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Entry  Wed Aug 15 18:56:46 2012, Yoichi, Update, IOO, MC Servo Transfer Function Measurements MC-Diagram.pngOPLG-10kHz-1MHz.pngSimpleServoDiagram.pngOPTG-100Hz-1kHz.png
    Reply  Thu Aug 16 01:52:52 2012, Yoichi, Update, IOO, MC Servo Transfer Function Measurements 6x
       Reply  Thu Aug 16 05:08:38 2012, Yoichi, Update, IOO, MC Servo Transfer Function Measurements MCBoard1.JPGMCBoard2.JPG
Message ID: 7198     Entry time: Wed Aug 15 18:56:46 2012     Reply to this: 7201
Author: Yoichi 
Type: Update 
Category: IOO 
Subject: MC Servo Transfer Function Measurements 

 I started working on the characterization of the MC servo.

The current MC servo topology is shown in the figure attached along with a simplified schematic diagram of the MC board. 

A usual way to measure the open loop gain of this servo is to inject a signal from, say, EXCA of the MC board and measure the transfer function from TP2A to TP1A. It works OK at frequencies around the UGF. The second attachment is the OPLTF measured in this way with the Agilent 4395A. The UGF is about 100kHz with the phase margin of 40 to 50 deg. 

Now we have two issues here. First, I expected the UGF to be more than 100kHz, like 300kHz or so. The phase babble is peaked around 100kHz. According to our old measurement (http://nodus.ligo.caltech.edu:8080/40m/1431) the phase babble peak was at a much higher frequency when the FSS was using the reference cavity. One reason could be that the MC is located much farther from the laser than the reference cavity, so that there is some phase lag caused by the time delay. I will make a model of the MC servo system later to check this theory.

The second issue is that, as you can see in the plot, the OPLTF measurement becomes noisy at lower frequencies. With 4395A, which has the minimum IFBW of 2Hz, OPLTF measurement below 10kHz was impossible with the traditional method. We could use SR785 with a long averaging time to improve the SNR, but it requires a patience which I don't have.

The measurement becomes difficult at low frequencies because the loop gain is too high. When the open loop gain (G) is high, the injected signal (x) from EXCA is immediately suppressed by a factor of 1/(1+G) at TP2A. This makes the injected signal hidden in other noises at TP2A.

How do we solve this problem ? Let's consider a simple servo model shown in the third attachment. A traditional OPLTF measurement is done by injecting a signal from EXC port and measuring the TF from TP2 to TP1. The problem was that at TP2, the signal is attenuated by 1/(1+G1*G2), which is too much when G (=G1*G2) is large. However, at TP3, the attenuated signal is amplified by G1. So the injected signal x becomes x*G1/(1+G) at TP3. If G1's contribution to the overall gain G is large enough,  the signal at TP3 is not so small. Then we can easily measure G2 using TP3 and TP1. In a typical situation, G1 is the transfer function of the electric circuits, which we can know either from standalone measurements or from model calculations, and G2 is an interferometer response, which we want to measure. So, by combining the knowledge of G1 and the measurement of G2, we can obtain the overall loop gain G even at lower frequencies.

 The final attachment shows an example of the measurement of G2. In our case, this is the transfer function from MC_Out_Mon to Q-Mon (see the first attachment) . G1 is the transfer function of the MC board. Since G1 is large at low frequencies, we can measure G2 down to 100Hz with a reasonable integration time (10000 cycles per point).

Last night, I took a bunch of TFs with this method. Now I'm analyzing the data to recover the overall gain G. I will post the results later.

Attachment 1: MC-Diagram.png  27 kB  | Hide | Hide all
Attachment 2: OPLG-10kHz-1MHz.png  74 kB  | Hide | Hide all
Attachment 3: SimpleServoDiagram.png  6 kB  | Hide | Hide all
Attachment 4: OPTG-100Hz-1kHz.png  67 kB  | Hide | Hide all
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