
I modeled the TF from the output of the mixer (U2 in D0901894-v1) to the input of the servo (U3 in LIGO-D040105 rev C). The model is compared below with the measured TF injected from Test1 to TP1 on the servo board. As plotted below, for both north and south paths, it is in ok agreement to within the tolerances of the components. Note that one discrepancy with how I measured the TF is that I injected into Test1 without 22 Ω in series. This doesn't seem to make a big difference. The bump at 50 MHz in the LISO model is an artifact of the AD829 but doesn't seem to turn up in the measured TF.
The original circuit is illustrated below:
Here a basic LP filter is formed between the C13 and C14 and L3. The combination of C12 and L3 form the notch.
For the best LP filter at the modulation frequency we want to lower the first (lowest) poles of the filter to as low as possible without lowering the required capacitance of C12 so low that parasitic capacitance is a concern for the notch. I've attached a notebook below, this includes some pyliso and widget sliders that where values can be varied to find the best combination. Also plotted below is a contour plot of the notch frequency as a function of the inductor (L3) and the notching capacitor in parallel (C12), this is also in the notebook.
For 36 MHz a good combination looks like L3 = 750 nH, C13 = C14 = 220 pF, C12 = 26 pF (green point labeled in above plot). Absolute tolerance of these components are 5% with a thermal drift of 30 ppm/K for the ceramic capacitors and +25 to 125 ppm/K for the ceramic core inductor (see see cap spec sheet and coil craft ceramic core spec sheet for 1206cs series). A box in the above plot shows the ±5% error level on components showing the range of potential error in the notch frequency due to manufacture variations.
The South TTFSS RF board was modified with L3 changed from 1200 nF to 750 nF and C12 being changed from 47 pF to a 18 + 1.5 + 1.5 + 1.0 pF = 22.0 pF stack (i.e. parallel). These values were initially guessed and then trial and error was used to swap out small value caps until the notch was centered on 36 MHz. The bottom of the dip was an attenuation of -58 dB (plotted below)
The North TTFSS RF board was modified with L3 changed from 1200 nF to 750 nF and C12 being changed from 47 pF to a 18 + 3.9 + 1.5 + 1.0 pF = 24.4 pF in parallel. This gave a notch at 37 MHz with a dip that was also -58 dB. The measured transfer function is plotted below.
This is a high(ish) Q narrow peak so we don't want it to drift too much. As mentioned above the thermal drift is 30 ppm/K for caps and 125 ppm/K for the inductor (worst case). The LISO model indicates that this corresponds to a drift of 0.5 kHz/K for the cap and 2.2 kHz/K for the inductor: this is a tolerable margin of error. Thermal drift, even for large 10's K variations in box temperature, is not a concern.
The LISO model indicated that we could squeeze some more attenuation by shifting C13 and C14 from 220 pF to a larger value. But when I tried 1 nF (for both) I found that there was some weird 1/f roll up below 200 kHz when I measured the TF (rather than flat). I got the same even when I tried 440 pF. Maybe its some impedance matching thing and the resistors need to be modified; I wanted to get the FSS back up and working so I didn't look further into this. C13 and C14 were left at 220 pF for both North and South TTFSS boxes.
It also looks like the real measured TF have a broader notch than the LISO model. There is probably some stuff that isn't modeled in the simple LISO model. This relaxes the requirments for the notch tuning a little.
TTFSS field boxes were reinstalled on the table, ready for the demodulation phase to be tuned for the new frequencies.
Data is commited into https://git.ligo.org/cit-ctnlab/ctn_labdata/tree/master/data/20180925_FSS_EllipticFilterRetuned_TF and zipped and attached below.