Capacitor-feedback for low noise

[Zigoteau]

Hi, all,

Does anybody know what components are used in capacitor-feedback
transimpedance amplifiers?

Since capacitors do not contribute any thermal noise of their own, a
JFET-input transimpedance amplifier with a capacitor as the feedback
element, followed by a differentiator, gives you the lowest possible
input noise. However since the DC input current is in general nonzero,
you have to discharge the feedback capacitance at regular intervals to
prevent the amplifier running into the stops. The differentiator has to
be disabled during the discharge cycle.

Does anybody know how you can discharge the capacitor fast? I believe
there is an amplifier on the market, for looking at the switching of
individual molecular ion channels, in which the discharge cycle lasts
only 50 us and occurs typically at a 10 Hz rate, so that you lose only
0.05% of the action. I can't work out what they could be using for the
discharge. A reed relay typically takes 1 ms to switch, and since it
requires tens of mA switching current to the pA you are trying to
measure, the differentiator would have to be blanked for the whole
millisecond. Light-controlled avalanche photodiodes might do the trick
- I believe their low-bias reverse current can be way sub-pA, but I am
not sure how you could get around the nonlinearity of the diode
capacitance at low bias.

Any ideas?

Cheers,

Zigoteau.

 

[John Larkin]

Hi, all,

Does anybody know what components are used in capacitor-feedback
transimpedance amplifiers?

Since capacitors do not contribute any thermal noise of their own, a
JFET-input transimpedance amplifier with a capacitor as the feedback
element, followed by a differentiator, gives you the lowest possible
input noise. However since the DC input current is in general nonzero,
you have to discharge the feedback capacitance at regular intervals to
prevent the amplifier running into the stops. The differentiator has to
be disabled during the discharge cycle.

Does anybody know how you can discharge the capacitor fast? I believe
there is an amplifier on the market, for looking at the switching of
individual molecular ion channels, in which the discharge cycle lasts
only 50 us and occurs typically at a 10 Hz rate, so that you lose only
0.05% of the action. I can't work out what they could be using for the
discharge. A reed relay typically takes 1 ms to switch, and since it
requires tens of mA switching current to the pA you are trying to
measure, the differentiator would have to be blanked for the whole
millisecond. Light-controlled avalanche photodiodes might do the trick
- I believe their low-bias reverse current can be way sub-pA, but I am
not sure how you could get around the nonlinearity of the diode
capacitance at low bias.

Any ideas?

Cheers,

Zigoteau.

See Knoll's classic book, Radiation Detection and Measurement, for
some ideas.

I think the ultimate discharge device is supposed to be a
photosensitive jfet or something. Knoll has an enormous number of
references at the end of each chapter. Some people just use a very
high-value resistor across a big feedback cap, which is continuous (no
dead time) and works fine in some situations.

APDs are high-voltage devices, probably not appropriate here. NEC has
some fairly low-capacitance photomos SSRs that might be interesting.

John

 

[Joerg]

Hello Zigoteau,

Any ideas?

I am not sure that I understand what you are doing and what DC level the
cap will be at. Can you use FETs to discharge? You'll probably have to
use a balanced scheme where the charge injection cancels out and any
residual imbalance can be trimmed away.

If on a high DC potential a FET can be driven via a little ferrite
toroid signal transformer.

Regards, Joerg

 

[Winfield Hill]

John Larkin wrote...

See Knoll's classic book, Radiation Detection and Measurement, for
some ideas.

I think the ultimate discharge device is supposed to be a
photosensitive jfet or something. Knoll has an enormous number of
references at the end of each chapter. Some people just use a very
high-value resistor across a big feedback cap, which is continuous (no
dead time) and works fine in some situations.

APDs are high-voltage devices, probably not appropriate here. NEC has
some fairly low-capacitance photomos SSRs that might be interesting.

We show in our book one way to solve the discharge-FET capacitance
problem (how to avoid interfering with the 1.0pF feedback cap).

 

[John Larkin]

John Larkin wrote...

We show in our book one way to solve the discharge-FET capacitance
problem (how to avoid interfering with the 1.0pF feedback cap).

P 1039?

There's also the old trick of collapsing the opamp power supplies
briefly, letting the esd diodes discharge the cap.

John

 

[John Larkin]

Hello Zigoteau,


I am not sure that I understand what you are doing and what DC level the
cap will be at. Can you use FETs to discharge? You'll probably have to
use a balanced scheme where the charge injection cancels out and any
residual imbalance can be trimmed away.

If on a high DC potential a FET can be driven via a little ferrite
toroid signal transformer.

The idea is that, for very small zots of charge, like from a
low-energy nuclear detector, you drive an opamp with just a cap for
feedback; this gives you low-noise gain without Johnson noise. You
differentiate the signal in later gain stages to get the spikes back.
But eventually the input charge piles up on the cap and saturates the
amp, so you have to time out data acquisition long enough to reset it,
then run for a while longer. Many clever variants exist in the nuclear
biz.

John

 

[Zigoteau]

Dear John, Joerg and Winfield,

Many thanks for all your suggestions.

John and Joerg, no, I don't think I can use a JFET to discharge,
because I will then be stuck with the reverse leakage current of the
gate-channel junction, which is typically a few nA. The noise spectral
density that I'm trying to reach is something like 1e-34 A^2/Hz, which
is equal to the shot noise from a few tens of fA. That's why a
photodiode has to be an avalanche type, because the usual run of PIN
photodiodes have reverse leakage currents in the nA range.

John, how does the idea of putting the op amp supply to zero for a
short period work? You've got to get the charge out of the end
connected to the summing junction as well.

A resistor across the capacitor to discharge it continuously is no good
because resistors are noisy. The noise level I'm trying to reach is
equal to the Johnson noise from more than a teraohm. I am quite au fait
with resistor feedback, and if you've got to have a resistor there,
then an additional capacitor is a waste of time (in any case high value
resistors have significant parasitic capacitance that you have to
compensate for somewhere).

Winfield, could you give me details of your book? Any clues about the
configuration you describe there?

Best regards,

Zigoteau.

 

[Winfield Hill]

Zigoteau wrote...

John and Joerg, no, I don't think I can use a JFET to discharge,
because I will then be stuck with the reverse leakage current
of the gate-channel junction, which is typically a few nA.

That's wrong. Take some measurements on small parts. And even
if it was right, which it isn't, there's a simple solution, as
we show.

John, how does the idea of putting the op amp supply to zero for
a short period work?

Using a fA opamp, reverse it, through 10k resistors. Uses the
matched protection diodes to quickly do the job. A very nice
elegant trick I've written about here on s.e.d. several times.

You've got to get the charge out of the end connected to the
summing junction as well.

I don't see the problem. It's not necessary to end up with
exactly 0V on the integrating capacitor, if that's what you're
implying. It's only necessary to reset the differentiator
capacitor to the same value, which is easy and automatic. But
watch out for dielectric absorption. That's an issue.

 

[Jeroen Belleman]

Hi, all,

Does anybody know what components are used in capacitor-feedback
transimpedance amplifiers?

Since capacitors do not contribute any thermal noise of their own, a
JFET-input transimpedance amplifier with a capacitor as the feedback
element, followed by a differentiator, gives you the lowest possible
input noise.

Did you consider transformer feedback? That doesn't generate any
additional noise either and it affords a flat frequency response.
It rids you of the problem of discharging the feedback cap and of
the differentiator.

What's the application?

Jeroen Belleman

 

[[email protected]]

Hi, all,

Does anybody know what components are used in capacitor-feedback
transimpedance amplifiers?

Since capacitors do not contribute any thermal noise of their own, a
JFET-input transimpedance amplifier with a capacitor as the feedback
element, followed by a differentiator, gives you the lowest possible
input noise.

I've followed this thread with interest. Not because I think I may have
something to add, but because I'm learning stuff.

That "throw away" line about caps not having thermal noise interests me.
Can someone put some more words around that concept? What are the fundamental
properties of caps that make them so different from every other component?
Would there not be an equivalent thermal noise voltage developed across a cap's
equivalent series resistance?

A successful explanation would also include transformers and inductors.

Jim

 

[Zigoteau]

Hi, Win,

the reverse leakage current
of the gate-channel junction [of a JFET] is typically a few nA.

That's wrong. Take some measurements on small parts.

Thanks for the tip, which I will check out.

And even if it was right, which it isn't,
there's a simple solution, as we show.

I take it you are referring to Paul Horowitz and Winfield Hill, The Art
of Electronics, Cambridge University Press (1989)?

Using a fA opamp, reverse it, through 10k resistors. Uses the
matched protection diodes to quickly do the job. A very nice
elegant trick I've written about here on s.e.d. several times.


I don't see the problem. It's not necessary to end up with
exactly 0V on the integrating capacitor, if that's what you're
implying.

Ah, are you talking about the protection diodes at the op amp input?
OK, I'm with you. And I guess that the protection diodes of a fA op amp
are guaranteed to have a reverse leakage of that order of magnitude.

Reversing the op amp power supply sounds dangerous, even with 10K
resistors. Is that covered in your book? Do you use decoupling
capacitors for the op amp supply?

It's only necessary to reset the differentiator
capacitor to the same value, which is easy and automatic. But
watch out for dielectric absorption. That's an issue.

Many thanks,

Ziggy.

 

[Winfield Hill]

[email protected] wrote...

Would there not be an equivalent thermal noise voltage
developed across a cap's equivalent series resistance?

That would be very low, e.g., e_n for 0.1 ohm is 0.04nV

 

[Zigoteau]

Hi, Jeroen,

Did you consider transformer feedback? That doesn't generate any
additional noise either and it affords a flat frequency response.
It rids you of the problem of discharging the feedback cap and of
the differentiator.

This sounds very interesting. Do you have a reference? Such an
amplifier would not be DC coupled - would there be stability issues at
either the upper or lower roll-off points? I will think about this.

What's the application?

The signal source is the current through a single protein molecule
bound to a bilayer lipid membrane immersed in an electrolyte. The
current flows through the protein molecule as ions, which are traded
for electrons in a metallic conductor at two electrodes. Typical
currents are of the order of pA, and switch between a number of
different values as the protein switches between different
conformations. The aim is to get as high a bandwidth as possible while
still being able to see the molecular transitions.

Cheers,

Ziggy.

 

[Phil Hobbs]

Zigoteau wrote...



That's wrong. Take some measurements on small parts. And even
if it was right, which it isn't, there's a simple solution, as
we show.




Using a fA opamp, reverse it, through 10k resistors. Uses the
matched protection diodes to quickly do the job. A very nice
elegant trick I've written about here on s.e.d. several times.




I don't see the problem. It's not necessary to end up with
exactly 0V on the integrating capacitor, if that's what you're
implying. It's only necessary to reset the differentiator
capacitor to the same value, which is easy and automatic. But
watch out for dielectric absorption. That's an issue.

There's still the sqrt(kT/C) reset voltage uncertainty to worry
about--but correlated double sampling fixes that.

It's sort of interesting the habits most of us have--at low frequency,
we're often tempted to look at the noise of a 300K resistor as an
unavoidable cost of doing business at room temperature, whereas at RF,
we'd be grousing about its indifferent 3 dB noise figure. The physics
is no different in the two cases.

Cheers,

Phil Hobbs

 

[Zigoteau]

Hi, Jim,

I've followed this thread with interest. Not because I think I may have
something to add, but because I'm learning stuff.

That "throw away" line about caps not having thermal noise interests me.
Can someone put some more words around that concept?

Capacitors have no noise because there is no dissipation. Jeroen is
right that inductors also have no noise.

What are the fundamental
properties of caps that make them so different from every other component?
Would there not be an equivalent thermal noise voltage developed across a cap's
equivalent series resistance?

A successful explanation would also include transformers and inductors.

If you want to calculate the noise you get from an arbitrary circuit,
then you need a model for the noise behavior. The thermal noise of an
impedance Z(f) can be modeled by a Thevenin equivalent circuit, where
the voltage source in series with Z(f) is random with a spectral
density of 4kTRe(Z(f)) V2/Hz. Equivalently, its thermal noise can be
modeled by a Norton equivalent circuit, where the current source in
parallel is random with a spectral density of 4kTRe(1/Z(f)) A2/Hz.

Cheers,

Zigoteau.

 

[Winfield Hill]

Zigoteau wrote...

... resistors are noisy. The noise level I'm trying to reach
is equal to the Johnson noise from more than a teraohm.

Nothing wrong with using 1 to 10T-ohms, easy, wire the sj end
floating in air, or on a Teflon standoff. Sources? Willow has
resistors to 100T, http://www.willow.co.uk/html/high_ohmic.html
Many others make these, and there's even some distributor stock,
DigiKey has several types to 1T, and Mouser has up to 1.5T ohms.

I am quite au fait with resistor feedback, and if you've got
to have a resistor there, then an additional capacitor is a
waste of time (in any case high value resistors have significant
parasitic capacitance that you have to compensate for somewhere).

Actually, a resistor makes plenty of sense. I often mention
what I call the R-C-R trick to remove the effect of resistor
self-capacitance. Alternately, I use a two-path scheme, with
an RC to insure only a low-frequency path through the high-
value resistor, and a precise capacitor feedback path for the
high frequencies. Followed by an appropriate opamp network to
bring everything back to flat response. The R-C crossover can
be precisely set, say in the 10Hz region, with one adjustment.
This approach avoids the problem of capacitance to ground with
long high-value resistors, which I've written about here before.

 

[Phil Hobbs]

If you want to calculate the noise you get from an arbitrary circuit,
then you need a model for the noise behavior. The thermal noise of an
impedance Z(f) can be modeled by a Thevenin equivalent circuit, where
the voltage source in series with Z(f) is random with a spectral
density of 4kTRe(Z(f)) V2/Hz. Equivalently, its thermal noise can be
modeled by a Norton equivalent circuit, where the current source in
parallel is random with a spectral density of 4kTRe(1/Z(f)) A2/Hz.

Yes, the physics behind it is summarized in the fluctuation-dissipation
theorem of statistical mechanics, which says that any mechanism that can
dissipate energy has associated fluctuations at finite temperature. If
this weren't so, you could make heat flow spontaneously from cold to hot.

The usual way to derive the Johnson noise formula for a resistor is to
use classical equipartition of energy, which predicts that any single
degree of freedom, e.g. the charge on a capacitor, has an RMS energy of
kT/2. Classical equipartition is a very general consequence of
statistical mechanics, and even in a quantum treatment, it can be shown
to hold for frequencies << kT/h, about 6 THz at room temperature. (The
high-frequency correction is due to the Planck function rolloff.) Since
E=CV**2/2, kT/2 of energy corresponds to voltage Vrms = sqrt(kT/C), and
charge Qrms = CV = sqrt(kTC).

If you have a parallel RC, isolated from the rest of the universe,
this fluctuation must be maintained in equilibrium by the resistor
noise--otherwise, the initial sqrt(kTC) would just discharge through the
resistor. This must be true regardless of the values of R and C.
Therefore, the open-circuit thermal fluctuations of the resistor, in the
bandwidth of the RC, must equal sqrt(kT/C) volts; since the noise BW is
1/(4RC) (noise BW = pi/2* 3 dB BW), the open-circuit resistor noise
voltage density is sqrt[(4RC)*(kT/C)] = sqrt(4kTR), which we all know
and love.

You have to work a little harder to make this demonstration completely
rigorous, e.g. by showing that the fluctuations have to be flat with
frequency, but this is the idea. It can also be shown directly from
statistical mechanics applied to a semiclassical electron gas model of
metallic conduction, but I don't know how that derivation goes.

Cheers,

Phil Hobbs

 

[Jeroen Belleman]

That "throw away" line about caps not having thermal noise interests me.
Can someone put some more words around that concept? What are the fundamental
properties of caps that make them so different from every other component?
Would there not be an equivalent thermal noise voltage developed across a cap's
equivalent series resistance?

A successful explanation would also include transformers and inductors.

Thermal noise only comes about where there's an exchange between heat and
electrical energy. So resistors have noise, but the AC impedance of coils and
capacitors do not. The equivalent *loss resistance* of those components *does*,
make noise, of course.

Also, it's possible to make room-temperature circuits with a real resistive
impedance that nevertheless produce less thermal noise than a room temperature
resistance of the same value.

Jeroen Belleman

 

[John Larkin]

Hi, all,

Does anybody know what components are used in capacitor-feedback
transimpedance amplifiers?

Since capacitors do not contribute any thermal noise of their own, a
JFET-input transimpedance amplifier with a capacitor as the feedback
element, followed by a differentiator, gives you the lowest possible
input noise. However since the DC input current is in general nonzero,
you have to discharge the feedback capacitance at regular intervals to
prevent the amplifier running into the stops. The differentiator has to
be disabled during the discharge cycle.

Does anybody know how you can discharge the capacitor fast? I believe
there is an amplifier on the market, for looking at the switching of
individual molecular ion channels, in which the discharge cycle lasts
only 50 us and occurs typically at a 10 Hz rate, so that you lose only
0.05% of the action. I can't work out what they could be using for the
discharge. A reed relay typically takes 1 ms to switch, and since it
requires tens of mA switching current to the pA you are trying to
measure, the differentiator would have to be blanked for the whole
millisecond. Light-controlled avalanche photodiodes might do the trick
- I believe their low-bias reverse current can be way sub-pA, but I am
not sure how you could get around the nonlinearity of the diode
capacitance at low bias.

Any ideas?

Cheers,

Zigoteau.

Wild idea:

Run the front-end as an integrator, add downstream gain maybe, and
digitize that, without any attempt to differentiate. Oversample a lot
so you can do digital filtering tricks. When the system gets close to
saturation, let the software kick in a weak current source to ramp
back towards ground, or wherever you like the start point to be. Since
the software controls everything and knows (or can calculate from
observation) the down-slope, it can fix the data appropriately.

No timeouts. All we need now is a very low-noise switchable current
source!

John

 

[John Larkin]

It's sort of interesting the habits most of us have--at low frequency,
we're often tempted to look at the noise of a 300K resistor as an
unavoidable cost of doing business at room temperature, whereas at RF,
we'd be grousing about its indifferent 3 dB noise figure. The physics
is no different in the two cases.

That's because most of us rarely have to process femtowatt signals at
baseband. And because uncooled high-Q-tuned amps *can* have very low
noise temps. And there's the 1/f thing, too.

John