amplifying a sub femtoamp of current

Just do not forget the capacitive loads. At 10 kHz the impedance of 1 pF is ~0.0159 G ohm. So try a (hf-) mosfet with low input capacitance.

4K is probably to low for a mosfet, but some cooling should lower the noise.

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Sven Wilhelmsson
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You can't usefully use a 1 MHz bandwidth with a femtoamp of current, at least not if it has full shot noise, which I imagine it does. If your current consists of N electrons per second, counting statistics predict that your SNR will drop to 0 dB in a measurement bandwidth of N/2 Hz. A femtoamp is only 6200 electrons/s, so assuming you want at least a 20 dB SNR (because below that you haven't got a measurement really), your bandwidth is going to be limited to 31 Hz.

Sorry about that.

Cheers,

Phil Hobbs

You have two problems with basic physics:

Problem One:

To get a 3dB corner frequency of 1MHz you need to keep your total capacitance down to about 160 atto farads, assuming I got my prefixes right. That implies a capacitor that's about 0.02mm on a side, with air dielectric.

You _may_ be able to get there from here with some custom IC operating at 4K, but I wouldn't know.

I would suggest that you need some other, more reliable, way of amplifying small currents. Hopefully someone will jump in with suggestions. All I can think of is that if you can get your voltages up high enough you may be able to do something with ionization, like a Geiger counter.

Problem Two:

One fA implies that you're flowing about 62400 electrons per second. Even at 10kHz the shot noise is going to be enormous, and at a 1MHz bandwidth you'll be seeing the electrons as individual events, not as anything resembling a continuous current.

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Tim Wescott
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Tricky. 1 fA integrated over 500 ns (1/2 cycle at 1 MHz) is 0.003 electrons. You're going to need some serious signal averaging.

And a charge amp with very low input current, probably a cold jfet.

What's the physics?

John

Great Comments, Now i see the problems - and am not that happy when i started this post:( I was planning to use GaAs MESFETs with the 1G resistor at gate bias. However, now it seems it won't work as i thought. Here i am trying to detect a motion of a single ion in a penning trap - people use tuned circuits to pick up this ~50 fA image current. But i want to build something for broadband detection (upto 1 MHz).

Damn. 6240, per Phil Hobbs. Apparently I was visiting a universe where

6.24*10^3 = 62400, but I'm back now.

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Tim Wescott
Wescott Design Services
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"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

Heisenberg's uncertainty rules, at least in principle.

--
Bill Sloman, Nijmegen

Mesfets are nasty, leaky, noisy, and have very strange changes of gain at low (KHz) frequencies, some sort of trapping-state thing. Jfets are often used cold, and work at liquid helium temps. The ultimate charge amp uses pure capacitive feedback to eliminate resistor noise, but has to be reset now and then to cancel offset drift buildup.

That may not be possible... there's just not enough signal. Signal averaging (lock-in technique, done in hardware or software) would work, but that's just equivalent to reducing the bandwidth. At least it's not fixed-tuned.

How do you get the signal out of the ion... tiny antennas? Optical?

Non-trivial, for sure.

John

My reading of the OPs comments doesn't rule out a narrow bandwidth around some carrier in the range he suggested. If this is the case, this won't be his biggest problem.

Figuring out how to amplify a signal that small accurately will be trouble too.

--
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kensmith@rahul.net   forging knowledge

In article , Tim Wescott wrote: [...]

He's already cold so maybe a SQUID is the answer.

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kensmith@rahul.net   forging knowledge

Remember that Millikan "measured" single electron "flow"; guesstimate

1 electronper ten seconds. So for 1000 electrons, theoretically that could be done in 10mSec or a rough bandwidth of 100Hz. Following that to 1MHz, one would need (crudely now) a flow of 10,000 electrons. But do not use a high value resistor, as displacement currents will kill what it would "see"; if you insist, then look into measuring the displacement current or the voltage it generates on a known capacitor. Say, use a huge 1.00 pF capacitor.... Or, try to be more nasty and get them electrons to "jump" thru a chamber with a view port, at one electron per oil drop (or other insulating liquid) - and *count* those or determine when they pass by (132 this time interval, 45 next one, etc...).

I will have you know, that *he* was NOT the principal of my school!

What kind of source ?

greetings, Vasile

As others have noted, you're going to have a heck of a time with noise if your signal is just 6200 electrons per second. Plus seeing a 1MHz signal is going to require a whole lot of auto-correlation and filtering.

Do you have a known frequency and bandwidth to look for? I suspect seeing that weak a signal is going to require like many many seconds of observation and a very narrow bandwidth, like 1Hz or so.

I'd suggest forgetting about measuring the voltage, and instead measure the current directly with a transimpedance circuit. You're getting so few electrons it's a shame wasting them heating up a 1Gohm resistor. :)

Yeah, by watching oil drops in a microscope and changing the voltage across two capacitor plates to levitate them. Doing that even 6200 times per second is a good trick, besides the fact that M. was wasting almost all the oil drops while concentrating on one at a time.

If the current starts out in a wire, i.e. it comes from displacement current due to ion motion, the OP going to have to use bandwidth narrowing of some sort. Signal averaging is generally much better than using a narrow bandwidth near DC, because you can get out of the 1/f noise and the drift pretty well. Tuned circuits are not a stupid idea at all, because you can set the fields in the trap up to get a particular cyclotron resonance frequency--i.e. you can tune the signal to the filter. (Superhets do the same thing.)

If the signal starts out as free electrons in a vacuum, then the situation is much better--a Channeltron or other electron multiplier is the way to go. It's trivially easy to put 140 dB of gain on those pulses, at which point you can probably even detect them with a neon bulb.

Cheers,

Phil Hobbs

Guys thanks again for the suggestions - though my eyes are so dilated from an eye exam that i am not able to read properly:). But let me tell more about the signal source, which might help. Ions of range of mass to charge ratio are made to rotate in a cubic electrode arrangement. The rotation of ions induces an image charge/current on the plates/electrodes of the cubic cell. The frequency of the induced current corresponds to the frequency of the rotation of ions and proportional to their mass to charge ratio. A typical Ion cyclotron resonance experiment. This current is in the order of 100's pA if their are lot of ions (generally a million). However i want to be able to detect single ion using some sort of amplification. And i want to do this for ions with a range of mass to charge ratio, hence a range of frequencies (10 KHz - 1MHz). The plates of the cell (cubic electrode arrangement) has a capacitange of around

20 pF, thus we model our source as an ideal current source in parallel with this 20 pF capacitor. Here we have put the cubic cell at 4 kelvin and i hope to put the preamplifier right on it - getting to cool the electronics and reduce the thermal noise.

I have to do a broadband detection, hence can't use tuned circuits.

The ICR detection is non-destructive i.e. you don't loose the ions which you are detecting. The signal starts as induced charge on the plates of the detector where as the ions keep rotating (damped slightly by the loss of energy during detection).

Thanks for the description. Interesting!

I understand we have 1 nV or less at 20 pF. I believe this is possible to detect provided data acquisition time is longer than life time of the ion. It is not a problem with Heisenberg, IMHO.

A capacitance of 20 pF is a lot. The signal would increase if C could be reduced. If this is not possible maybe one could raise the impedance by means of an inductor to form a tuned circuit at the amplifier input.

I hope someone can give advice on the best choice of 4 Kelvin charge amplifier. John Larkin suggested a cold jfet. I guess that is a good suggestion. Some semiconductors do not work at 4K as minority carriers are not generated thermally as they are at room temp.

--
Sven Wilhelmsson
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Sorry, I mean "I believe this is possible to detect provided the NEEDED data acquisition time is NOT longer than life time of the ion."

I saw Werner Heisenberg once. The closer he came, the more uncertain I was whether it was really him.

--
Sven Wilhelmsson
http://home.swipnet.se/swi