Pete, Rob, Alberto,

yesterday we thought that some of the problems we were having in locking the IFO might be related to a change of the length of the mode cleaner. So today we decided to measure it again.

We followed the Sigg-Frolov technique (see 40m Wiki, Waldman, Fricke). For the record, the MC_AO input corresponds to IN2 on the MC Servo board.

We obtained: L = 27.092 +/- 0.001 m

From the new measurement we reset the frequencies of the Marconis to the following values:

33196450 Hz

132785800 Hz

165982250 Hz

199178700 Hz

For the 40m Upgrade, we plan to eliminate the Mach-Zehnder and replace it with a single EOM driven by all three modulation frequencies that we'll need: f1=11MHz, f2=5*f1=55MHz, fmc=29.5MHz.

A frequency generator will produce the three frequencies and with some other electronics we'll properly combine and feed them to the EOM.

The frequency generator will have two crystals to produce the f1 and fmc signals. The f2 modulation will be obtained by a frequency multiplier (5x) from the f1.

The frequency multiplier, for the way it works, will inevitably introduce some unwanted harmonics into the signals. These will show up as extra modulation frequencies in the EOM.

In order to quantify the effects of such unwanted harmonics on the interferometer and thus to let us set some limits on their amplitude, I ran some simulations with Optickle. The way the EOM is represented is by three RF modulators in series. In order to introduce the unwanted harmonics, I just added an RF modulator in series for each of them. I also made sure not to leave any space in between the modulators, so not to introduce phase shifts.

To check the effect at DC I looked at the sensing matrix and at the error signals. I considered the 3f error signals that we plan to use for the short DOFs and looked at how they depend on the CARM offset. I repeated the simulations for several possible amplitude of the unwanted harmonics. Some results are shown in the plots attached to this entry. 'ga' is the amplitude ratio of the unwanted harmonics relative to the amplitude of the 11 & 55 MHz modulations.

Comparing to the case where there are no unwanted harmonics (ga = 0), one can see that not considerable effect on the error signals for amplitudes 40dB smaller than that of the main sidebands. Above that value, the REFL31I signals, that we're going to use to control PRCL, will start to be distorted: gain and linearity range change.

So 40 dB of attenuation in the unwanted harmonics is probably the minimum requirement on the frequency multiplier, although 60dB would provide a safer margin.

I'm still thinking how to evaluate any AC effect on the IFO.

** TODO: Plot DC sweeps with a wider range (+/- 20 pm). Also plot swept sines to look for changes in TFs out to ~10 kHz.

The beam scan (which has been living in the bridge subbasement for a bit now) is in a state of imperfection.

I noticed that:

• The waist reading seems to change by not insignificant amounts as you move the spot across the head, even for just small perturbations about the center.
• None of the features which require two slits seem to be working (unsure if this is software or hardware related)

I took some pictures to try and illuminate the situation - The inverted images are included to make it easier to see the flecks (?) in the slits

I am not sure how to figure out if any bit of the scan is/has been fried.

Pending further investigation, enjoy large error bars in your scan measurements!

PICTURES OF BOTH SLITS ON THE BEAMSCAN HEAD:

Koji and I were looking for an extender card to aid with MZ board testing.  Rob went off on a quest to find one.  He found 2 (in addition to the one in the drawer near the electronics bench which says "15V shorted"), and put them in some empty slots in 1X1 to test them out.  Somehow, this burned a few pins on each board (1 pin on one of them, and 3 pins on the other). We now have 0 functioning extender cards: unfortunately, both extender cards now need fixing.  The 2 slots that were used in 1X1 now have yellow electrical tape covering the connectors so that they do not get used, because the ends of the burnt-off pins may still be in there. 

In other, not-Rob's-fault news, the Martian network is down...we're going to try to reset it so that we have use of the laptops again.

This happened when I plugged the cards into a crate with computers, which apparently is a no-no.  The extender cards only go in VME crates full of in-house, LIGO-designed electronics.

I took the pictures of all racks of electronics yesterday, and then uploaded these pictures on the wiki.

http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics

You can see them by clicking "pictures" in the wiki page.

Its back in and re-centered. Our next move on IPPOS should be to replace its steering mirror with something bigger and more rigid.

Electronics changes:

20K -> 3.65 K  (R6, R20, R42, R31) (unused)

20K -> 3.65 K  (R7, R21, R32, R43, R11, R24, R35, R46)

If you look in the schematic (D990272), you see that its an AD797 transimpedance stage with a couple of LT1125 stages set to give some switchable gain. It looks like some of these

switches are on and some are not, but I am not sure where it would be controlled from. I've attached a snapshot of one quadrant of the schematic below.

The schematic shows the switches in the so-called 'normally closed' configuration. This is what the switches do with zero volts applied to the control inputs. As the schematic also shows,

just disconnecting the 'switch' inputs cause the switch's control inputs to go high (normally open configuration, i.e. pins 2-3 connected, pin4 open). For the record, the default positions of the IPPOS switches are:

switch1   high

switch2   low

switch3   low

switch4   high

** EDIT (Nov 2, 2009): I forgot to attach the before and after images; here they are:

I tried to compare the IP_POS time series with the IPANG and MC_TRANS but was foiled at first:

1) The IPANG scan rate was set to 0.5 second, so it doesn't resolve the pendulum motions well. Fixed in the .db file.

2) Someone had used a Windows/DOS editor to edit the .db file and it was filled with "^M" characters. I have removed them all using this command:   tr -d "\r" <ETMXaux.db > new.db

3) The MC_TRANS P/Y channels were on the MC Lock screen but had never been added to the DAQ. Remember, if there's a useful readback on an EPICS screen. its not necessarily in the frames unless you add it to the C0EDCU file. I have done that now and restarted the fb daqd. Channels now exist.

4) Changed the PREC of the IPPOS channels to 3 from 2.

5) changed the sign for the IBQPD (aka IPANG) so that bigger signal is positive on the EPICS screen.

                2.2 uF
In ----o-------- | | --------o-------- Out
       |                     |
       _                     |
       _  1uF                R  7.5 kOhms
       |                     |
       |                     |
      GND                   GND

I have been working about multi-resonant EOM since last week.

In order to characterize the behavior of the each components, I have made a simple LC tank circuit.

You can see the picture of the circuit below.

Before constructing the circuit, I made an "ideal" calculation of the transfer function without any assumptions by my hand and pen.

Most difficult part in the calculation is the dealing with a transformer analytically. Eventually I found how to deal with it in the analytical calculation.

The comparison of the calculated and measured transfer function is attached.

 It shows the resonant frequency of ~50MHz as I expected. Those are nicely matched below 50MHz !!

For the next step, I will make the model of the circuit with stray capacitors, lead inductors, ... by changing the inductance or something. 

I have measured the impedance of the LC tank circuit which I referred on my last entry.

The configuration of the circuit is exactly the same as that time.

In order to observe the impedance, by using Koji's technique I injected a RF signal into the output of the resonant circuit.

In addition I left the input opened, therefore the measured impedance does not include the effect of the transformer.

- - - - - - - - - - - - results

The measured impedance is attached below; "LCtank_impedance.png"

The peak around 50MHz is the main resonance and it has impedance of ~1500 [Ohm], which should go to infinity in the ideal case (no losses).

In fact the impedance looked from the input of the circuit gets reduced by 1/n^2, where "n" is the turn ratio of the transformer.

By putting the n=4, the input impedance of the circuit should be 93 [Ohm]. This is a moderate value we can easily perform impedance-matching by some technique.

I also fitted the data with a standard model of equivalent circuit (see attachment 2).

In the figure.2 red component and red letter represents the design. All the other black stuff are parasites.

But right now I have no idea the fitted value is reasonable or not.

For the next I should check the input impedance again by the direct way; putting the signal into the input.

I measured the input impedance of the LC tank circuit with the transformer. The result is attached.

It looks interesting because the input impedance is almost dominated

by the primary coil of the transformer with inductance of 75nH (see attachment 1).

The impedance at the resonance is ~100 [Ohm], I think this number is quite reasonable because I expected that as 93 [Ohm]

Note that the input impedance can be derived as follower;

(input impedance) = L1 + Z/n^2.

Where L1 is the inductance of the primary coil, Z is the load in the secondary loop and n is the turn ratio.

I think now I am getting ready to enter the next phase \(^o^)/

It looked like the Busby Low Noise Box had too much low frequency noise and so I upgraded it. Here is a photo of the inside - I have changed out the 0.8 uF AC coupling cap with a big, white, 20 uF one I found on Rob's desk.

The Busby Box is still working well. The 9V batteries have only run down to 7.8V. The original designer also put a spare AD743 (ultra low current FET amp) and a OP27 (best for ~kOhm source impedances) in there.

Here's the noise after the fix. There's no change in the DC noise, but the AC noise is much lower than before:

I think that the AC coupled noise is higher because we are seeing the current noise of the opamp. In the DC coupled case, the impedance to ground from the input pins of the opamp is very low and so the current noise is irrelevant.

The change I implemented, puts in a corner frequency of fc = 1/2/pi/R/C = 1/2/pi/10e3/20e-6 = 0.8 Hz.

Overall, the box is pretty good. Not great in terms of current noise and so it misses getting an A+. But its easily a solid A-.

I've measured the voltage noise of the SR560's lead acid battery outputs; they're not so bad.

Steve ordered us some replacement lead-acid batteries for our battery powered pre-amps (SR560). In the unit he replaced, I measured the noise using the following setup:

SR560                              Busby Box

(+12V/GND) -------------AC Input      Out  ----------------   SR785

The SR785 was DC coupled and auto-ranged. The input noise of the SR785 was measured via 50 Ohm term to be at least 10x less than the SR560's noise at all frequencies.

Its clear that this measurement was spoiled by the low frequency noise of the Busby box below 10 Hz. Needs a better pre-amp.

The circuit design of multi-resonant EOM have proceeded.

By using numerical method, I found the some best choice of the parameters (capacitors and inductors).

In fact there are 6 parameters (Lp, L1, L2, Cp, C1, C2) in the circuit to be determined.

In general the less parameter gives the less calculation time with performing the numerical analysis. Of course it looks 6 parameters are little bit large number.

In order to reduce the arbitrary parameters, I put 4 boundary conditions.

Each boundary conditions fixed resonant peaks and valleys; first peak=11MHz, third peak=55MHz, first valley=19MHz, second valley=44MHz.

So now the remaining arbitrary parameters successfully get reduced to 2. Only we have to do is optimize the second peak as it to be 29.5MHz.

Then I take C1 and C2 as free parameters seeing how the second peak agree with 29.5MHz by changing the value of the C1 and C2.

the red color represents the good agreement with 29.5MHz, in contrast blue contour represents the bad.

 You can see some best choice along the yellow belt. Now what we should do is to examine some of that and to select one of those.

In designing the whole circuit it is better to know the characteristic of the EOM.

I made impedance measurement with the EOM (New Focus model 4064) and I found it has capacitance of 10pF.

This is good agreement with the data sheet which says "5-10pF".

The measured plot is attached below. For comparison there also plotted "open" and "10pF mica".

In the interested band( from 1MHz to 100MHz), EOM looks just a capacitor.

But indeed it has lead inductance of 12nH, resistance of 0.74[Ohm], and parasitic capacitance of 5.5pF.

In some case we have to take account of those parasites in designing.

How can I get those values from the figure?

Now I am studying about the behavior of the Q-factor in the resonant circuit because the Q-factor of the circuit directly determine the performance as the EOM driver.

Here I summarize the fundamental which explains why Q-factor is important.

 --------------------------------------

The EOM driver circuit can be approximately described as shown in figure below

Z represents the impedance of a resonant circuit.

In an ideal case, the transformer just raise the voltage level n-times larger.  Rin is the output impedance of the signal source and usually has 50[Ohm].

The transformer also makes the impedance Z 1/n^2 smaller. Therefore this configuration gives a following relation between Vin and Vout.

 Where G is the gain for the voltage. And G goes to a maximum value when Rin=Z/n². This relation is shown clearly in the following plot.

 Note that I put Rin=50 [Ohm] for calculating the plot.

Under the condition  Rin=Z/n²( generally referred as impedance matching ), the maximum gain can be expressed as;

It means that larger Z makes more efficient gain. In our case, interested Z is considered as the impedance at a resonance.

So what we should do is making a resonant circuit which has a higher impedance at the resonance (e.g. high Q-resonant circuit).

The key point of the story is:
"The recipe to exploit maximum benefit from a resonant EOM"
- Make a resonant EOM circuit. Measure the impedance Z at the resonance.
- This Z determines the optimum turn ratio n of the step-up transformer.
  (n² = Z/Rin where Rin is 50Ohm in our case.)
- This n gives the maximum gain G_max (= n/2) that can be obtained with the step up transformer.
  And, the impedance matching is also satisfied in this condition.

OK: The larger Z, the better. The higher Q, the Z larger, thus the better.
(Although the relationship between Z and Q were not described in the original post.)

So, how can we make the Q higher? What is the recipe for the resonant circuit?
=> Choose the components with smaller loss (resistance). The details will be provided by Kiwamu soon??? 

When I was young (3 months ago), I thought...

• Hey! Let's increase the Q of an EOM! It will increase the modulation!
• Hey! Let's use the step-up transformer with n as high as possible! It will increase the modulation!
• Hey! Take the impedance matching! It will increase the modulation!

I was just too thoughtless. In reality, they are closely related each other.

A high Q resonant circuit has a high residual resistance at the resonant frequency. As far as the impedance is higher than the equivalent output impedance of the driving circuit (i.e. Z>Rin n²), we get the benefit of increasing the turn ratio of the transformer. In other words, "the performance of the resonant EOM is limited by the turn ratio of the transformer." (give us more turns!)

OK. So can we increase the turn ratio infinitely? No. Once Rin n² gets larger than Z, you no longer get the benefit of the impedance transforming. The output impedance of the signal source yields too much voltage drop.

There is an optimum point for n. That is the above recipe. 

So, a low Q resonant EOM has a destiny to be useless. But high Q EOM still needs to be optimized. As far as we use a transformer with a low turn ratio, it only shows ordinary performance.

Need to measure the length of the cable, but too lazy to use a measuring tape?

Then you too can become an expert cable length measurer by just using an RF signal generator and a scope:

1. Disconnect or short (not 50 Ohm term) the far side of the cable.
2. Put a T on the near side of the cable.
3. Drive the input of the T with your signal source.
4. Look at the output of the T with the scope while sweeping the signal source's frequency knob.

The T is kind of acting like a beamsplitter in an asymmetric length Michelson in this case. Just as we can use the RF phase shift between the arms to measure the Schnupp asymmetry, we can also use a T to measure the cable length. The speed of light in the cable is documented in the cable catalog, but in most cases its just 66% of the speed of light in the vacuum.

 I shorted the input to the box and then put its output into the SR560 (low noise, G = 100, AC). I put the output of the SR560 into the SR785.

*** BTW, the 2nd channel of the SR785 is kind of broken. Its too noisy by a factor of 100. Needs to go back for repair once we get started in the vac.

The attached PNG shows its input-referred noise with the short.

The picture shows the inside of the box before I did anything. The TO-5 package metal can is the meaty super dual-FET that gives this thing all of its low noise power.

In the spectra on the right are two traces. The BLUE one is the noise of the box as I found it. The BLACK one is the noise after I replaced R1, R6, R7, & R10 with metal film resistors.

The offset at the output of the box with either an open or shorted input is +265 mV.

I think we probably should also replace R2, R3, & R1, but we don't have any metal film resistors lower than 100 Ohms in the kit...but hopefully Steve will read this elog and do the right thing.

The validation for high impedance measurement has been well done.

The impedance measurement is one of the keys for designing the EOM circuit.

So far I was very struggling to measure the high impedance ( above several 1000 Ohm) at RF because the EOM circuit has a high impedance at its resonance.

Finally I realized that the measured impedance was suppressed by a parasitic resistance, which especially reduces the impedance at the resonance.

Also I found that we can extract the TRUE impedance data by subtracting the effect of the parasitic resistance from resultant data.

In order to confirm whether this subtraction works correctly or not,  the impedance was directly re-measured with another analyzer for crosscheck.

(measurement )

The measurement has been performed with help from Peter and Frank. ( Thank you !)

By using  network analyzer AG4395A with the impedance test kit AG43961A (these are at the PSL lab.), the impedance of resonant circuit with EOM was measured.

The picture of setup is attached. This impedance test kit allows to measure typically 0.1 [Ohm]-1M [Ohm] and frequency range of 100kHz-500MHz.

(result)
The resultant plot is attached. In the plot the blue curve represents the impedance measured by usual analyzer at 40m.

Note this curve is already subtracted the effect of the parasitic resistance.

( the parasitic resistance is in parallel to the circuit and it has ~7.8k Ohm, which is measured while the probe of the analyzer stays open. )

The red curve is the re-measured data using the impedance test kit.

The important point is that; these two peak values at the resonance around 40MHz show good agreement in 10%.

The resonant frequencies for two data differs a little bit, which might be the effect of a stray capacitance ( ~several [pF] )

The red curve has a structure around 80MHz, I think this comes from the non-coaxial cables, which connect the circuit and analyzing kit.

You can see these cables colored black and red in the picture.

( conclusion )

Our measurement with the subtraction of the  parasitic resistance effect is working reliably !

 This is indeed sad. But, we can perhaps bypass all of this by just using the individual segment outputs. According to the circuit diagram and the c1iool0 .db file, we should be able to just do the math on the segments and ignore the VERT/HOR/SUM signals completely. In that case, we can just use high impedance for the sum/diff buffers as Koji says and not suffer from the calibration errors at all I think.

Unfortunately, the signals for individual segments also suffer from the voltage drop as all of the low impedance amplifiers are hung from the same input.
In order to utilize the individual channels, we anyway have to remove the resistors for the VERT/HOR/SUM amps.
That is possible. But does it disable some fast channels for future ASC purposes?

FYI: I stored the Universal PDH boxes in the RF cabiner in the Y arm.

The first design of the triple resonant EOM circuit has been done.

If only EOM has a loss of 4 Ohm, the gain of the circuit is expected to be 11 at 55MHz

So far I've worked on investigation of the single resonant circuit and accumulated the knowledge about resonant circuits.

Then I started the next step, designing the triple resonant circuit.

Here I report the first design of the circuit and the expected gain.

( What I did )

At first in order to determine the parameters, such as inductors and capacitors, I have solved some equations with numerical ways (see the past entry).

In the calculation I put 6 boundary conditions as followers;

(first peak=11MHz, second peak=29.5MHz, third peak=55MHz, first valley=22MHz, second valley=33MHz, Cp=18pF)

The valley frequencies of 22MHz and 33MHz are chosen in order to eliminate the higher harmonics of 11MHz, and Cp of 18pF represents the capacitance of the EOM.

Basically the number of parameters to be determined is 6 ( L1, L2, ...,), therefore it is completely solved under 6 boundary conditions. And in this case, only one solution exists.

The point is calculation does not include losses because the loss does not change the resonant frequency.

( results )

As a result I obtained the 6 parameters for each components shown in the table below.

Then I inserted the loss into the EOM to see how the impedance looks like. The loss is 4 Ohm and inserted in series to the EOM. This number is based on the past measurement .

Let us recall that the gain of the impedance-matched circuit with a transformer is proportional to square-root of the peak impedance.

It is represented by G = sqrt(Zres/50) where Zres is the impedance at the resonance.

 As you can see in the figure, Zres = 6.4 kOhm at 55MHz, therefore the gain will be G=11 at 55MHz.

Essentially this gain is the same as that of the single resonant circuit that I've been worked with, because its performance was also limited mainly by the EOM loss.

 An interesting thing is that all three peaks are exactly on the EOM limited line (black dash line), which is represented by Zres = L/CR = 1/ (2pi f Cp)^2 R. Where R = 4 Ohm.

( next plan )

There are other solutions to create the same peaks and valleys because of the similar solution.

 It is easy to understand if you put Cp' = Cp x N, the solutions must be scaled like L1'=L1/N, C1'=C1 x N, ...,  Finally such scaling gives the same resonant frequencies.

So the next plan is to study the effect of losses in each components while changing the similar solution.

After the study of the loss I will select an optimum similar solution.

Very cool.         

The design of the triple resonant circuit has been fixed.

I found the optimum configuration, whose gain is still 11 at 55MHz even if there are realistic losses.

As I mentioned in the last entry, there are infinite number of the similar solutions to create the same resonant frequencies.

However owing to the effect of the losses, the resultant gain varies if the similar solution changes

The aim of this study is to select the optimum solution which has a maximum gain ( = the highest impedance at the resonance ).

In order to handle the losses in the calculation, I modeled the loss for both inductors and the capacitors.

Then I put them into the circuit, and calculated the impedance while changing the solutions.

(method)

1). put the scaling parameter as k in order to create the similar solution.

2). scale the all electrical parameters (L1, L2,...) by using k, so that C1'=C1 x k, L1'=L1/k ,...

3). Insert the losses into all the electrical components

4). Draw the impedance curve in frequency domain.

5). See how the height of the impedance at the resonance change

6). Repeat many time this procedure with another k.

7). Find and select the optimum k

There is a trick in the calculation.

I put a capacitor named Cpp in parallel to the EOM in order to scale the capacitance of the EOM (see the schematic).

For example if we choose k=2, this means all the capacitor has to be 2-times larger.

For the EOM, we have to put Cpp with the same capacitance as Cp (EOM). As a result these two capacitors can be dealt together as 2 x Cp.

So that Cpp should be Cpp = (k-1) Cp, and Cpp vanishes when we choose k=1.

The important point is that the scaling parameter k must be greater than unity, that is k > 1.

This restriction directly comes from Cp, the capacitance of the EOM, because we can not go to less than Cp.

If you want to put k < 1, it means you have to reduce the capacitance of the EOM somehow (like cutting the EO crystal ??)

(loss model)

I've modeled the loss for both the inductors and the capacitors in order to calculate the realistic impedance.

The model is based on the past measurements I've performed and the data sheet.

   Loss for Capacitor :  R(C) = 0.5 (C / 10pF)^{-0.3} Ohm

   Loss for Inductor :    R(L) = 0.1 ( L / 1uH) Ohm

Of course this seems to be dirty and rough treatment.

But I think it's enough to express the tendency that the loss  increase / decrease monotonically as  L / C get increased.

These losses are inserted in series to every electrical components.

( Note that: this model depends on both the company and the product model. Here I assume use of Coilcraft inductors and mica capacitors scattered around 40m )

( results )

The optimum configuration is found when k=1, there is no scaling. This is the same configuration listed in last entry

Therefore we don't need to insert the parallel capacitor Cpp in order to achieve the optimum gain.

The figure below shows the some examples of the calculated impedance. You can see the peak height decrease by increasing the scale factor k.

The black dash line represents the EOM-loss limit, which only contains the loss of the EOM.

The impedance at the resonance of 55MHz is 6.2 kOhm, which decreased by 3% from the EOM-loss limit. This corresponds to gain of G = 11.

The other two peaks, 11MHz and 29.5MHz dramatically get decreased from EOM-loss limit.

I guess this is because the structure below 50MHz is mainly composed by L1, L2, C1, C2.

In fact these components have big inductance and small capacitance, so that it makes lossy.

( next step )

The next step is to choose the appropriate transformer and to solder the circuit.

The design looks very good. I have some questions.

1. As far as I remember, you've got the gain of slightly worse than 10 for a 55MHz single resonant case. Why your expectation of the gain (G=11) for the highest resonance better than this?

Supposing the loss exists only on the EOM, the other part of the LC network for the triple work as an inductor at the resonant frequency. This is just equivalent as the single resonant case. So the expected gain at 55MHz should coincides with what we already have. Probably, the resistance of 4 Ohm that is used here had too rough precision???

2. How can you adjust the resonances precisely?

Do we need any variable components for Cs and Ls, that may have worse quality than the fixed one, generally speaking.
I myself has no experience that I had to tune the commercial EOM because of a drift or whatever. I hope if you can adjust the resonance with a fixed component it should be fine.

3. Changing Cp. What does it mean?

Do you put additional cap for Cp?

4. The resonances for the lower two look very narrow. Is that fine?

This will show up in a better shape if we look at the transfer function for the gain. Is this right?

If we have BW>100kHz, it is sufficient.

5. Impedance matching for the lower two resonances.

Yep. You know this problem already.

Self-follow:

I got the answer of Q3 from the follow-up entry.

For Q4, once you get the impedance of the LC network lower than n^2*50, the EOM gain will be quite low. This means that the resonance is anyway narrow.
I did some simple calculation and it shows that the width of the resonance will be 100kHz~500kHz. So it maybe OK.

First I was confused, but now I think I understood.

My confusion:
If the k get bigger, L get smaller, C get bigger. This makes R(L) smaller and R(C) smaller. This sounds very nice. But why smaller k is preferable in the Kiwamu's result?

Explanation:
The resultant impedance of the network at a resonance is determined by Zres = L/(R C) or something like that. Here R = R(L)+R(C). (I hope this is right.)

Here larger Zres is preferable. So smaller R is nice.

But If the speed of reduction for R is slower than that of L/C (which is proportional to k^-2), increasing k does not help us to increase of Zres. And that's the case.

This means "if we can put the LC network in the box of EOM, we can do better job!" as we can reduce Cp.

1. You are right, the gain for the single resonant circuit was about 9.3 in my measurement.

But the reason why the triple is better than the single resonant circuit comes from the transformer.

The impedance can be degraded by a loss of the transformer, because it got worse after applying the transformer in the past measurement.

Also I definitely confirmed that the circuit had the impedance of 7.2 kOhm at the resonance of 52.9MHz without the transformer.

So it shall give the gain of 12, but did not after applying the transformer.

2.  Yes, I think we need some variable components just in case.

5.  For the impedance matching, I will select a transformer so that 55MHz is matched. In contrast I will leave two lower resonances as they are.

This is because 11MHz and 29.5MHz usually tend to have higher impedance than 55MHz. In this case, even if the impedance is mismatched, the gain for these can be kept higher than 11.

I will post the detail for this mismatched case tomorrow.

Here the technique of the impedance matching for the triple resonant circuit are explained.

In our case, the transformer should be chosen so that the impedance of the resonance at 55MHz is matched.

We are going to use the transformer to step up the voltage applied onto the EOM.

To obtain the maximum step-up-gain, it is better to think about the behavior of the transformer.

When using the transformer there are two different cases practically. And each case requires different optimization technique. This is the key point.

By considering these two cases, we can finally select the most appropriate transformer and obtain the maximum gain.

( how to maximize the gain ?)

Let us consider about the transformer. The gain of the circuit by using the transformer is represented by

         (1)

Where ZL is the impedance of the load (i.e. impedance of the circuit without the transformer ) and n is the turn ratio.

It is apparent that G is the function of two parameters, ZL and n.  This leads to two different solutions for maximizing the gain practically. 

  - case.1 : The turn ratio n is fixed.

In this case, the tunable parameter is the impedance ZL.  The gain as a function of ZL is shown in the left figure above.

In order to maximize the gain, Z must be as high as possible.  The gain G get close to 2n when the impedance ZL goes to infinity.

There also is another important thing; If the impedance ZL is bigger than the matched impedance (i.e. ZL = 50 * n^2 ), the gain can get higher than n.

  - case.2 : The impedance ZL is fixed.

In contrast to case1, once the impedance ZL is fixed, the tunable parameter is n. The gain as a function of n is shown in the right figure above.

In this case the impedance matched condition is the best solution, where ZL=50*n^2. ( indicated as red arrow in the figure )

The gain can not go higher than n somehow. This is clearly different from case1.
 

( Application to the triple resonant circuit )

Here we can define the goal as "all three resonances have gain of more than n, while n is set to be as high as possible"

According to consideration of case1, if each resonance has an impedance of greater than 50*n^2 (matched condition) it looks fine, but not enough in fact.

For example if we choose n=2, it corresponds to the matched impedance of 50*n^2 = 200 Ohm. Typically every three resonance has several kOhm which is clearly bigger than the matched impedance successfully.

However no matter how big impedance we try to make,  the gains can not be greater than G=2n=4 for all the three resonance. This is ridiculous.

What we have to do is to choose n so that it matches the impedance of the resonance which has the smallest impedance.

In our case, usually the resonance at 55MHz tends to have the smallest impedance in those three. According to this if we choose n correctly, the other two is mismatched.

However they can still have the gain of more than n, because their impedance is bigger than the matching impedance. This can be easily understand by recalling the case1.

(expected optimum gain of designed circuit)

 By using the equation (1), the expected gain of the triple resonant circuit including the losses is calculated. The parameters can be found in last entry.

The turn ratio is set as n=11, which matches the impedance of the resonance at 55MHz. Therefore 55MHz has the gain of 11.

The gain at 11MHz is bigger than n=11, this corresponds to the case1. Thus the impedance at 11MHz can go close to gain of 22, if we can make the impedance much big.

I have made a prototype circuit of the triple resonant EOM.

The attached is the measured optical response of the system.

The measured gains at the resonances are 8.6, 0.6 and 7.7 for 11MHz, 29.5MHz and 55MHz respectively.

I successfully got nice peaks at 11MHz and 55MHz. In addition resultant optical response is well matched with the predicted curve from the measured impedance.

However there is a difference from calculated response (see past entry) (i.e. more gains were expected)

Especially for the resonance of 29.5MHz, it was calculated to have gain of 10, however it's now 0.6. Therefore there must a big loss electrically around 29.5MHz.

I am going to re-analyze the impedance and model the performance in order to see what is going on.

Hey, this looks nice, but can you provide us the comparison of rad/V with the resonant EOM of New Focus?

The commercial resonant EOM of New Focus has the modulation efficiency of 50-150mrad/Vrms. ( This number is only true for those EOM made from KTP such as model4063 and model4463 )

Our triple-resonant EOM (made from KTP as well) has a 90mrad/Vrms and 80mrad/Vrms at the reosonances of 11MHz and 55MHz respectively.

Therefore our EOM is as good as those of company-made so that we can establish a new EOM company

I have measured the linearity of our triple resonant EOM (i.e. modulation depth versus applied voltage)

The attached figure is the measured modulation depth as a function of the applied voltage.

The linear behavior is shown below 4Vrms, this is good.

Then it is  slowly saturated as the applied voltage goes up above 4Vrms.

However for the resonance of 29.5MHz, it is difficult to measure below 7Vrms because of the small modulation depth.

 - - - - result from fitting - - -

11MHz: 91mrad/Vrms+2.0mrad

29.5MHz: 4.6mrad/Vrms+6.2mrad

55MHz:82mrad/Vrms+1.0mrad

Looks good. I just thought of the idea that we also can use Alberto's PLL setup to sense the modulation with more sensitivity.  ;-)

In this LVC meeting I discussed about triple resonant EOMs with Volker who was a main person of development of triple resonant EOMs at University of Florida.

Actually his EOM had been already installed at the sites. But the technique to make a triple resonance is different from ours.

They applied three electrodes onto a crystal instead of one as our EOM, and put three different frequencies on each electrode.

For our EOM, we put three frequencies on one electrode. You can see the difference in the attached figure. The left figure represents our EOM and the right is Volker's.

Then the question is; which can achieve better modulation efficiency ?

Volker and I talked about it and maybe found an answer,

 We believe our EOM can be potentially better because we use full length of the EO crystal.

This is based on the fact that the modulation depth is proportional to the length where a voltage is applied onto.

The people in University of Florida just used one of three separated parts of the crystal for each frequency.

Did you find what is the merit of their impedance matching technique?

Yes, I found it.

Their advantage is that their circuit is isolated at DC because of the input capacitor.

And it is interesting that the performance of the circuit in terms of gain is supposed to be roughly the same as our transformer configuration.

It took too long to get this box ready for action. I implemented all of the changes that I made on the previous one (#1437). In addition, since this one is to be used for phase locking, I also made it have a ~flat transfer function. With the Boost ON, the TF magnitude will go up like 1/f below ~1 kHz.

The main trouble that I had was with the -12V regulator. The output noise level was ~500 nV/rHz, but there was a large oscillation at its output at ~65 kHz. This was showing up in the output noise spectrum of U1 (the first op-amp after the mixer). Since the PSRR of the OP27 is only ~40 dB at such a high frequency, it is not strange to see the power supply noise showing up (the input referred noise of the OP27 is 3.5 nV/rHz, so any PS noise above ~350 nV/rHz becomes relavent).

I was able to tame this by putting a 10 uF tantalum cap on the output of the regulator. However, when I replaced the regulator with a LM7912 from the blue box, it showed an output noise that went up like 1/f below 50 kHz !! I replaced it a couple more times with no benefit. It seems that something on the board must now be damaged. I checked another of the UPDH boxes, and it has the same high frequency oscillation but not so much excess voltage noise. I found that removing the protection diode on the output of the regulator decreased the noise by a factor of ~2. I also tried replacing all of the 1 uF caps that are around the regulator. No luck.

Both of the +12 V regulators seem fine: normal noise levels of ~200 nV/rHz and no oscillations.

Its clear that the regulator is not functioning well and my only guess is that its a layout issue on the board or else there's a busted component somewhere that I can't find. In any case, it seems to be functioning now and can be used for the phase locking and PZT response measurements.

For your reference: Voltage noise of LM7815/LM7915 (with no load)

Recorded transfer functions for the 1cm Si-PD as described on p. 2708

for different biases. I put the plots in there, to keep the info in one place,

where the label on the PD case (which Steve made without asking him) points

to.

I talked to some people recently about the fact that the responsivity (A/W) of the PD

changes even at DC for different biases. I tested this again and should be more precise about this:

The first time I observed this was in the transfer functions as shown on p. 2708.

With 'DC' I meant 'low frequency' there, as you can still see an effect of the bias as low as 100kHz.

Then at one point I saw the responsivity changing with bias also at true DC.

However, it turned out that this is only the case if the photocurrent is too high.

If the photocurrent is 4mA, you need 400mV bias to get the max. responsivity.

For 2mA photocurrent, the responsivity is already maximal for 0V bias.

An effect for relative low frequencies remains however.

The DC check of responsivity was done with white light from a bulb.

We tested out the functionality of the EG&G 113 preamp that I found in one of the cabinets. This is one of the ancestors of the SR560 preamp that we are all used to.

It turns out that it works just fine (in fact, its better than the SR560). The noise is below 3nV/rHz everywhere above 30 Hz. The filter settings from the front panel all seem to work well. And the red knob on the front panel allows for continuous (i.e. not steps) gain adjustment. In the high-bandwidth mode (low pass filter at 300 kHz), there is ~35 deg of phase lag at 100 kHz. So the box is pretty fast.

I would easily recommend this above the SR560 for use in all applications where you don't need to drive a 50 Ohm load. Also the battery is still working after 17 years!

There's several more of the this vintage in one of the last cabinets down the new Y-arm.

This morning the pencil soldering iron of our Weller WD2000M Soldering Station suddenly stopped working and got cold after I turned the station on. The unit's display is showing a message that says "TIP". i checked out the manual, but it doesn't say anything about that. I don't know what it means. Perhaps burned tip?

Before asking Steve to buy a new one, I emailed Weller about the problem.

 There should be a supply of extra tips in the Blue Spinny Cabiney (I can never remember it's French name....)  The drawer is something like the top row of one of the bottom sets of drawers.  You can pick the shape of tip you want, and stick it in.

Albeto and Koji

We took the tip replacement from the blue tower.

I am looking at http://www.cooperhandtools.com/brands/weller/ for ordering the tips.

The burnt one seems to be "0054460699: RT6 Round Sloped Tip Cartridge for WMRP Pencil" We will buy one.

The replaced one is "0054460299: RT2 Fine Point Cartridge for WMRP Pencil" We will buy two.

I like to try this: "0054460999: RT9 Chisel Tip Cartridge for WMRP Pencil" We will buy one.

#
#                 gnd
#                 |
#                 Cw2
#                 |
#                 n23
#                 |
#                 Lw2
#                 |
#   gnd           n22
#   |             |
#   Rip           Rw2
#   |             |                   |\
#   nt- Rsi-n2- - - C2 - n3 -  - -  - |  \
#            |    |      |   |        |4106>-- n5 - Rs -- no                                                            
# iinput    Rd   L1     L2 R24    n6- |  /     |           |
#    |- nin- |    |      |   |    |   |/       |         Rload
#           Cd   n7     R22 gnd   |            |           |
#            |    |      |        | - - - R8 - -          gnd
#           gnd  R1     gnd      R7
#                 |               |
#                gnd             gnd
#
#
#

What??? I don't see any gray trace of Rs in the plot. What are you talking about?

Anyway, if you are true, the circuit is bad as the noise should only be dominated by the thermal noise of the resonant circuit.