Noise in JFET analogue switches

[Cerebus]

But wait a minute, you can’t have it both ways In the OFF state, does the channel behave as a very high value resistance such as 1E12 ohms, or does it become a  no-movement zone for charge carriers meaning infinite resistance? Your reasoning appears to be that it is the latter, because if it did (if it did behave as 1E12 ohms) JFET switches would be next to useless just because of the noise levels involved.

With sincere politeness and respect, I believe you are wrong, and still apparently don’t ‘get it’. JFET switches when OFF do not behave as a no-movement zone for charge carriers at all. On the contrary, they have a high resistance, such as 1E12 ohms, with corresponding Johnson noise. By your reasoning that would make them next to useless because of the high noise levels involved, but that is also not true in any realistic circuit implementation, and was largely the thrust of my posting. Rather than repeat myself here, please read my previous posting carefully. If what I say above is wrong, then of course I want to know about it, and know why I am wrong, that’s what I am here for, that’s how we learn.

OK, it seems we still haven't got to the bottom of this. [Fx: Sigh] And I thought we had.

By the way, you should realize that 'no-movement zone for charge carriers' isn't mean to be taken completely literally, especially not to imply infinite resistance. Again, what I actually said was "essentially becomes a no movement zone" - that "essentially" you omitted means "in essence", "reduced to its essentials", it implies that I'm omitting fine details and it's often used to make a short explanation out of a long one. If you prefer, a region of reduced charge carrier mobility caused by the field effect of the field effect transistor leading to a highly increased resistance of the channel.

My reason for believing that an 'OFF' JFET switch is quieter than the Johnson noise implied by the off channel resistance is that I've seen circuits that would be ruined by this and yet aren't. Take a look at the input stages of the HP 3458A. There are as many as 8 turned off JFET switches (and 1 on) feeding in parallel directly into the gate of the input amplifier (i.e. a very high-Z situation with no shunting impedance except the source resistance of the DUT which could still be very high). If we take a nominal 127uV rms as the noise of one switch, the noise contribution of those turned off switches would be on the order of sqrt (8 * 127uV^2) = 359 uV rms. That meter doesn't make high-Z readings as if 300 odd uV of noise have been thrown into the mix and has a 1uV rms noise spec (0.1 ppm of 10V range) into >10 G input impedance - equally I haven't seen a graph of noise versus source resistance for it.

I think we're going to have to make Bob happy and actually do some real measurements. I can't physically do any electronics for a few days - I've got relatives visiting and that has necessitated a tidying up and clearing of the boards. Thinking about it, that's more like a week or two. When I get a chance I've got a rare hoarded U421 (that has a maximum gate operating current of 250 fA at room temperature) that I can air wire into a small high-Z pre-amp and follow it with a stage with a gain of, say, 1000 and plug it into the scope. I've got some MMBF4393s and J113s that can be used to create switches to test. I might have to order up a few quiet op amps too as the only truly quiet and low offset thing I have at the moment is a single OPA277 (220 nV 0.1-10Hz e_in and 20uV offset). Yup, quick check shows that the next best I have is some AD712s at 2uV e_in and 300 uV offset. That should put to bed once and for all whether you can see the full Johnson noise of the channel's off resistance or not.

I kinda hoped (assumed really) that someone knew a lot more than me about this and would just throw out a definitive answer early in the game. I'm really surprised that is not apparently the case.

[Cerebus]

*Cough*...

Yes, you can model it as a very high resistance, but at that point, you're probably better off modeling it as a current source, which is what I implied ("leakage current shot noise").

You'll get so-and-so fA/rtHz or whatever, which simply develops a noise voltage V = I*R on your system impedance R.  Well okay, Z to be general, not R, but whatever.

There's nothing wrong about Thevenin-Norton source equivalency, it's just a matter of which is most appropriate for the case.

Tim

You'll notice that I started early on with A²/Hz as my unit of choice. I couldn't agree more that this is the kind of situation that's much easier to think of in terms of current, well at least it is for me.

I don't know why, but I've noticed a really heavy bias among electronics folks in general to always think and discuss in voltage rather than current terms whenever they can. The odd thing about this is that current (essentially electron flow per unit time) is, to my mind at least, a much more concrete idea than voltage (potential to do work). There are a whole bunch of things I never really got a handle on until I saw them in current terms rather than voltage terms although an example refuses to come to mind just now when I could use it.

[T3sl4co1l]

I don't know why, but I've noticed a really heavy bias among electronics folks in general to always think and discuss in voltage rather than current terms whenever they can. The odd thing about this is that current (essentially electron flow per unit time) is, to my mind at least, a much more concrete idea than voltage (potential to do work). There are a whole bunch of things I never really got a handle on until I saw them in current terms rather than voltage terms although an example refuses to come to mind just now when I could use it.

And even more so, power and impedance.  Or frequency and impedance (versus inductance and capacitance).

Believe it or not, the humble LM358 is just as low-noise as the famed LT1028... on a power basis.  The difference is, if all you're interested in is voltage, period, and you have a really low source impedance (1k or less), LT1028 can only be beaten by a few select discretes, or by building a parallel array.  LM358 only breaks even for a source impedance of nearly 1Mohm -- in fact, a source resistance so high that you have trouble biasing the poor thing, given its input bias current (and especially input bias offset).

So the difference is, it's impractical to try to use an LM358 at its optimal source resistance, whereas in most LT1028 applications, the low impedance isn't a problem.

Just as equally, you'd never use an LT1028 in an oscilloscope front end, where the input impedance must be high.  The noise appearing on the input pins, when unloaded (open circuit, or at least high Z) would be huge!  And anyway, you can't win against such a constraint: that is, expecting 50-ohm noise levels from a 1M probe.  Though, a discrete circuit with e.g. LSK389 can do pretty damn well, especially after adding some tricks to control 1/f noise.  (Some ideas in AoE3.)

As has always been the case: use what is most appropriate.  If your JFET switch circuit is too noisy (perhaps because of excessively high impedances being sensitive to leakage noise; or too low, and Rds(on) is adding too much), consider using relays (and deal with the slow and bouncy operation).  Speaking only in terms of voltage, or only in terms of current, is meaningless.  Speaking of both, however, you can at least put an optimum resistance on the part: if Rds(on) is 100 ohms and Roff ~ 1G, then the least noise will be had at a resistance which is the geometric average of these, i.e., ~320kohms.  The noise factor will be quite good, because the ratio is very high; reasonable performance would be had from 1k to 100M.

Incidentally, there's never such a thing as "open circuit".  Despite needing a low source resistance for optimal operation, an amplifier might still not produce much noise when unloaded -- except it is loaded, into its own internal resistance and capacitance.  It's very likely the bandwidth of the input stage changes with resistance.  It might be that the only frequencies where e_n = sqrt(4*kB*T*Rs) holds true, is at very low frequencies (namely, where Rs dominates over any filtering effect from L or C).  But the integrated noise can still be small, because the bandwidth is small (1nV/rtHz out of a 1Hz bandwidth is, *calculates furiously*, all of 1nV!).  Loaded into nominal resistance, the noise will be small, but the bandwidth can be many times higher, so that similar (total, RMS) noise is present.

Tim

[Zeranin]

*Cough*...

Yes, you can model it as a very high resistance, but at that point, you're probably better off modeling it as a current source, which is what I implied ("leakage current shot noise").

You'll get so-and-so fA/rtHz or whatever, which simply develops a noise voltage V = I*R on your system impedance R.  Well okay, Z to be general, not R, but whatever.

There's nothing wrong about Thevenin-Norton source equivalency, it's just a matter of which is most appropriate for the case.

Tim

Yes, think in terms of current if you prefer. If we are talking about an equivalent noise current source to a 1E12 resistor voltage source, then don't forget that the equivalent current source is in parallel with 1E12 resistance. If you don't include the parallel resistance, then the noise voltage of the current source would be infinite. The magnitude of the current source is of course Vnoise/R.

Cerebus, I'll get back to you re your posting. You raise interesting questions that demand answers.

[T3sl4co1l]

Yeah, but the handy thing is, 1e12 is way fuckin' bigger than 3e5, so much that you don't need to calculate the parallel combination.  T'other way around, you need to scratch your head about a voltage divider.

Like I said, horses for courses...

Tim

[Zeranin]

OK, it seems we still haven't got to the bottom of this. [Fx: Sigh] And I thought we had.

My reason for believing that an 'OFF' JFET switch is quieter than the Johnson noise implied by the off channel resistance is that I've seen circuits that would be ruined by this and yet aren't. Take a look at the input stages of the HP 3458A. There are as many as 8 turned off JFET switches (and 1 on) feeding in parallel directly into the gate of the input amplifier (i.e. a very high-Z situation with no shunting impedance except the source resistance of the DUT which could still be very high). If we take a nominal 127uV rms as the noise of one switch, the noise contribution of those turned off switches would be on the order of sqrt (8 * 127uV^2) = 359 uV rms. That meter doesn't make high-Z readings as if 300 odd uV of noise have been thrown into the mix and has a 1uV rms noise spec (0.1 ppm of 10V range) into >10 G input impedance - equally I haven't seen a graph of noise versus source resistance for it. I think we're going to have to make Bob happy and actually do some real measurements. I can't physically do any electronics for a few days - I've got relatives visiting and that has necessitated a tidying up and clearing of the boards. Thinking about it, that's more like a week or two. When I get a chance I've got a rare hoarded U421 (that has a maximum gate operating current of 250 fA at room temperature) that I can air wire into a small high-Z pre-amp and follow it with a stage with a gain of, say, 1000 and plug it into the scope. I've got some MMBF4393s and J113s that can be used to create switches to test. I might have to order up a few quiet op amps too as the only truly quiet and low offset thing I have at the moment is a single OPA277 (220 nV 0.1-10Hz e_in and 20uV offset). Yup, quick check shows that the next best I have is some AD712s at 2uV e_in and 300 uV offset. That should put to bed once and for all whether you can see the full Johnson noise of the channel's off resistance or not.

I kinda hoped (assumed really) that someone knew a lot more than me about this and would just throw out a definitive answer early in the game. I'm really surprised that is not apparently the case.

Hmm. Interesting. Let me come at this from 2 angles. It is a generally observed fact that the Johnson noise of any resistance (as defined by V/I) is never less than the calculated value. Very often it is more, but never have I seen a case where it is less. For example, if the ON resistance is 100 ohms, then I would be amazed if the Johnson noise of this ON resistance was less than for a perfect 100 ohm resistor, and I suspect we all agree. Just think, we could use the ON resistance of a JFET for the feedback resistors in an uber-low-noise amplifier circuit, and beat the Johnson noise that plagues ‘normal’ resistors. But I suspect Mr Johnson won’t be fooled that easily. By the same reasoning, it seems highly unlikely to me that the OFF leakage resistance could exhibit lower noise than an equivalent resistor, either. I can’t tell you how much I would like to be shown wrong on that, because boy could I build some great circuits and make a lot of money, but it’s not going to happen, I reckon.

But real world specifications and measurements are the ultimate bottom line, so how can the specifications of the HP3458A be what they are? I think you hit the nail right on the head :-

That meter doesn't make high-Z readings as if 300 odd uV of noise have been thrown into the mix and has a 1uV rms noise spec (0.1 ppm of 10V range) into >10 G input impedance - equally I haven't seen a graph of noise versus source resistance for it.

If all I have claimed is right, even the best DVM will be relatively noisy when configured for 1Gohm input impedance, and with nothing connected to the input, and that is certainly my experience. I don’t have an HP3458 just to hand, but tried that experiment with a Tektronix and Agilent 6.5 digit DVM, and sure enough, they are quite noisy with an open-circuit input, way, way noisier than their DC spec.

If you are right, then it would be easy to prove for anyone with an HP3458 at hand. You claim that with no external connection to the input, just the internal 1 Gohm, that the measured noise will be way less than calculated for 1 Gohm. Of course, bandwidth needs to be taken into account. If the input is 10 Gohm, and total input capacitance is 10 pF, then RC=0.01 seconds, for a cutoff frequency of 16 hz. Depending on the chosen measurement integration time, the actual bandwidth may be less. This experiment is easily performed, and I would be taken aback if the measured noise was less than for a 1 Gohm resistor at the same bandwidth.

What do you think?

Being a hands-on person myself, I support your idea of measuring the noise of the OFF channel resistance. However, it might be challenging, though doubtless possible. For a start, you will need to measure what the actual OFF resistance is, remembering that it may well be an order of magnitude less than spec. As a check on your measurement, I suggest you find a conventional resistor of about the same value, and measure it’s noise as well. Keep in mind, the measured noise is expected to decrease when the resistor is connected across your amplifier input.

[Zeranin]

Yeah, but the handy thing is, 1e12 is way fuckin' bigger than 3e5, so much that you don't need to calculate the parallel combination.  T'other way around, you need to scratch your head about a voltage divider.

Like I said, horses for courses...

Tim

Yes indeed Tim, says me chuckling, I do indeed realize all you say, but I'm a pedantic bastard, and would not like us to be imprecise or incomplete in our understanding. Most time 1E12 is so much bigger than anything else that it can be ignored, but sooner or later you'll come across a situation or argument where it does matter, and then you'll get bitten unless you are at least aware that it is there. 

[Cerebus]

*Cough*...

Yes, you can model it as a very high resistance, but at that point, you're probably better off modeling it as a current source, which is what I implied ("leakage current shot noise").

You'll get so-and-so fA/rtHz or whatever, which simply develops a noise voltage V = I*R on your system impedance R.  Well okay, Z to be general, not R, but whatever.

There's nothing wrong about Thevenin-Norton source equivalency, it's just a matter of which is most appropriate for the case.

Tim

Yes, think in terms of current if you prefer. If we are talking about an equivalent noise current source to a 1E12 resistor voltage source, then don't forget that the equivalent current source is in parallel with 1E12 resistance. If you don't include the parallel resistance, then the noise voltage of the current source would be infinite. The magnitude of the current source is of course Vnoise/R.

Cerebus, I'll get back to you re your posting. You raise interesting questions that demand answers.

After a chance to sleep on it I've spun some numbers. The short answer is that the noise mechanism is irrelevant as it's all going to be dominated by the gate leakage current as that path is relatively low impedance compared to the channel. That is going to be the path that shunts most of the noise current away from the 'output*' of the switch.

To get to this point I just made the assumption, for arguments sake, that the full Johnson noise for the channel just treated as a resistor was there and the full shot noise due to channel leakage current was there too. Further I assumed Vds = 0, Vgs = -10, and Vgd = -10 and a channel resistance of 10^12 ohms, typical voltages for an 'OFF' condition and mid rail signal. Then turned the Johnson noise into current noise, calculated the shot noise caused by the channel leakage and came up with the total current noise (rss) which is going to be something on the order of 2 fA BUT I know from experience that the gate leakage current under those initial conditions is on the order of 50 pA for a typical switching JFET (MMBF4393). So although it's a paltry 50 pA it represents an equivalent resistance of 200G which ordinarily sounds large but isn't in the face of a 2fA (12,500 electrons/sec) current. It still comes out noisier than I'd have  expected.

Note, that really is back-of-the-fag-packet numbers and they're just for argument's sake to show the magnitude of the effect and any individual numbers should be taken with a pinch of salt.

* I'm finding it really frustrating not being able to say 'source' and 'drain' but they swap around depending on which side of the switch is at lower potential.

(N.B. For the most part I've not bothered with signs e.g. That leakage current ought to be negative.)

[Cerebus]

OK, it seems we still haven't got to the bottom of this. [Fx: Sigh] And I thought we had.

My reason for believing that an 'OFF' JFET switch is quieter than the Johnson noise implied by the off channel resistance is that I've seen circuits that would be ruined by this and yet aren't. Take a look at the input stages of the HP 3458A. There are as many as 8 turned off JFET switches (and 1 on) feeding in parallel directly into the gate of the input amplifier (i.e. a very high-Z situation with no shunting impedance except the source resistance of the DUT which could still be very high). If we take a nominal 127uV rms as the noise of one switch, the noise contribution of those turned off switches would be on the order of sqrt (8 * 127uV^2) = 359 uV rms. That meter doesn't make high-Z readings as if 300 odd uV of noise have been thrown into the mix and has a 1uV rms noise spec (0.1 ppm of 10V range) into >10 G input impedance - equally I haven't seen a graph of noise versus source resistance for it. I think we're going to have to make Bob happy and actually do some real measurements. I can't physically do any electronics for a few days - I've got relatives visiting and that has necessitated a tidying up and clearing of the boards. Thinking about it, that's more like a week or two. When I get a chance I've got a rare hoarded U421 (that has a maximum gate operating current of 250 fA at room temperature) that I can air wire into a small high-Z pre-amp and follow it with a stage with a gain of, say, 1000 and plug it into the scope. I've got some MMBF4393s and J113s that can be used to create switches to test. I might have to order up a few quiet op amps too as the only truly quiet and low offset thing I have at the moment is a single OPA277 (220 nV 0.1-10Hz e_in and 20uV offset). Yup, quick check shows that the next best I have is some AD712s at 2uV e_in and 300 uV offset. That should put to bed once and for all whether you can see the full Johnson noise of the channel's off resistance or not.

I kinda hoped (assumed really) that someone knew a lot more than me about this and would just throw out a definitive answer early in the game. I'm really surprised that is not apparently the case.

Hmm. Interesting. Let me come at this from 2 angles. It is a generally observed fact that the Johnson noise of any resistance (as defined by V/I) is never less than the calculated value. Very often it is more, but never have I seen a case where it is less. For example, if the ON resistance is 100 ohms, then I would be amazed if the Johnson noise of this ON resistance was less than for a perfect 100 ohm resistor, and I suspect we all agree. Just think, we could use the ON resistance of a JFET for the feedback resistors in an uber-low-noise amplifier circuit, and beat the Johnson noise that plagues ‘normal’ resistors. But I suspect Mr Johnson won’t be fooled that easily. By the same reasoning, it seems highly unlikely to me that the OFF leakage resistance could exhibit lower noise than an equivalent resistor, either. I can’t tell you how much I would like to be shown wrong on that, because boy could I build some great circuits and make a lot of money, but it’s not going to happen, I reckon.

But real world specifications and measurements are the ultimate bottom line, so how can the specifications of the HP3458A be what they are? I think you hit the nail right on the head :-

That meter doesn't make high-Z readings as if 300 odd uV of noise have been thrown into the mix and has a 1uV rms noise spec (0.1 ppm of 10V range) into >10 G input impedance - equally I haven't seen a graph of noise versus source resistance for it.

If all I have claimed is right, even the best DVM will be relatively noisy when configured for 1Gohm input impedance, and with nothing connected to the input, and that is certainly my experience. I don’t have an HP3458 just to hand, but tried that experiment with a Tektronix and Agilent 6.5 digit DVM, and sure enough, they are quite noisy with an open-circuit input, way, way noisier than their DC spec.

If you are right, then it would be easy to prove for anyone with an HP3458 at hand. You claim that with no external connection to the input, just the internal 1 Gohm, that the measured noise will be way less than calculated for 1 Gohm. Of course, bandwidth needs to be taken into account. If the input is 10 Gohm, and total input capacitance is 10 pF, then RC=0.01 seconds, for a cutoff frequency of 16 hz. Depending on the chosen measurement integration time, the actual bandwidth may be less. This experiment is easily performed, and I would be taken aback if the measured noise was less than for a 1 Gohm resistor at the same bandwidth.

What do you think?

See my previous post for what I think's going on. In that I derive a parallel leakage resistance for one switch of something in the order of 200G. I don't think that the 3458's input resistance spec of >10G, the fact that there are 9-10 JFET switches in parallel and that figure of 200G for one switch are coincidences. I'm ignoring the input leakage of the amplifier that follows but I suspect that it is on the order of a few 100fA based on similar designs I do know in detail. I can't be more precise because the JFETs used both for the switches and input pair are a) obsolete, b) listed with internal part numbers and c) I've never managed to unambigiously match the HP part numbers to a standard datasheet parts.

Being a hands-on person myself, I support your idea of measuring the noise of the OFF channel resistance. However, it might be challenging, though doubtless possible. For a start, you will need to measure what the actual OFF resistance is, remembering that it may well be an order of magnitude less than spec. As a check on your measurement, I suggest you find a conventional resistor of about the same value, and measure it’s noise as well. Keep in mind, the measured noise is expected to decrease when the resistor is connected across your amplifier input.

I may back off on that for a bit, the reason being, although I've pushed very hard to keep this a theoretical discussion, that there is some practical end to this and it'd be much easier to measure all this on a neat shielded PCB. I came at this because I wanted to do some noise budgeting on my draft designs to see if I was getting into the right ball-park and I realised that I had zero clue how to figure out the noise contribution of the JFET switches.

Oh, and Tim, don't worry, there will be relays too - not worth building anything if you can't hear the clack of a few relays on your calibration cycle.