G_L = G_0 * ------------ = 149 +/- 3 V/(m/s)
R_x + R_c
G_0 = 340 V/(m/s) (generator constant)
R_x = 4300 Ohms (external damping resistor in Pomona box)
R_c = 5500 Ohms (internal coil resistance)
m * x = (x_G - x) * k + d(x_G - x) * b
x w0^2 + i*w*w0/Q
---- = -----------------------
x_G w0^2 + i*w*w0/Q - w^2
d (x - x_G) ( w0^2 + i*w*w0/Q ) . w^2 .
dt = ( ----------------------- - 1 ) * x_G = ----------------------- * x_G
( w0^2 + i*w*w0/Q - w^2 ) w0^2 + i*w*w0/Q - w^2
PMC_cal (m/V) = (1064 nm)/2 / V_FSR
I've been measuring a bunch of transfer functions of the FSS related stuffs.
There are a lot to be analyzed yet, but here I put one mystery I'm having now.
Maybe I'm missing something stupid, so your suggestions are welcome.
Here is a conceptual diagram of the FSS control board
RF PD -->--[Mixer]-----[Sum Amp]------>--[Common Gain]--->----[Fast Gain]----[Filter]--> NPRO PZT
^ | ^ | |
| V | V |
LO ---->------- TP1 IN TP2 -->---[Filter]--[High Volt. Amp.] --> Phase Corrector
What I did was first to measure a "normal" openloop transfer function of the FSS servo.
The FSS was operated in the normal gain settings, and a signal was injected from "IN" port.
The open loop gain was measured by TP1/TP2.
Now, I disconnected the BNC cable going to the phase corrector to disable the PC path and locked the ref. cav.
only using the PZT. This was done by reducing the "Common Gain" and "Fast Gain" by some 80dB.
Then I measured the open loop gain of this configuration. The UGF in this case was about 10kHz.
I also measured the gain difference between the "normal" and "PZT only" configurations by injecting
a signal from "IN" and measuring TP3/TP2 and TP4/TP3 with both configurations (The signal from the Mixer was
disconnected in this measurement).
The first attachment shows the normal open loop gain (purple) and the PZT only open loop gain scaled by the
gain difference (about 80dB). The scaled PZT open loop gain should represent the open loop gain of the PZT
path in the normal configuration. So I expected that, at low frequencies, the scaled PZT loop TF overlaps the normal
open loop TF.
However, it is actually much larger than the normal open loop gain.
When I scale the PZT only TF by -30dB, it looks like the attachment #2.
The PZT loop gain and the total open loop gain match nicely between 20kHz and 70kHz.
Closer look will show you that small structures (e.g. around 30kHz and 200kHz) of the two
TFs also overlap very well. I repeated measurements many times and those small structures are always there (the phase is
also consistently the same). So these are not random noise.
I don't know where this 30dB discrepancy comes from. Is it the PC path eating the PZT gain ?
I have measured many other TFs. I'm analyzing these.
Here is the TO DO list:
* Cavity response plot from AOM excitation measurements.
* Cavity optical gain plot.
* Reconstruct the open loop gain from the electric gain measurements and the optical gain above.
* Using a mixer and SR560(s), make a separate feedback circuit for the PZT lock. Then use the PC path
to measure the PC path response.
* See the response of the FSS board to large impulse/step inputs to find the cause of the PC path craziness.
f (MHz) | before filter (dBm) | after filter (dBm)
21.5 | -12.8 -13.1
43 -24 -46
64.5 -50 < -80
86 -64 < -80