Hi,

I'm currently working on a board design for an EEG pre-amplifier (first draft posted here in case interested).

EEG is a very weak floating differential signal, about 20uV p-p and a source impedance of 5k at best. So I am using an instrumentation amplifier, with filters and bias return in front of this. I can get e.g. resistors with 0.1% tolerance without too much difficulty, capacitors is a bit harder.

But one thing that I was interested in was the idea of placing multiple lower-/higher-value passives in series/parallel to reduce the effective tolerances.

I have looked online and it seems (unsurprisingly) that the probability distributions of component values dpeend on the manufacturing process - with tighter tolerances we often see something like a Gaussian distribution; with maybe 5% or 10% tolerance it's not uncommon to see the middle section of a bell curve removed, where the manufacturer has chosen to extract those closer to the intended value and sold them as lower-tolerance, so we see the fringes around that corresponding to a normal distribution. And sometimes other distributions appear for yet more approaches as to how components are discarded or managed between batches.

However, if we assume a Gaussian distribution for now, N observations should improve the effective tolerance by a factor of √N, which should improve our CMRR. I.e. we could place five 1k 1% resistors instead of one 5k one and expect to be within 0.4% of the target value overall. The cost of this though is longer traces, more junctions/changes in material, and I would presume would overall worsen parasitics. For this project I have only laid my circuitboard very very roughly for the time being, whilst I am trying to get some feedback on the schematic - but to illustrate the idea, the below images contrast using literal values or by repeatedly placing the same lower-valued components to get the same equivalent:

I would hazard I guess placing extra components like this with the aim of improving matching would backfire and worsen my signal integrity overall - but my question is, can I quantify this without difficult maths or a lot of work?

PCB layout can be simulated, but this is pretty difficult just for the shape of the copper, and I'm not aware of any (at least widely available) simulators that also include the multiple different materials and 3D layouts involved. It would probably be highly dependent on heat and nearby signals too. Even if there's a rough analytic solution, I'm guessing the equations would be very complicated.

So, I'm wondering, does anyone who's laid out a lot more PCBs than me (this is my first!) have a rough idea or rule-of-thumb as to if this is a good idea or not? Are there any very rough ways to estimate parasitic effects to within one or two orders of magnitude, that I could then compare to the expected improvement in CMRR? Does this sound like a bad plan, or conversely, does this seem an okay approach to try out?

Thanks a lot!

 

Are you planning on making so many of these that you can't measure and select your components so that they meet your needs?

If not, then you are pretty much buying the worst of both worlds. You are creating more parasitics and reducing your noise immunity to EMI while probably not getting any more accuracy.

First off, while some manufacturers still do some binning, today's manufacturing processes are sufficiently tight that they don't need to go to that expense. In fact, if you buy 5% resistors today, it is very likely that they are all within 1% to 2% of their nominal value at room temperature. But even if that weren't the case, you Gaussian distribution assumption doesn't really buy you anything in practice unless you are getting your resistors from independent batches. If they are all coming from the same lot, their part-to-part variations is going to be much smaller than the allowed tolerance -- it's the mean of that sample that is going to be located somewhere within the allowed range.

You also need to decide what is important about your resistors -- that they be close to the nominal value (i.e., accuracy matters), or that they be closely matched to each other (i.e., precision matters). The answer will likely be different for different resistors in your circuit (same for other components, too).

 

You will lose more than gain by using multiple components.
Variations of capacitance will affect the roll-off frequency of the filters. You are not likely to observe an effect on CMRR.

 

Absolute accuracy of gain in an EEG is irrelevant, but CMRR is vital. Resistors in resistor arrays are extremely well matched, especially ones designed for the purpose such as the LT5400. Overall tolerance is only ±7.5% but matching is within 0.01% which would give 80dB CMRR.
I think that a standard resistor network with 2% tolerance would have rather better matching than 2%.

 

At one point resistors were sorted and so if you bought 5% tolerance, none will be within 1%. So to improve resistor value accuracy you need to buy more accurate resistors. AND it will help if you also select those with lower noise levels.
If you need more accurate components then the solution is to buy more accurate components FROM A KNOWN GOOD SUPPLIER!!

 

Thanks,

I will be getting this assembled, and components need to be SMT, so measuring by hand isn't possible and I'm partly limited by what they have in stock. And yes, the matching between each other is what matters. As much as a 10% joint variation in filter co-efficients wouldn't bother me much, those are already a compromise anyway, but as far as I know it is much more important that both leads be treated identically. Any variation between the inverting and non-inverting leads can make an EMI filter for example worse than going without, by causing the common-mode to appear differentially on one side, where it will be amplified, versus having no filter - the InAmp may struggle to handle that frequency, but you'll get some common-mode rejection as long as it's identical on both inputs.

I would have thought also that multiple units on a tape might be closer to each other than any random two picked of the same model, but EEVBlog did a quick test in a video here and in a follow-on, and that seemed not to be the case in the batch he tested at least. Those were somewhat older through-hole resistors so I don't know if it's different for tape-reel, googled but not found an answer, be interested ot hear anyone's experiences.

I did initially lay out some resistor networks, but these seem to be extremely expensive, and this is the very first prototype; meanwhile I can get ±0.02% thin film for about 20p each, so, negligible. I'm also assuming that like you say, this is much tighter than what was available at the time the literature I've been using (The Designer's Guide to Instrumentation Amplifiers from AD as being a major one) was written - so 0.02% may be more than adequate than the 1% quoted there, and I can perhaps remove the differential filter inbetween compensating for variation in the common-mode components.

However it did all get me thinking, and wondering if there would be any way to put a vague number on the parasitics without assembling both ways and measuring or relying on the gut feel of someone experienced as to if one almost definitely outweights the other.

Capacitors I don't have nearly as many options as they need to be so large to handle the corner frequency below 1Hz without pushing the resistors above the Johnson level mathcing that of the InAmp. It seems in excess of 100uF, my options are pretty much between X75/Class II or electrolytics (that will be reverse-biased about half the time) so neither seems great.

 

If you have any similar sized resistors still on a tape-pack, you can check the values of 10 or 20 and see what sort of spread there is in the resistance values. Knowing is often much better than guessing.
Keep in mind, though, that a well-controlled automated manufacturing process is not likely to have a wide distribution of variations.

 

Capacitors I don't have nearly as many options as they need to be so large to handle the corner frequency below 1Hz without pushing the resistors above the Johnson level mathcing that of the InAmp. It seems in excess of 100uF, my options are pretty much between X75/Class II or electrolytics (that will be reverse-biased about half the time) so neither seems great.

Use bipolar electrolytics. They are much better for signal integrity than polarised electrolytics, even pairs of polarised electrolytics back to back.
The usual method of reducing the DC offset is by putting a capacitor in series with R3. Because it only appears once in the circuit, not once in each leg, there is nothing you have to match it with.
You will need 2200uF, but that is not impossibly large.
https://www.mouser.co.uk/ProductDetail/Panasonic/ECE-A1AN222UB?qs=rMMd5vBiahpHWoCpTXCjbw==

 

> Knowing is often much better than guessing.

Thanks, but I don;t have anything lying around, there's zero chance I can do SMT soldering by hand, hence I've never tried and can't rely on measuring anything beforehand. I could potentially add holes for through-hole components but this makes the traces longer and so I think adds further risks of parasitics.

> Use bipolar electrolytics. They are much better for signal integrity than polarised electrolytics

Thanks, do you have a source or anything covering them you'd recommend on this? It's something I had considered, and I would have to look back at the notes I made on all the different zoo of capacitors out there, but from memory I think there were some other relative disadvantages of electrolytics compared to ceramics, not least again their size and the lengthening of the traces. However I know there are audio crossover caps for this purpose so they may perform better at low frequencies so it was on my radar. Bipolars seem much rarer so I haven't found as much discussing them, and I may have put it to the side as it was harder to find in the parametric searches for assembly.

By R3 do you mean the gain resistor (or the one taking the same function in my front-half, labelled R3 on the diagram in the AD forum post), to confirm?

 

> Use bipolar electrolytics. They are much better for signal integrity than polarised electrolytics

Thanks, do you have a source or anything covering them you'd recommend on this?

https://linearaudio.net/cyril-batemans-capacitor-sound-articles
it is in Part 5

By R3 do you mean the gain resistor (or the one taking the same function in my front-half, labelled R3 on the diagram in the AD forum post), to confirm?

Yes.
You would always find a bipolar electrolytic there in professional microphone preamps.

 

Thanks, sorry I haven't replied, I will look into it but want to have time to read on both those points.

 

There are common mode rejection circuits around. That has not been a problem for me so I did not work on it.

 

Yes, the instrumentation amp should be rejecting the common-mode. The issue though is about if mismatches in the signal chain between the inputs causes part of the common-mode signal to become differential.

 

Yes, the instrumentation amp should be rejecting the common-mode. The issue though is about if mismatches in the signal chain between the inputs causes part of the common-mode signal to become differential.

Yes, they will. But that is properly solved by tightening the absolute tolerances of the signal chain, not in trying to reduce it from a statistical perspective. Doing that actually worsens the absolute tolerances.

 

Well yes, but at some point I hit the limits of what components are available, or at the very least, are available at a reasonable cost. Hence I'm wondering how it can be quantified, even with broad order-of-magnitude numbers.

 

Well yes, but at some point I hit the limits of what components are available, or at the very least, are available at a reasonable cost. Hence I'm wondering how it can be quantified, even with broad order-of-magnitude numbers.

You model the distribution and perform a statistical analysis. But, again, you can't just look at the expected mismatch, you need to consider the potential worst-case mismatch because, sooner or later, you are going to have a unit that is out near the edges of the distribution, and that's the one that is going to be the center of the lawsuit filed against you when it doesn't perform nearly as well as you've led your customers to believe based on the expected mismatch.

Instead of playing games with ensembles of poorly-matched components and hoping that they average out nicely, use well-matched components, such as resistor arrays. They are readily available with matching ratios of well under 0.01%.

 

In addition to the solution described in post #16, WHICH WILL CERTAINLY WORK, there is also the option of providing an adjustment so that the resistance can be adjusted to the exact value required for the specified performance. The inclusion of an adjustment might have a cost penalty, but it may also allow a price increase, due to increased quality.