DIY 0.1 to 10Hz Noise Amplifier

[trtr6842]

I'm starting some projects where it will be useful to measure low frequency noise, so I designed and built this 0.1Hz to 10Hz noise amplifier.

(I know my handwriting sucks)


It has a gain of 2,000 V/V, which is plenty to get above the noise floor of my RTB2000 scope.  My main goal was not ultra-low noise performance, as nothing I'm working on requires measuring noise less than 1µV p-p.  Instead I wanted something that settled within a reasonable time, and wasn't picky about finding the perfect low-leakage input capacitor.  To achieve that, I went with a multi-stage design.  I also wanted it to run off a single 9V battery with decent life.




The input stage is just the high-pass RC network with some diode clamps.  While breadboarding the design I found out the hard way that hot-plugging the input to a +10V supply can very easily fry the input to the first opamps.  Also with higher input voltages, the input resistors have to dissipate a significant amount of energy, so I used a total of 4x 1206 sized parts. 

The first amplification stage is 4x parallel OPA2188's with a gain of 200.  OPA2188's are reasonably priced and have pretty good noise performance.  There are less noisy options, but all I've seen consume quite a bit of current, which would kill the 9V battery life.  A gain of 200 is plenty to get the input completely clear of the op amp noise floor, but is low enough to allow typical electrolytic capacitor leakage currents to cause minimal offsets with the 2k input resistance.  Assuming a partially depleted 9V battery, the power rails will be about ±4V, so the input capacitor leakage can be as high as 10µA before the output hits the rails.  This is no problem for most electrolytics, and this strategy worked well as every cap that came on my stuffed boards worked just fine.

Right after the 200x input stage comes a high pass filter.  This removes any DC offsets from input cap leakage and allows more gain to be applied later.  After that is is a 4th order 10Hz high-pass filter, and a final 10x gain stage.  The output is high-passed at 0.1Hz as well, taking into account a 1MΩ scope input impedance.

Overall the performance is good enough for me, but not ultra-low noise.  With a shorted input I get about 261nVp-p.  That's plenty low for what I test, which is more like LM399's in stead of LTZ1000's.  It's also been very consistent, and the FFT of it shows no significant spikes.  If I can make the assumption that my amplifier and the device under test both have truly random noise sources, I could just do the math to subtract my amplifier un-correlated noise from any measurement's I'm taking that are below 1µVp-p, but I honestly don't expect I'll need to do that with what I'm working with.

Intrinsic Noise with Shorted Input



131kPt FFT of shorted input, done with scope data and a python script, since my scope won't do such low frequency FFT's



I tested the gain by using a 1Hz 1Vp-p signal and a 1MΩ / 100Ω resistor divider, and the gain was spot-on.



I tested the frequency response with a 200 second 0.05Hz to 20Hz logrithmic sweep.  The low frequency cutoff is a little high, but not bad.  (The vertical cursors represent 0.1Hz and 10Hz on the sweep)



The inter-stage high pass filter makes the settling time pretty quick, about 30 seconds for a 100µV step.  It can take up to 2 mins when first plugging into a new DUT, but that's not bad at all.  Better than waiting forever for the input cap to re-form!


The current consumption is 5.66mA at 9V, so that should give me a good 50 hours or more on a single battery, which seems pretty reasonable for my use.

Overall I'm really happy with the design, and it has proven very useful so far.  A while back I built a 4-20mA signal calibration source based around an LM399 and some goofy configurations of some NOMCA 8 resistor networks.  It also has a +10V output, and turns out its not too bad at about 6.5Vµp-p.



Another thing I learned is that the cheap 79L12 linear regulators I'm using on a project are about 15x noisier than their 78L12 counterparts! (1mVp-p vs 70µVp-p)  I didn't expect that, but I confirmed it on a sample size of 5 boards, so that's good to know.

I got 5 of these made through JLCPCB's SMT service, so I have 4 extra if anyone is interested in board-only or fully-enclosed one!

[mawyatt]

Nice work 

Curious as to why you chose SMD chip caps for use in the Sallen-Key Filters and output DC blocking cap. Are these ceramic because they are physically small size? Also are they C0G/NP0 types, or one of the higher dielectric constant ceramics?

Best,

[trtr6842]

I chose ceramics simply for size and convenience.  They are X7R types, nothing special.

My thought process was yes, they will be very imperfect, but their impact should be fairly small since they all come after the initial 200x gain stage.  The most critical ones are the two 10µF ones used in the sallen-key high pass filter since any noise the generate from capacitance variance could show up in the 0.1Hz to 10Hz bandwidth.  However, 10µF film caps are too big to fit in this enclosure.  1µF film caps are a bit more reasonable, but that would push the resistor values to 1.6M and 3.3M.  That's not too bad for thermal noise since it's after the 200x stage, and is actually a really good option.

For the low-pass caps, they are only dominant at 10Hz and above, and their effect is divided by the 200x first stage gain.

Overall I think the 260nVp-p is still dominated by the input resistor and opamps, but exploring film caps could be interesting if I ever need to improve this circuit!

[mawyatt]

Yes, the Sallen-Key HP would be the most sensitive with the 10uF X7R.

Agree the 10uF film are huge (used in our LCR DC Bias adapter), so maybe a 2.2uF Film, 10uF Tantalum, Electrolytic, or Poly. All these should be better than a X7R cap, altho larger.

Awhile back we developed a DC Bias adapter for our lab bench LCR meters to test some various caps including SMD ceramic types. This allowed studying DC Bias effects, but we also found that the High K ceramic types not only vary significantly with DC bias & temp, but just about everything, even the quality X7R from Samsung!! Just taping on them creates a huge piezo electric effect, not to mention PCB stress and so on. We decided to only use the High K ceramic caps for supply decoupling and bypassing and nothing else.

Best,

[MasterT]

High pass filter is likely to be off, since it is not expecting 3k /( 2-4 ) output impedance from first stage

[mawyatt]

The HP input impedance is too high for a few K source impedance to have much of an effect.

Best,

[trtr6842]

For the high-pass sallen-key I couldn't use polarized caps because they could see some significant negative voltages.  With larger supply rails I could have done some creative biasing and used them, but that was beyond what I could do with a single 9V battery.  I am actually working on some simple mods right now and will include changing the 10µF X7R caps to 1µF film ones and will update the resistors accordingly, I'll post those results soon.

For the high pass error in cutoff frequency, its definitely not the extra 250Ω of input impedance, here's an LTspice sim with input impedance of the high-pass filter, and the frequency response.  The sim steps the input resistor from 1µΩ to 250Ω and almost no effect is visible.  My guess is it's either tolerance on the 10µF ceramic caps, or I did the math wrong on where to put the vertical cursor!!!

[MasterT]

The HP input impedance is too high for a few K source impedance to have much of an effect.

Best,

My excel tells 10u has 1.6k at 10 Hz.

I recently get opa2182 to evaluate, and noticed that if I set G=1000 with 1k & 1M opa behaves as "normal" - noisy. But if I tried to put a cap in parallel with 1M ( 10 nF or so to get 10Hz) broadband noise drops as it should, But to my surprise in the  low frequency 0.1-10 Hz band noise jumps up! I can't say it was the first time I've seen abnormality when AZ interact and getting upset by caps - at the input or outputs, so I make a rules for myself not to connect any caps directly to az w/o isolating R in series. Any new az I buy first checked for this phenomenon.

[mawyatt]

The HP input impedance is too high for a few K source impedance to have much of an effect.

Best,

My excel tells 10u has 1.6k at 10 Hz.

As shown by the simulation above, the source impedance doesn't have much effect as we mentioned earlier.

The 10uF cap is working in a very high impedance circuit as can be seen by the 82K and 330K resistors, thus the source impedance of <1K doesn't matter.

Best,

[mawyatt]

For the high-pass sallen-key I couldn't use polarized caps because they could see some significant negative voltages.  With larger supply rails I could have done some creative biasing and used them, but that was beyond what I could do with a single 9V battery.  I am actually working on some simple mods right now and will include changing the 10µF X7R caps to 1µF film ones and will update the resistors accordingly, I'll post those results soon.

Another possibility is a non-polarized electrolytic, or back to back regular electrolytics.

Best,

[trtr6842]

I tried a couple mods on one of the other boards, and here are the results:


Up first was swapping the input 1206 thick film resistors for metal foil ones.  The effect was negligible.



Next I left the metal film input resistors, and also modded the high-pass sallen-key circuit.  I changed the caps to 1µF 50V film caps, and replaced the resistors with 10x the original value for the same frequency response.  Again, the effect was negligible, so those 10µF caps weren't a significant cause of noise, or if they were, the slight added noise from the 10x resistor values cancelled it out.



I went back to look at my initial noise analysis too.  I realized my gain stages were different than stated, they are 500x then 4x!  (pdf had outdated values, original writeup and .jpg schematics were correct).  Same overall concept, but I was back-and forth on what combinations to do and I ended up forgetting what I actually ordered.  Anyways... I did a full LTspice noise sim of the circuit as-ordered.  I modeled the OPA2188's as an ideal noiseless op amp with a 4.9k input resistor for an effective flat noise density of 9nV√Hz, which is what they're spec'd at.  The overall noise of the whole circuit with ideal passive components was calculated at 31.44µV RMS integrated from 0.05Hz to 20Hz. 

All of my measurements are within a couple percent of that!  So that means all the generic thick-film 0603 resistors and X7R caps I used are acting fairly ideally, and/or the input noise is dominated by the input stage.  The same LTspice sim shows that the 0.05Hz to 20Hz noise just after the 500x stage is 37.46nV RMS, slightly higher than the output noise.  This is due to the higher bandwidth before all the filtering.

[Kleinstein]

The design looks very reasonable. I like having the input AC coupling at a lower frequency than the later low pass filter.
The 10 µF X7R capacitors should see very little voltage and under these conditions they may be OK. They still may have quite some dirft with time and temperature and this could effect the bandwidth. The tolerance may also be an issue. The bandwidth for noise tests a tricky point anyway, as the noise BW is different from the -3dB BW. This is also a problem with data found in datasheets.

I don't see a major noise noise besides the OP-amps and R22+R31. So I would have expected a less noise as the specs for a single OPA2182 are at 120 nV_PP.
With 4 OP-amps in parallel the resistor noise is expected to be even more then the amplifier noise.
Another possible noise source is the input capacitor, as the leakage current is expected to be somewhat noisy.
For a test it may make sense also to also measure with a short behind the capacitor.

For comparing the noise performance the RMS noise is often more practical than the PP noise as it has less scattering. If the PP noise is used one should use "PPA" and not "PPP" as this would be PP over a longer interval.

At least from the plan the gain of the final stage is still x 10 and not x 4. The extra gain could about explain the higher than expected noise.

[trtr6842]

So it turns out my original write up had all the right values, first stage is 200x, second is 10x.  The pdf I attached had outdated values for a 5,000x design.  In reconciling those mixups, I found the cause of the bad low-frequency response:  R11 should be 82k in stead of 160k, so the Q of that filter was too low.

I fixed my LTspice noise sim, and I actually should be getting about 27.8nV RMS, so my circuit has about 14nV RMS of extra noise somewhere, my gut is that it's current noise through the input 2k resistor, since that isn't present in my simulation at all.

For noise measurements, I'm mainly going off of the standard deviation measurements, since those are simply AC RMS calculations.  My scope has a significant DC offset, so the RMS values are skewed, but the standard deviation (σ) values are perfect.  I confirmed that by taking RMS, σ, and mean measurements, and they all lined up where RMS^2 = mean^2 + σ^2.  While I'm talking about the scope, it's noise floor with the 0.0005x attenuation factor shows <=65nVp-p and <=7nV RMS when using the high-res acquisition mode, which is what was used for all previous screenshots & measurements.  As for the "Vppp" and "Vppa" measurements, I had no idea if those were any sort of standard notation, I just made that up on the spot.  My logic for taking the highest Vpp value of 10 separate 12-second captures is twofold:  The high pass filter is 3rd order, and removes a lot of noise beyond the 10-second span, so doing longer Vpp captures doesn't make too much sense.  Also, 10-second @ 1s/div captures are standard on datasheets, and my scope simply has a 12 division horizontal span.

On to some more test results:


Reducing the input resistance to 1k offered a good improvement, down to about 200nVp-p.  In theory the 2k input resistor had 18.2nV RMS of thermal noise, and the 1k one has 12.86nV RMS.  Ignoring op-amp current noise, swapping the two should have brought the noise from 31.27nV RMS to 28.5nV RMS.  Instead, the noise dropped down to 26.28nV RMS, indicating that 11nV RMS of current noise was also removed, putting the total 4x averaged input current noise of the OPA2188 at around 3.4pA√Hz, assuming a 10Hz bandwidth. 

Shorting R22 and R31 effectively makes this circuit very similar to the other designs I've seen around here which have around 100Ω of input impedance.  With some care that can be used, but input impedance that low with clamping diodes scares me.  I am very hesitant to reduce the input resistance, since I see that as dangerous for the potentially sensitive DUT's that I'll be plugging this into.  Since reference aging is so common, hot-plugging noise testers like this seems to be the default to avoid power-cycling the DUT.  Since the input cap is so large, a design with only 100Ω of series input impedance before the clamp diodes would draw a surge of 100mA with a decay time constant of ~220ms from a +10V reference.  Depending on the reference buffer (if there even is one!), that might not be trivial.  The 2k||2k design I made would only draw 10mA from a +10V reference, which is within the safe range for many common buffer op amps. 

An easy solution would be to integrate a precharge and bypass switch.  Have something like 2k||2k  always connected to charge up the input cap in about 10 seconds, then flip a switch to bypass the input resistance (R22 and R31 in my case).  I don't like that idea because I know I would forget to turn off the bypass switch before connecting to a new DUT!!

I'm curious if taking advantage of the high voltage supply handing of the opamps could be useful...  For example, change the input clamp circuit so that it clamps at -0.7V for negative voltages, but at something like +24V for positive voltages using a zener.  Add a schottky in series with the positive supply rail after the large decoupling caps to prevent reverse current, and that should allow the input to swing up without drawing huge surges of current.  As the input cap charges up the opamp supply rails would settle and return to the 9V battery supply, and then everything should work as normal.  I might have to breadboard that!

[trtr6842]

The frequency response was all cleaned up when I fixed the Q of the high-pass sallen key.  R11 should be 82k if the 10µF caps are used, or 820k if the 1µF caps are used.

[mawyatt]

I tried a couple mods on one of the other boards, and here are the results:


Up first was swapping the input 1206 thick film resistors for metal foil ones.  The effect was negligible.



Next I left the metal film input resistors, and also modded the high-pass sallen-key circuit.  I changed the caps to 1µF 50V film caps, and replaced the resistors with 10x the original value for the same frequency response.  Again, the effect was negligible, so those 10µF caps weren't a significant cause of noise, or if they were, the slight added noise from the 10x resistor values cancelled it out.

The 10X resistors should produce root(10) more voltage noise per resistor, so yes likely they are contributing more noise and offsetting the film capacitor effect. A better test would be to use a 10uF film cap with the same resistors as used with the X7R capacitors, but they are big. You might want to try an 10uF electrolytic, which is much smaller than even the 1uF film you've shown.

Another crude test would be to tap on the case with various capacitors for comparisons, the X7R are notorious for mechanical vibration sensitivity (piezo effect), the other types are much less prone to such.

Anyway, if the X7R caps are working acceptability, then that's good news

BTW what grade of X7R cap did you use?

Best,

[trtr6842]

Since all the filtering is after the initial 200x gain stage, noisy components there don't really contribute much to the input-referred noise.  My LTspice sim shows 27.89nV RMS noise with ideal 10µF / 10µF 82k, 330k for the high-pass sallen-key, and 27.915nV RMS  (Both values are input-referred). 

The specific caps are GRM21BR61H106KE43L, but again I think that everything after the 200x stage is essentially trivial. 

My testing with the lower and shorted input resistor is interesting though, since it's suggesting that the opamps might have higher than expected current noise, or that my clamp diodes are somehow introducing current noise...

[mawyatt]

An easy solution would be to integrate a precharge and bypass switch.  Have something like 2k||2k  always connected to charge up the input cap in about 10 seconds, then flip a switch to bypass the input resistance (R22 and R31 in my case).  I don't like that idea because I know I would forget to turn off the bypass switch before connecting to a new DUT!!

Think you could use a Push to Test button which would Set and close the input relay, which would shunt the larger input series resistor with a smaller resistor. Add a high value resistor in parallel with the input, so when the input test source is removed the large voltage across the input cap will drive the input op-amps to rail, then detect such and use this to Reset the relay (also could include a simple timer (CD4060) to time out Reset as a "Just in Case".

Anyway, just a thought on the series input resistor shunt relay operation.

Best,

[Kleinstein]

If a high initial input current is the problem, there is the option to use 2 JFETs and a resistor as a current limiter in bettween instead or parallel to R22+R31. This could give a 2-3 mA current limit with some 500 Ohm of resistance.

With a gain of 200 from the input stage the resistors in the filter part should not give relevant noise, even with 1 µF and 3.3 M. Anyway the resistor part would only be relevant at the lower bad edge not with the full 10 Hz BW.

3.4 pA/sqrt(Hz) would be quite a lot of current noise. The specs are way more optimistic, but the specs on AZ amplifier current noise are sometimes a bit scetchy. The current noise may depend on the circuit (e.g. capacitance directly at the input) and symmetry between the inputs. The current circuit at least looks symmetric for the higher frequencies, which is normally a good thing.

I don't think a higher supply would really help much. Chances are the current noise and input bias may get worse with a high supply.

[trtr6842]

Think you could use a Push to Test button which would Set and close the input relay, which would shunt the larger input series resistor with a smaller resistor. Add a high value resistor in parallel with the input, so when the input test source is removed the large voltage across the input cap will drive the input op-amps to rail, then detect such and use this to Reset the relay (also could include a simple timer (CD4060) to time out Reset as a "Just in Case".

Anyway, just a thought on the series input resistor shunt relay operation.

Best,

I like the "push to test" idea!  I think rather than a timer, simply re-setting the bypass switch whenever the 200x stage hits the rails could work.  Any time I unplug the input it rails, and could be a reliable way to ensure the bypass gets turned off.  It's unfortunate how little circuitry fits in a Hammond 1590B enclosure though!  The dual comparator, flip-flop, and analog switch required to do that would take up almost as much room as the rest of the circuit!!

[mawyatt]

Since all the filtering is after the initial 200x gain stage, noisy components there don't really contribute much to the input-referred noise.  My LTspice sim shows 27.89nV RMS noise with ideal 10µF / 10µF 82k, 330k for the high-pass sallen-key, and 27.915nV RMS  (Both values are input-referred). 

The specific caps are GRM21BR61H106KE43L, but again I think that everything after the 200x stage is essentially trivial. 

My testing with the lower and shorted input resistor is interesting though, since it's suggesting that the opamps might have higher than expected current noise, or that my clamp diodes are somehow introducing current noise...

The 200X front end gain certainly helps and the correct approach to making things "downstream" almost insignificant. Even tho I'd wager that if you lightly tap those X7R caps the output will jump all over the place, even sweeping a heat gun across them will likely induce some response, that's our experience with High K dielectrics in high sensitivity signal paths and why we avoid them.

Of course YMMV.

Thanks for the cap information, that's a muRata 10uF 50V, which is a very good source!! BTW its a X5R and not a X7R!!!

Best,

[trtr6842]

If a high initial input current is the problem, there is the option to use 2 JFETs and a resistor as a current limiter in bettween instead or parallel to R22+R31. This could give a 2-3 mA current limit with some 500 Ohm of resistance.

With a gain of 200 from the input stage the resistors in the filter part should not give relevant noise, even with 1 µF and 3.3 M. Anyway the resistor part would only be relevant at the lower bad edge not with the full 10 Hz BW.

3.4 pA/sqrt(Hz) would be quite a lot of current noise. The specs are way more optimistic, but the specs on AZ amplifier current noise are sometimes a bit scetchy. The current noise may depend on the circuit (e.g. capacitance directly at the input) and symmetry between the inputs. The current circuit at least looks symmetric for the higher frequencies, which is normally a good thing.

I don't think a higher supply would really help much. Chances are the current noise and input bias may get worse with a high supply.

I like the idea of a low-noise current limiter.  I've actually never worked with JFETs, so I'll have to read up on this and get some parts to prototype with.  Any common JFETs parts that you can recommend of the top of your head?  Preferably through hole for easy prototyping, but I've got plenty of SOT-23 breakouts as well.

I agree that something sketchy is going on at the input, and probably related to current noise.  I wonder if the clamp diodes are contributing at all, that's something I could test, at least for a short-circuit input.  Maybe the 10nF feedback caps are causing issues too.  They're not crucial to the overall frequency response, so I can try removing them.

For the supply changes, I wasn't thinking about increasing the supply voltage, I was considering letting an input transient push the supply voltage up temporarily, since most low-noise opamps are good to +36V.  This wouldn't reduce the peak input current on a hot +10V plugin, but with the right clamping circuit only the opamp bypass caps would have to be charged up, so the time constant would be ~20µs instead of 200ms!

[Kleinstein]

For the current limiter one would like low threshold JFETs, like SK209 or SK3557. No need to have low noise, but these are the ones that come with a low threshold.  For a test J113 or similar PN4393 would be candidates in a TO92 case.

[trtr6842]

The 200X front end gain certainly helps and the correct approach to making things "downstream" almost insignificant. Even tho I'd wager that if you lightly tap those X7R caps the output will jump all over the place, even sweeping a heat gun across them will likely induce some response, that's our experience with High K dielectrics in high sensitivity signal paths and why we avoid them.

Of course YMMV.

Thanks for the cap information, that's a muRata 10uF 50V, which is a very good source!! BTW its a X5R and not a X7R!!!

Best,

Since the ceramic high-pass caps seem to be such a concern, I ran this rough test for microphonics.
Board on the left is CH1 on the scope.  The high pass sallen-key parts are 1µF film, 1µF film, 820k, and 3.3M.
Board on the right is CH2 on the scope.  The high pass sallen-key parts are 10µF X5R, 10µF X5R, 82k, and  330k.

Both boards exhibit some microphonics, but from my time using the one I already have in an enclosure once I stop touching the test setup everything stays very consistent.

[trtr6842]

For the current limiter one would like low threshold JFETs, like SK209 or SK3557. No need to have low noise, but these are the ones that come with a low threshold.  For a test J113 or similar PN4393 would be candidates in a TO92 case.

Thank you for the suggestions, looks like Mouser has J113's in stock so I'll be ordering those! So far this is my favorite idea for current limiting so I will be trying it out as soon as I get parts.

[trtr6842]

I tried removing the input clamp diodes D2 and D3, and they offered no improvement when the input resistance was only 100Ω (Cfg#6).  But when the input resistance was 1kΩ noise is better with them removed vs installed (Cfg#7).  In that case σ dropped from 25.79nV to 25.31nV, meaning the diodes contributed about 5nV RMS of input noise, which is significant, but input protection is important.  I think if the JFET current limiter idea works well then I could just rely on the opamp internal clamp diodes safely.