Third order IMD in photomultipliers--weird behaviour

Well, 'most' means more than half, and 'scientists' is plural. So, this is about at least three persons. There's no such thing as a 'climate change scientist' (but maybe you mean 'climate scientist'?). Name three climate scientists. If you can't, that comment is meaningless and its source uninformed.

If you can, tell us how two scientists have a better option that could substitute for a computer-resident model.

Climate change scientists run lots of different computer models, and trust the results just as far as they agree. Where they've got good enough historical information, they also check out how well their models fit what actually happened.

Peter Land clearly hadn't compared his - single - computer model with any kind of reality.

Sloman, A.W. "Comment on 'Computer aided simulation study of photomultiplier tubes'", IEEE Transactions on Electron Devices, ED-38 679-680 (1991).

comments on a equally horrible, but more modern, example of the same pathology

M.E.Zaghloul and D.J. Ree IEEE Trans. Electron Devices vol. 36(9) pp.2005-10 Sept. 1989.

--
Bill Sloman, Sydney

uter model - and >hadn't noticed that the last stage of a resistive divider dynode chain provides only >the anode collection bias and no gain, despite the fact that my comment - and Lush's paper - >had both emphasised this po int, as does the chapter in "Experimental Physics".

Well, I got the gizmo done; it turns out that in this tube, at the desired moderate gain (6-700V total), up to at least 350 uA average anode current (

540 uA peak), you can push the IM3 to completely invisible levels by changi ng the bias distribution (relatively more bias on the first and last three dynodes) and putting Darlington emitter followers on the last 3 stages and a regular follower on the fourth-from-last.

(How's that for a one-sentence summary?)

Fun. Customer's happy.

Cheers

Phil Hobbs

mputer model - and hadn't noticed that the last stage of a resistive divide r dynode chain provides only the anode collection bias and no gain, despite the fact that my comment - and Lush's paper - had both emphasised this poi nt, as does the chapter in "Experimental Physics".

d moderate gain (6-700V total), up to at least 350 uA average anode current (540 uA peak), you can push the IM3 to completely invisible levels by chan ging the bias distribution (relatively more bias on the first and last thre e dynodes) and putting Darlington emitter followers on the last 3 stages an d a regular follower on the fourth-from-last.

"Lush was right" is shorter.

He'd have been even happier if you'd got the dynode voltages right first ti me around, but phootmultipliers are cranky beasts and you can waste a lot o f time solving problems that don't turn out to be significant in real appli cations.

540uA peak strikes me as quite a lot of anode current - and 350uA average w ould get the last couple of dynodes quite warm.

--
Bill Sloman, Sydney

You know, Bill, I think maybe you don't even realize when you insult people--you've been doing it so consistently for so long that it's now apparently second nature.

This _was_ my first try. The customer was using a Hamamatsu C-W socket, as I said in a previous post, and one might expect the manufacturer to know something about their own tubes. I started my measurements with that as a baseline, which is where I discovered the effect that I first posted about.

The absence of any apparent space-charge effect even up near 1 mA is fairly new news, at least to me. There's a lot of crape-hanging in the literature about space charge, but at least in this tube it's not a limitation at all if you get the bias distribution right.

The most interesting thing about this work (I think) was discovering a mechanism where one can get third-order IM products with a linear amplitude dependence, due to time correlations in the amplified shot noise. I've never ever seen that one, either in real life or in the literature. It was great having the assembled multitude here to kick it around with--I might never have figured it out otherwise. I'm writing it up for my planned third edition.

Right, but that's where the customer wants to work, because that's where he gets the best SNR, apart from his previous problem with IM3 causing image ghosts. According to Hamamatsu, over its useful life, a tube will typically give you about 1000 coulombs of anode charge per cm**2 of photocathode area. (Overheating will shorten this, for sure.) So it should last very roughly

3 cm**2 * 1000 C/cm**2 / 500 uA = 6E6 seconds,

i.e. a bit under a year, figuring continuous operation on one shift per day. That's not horrible for a research instrument, especially since changing tubes is pretty easy with side-lookers.

Point is, you can get rid of the IM3 to below -70 dBc even way up there, which I think is interesting and useful.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

If/when you write something up (with perhaps some pretty pictures for us mere mortals) would you put it on your web site and alert us?

Thanks, George H.

No, he does it deliberately. I can't begin to conjecture why.

Hi, George,

Yeah, it's about time for my annual fit of website maintenance, it's true. Probably after Christmas.

I'm not sure I know enough statistics to really do justice to the theory, but thinking about an ensemble of random processes with the same time-dependent signal should get me close enough.

The interesting thing in the math will be figuring out exactly how the delta-function autocorrelation of the noise makes the shot noise * shot noise contribution come out partly in narrow spikes.

It's not the same as AMing the noise, which would be easy, because the variance is always equal to the mean in a Poisson process.

I'm looking forward to it, but I'm too tired at the moment. A few days off in a row would be the ticket.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

That pretty much sums up why I like coming to work every morning.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

Getting paid helps too. ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

That is a nice side effect. There are tons of interesting electronic-related problems out there, and surprisingly few people who can think about them clearly.

Yeah well hairy math is not going to help me at all. If I had some picture/ image of what you think is happening that would be enough.. (for me... but I'm selfish :^)

You should mostly color me confused, since from your report, getting rid of the non-linearities in the PMT drive/ bias seems to have cured your problem. Which implies it's a non-linear thing... so how are the third IM products linear in input???? (I hate to call into question your technique... but maybe it wasn't linear... but just looked linear over some smallish range?)

George H.

Hi, George,

The IM3 with the linear amplitude dependence is the central mystery that I was wondering about two weeks ago when the thread started. I tried all the usual things to narrow them down:

• checking the sources -- no IM3

• turn off one source -- no IM3

• putting a pad in front of the output amplifier -- no change in SFDR

• changing bias voltage -- SFDR constant over a wide range

• optical attenuation -- SFDR constant over a wide range

This was all without touching the reference level on the spectrum analyzer. Everything just went up and down together, except above 50 uA anode current. It didn't matter if I changed the anode current by changing the gain or by attenuating the light.

The spurs appear to come from a quadratic nonlinearity affecting correlated shot noise contributions.

The instantaneous shot noise depends on the instantaneous photocurrent. Since it's nonstationary, you have to think of it in ensemble-average terms. The ensemble-average noise current is

= sqrt(2 e Iphoto)

Iphoto = A( 2 + sin(omega1 t) + sin(omega2 t)) + B sin (2 omega1 t)...

(which is roughly right for 50% modulation, which is what I have).

This has terms of all orders, and they aren't particularly small, either--the series becomes singular right nearby.

So either some contribution from the square root, or some quadratic nonlinearity, is giving me those spurs.

The instantaneous amplitude of each signal component modifies the shot noise due to all the others, so the noise contributions of each one are correlated. That makes it not unreasonable that there would be some narrowband result when you multiply them together, but I don't know how that turns out yet.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

OK, hopefully just the B terms are enough. What do you mean by singular? it approaches one?

Yeah I kinda see this, but it's also where my brain starts to hurt, as I start switching between the time and frequency domains.

Since the customer is happy this is mostly for your own edification, no?

Phil, let me end with a general comment. I think we both like coming here (SED) for similar reasons. Given that we are no longer at research institutions or big companies we seek an intelligent audience (IA) to bounce idea's/ problems off of. (I can no longer go down the hall and knock on a door.) And lots of times I don't have to actually post my question. The act of laying out the problem (for the IA) is enough for me to see the part I'm missing. So (for you) we don't always need to be an IA, it's enough if you think we are one. :^) I'm trying to do my part and hold up my charade as an IA, but I fear you can see my feet showing below the curtain.

I know a little about shot noise, and less about IMD. (A pretty good time can be had with a spectrum analyzer, an analog multiplier and a few sig. gens.) Mixing the two is not something I've thought about.

But as I said if you write something that makes sense I'd like to read it.

George H.

That's not an insult - it's an expression of a universal law.

The manufacturer knows enough about their tubes - and how they are usually used - to produce a dynode chain that works well-enough at at 10uA anode cu rrents.

540uA peak and 350uA average are high enough anode currents to be immediate ly worrying.

Sauerbrey does talk about space charge between the photocathode and the fir st dynode. Both the old EMI and Philips application notes talk about space charge near the anode - the tendency is to put the last two dynodes on eith er side of the anode in fast focussed 14-stage tubes so you do tend to get a lot of electrons in that region - but you seem to need anode currents abo ve about 100mA (from memory) before you have to start using higher voltages between the last dynodes.

Do publish. The photomultiplier linearity literature is rather sparse.

Sloman, A.W. "Comment on 'Computer aided simulation study of photomultiplie r tubes'", IEEE Transactions on Electron Devices, ED-38 679-680 (1991)

has only got six references, but it does reference Sauerbrey who lists abou t 14 (including Peter Land which is taking completeness a bit too far).

--
Bill Sloman, Sydney

It's not an insult, but an ironic observation.

John Larkin is pathologically thin-skinned. I had thought that Phil Hobbs was less sensitive, but I have to remind myself that he's selling his (largely justified) air of omniscience, and works hard on the brand image.

--
Bill Sloman, Sydney

Considered seeing doctor Bill? all you write these days is bitterness and barely hidden insults and it seems to be getting worse

-Lasse

That wasn't any kind of "barely hidden insult" but an assertion of the obvious.

John Larkin sees an insult when anybody fails to praise him as enthusiastically as he feels to be his due, but the rest of the world ought to be less prickly.

--
Bill Sloman, Sydney

Bill, I like having you here. But I ignore your flame wars, and your continuing name calling is to me, simply childish. I've got a pretty good idea of the politics etc of all those who post here. (Politics in the US is in a sad state, two echo chambers, and the other ~third of us saying wtf... which explains (in part) the appeal of any outsiders... president-wise... but let's not get distracted.) I don't want to engage in your playground tactics, but let me say that every time you insult someone I also very much like having here on SED, I'm saddened/ disappointed. (perhaps that's not important to you.)

I mostly want to talk about electronics/ instruments/ design*, how to get the job done. If the "job" works best with a pmt cranked to ~1ma, (which seems like a lot to me but not "out of bounds") then so be it. (We use the hamamatsu CW pmt HV sockets.. they leave a lot to be desired.. You could make some money building a better one. In my experience I've found commercial electronics to be disappointing. And I end up building my own.)

If your comment is humorous or ironic, then add an emoticon, or expect to be mis-understood.

enough, George H.

*after that, tools, repair, food,...

,

y used - to produce a dynode chain that works well-enough at at 10uA anode currents.

tely worrying.

irst dynode. Both the old EMI and Philips application notes talk about spac e charge near the anode - the tendency is to put the last two dynodes on ei ther side of the anode in fast focussed 14-stage tubes so you do tend to ge t a lot of electrons in that region - but you seem to need anode currents a bove about 100mA (from memory) before you have to start using higher voltag es between the last dynodes.

t e l ,

ier tubes'", IEEE Transactions on Electron Devices, ED-38 679-680 (1991)

out 14 (including Peter Land which is taking completeness a bit too far).