### Author Topic: Statistical arrays  (Read 13347 times)

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#### Kleinstein

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##### Re: Statistical arrays
« Reply #25 on: December 12, 2018, 10:04:08 pm »
The 13:1 divider is a really nice solution. However it would provide only a limited amount of averaging. So I am not so sure it would be really stable and low TC.

For the 15:1 ratio, there is an easier solution: 5 in series and 3 in parallel.

#### doktor pyta

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##### Re: Statistical arrays
« Reply #26 on: December 12, 2018, 10:44:54 pm »
razvan784, thanks for the inspiration!

Below is my version of divider by 14.
1.6k output resistance should not be a problem.
The resistors are grouped in pairs with same power dissipation.

What do You think guys ?

Edit: tempco measured for comparision.
Let's call it layout v.1.

T1=25.2'C
T2=60.4'C
mean T.C. of division ratio -3.9ppm/'C

and

division coefficient measured: 14.00088
« Last Edit: December 31, 2018, 07:11:35 pm by doktor pyta »

#### razvan784

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##### Re: Statistical arrays
« Reply #27 on: December 13, 2018, 03:38:44 pm »
Thank you doktor pyta. Yes, your design is better, more symmetric.
Kleinstein, I agree that averaging is limited; these designs would work well however if the individual TCs were not just randomly distributed but more like a gradient, as you noted earlier. On the other hand I have done no such measurements; I finally abandoned this design in favor of just using two selected foil resistors.

#### doktor pyta

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##### Re: Statistical arrays
« Reply #28 on: December 13, 2018, 09:34:03 pm »
Update: divider /14 with slightly corrected layout.

Edit: tempco finally measured.

T1=25.2'C
T2=60.0'C
mean T.C. of division ratio 0.41ppm/'C

and

division coefficient measured: 14.00055

« Last Edit: December 30, 2018, 12:39:38 pm by doktor pyta »

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#### Kleinstein

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##### Re: Statistical arrays
« Reply #29 on: December 14, 2018, 09:04:42 am »
For the layout, selecting the resistor positions, the power dissipation should not be that important, if used at a reference, as the power dissipation would be constant. The power dissipation could be important if the divider is used at variable voltage, e.g. to set an amplifier gain.

So It is not sure the 2 nd version is actually better than the 1 st. It is likely more about a gradient in the resistor properties, so to have the resistors well mixed and evenly distributed. Here the 1st version is still not that good as it has the resistors towards ground are in the center - so a difference from center to edges would show up. The 2nd version is more like a little biased left to right.

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#### Magnificent Bastard

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##### Re: Statistical arrays
« Reply #30 on: December 14, 2018, 05:51:09 pm »
The idea is to keep the temperature as uniform as possible across the ceramic substrate.  This will allow for better tracking over time and temperature-- (the Ta2N resistors "age" by heat and oxygen availability-- keeping them close to each other in temperature will aid in uniform aging characteristics).  Also, the farther away from the center of the package, the less the resistors will track; and resistors next to each other will track better than resistors far apart; and this is due to the difference in TCE between the ceramic substrate and the epoxy package; and also-- humidity will have a similar (more pronounced) effect.  The layout should be as symmetrical as you can get it while observing the above constraints.  As oxygen attacks the tantalum nitride compound-- tantalum pentoxide is formed, which is not conductive (and is unaffected by water molecules-- even under power).  Since these are thin-film resistors, that leaves only one drift mechanism-- and they always drift "up" in value.  When a thick enough layer of tantalum pentoxide forms-- the resistors will slow their drift rate to almost zero.  This is what the 90-day burn-in at 125oC is all about-- to artificially age these resistors so that the subsequent drift over time is almost zero-- doing this in an ozone-rich environment will speed up this process.

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#### branadic

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##### Re: Statistical arrays
« Reply #31 on: December 14, 2018, 06:31:28 pm »
I'm pretty sure the resistors are processed in a panel for economic reasons and cut into pieces after PVD process. So one can expect the resistors to be very uniform within one ceramic die. So it's all about heat distribution across the ceramic die.

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#### doktor pyta

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##### Re: Statistical arrays
« Reply #32 on: December 14, 2018, 06:36:38 pm »
I wonder if the temperature distribution inside statistical array could be evaluated objectively before practical measurements.
Some simple freware thermal simulation software would be useful but without knowing dimensions, thermal conductivities specifc to the array it may not be good enough.
Any ideas?
« Last Edit: December 14, 2018, 07:15:11 pm by doktor pyta »

#### branadic

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##### Re: Statistical arrays
« Reply #33 on: December 14, 2018, 07:20:28 pm »
Well, it's not that you now nothing about the array... you can estimate the size of the ceramic, you now it's alumina (Al2O3) substrate and know about thermal conductivity and that there are 7 or 8 resistors on it. But I'm sure there is no need to simulate the heat distribution, but to think about how heat will spread.
On the other hand you can use any thermal simulation program available to get an idea of what is thermally going on. If you want to do a real world simulation you need to sacrifice one unit, crack it open and measure the dimensions including the thickness of the TaN layer.

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#### Magnificent Bastard

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##### Re: Statistical arrays
« Reply #34 on: December 14, 2018, 08:08:57 pm »
OR, you can just measure it!  Measure R2-R8 while applying power to R1 (vs. no power).  Now do the same by powering R2, and measuring the other resistors.  Same with R3 (and so on) until you have a complete set of measurements.  With some mathematical magic, you should be able to understand how each resistor's dissipation affects the other resistors.  Intuitively, it "feels" like having the higher-dissipation resistors on the ends of the package will help keep the substrate temperature gradients lower (as opposed to having the higher dissipation resistors in the center of the package).  This can be verified with the above experiment.  An additional interesting question is: "Do the temperature gradients of the substrate change when mounted to a PCB vs. a package in "free air"?

Fun stuff!

#### JimmyJo

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##### Re: Statistical arrays
« Reply #35 on: December 15, 2018, 06:53:54 am »
Inspired by Zlymex, I present to you this 1K version of the NOMCA1603.  Upper right corner is Pin1 in both pictures.

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#### doktor pyta

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##### Re: Statistical arrays
« Reply #36 on: December 15, 2018, 10:25:08 am »
Nice job JimmyJo!

Below distances measured from the image.

#### branadic

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##### Re: Statistical arrays
« Reply #37 on: December 15, 2018, 01:09:15 pm »
Since Vishay is not a european company the distance between the resistors is most likely 0,3175mm or 0,0125". There seems to be a small parallax error from the microscope.

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#### branadic

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##### Re: Statistical arrays
« Reply #38 on: December 15, 2018, 07:50:01 pm »
Just curious if NOMCA16035001 could perform as temperature stabilized 10k resistance reference just as good as Fluke SL935 from TiN? There are enough 5k resistors inside one package to realize that.

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#### Kleinstein

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##### Re: Statistical arrays
« Reply #39 on: December 15, 2018, 08:12:19 pm »
One could use 1 or 2 of the resistors for heating, but even than the resistor is encapsulated in epoxy. So there can be humidity effects.

Extra heating might be useful to compensate for self heating, if the resistors are used for something like a divider with a variable voltage.

#### splin

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##### Re: Statistical arrays
« Reply #40 on: December 16, 2018, 03:42:48 am »
One issue with statistical arrays is that they multiply the number of leakage paths and also makes guarding more of a problem. If, for example, you have 10 resistors in series forming the bottom leg of a divider, then to fully guard it you would need 10 guard voltages.

In practice, given the lower voltage drop across each resistor, you would probably compromise by guarding fewer nodes at the expense of potentialy a bit more leakage. The calculations might be interesting if the leakage resistance of the PCB is significantly non-linear with voltage - perhaps due to humidity and/or surface contamination (I've no idea if it is).

#### branadic

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##### Re: Statistical arrays
« Reply #41 on: December 16, 2018, 11:42:54 am »
I was thinking about a pcb with the 5k resistor array connected as a 10k reference on the component side of the board and an oven control circuit on the back or the pcb with a big copper area on the back mounted to some BPR10 resistor forming an oven that is running at 35°C ... 40°C.
The thermistor could be some SMD longterm stability type mounted on the component side close to the resistor array. If permanently powered there should be no problem with humidity after a small run in phase. It's then a question of thermal insulation and oven temperature stability (0.1°C, 0.01°C or 0,001°C). But the oven could be of much smaller size compared to SL935.

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« Last Edit: December 16, 2018, 12:55:18 pm by branadic »
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#### doktor pyta

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##### Re: Statistical arrays
« Reply #42 on: December 30, 2018, 11:09:47 pm »
Little update in first post and Reply #28 and Reply #26.

In short, T.C. :

-from Reply #26: -3.9ppm/'C
-from Reply #28: +0.41ppm/'C

I couldn't believe my eves so I double checked everything and I made multiple measurements.
Both layouts were using the same specimen of NOMCA array.
« Last Edit: December 31, 2018, 08:01:38 am by doktor pyta »

#### branadic

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##### Re: Statistical arrays
« Reply #43 on: December 31, 2018, 12:02:20 am »
Can you rearrange the resistors and repeat the measurement? R7 + R8 as the center resistors, R5 + R6 symmetrical an both sides, followed by R3 + R4 and finally R1 + R2 (see attachement).

-branadic-
« Last Edit: December 31, 2018, 08:49:23 am by branadic »
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#### doktor pyta

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##### Re: Statistical arrays
« Reply #44 on: December 31, 2018, 12:27:53 am »
@branadic

proposed layout is definitely worth testing.
I will do it within one or two days.

P.S. please remove connections on the layout part of the attached drawing so the readers won't be confused.
I will post new layout drawing soon.

#### doktor pyta

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##### Re: Statistical arrays
« Reply #45 on: December 31, 2018, 12:23:11 pm »
Measurements of the layout suggested by branadic.
Proper drawings below.

T1=25.3'C
T2=63.6'C
mean T.C. of division ratio -5.8ppm/'C

and

division coefficient measured: 14.00017

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#### branadic

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##### Re: Statistical arrays
« Reply #46 on: December 31, 2018, 04:34:47 pm »
There are a few possibilities left, like having R7 and R8 on the outer ends and R5 and R6 in the center.

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#### Andreas

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##### Re: Statistical arrays
« Reply #47 on: December 31, 2018, 11:31:55 pm »
Hmm,

did you use one and the same sample for all these 3 wirings
or are that different samples for each wiring?

with best regards

Andreas

#### doktor pyta

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##### Re: Statistical arrays
« Reply #48 on: January 01, 2019, 12:02:12 am »
I used one sample in these 3 layouts. Otherwise it would not make big sense.
Cheers! Happy New Year!

#### e61_phil

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##### Re: Statistical arrays
« Reply #49 on: January 01, 2019, 08:47:31 pm »
Did you measure the individual TCs?

I wonder if these measurements are due to the position or due to lucky matching of the resistors for the different sides. Or is that already clear and I overlooked something?

Smf