Saturday, December 1, 2007

Transimpedance Amplifiers

A while back I made an off hand comment (can't remember where) about using a transimpedance amplifier to bring broader bandwidth diagnostics to the plasma community in general and IEC Fusion in particular.

Let me start with the MIT paper [pdf] by Carl C. Dietrich. Let us look at his Ion Detector on page 49 of the pdf. He has a nice picture of the probe on that page. On the following page he gets to the heart of the matter, a schematic representation of the detector circuitry. For frequency response estimation purposes the detector can be modeled as a 100K resistor in parallel with a 100 pF capacitor (which accounts for a probe capacitance of 5pF). The 3 dB roll off point is = .15/(R*C) - within 5%. which would be .15/(1E5*1E-10) = .15E5 = 15KHz. Pitiful. I think the scope impedance and frequency response is so limited because he has to use the very highest gain (where scope bandwidth is less) to see any signal at all. So we can estimate the signal at 1 mV p-p. Into 100 K ohms that means a current of 1E-8 Amps. About 10 nano Amps.

Can we do better? Yes. But we have to do a couple of things. One is to reduce the input impedance to get wider bandwidth and second we are going to have to amplify that current. Thanks to the proliferation of fiberoptic technology we have exactly the tool we need to do the job.

I like the Philips SA5211. It is low noise and high gain with a maximum output swing of a few volts with a 5 volt supply. It is also bipolar technology tending to make the input a bit more robust than JFET or MOSFET input technology.

So let us start with gain. The transimpedance gain (minimum) is about 20K ohms differential. What does that mean? A current of 1E-8 Amps will be multiplied by that resistance to give 2E-4 volts change between the two outputs. About 200 uV p-p or about 70 uV rms. That is a fair signal for spectrum analyzer and other RF work. Feed that into a transformer like the Mini-Circuits T1-6T and you have a package with good gain from 30 KHz out to 150 MHz and almost flat from 300KHz to 50 MHz. To look at lower frequency signals I'd use an ordinary instrumentation op amp from the differential output of the transimpedance amplifier. The AD8253[pdf] looks nice with a bandwidth of 3 MHz at a gain of 100 (40 dB). That gets us to 20 mV p-p at the output for signals in the audio to low RF range. Not bad. For the higher frequency signals I'd follow the transimpedance amplifier with a couple of 20 dB gain stages (at least) to get the signals up to the mid mV range. I like the Mini-Circuits MAR-8A which is rated out to 1,000 MHz (25 dB gain typ) and is not too hot in the high frequency gain department so that taming the circuit will not be too difficult. It also has gain from DC to 1,000 MHz - meaning we can use it to amplify RF in the mid kHz range without problems. Some amplifiers of the type do not like low frequencies because the slow waves can cause the circuits to either over heat or become unstable.

So now we are facing the last question. Bandwidth. The feedback resistance for the transimpedance amp is about 14K (I used 10 K - above multiplied by 2X to account for the differential output) with the gain of the input stage a factor of 70. So what is the input impedance seen by our current (ion) source? That would be 14K divided by the gain of the input stage (70) or 200 ohms. It has an input capacitance of 4 pF. Let us say the probe is another 6 pF or 10 pF total. Double that to account for a lot of slop in the installation.

Let us plug that into our frequency formula: .15/(200*2E-11) = 37 MHz. Not too shabby. We can double that without too much effort if we work to keep stray capacitance down. Which means that our SA5211 at 200 MHz bandwidth should be more than adequate for the job with the subsequent Mini-Circuits amplifiers making a very small contribution to reduced high frequency gain.

So there you have it - a very nice high frequency ion probe. With a minimum AC signal of 1E-8 Amps p-p and a maximum signal of 4E-5 Amps p-p (at the transimpedance amplifier - gains of the other amplifiers would need adjusting if the signal is near maximum).

Update: The 1E-8 Amp current limit is where the signal = the noise for a 50 MHz bandwidth. If a narrow band detector is used (1 KHz) the detection limit goes down to 1E-10 Amps p-p.


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Tom Cuddihy said...

Hey Simon, enjoyed the Carl C. Dietrich MIT paper you linked too -- another approach to IEC I hadn't considered! (beam shaping with grids to minimize e- and ion losses instead of magnetic protection of the grids).

I wonder if there's a way to combine the two methods in order to further increase power scaling? That would allow even smaller and lighter breakeven reactors, I believe?

M. Simon said...


I think it is worth a look.

I might keep the magnetic grid and add others for better beam formation.

They do point out that beam losses are not sufficiently low for net power. Thus I would keep the magnetic grid to "shield" the others.