DC-accurate Low-pass-filter

[Roehrenonkel]

Hi voltnuts,
 
for my voltage-reference(s) i'd like to add a DC-accurate Low-pass-filter. (See PDF)
Okay, we have to deal with the OP-Amp-offset-voltage, i know.

Here we have the standard Sallen-Key Butterworth 2nd order LP
(fc10Hz) modified to cancel the leakage-current through C2.
Step-response is 0.2 seconds.

Meassured leakage of foil-caps is 100...200 pA at 45 to 50 Volts
that result in 225...500 Gigaohms.
And there are my precious ppms escaping to ground. 8-O
In the modified LP there is no DC over C1 and C2 anyway, nice. :-)


What do you think?
Is this a good idea, or did i overlook something?
Should i make a 1Hz- or even 100mHz-Version?

Best regards

[macaba]

Have you investigated the attached topology? I use this in practical DC accurate circuits a lot.
Attached image shows a 3rd order response, it can be extended to further orders but my experimentation shows it tends to be better to chain multiple 3rd order stages instead.

[trtr6842]

I have been working on a DC accurate low-pass filter too!  I actually just got my prototype boards made, but I have yet to test them.
I got the idea when I was working on my LNAs.  I figured if you can measure the noise on a voltage reference, then you can cancel it out!

Obviously a low-pass filter will not help long term stability, but I do think it could have great value in reducing measurement times, or helping measurements that have to be fast (i.e. scanner cards) be a little less noisy.

The main challenge is making it such that the filter doesn't add more noise than it filters out...
@Roehrenonkel I did a quick simulation of your design, and it appears that it would have a noise floor of approximately 19nV/√Hz.  This would be about 600nVpp in the 0.1-10Hz range, even with a shorted input, which is great for bandgap or LM399 references, but falls short of LTZ/ADR1000 territory.  To reduce that you have to increase all capacitances and reduce all resistances, that's the only way around it.  This simulation even ignores opamp input voltage and current noise too.


I also simulated @macaba's topology, and it has similar noise results, about 500nVpp form 0.1-10Hz.


I attached the schematic for the active filter I'm working on, I decided to call it "PARF" for Precision Active Reference Filter, just because I thought it was kindof funny. 
Based on simulations I think it should get to about 175nVpp of input referred noise, including contributions from the opamps, and it is effectively a single pole 15mHz low-pass filter.
I essentially took my LNA design, modified the input for a 15mHz high-pass cutoff, then feed it's inverted output back into the buffered input to cancel out noise.  Since the noise is amplified, I can AC couple it back into the DC path using ceramic caps and a voltage divider.  The maximum attenuation depends on how well the gains are matched between the LNA gain and the AC injection divider, but with most voltage references it doesn't take much attenuation before you reach the noise floor of the low-pass filter, so you don't need a lot.  This circuit is definitely a bit over-the-top, and I admit I have no idea if it will have any practical applications, but I'm working on it anyways!




Anyways, I haven't yet powered it on and tested with it, but I'll provide updates when I do!
I'm also well stocked with LNA's to measure the input vs output noise!

[Roehrenonkel]

Hi,
 
thank you both for your inputs.
@macaba: "Gyrator" was the first think that came to my mind.
How do you calculate it? Is there more info about it?
One could even use the buffer U1 to amplify 7V-->10V.

@trtr6842: Good job on the LNA, Kudos.
Noise-cancelation only works if you're in time to be 180° out of phase.
Resistor-noise within the LP-filter: Yes these are critical.
22k seems to be the upper limit with regards to noise.
But, i'll definetly will scale the resistors down.
Let's see what else i'll find in my stock:
500* 1u 63V 15mm Pinspacing.
That look's promissing. :-))
Now we have to wait what the SMU says about leakage (See you in a few hours).

I have got over 18.000 Mica-caps, but not ONE Teflon-/PTFE-cap! Someone wants to trade?

Ciao4now

[Roehrenonkel]

Hi again,
 
turns out, that distance is king for low-leakage.
The best cap so far with some old Wima MKS-3.
Fast setling in regards to my other samples (ERO 1818 & 1826 / Wima MKS).
Picture shows sample-# and leakage-current, 10 seconds between samples.

Could become a big pcb, but i'm a 19"-guy anyway. ;-)

Ciao4now

Edit: It's an ERO (Emil Roederstein) MKC-cap.

[trtr6842]

Noise-cancelation only works if you're in time to be 180° out of phase.

Definitely, which is why the high-pass input to the amplifier section has a 3.6mHz -3dB frequency, but the overall low-pass -3dB point doesn't occur until 15mHz.
This topology results in a slight increase in noise between those two frequencies, but the overall the output noise is reduced.

Hi again,
 
turns out, that distance is king for low-leakage.
The best cap so far with some old Wima MKS-3.
Fast setling in regards to my other samples (ERO 1818 & 1826 / Wima MKS).
Picture shows sample-# and leakage-current, 10 seconds between samples.

What capacitance was the part tested for leakage, 1µF?
If so, even ~25pA you measured might cause significant offsets in a ≤1Hz low-pass, since 160kΩ * 25pA = 4µV.  It would be 40µV for a 0.1Hz cutoff.  Even if you add more parallel capacitors and reduce the resistance to keep the same cutoff frequency, the offset will still stay the same.  If that offset is fixed, then its not too bad, but if isn't stable with time & temp it might cause issues.

[Roehrenonkel]

Hi trtr6842,
 
yes 1 Microfarad, i went through my stock of 1u's to see what's best.
Test was done with Keithley 237, charged the cap to 50V (or 45V for 50V-caps),
and took current-samples every 10 seconds. No shield or guard.

In my design there is no DC-voltage over C1 and C2a anyways.

Best regards, CU

[mawyatt]

Have you investigated the attached topology? I use this in practical DC accurate circuits a lot.
Attached image shows a 3rd order response, it can be extended to further orders but my experimentation shows it tends to be better to chain multiple 3rd order stages instead.

Agree, this is a very practical topology with good component insensitivity. One weakness, as common with VCVS (Sallen-Key) types, is the Op-Amp output impedance limits Stop-Band attenuation. This can be dramatically improved without self generated noise penalty by splitting the input resistor with a shunt C to ground. This provides a 1st order Low-Pass with the split input R to keep higher frequency signals from entering the feedback control loop with the Op-Amp.

We don't have a OPA140 model, so just used a OP07 for comparisons, see below with added 0.1uF shunt.

Best,

[trtr6842]

You don't need much stop-band attenuation when working with voltage references.  For something like a good bandgap reference with maybe 5µVpp of 0.1-10Hz noise, you only need 20dB of attenuation before you hit the 0.5Vpp noise floor of a filter using the 11.2k + 2µF values.  You need even less attenuation for lower noise references.

[DeltaSigmaD]

Low-noise lowpass filter

An addition to the circuits here:  the filter circuit shown below is calculated as Bessel 4th-order filter, but other filter characteristics are possible. The resistance values in the signal path are relatively low to reduce noise. The filter output is free of 1/f-noise, if we neglect the 1/f-noise of the resistors. The single inductor determines the lower limit for the cut-off frequency which can be realised.

[Kleinstein]

Using an LC instead of RC filter could indeed help, but real inductors have there downside. One is that they may pick up hum from external magnetic fields. To get high inductance one would essentially need a magnetic core (e.g. use a rel. high voltage transformer) and the core material may show Barkhausen jumps from the magnetic core material. One would still get some noise in the transition region from the resistance needed for dampening resonance.

For a low leakage capacitor I would look at polypropylene types. One may even get away with PP type motor run capacitors that are available to some 100 µF, though a bit bulky. Testing the capacitor leakage is not easy as there is also dielectric absorption (especially with polyster types, PP is about 10 x better, but still not perfect).

Especially the electrolytic capacitor used in the PARF circuit can also react to temperature fluctuations and the dielectric absorbtion can take a long time (e.g. days) to settle.

[DeltaSigmaD]

@Kleinstein: You are right, the Barkhausen noise is a problem. This was the reason for using huge air coil inductors (ca. 50 cm height and 20 cm diameter) to filter the input power of a furnace required for a key comparision noise-vs-radiation thermometry. The results were excellent.

[macaba]

mawyatt - Good suggestion, I was thinking about voltage reference filtering here, I do the split input on the first stage of PWM DAC filters.

DeltaSigmaD - Neat extension of the principle. I use a simple response in my circuit because I usually prioritise "settling time to 1uV" (say, around -1udB from nominal fully settled gain) characteristic.

[mawyatt]

Have you investigated the attached topology? I use this in practical DC accurate circuits a lot.
Attached image shows a 3rd order response, it can be extended to further orders but my experimentation shows it tends to be better to chain multiple 3rd order stages instead.

BTW a BPF rendition of this topology is shown here, concept credited to Bob Pease.

https://www.eevblog.com/forum/projects/edn-published-active-bpf-in-error/msg5563865/#msg5563865

Best,

[Roehrenonkel]

Hi DeltaSigmaD,
 
thank you for your input.
Besel is very good (Q=0,5) - for audio.
Here i want a steep slope, critical damping (Q=0,7).
What about the leakege of the first cap?
As @Kleinstein pointed out inductors are haunted by parasitics and other ill-effects.
Is there even a core-material for such low frequencies?
I'm useing lots of inductors/tranfos in my tube-amps: Input, Anode-choke, Drive- & Output-transfos.
And they (Lundahl/Reinhöfer) work really well in their frequency-band.
My biggest choke is a 5Hy 600mA that has 32.5 Ohms (and over 6kg) and will have a very low Q
at thouse frequencies.

In theory fine, but not practical.
Best regards

[Kleinstein]

The inductors get better (less resistance) the larger they get. The chokes are usually for a certain DC current, for the ref. filter one could use a core without a gap as there is essentially no DC current. A mains transformer primary or an evenen higher voltage winding could be a first start. No need for really special material for low frequency, but a hi µ material (e.g. grain oriented iron in a toroid or Nonoperm, maybe metglass) can help to get high inductance.

[CurtisSeizert]

Hi again,
 
turns out, that distance is king for low-leakage.
The best cap so far with some old Wima MKS-3.
Fast setling in regards to my other samples (ERO 1818 & 1826 / Wima MKS).
Picture shows sample-# and leakage-current, 10 seconds between samples.

Could become a big pcb, but i'm a 19"-guy anyway. ;-)

Ciao4now

Edit: It's an ERO (Emil Roederstein) MKC-cap.

When I was working on an LNA with a high input impedance I tested a number of caps for leakage current and DA. For film caps, the major mechanism of apparent leakage is DA based on a reference cited in AOE3 that measured over a year. My measurement setup just used two points spaced a couple hours apart (the ones here were 2.4 to 4 h except the PTFE, which was 8.75 h) and assumed linearity because I was measuring a lot of samples, the FOM I was looking at was self discharge time constant, which I recorded in ks. Here are a couple highlights:

C0G 470nF (Murata): 162 ks
PPS 470nF: 203 ks
PE 6.8uF (WIMA MKS2): 246 ks
PTFE 470nF (Soviet surplus): 39400 ks
PP 1uF (Panasonic): 3840 ks
PP 4.7uF (Panasonic): 6850 ks
PP 12uF (Kemet): 14400 ks

I did not do a ton of measurements with PE because PP was so much better, but with PP, the time between points and whether a sample was pre-charged for 24 hours prior to the measurement were big factors, which is consistent with most of the apparent leakage being a result of DA.

That said, I have successfully used bootstrapped SMD tantalum caps for voltage reference filtering down to a breakpoint of 2.7 Hz (single pole). In the case I tested most thoroughly with an ADR1000 reference, the concern was more TC than absolute accuracy, and settling time was not a major concern. The higher voltage cap was biased with about 10 mV because the R of the filter was part of a divider, and I wanted a bit of margin on the bootstrap node to ensure there was a positive bias on that cap. The ratio TC I got before and after the filter was negligible, i.e., <10 ppb/K. I have generally used this in preference to RC LP filters using Rubycon multilayer film caps, which you can get in fairly large sizes as SMD components (up to 22 uF I think) because it's cheaper and the solution size is less than a single 2220 cap. I like using fairly small (i.e., 3k3 or lower) R values because of the current noise characteristics of my preferred buffer amp, the OPA2205. Also, if I am going to this trouble, I use the standard RC filtered buffer amp topology at the output with something like 10R/47uF and appropriate feedback R and C values to maintain stability. I attached a screenshot of a schematic where I implemented this sort of thing for providing a 5V reference to an AD4030-24.