Here is the TF of LIGO's VCO. I measured the TF at 3 different RF output voltage levels (C3:PSL-FSS_VCOMODLEVEL) and plotted them together.
To measure the TF of the VCO box, I reduced the VCO RF before disconnecting any cables.
Source out from SR785 is split by a splitter. One goes to Ref ch A on SR785, another goes to VCO wide band input.
RF out to AOM is connected to Response ch B on SR785.
The TF looks bad when I turned the RF output V to 5 which is normally used during the lock. I'm not sure if there will be
reflection of signal or not, so I decide to lower the RF output V.
The magnitude from each measurements on the plot are offset for comparison purpose.
As we can see, VCO does not have flat freq response. This should be able to explain the different shape between
Beat note freq and VCO feedback signal.
I measured the calibration df/dV for VCO to be ~48 kHz/V. Then I convert the Vnoise fro VCO to frequency noise.
I injected the signal at 90 Hz and 1 kHz and measure the corresponding peaks from beat noise and VCO.
Then I rescale both data to match the peaks to get the conversion factor.
f=90 Hz, pk/floor f =1kHz pk/floor
VCO 1.43mV/20uV 2.95 mV/20 uV
BEAT 2.18mV/ 25uV 4.11 mV / 25uV
beat = VCO x K = 1.53 1.37
let's use 1.4 for average
Since df/dV for beat is 71kHz/ V, df/dV for VCO is 71/1.4 kHz/V = 51kHz/ V.
The plot below shows RC noise as measured by VCO and beat note.
What about the frequency response. Why did we see the different shapes between the spectra even with the coherence ~1.
You can measure the transfer function between those two VCO feedback and should try to explain it.
Is there any transfer function in the AOM VCO, for example?
If I can believe D980401-B.pdf, the VCO freq control path seems to have pole-zero pair at 1.5Hz and 41Hz.
The Voltage vs Frequency conversion for VCO is here.
It's not linear over the range. I have to check what is the average value of the VCO during our measurement.
Then, if it's small enough, linear approximation can be used to convert the data from VCO to Hz/rt Hz.
I think It's better to use linear fit because the psd of the voltage does not contain information about the sign of the signal.