Laser locking (control loops with two feedback paths.)

Laser locking (control loops with two feedback paths.)

So I finally had a user ask about side locking our diode laser. (That?s where you lock the frequency to the side of an absorption feature.) Now, you can change the laser frequency in two ways. There?s a piezo stack that changes the angle of a diffraction grating. And you can change the laser current. The electronics is all set up to lock the laser with the piezo. Signal chain looks like,

Photodiode->low pass (1 pole, tc = 100ms)-> DC offset->gain->modulation input of piezo control.

With some other bits of gain adjustment sprinkled in there. (The low pass is working as both integrator and gain (PI), you crank up the overall loop gain till it oscillates and then back off a bit.) This works fine, up to ~3kHz the oscillation frequency.

Now I?ve heard tell of a trick where I break the error signal into a low frequency and high frequency part. And then send the high frequency part into the laser current modulation input. It seems I should pick off the error signal before the lowpass (P/I part of signal chain).(?) But I'm wondering how to deal with the 'break frequency' What frequency for the HP? And do I roll off the 'DC' part at the break frequency too? (1 pole each) Or can I leave the rest of the 'DC' signal chain the same if I pick the right frequency?

Thanks, George H.

Reply to
George Herold
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Too many variables.

What are the characteristics of the modulation you get from the piezo vs. modulating the laser current?

Why does your piezo loop tend to oscillate at around 3kHz?

Why can't you just control the laser current?

Do you want to have closed-loop control using the laser current, with increased loop bandwidth, or do you just want to push the laser around open loop at those high frequencies?

--
Tim Wescott 
Control system and signal processing consulting 
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Reply to
Tim Wescott

freq error -o-> prop. gain - + --> laser | A '-> integrator --'

If your loop is crapping out at 20kHz with your 20kHz photodiode, chances are that even with a better photodiode in there you'll need some derivative action to push much above 20-ish kHz:

freq error -o-> prop. gain - + --> laser | A o-> integrator --+ | A '-> derivative --'

If you're doing this in analog, or if you're sampling good and fast in digital-land, you'll almost certainly want to band-limit the derivative.

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Reply to
Tim Wescott

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But with two feed back paths should there be an integrator in each loop?

Not to worry first I need a faster PD.

Oh all analog.

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Reply to
George Herold

Interestingly, the analog controls guys tend to do

| | | | +----int----->|sum-------- | | | | +----der----->|

because it's easier for people to tune.

--
John Larkin                  Highland Technology Inc 
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John Larkin

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That's how I've always done it.

But now (I think, according to Phelan)

Hmm Phelan's at work... I might have screwed that up. (Is there gain in JL's gain of one path?)

George H.

.highlandtechnology.com  jlarkin at highlandtechnology dot com

Reply to
George Herold

Only if you want things screwed up! With an integrator in each loop you'll have an uncontrollable, metastable mode -- said mode being the difference between the two integrator states, and metastable because it'll be integrating. So what will happen is that your loop will hold just fine until either the piezo or the current goes to the positive rail, and the other one goes to the opposite rail.

Besides, if you take my suggestion on this you'll have a DC-blocking filter between the one "laser" input and the current -- only the piezo will respond to the integrator at any rate.

I gathered that, it being the size of a dinner plate (well, for cockroaches, perhaps). I'm not on top of the physics of photodiodes, but I thought that -- given low enough impedances -- your bandwidth is more limited by your amplifier than by your photodiode itself. Am I all wet here?

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Reply to
Tim Wescott

That depends on how the people in question are doing the tuning.

The topology that I showed is easier to apply the "seat of the pants" method where you get derivative tuned in, then proportional, then integral. The one you favor is easier if you do a Bode plot, tune the integrator zero, then tune the derivative zero, then bring the gain up.

By the time you get to the point where you're fussing with the last few dB and degrees of margin, they're about equal.

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Tim Wescott

There are some ancient PID tuning procedures from the pneumatics days, that assume the config I drew. I heard the story that PID was actually discovered accidentally as a consequence of a leak in a bellows or something.

Equation 4 here

formatting link

is equivalent to a controller gain of Kp*(1+integral).

formatting link

Fresh EEs tend to sum P+I+D, which I did at first, until an old marine engineer pointed out the advantages of P * (1+I+D)

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John Larkin                  Highland Technology Inc 
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John Larkin

The gain of 1 is - computes furiously - 1!

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John Larkin                  Highland Technology Inc 
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John Larkin

From "On Governors", James Clerk Maxwell, 1868:

"But if the part acted on by centrifugal force, instead of acting directly on the machine, sets in motion a contrivance which continually increases the resistance as long as the velocity is above its normal value, and reverses its action when the velocity is below that value, the governor will bring the velocity to the same normal value whatever variation (within the working limits of the machine) be made in the driving-power or the resistance."

Or, translated into modern English, integrators.

He follows that a bit later with:

"The first and third cases are evidently inconsistent with the stability of the motion; and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative."

Or, in modern control-ese, that all of the poles are in the left half plane.

It goes on. And on. This is the seminal English-language paper on stability and control (Tchebychev wrote one in German or Russian). Most of the elements that we all deal with to make stable, well-behaved loops are in there, in some embryonic form. Only the math that makes it easy (like the Laplace transform) is missing. Maxwell did it all The Hard Way

-- and he made it work.

He also systematized electromagnetics, unified electricity with magnetism (before vectors had been invented, even), and did serious work in optics (which was not understood to be an electromagnetic phenomenon at the time because E&M didn't _exist_ yet).

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Reply to
Tim Wescott

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What I usually do is to make both I and T loops more or less integrating, with the T loop dominating at

very low freq, and make sure the I loop rails safely. Then just run them together. The T loop will keep the I loop centred, and nobody has any excess phase down at 0.1 Hz or wherever the low frequency cross is.

Cheers

Phil Hobbs

(Via Google Groups, from the Carnival Miracle at Port Canaveral-- heading for the beach bar. Having a daughter in the travel industry means we can't afford not to go. )

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Phil Hobbs
[...]

Unfortunately not with many governors voted into office these days.

--
SCNR, Joerg 

http://www.analogconsultants.com/
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Joerg

A farm hand was driving down the road with a load of manure, going fast. He got pulled over by a state trooper.

"Good morning young man -- fine day to be driving farm products, isn't it"

"Yes sir"

"You were going rather fast there -- is there a governor on this truck?"

"No sir -- that's _real_ bull shit you smell!"

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Tim Wescott 
Control system and signal processing consulting 
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Tim Wescott

Not lowest-lowest, but lowest nominal. In a normal resistive-FB TIA, shot noise equals Johnson noise at 50 mV, so you lose 1dB if the output is 200 mV, 0.25 dB at 400 mV. Normally the other parts of the system are way more expensive than the TIA, so from a cost-benefit POV you want the TIA to be unobtrusive.

Alas, 'tis true. You can still get BFT25As, but they're not as good.

Cheers

Phil Hobbs

I had a 6-hour pass, sir. Honest.

Reply to
Phil Hobbs

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Hi Tim, thanks again for the sage advice.

So at the moment the gain vs freq looks like,

~1Hz L ^ | O |-- G | \ | \ g | \ a | \ i | \ ~1kHz n | \| +--------\---------> gain=1 LOG frequency

So If I make a break point (LF to piezo and HF to current) at say 100 Hz do I still want the high frequency part of the gain to have a one pole roll-off... or maybe the gain can be flat (for a while.... I gotta roll off the HF eventually.)

Not to worry, I?ll play around and maybe learn something.

ut

As far as the photodiode design goes, I don?t know of any ?new? tricks*. But the old rule of thumb (for TIA?s) is that the max. frequency is the geometric mean of the RC ?frequency? and the opamp GBW. For my pedestrian circuit, with unbiased photodiode C=~700pF, R=1Meg, GBW =1.5MHz,(opa124) for which I get an f(rc)~240Hz and sqrt(f(rc)*GBW)~19kHz.. (I thought the opa124 had a 1MHz GBW, but the number was then a bit off.)

George H.

*well there are ways to reduce the capacitance. reverse bias the PD, bootstrapping, and then Phil H.'s cascode between the PD and TIA. I've never tried the cascode.

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Reply to
George Herold

I'm not sure what you're showing me the gain _of_ here.

It's a really good idea to have the open-loop gain be descending at around 20dB/decade with 60 to 120 degrees of lag at the loop closure point. Too little slope on the gain curve gives you these weird broad low peaks (or troughs, depending on the phase).

Going back to my original suggestion, you want a block that you can call "laser" which _internally_ has the high & lowpass filters, and the feed to the diode and piezo, and the feedback from the PD. Whatever the response of that block is, it should be well-behaved. I've been assuming that its frequency response would be fairly constant up to some cut-off frequency, at which point it would start dropping by 20 or 40 dB/decade. Then you'd wrap that with your controller to get a nice descending characteristic, with a gain=1 point as high as you can push it.

You're not bothering to bias your photodiode?!?!?! In a world of easy-to- get 10MHz or better op-amps you're using 1.5MHz?!?!?!?!

Um -- I think there's some circuit improvements that you could make, there.

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Tim Wescott 
Control system and signal processing consulting 
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Reply to
Tim Wescott

up

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I hope it's the closed loop gain of the piezo feedback circuit.

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ricks*.

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Hangs head in shame, kicks dirt. "Gee Tim, there's no need to rub it in".

But seriously, I did this in 2001, when it seems like, I harldy knew anything electronics-wise. There are several hundred of these "slow as molasses" detectors out there. I can't write up some side locking technique that uses modified detectors. But maybe I can sell them all newer faster detectors?

Anyway again thanks,

George H.

e quoted text -

Reply to
George Herold

Sorry, I didn't realize you were working on improvements to fielded products.

You may be able to shove a lead-lag network in there that kicks in at around 20kHz that'll boost your bandwidth up a little bit.

And hey -- 20kHz is better than 2, or whatever you get with your piezo, right?

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Tim Wescott

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