Resistor matching error starting with six 1% resistors

benb · 2021-11-13 10:15 pm

Mark Johnson said:
I got interested in obtaining better-than-1% matching of metal film resistors, especially "uncommon" values among the E96 series of standard resistors, that are not offered / are not stocked in the (much more expensive) 0.1% tolerance grade.

I decided I was willing to buy six resistors and pick the best matching pair among them, then discard the other four. So I put together a little Monte Carlo simulation to see just how good or just how bad the results might be. Assumptions built into the simulation
[*]Resistors are "100 ohm, 1% metal film" devices. Smallest possible resistance is 99.00 ohms, largest possible resistance is 101.00 ohms

A worst-case assumption is six values uniformly distributed from 99 to 101 inclusive - that's five divisions starting a t 99 and incrementing by 2/5 of an ohm:

Code:

As your simulation showed, you're guaranteed to have worst case 0.4% difference, and since they're rarely uniformly spread, you usually find a pair much closer.

What I'm wondering is why you don't buy 100 or 250 resistors and have a bunch extra in stock for other projects, as they're around a cent (0.01 USD) each. With that you can number each resistor (just put them in a cardboard edge or somehow kept separate left to right), measure each and put its value in a spreadsheet with each number, and sort both fields by resistance, as I show below. You'll get dozens of pairs that are arbitrarily close.

simon7000 said:
Mark,

My experience is that resistors made together match better than random spreads would indicate.

They certainly match better than a UNIFORM spread would indicate!

Code:
So I measured 30 Xicon 1% metal film 1/4 W 1,000 ohm resistors on my GR bridge. (Ignoring decimal points!)
What model is this? I've used a GR-1603A, but that was back in college, and I don't think it gave as good accuracy as you're indicating here...

The worst was 992.4 ohms or off by .76%

I suspect from the measure values, the manufacturer also tests the resistors and any that are within .1% of target value are selected and marked for .1%!

Results

Code:

9965 9974 9969 9953 9959 9944 9956 9952 9963 9961 9969 9979 9971 9992 9964 9953 9954 9966 9948 9968 9953 9970 9996 9961 9932 9961 9971 9953 9956 10005

The secret to measuring resistors precisely is to not touch the body of the resistor and change its' temperature.

Mean 9963.666 SD .16%

So I put these into LibreOffice Calc (much like Excel but a lot less expensive) and numbered each:

Code:

and I selected both fields and sorted by the second field, getting this:

Code:

This shows resistors #4, 16, 21 and 28 all measure 9953, or (within whatever resolution there really is in such measurements) within about 0.01 percent of one another. There are similar runs of other values.

Mark Johnson · 2021-11-13 10:16 pm

Here's a dump of the first 200 Monte Carlo trials. The six resistor values are printed (in sorted order for ease of reading), then the best match. If the best match is less than or equal to 0.05%, an E (for Excellent) is printed. In those 200 trials, 113 were Excellent, which is 56.5%. Not 93%.

All 200*6 = 1200 random numbers are included in the dump. If you sort them and plot the data, you see a straight line, just as expected from uniformly distributed random numbers.

Code:

 99.07111  99.30365  99.71210 100.00867 100.27026 100.28345 match 0.0131 % E
 99.00482  99.73438 100.20691 100.35260 100.75793 100.77838 match 0.0203 % E
 99.09967  99.67633  99.87744  99.99481 100.26343 100.53802 match 0.1175 %  
 99.17236  99.37695  99.71698 100.37799 100.38153 100.76239 match 0.0035 % E
 99.21002  99.42523 100.10388 100.14465 100.31165 100.50635 match 0.0407 % E
 99.13080  99.78918  99.84540 100.13922 100.21204 100.62372 match 0.0563 %  
 99.25842  99.52063  99.53174 100.14014 100.21387 100.50153 match 0.0112 % E
 99.57397  99.58246  99.63226  99.85870 100.58478 100.67273 match 0.0085 % E
 99.06421  99.25861  99.26569  99.47308 100.01862 100.19611 match 0.0071 % E
 99.70068  99.95331 100.03412 100.38593 100.67743 100.84027 match 0.0808 %  
 99.00525  99.45300 100.44885 100.57257 100.61652 100.75653 match 0.0437 % E
 99.44000  99.49170  99.98132 100.08295 100.45990 100.93890 match 0.0520 %  
 99.62115  99.71924 100.08850 100.19873 100.58374 100.64917 match 0.0650 %  
 99.04419  99.14777 100.12183 100.13940 100.61829 100.78668 match 0.0176 % E
 99.20123  99.33636  99.62628 100.34174 100.47906 100.59332 match 0.1137 %  
 99.24426  99.41443  99.81775  99.93280  99.93964 100.64435 match 0.0068 % E
 99.35938  99.70856  99.84521  99.89948 100.24615 100.49585 match 0.0543 %  
 99.59937  99.69037  99.69720  99.97784 100.28168 100.77576 match 0.0069 % E
 99.07489  99.22076  99.48834  99.82965 100.00348 100.11731 match 0.1138 %  
 99.11249  99.54388 100.25183 100.35199 100.57104 100.89215 match 0.0999 %  
 99.03516  99.18512  99.29114  99.89069 100.31665 100.39838 match 0.0815 %  
 99.34827  99.39423  99.44098 100.20227 100.68274 100.68433 match 0.0016 % E
 99.17938  99.28320  99.38654  99.64807 100.20972 100.62683 match 0.1041 %  
 99.16144  99.56116  99.74603 100.20630 100.21112 100.43176 match 0.0048 % E
 99.09338  99.49188  99.61292 100.11505 100.51563 100.68317 match 0.1217 %  
 99.57080  99.79596 100.21466 100.25934 100.80493 100.93097 match 0.0446 % E
 99.02502  99.11969  99.16742  99.16974  99.90485 100.41760 match 0.0023 % E
 99.75793  99.85071  99.87537 100.35968 100.43048 100.86639 match 0.0247 % E
 99.00507  99.45166  99.98035 100.39374 100.54822 100.57703 match 0.0287 % E
 99.33368  99.37823  99.92041  99.93555 100.71741 100.76538 match 0.0151 % E
 99.86438 100.20526 100.68689 100.70563 100.86725 100.95825 match 0.0186 % E
 99.06360  99.49585  99.51489 100.27594 100.29071 100.96771 match 0.0147 % E
 99.05084  99.06683  99.47504 100.08203 100.16565 100.62476 match 0.0161 % E
 99.13153  99.30865  99.45160  99.54321  99.57190 100.42572 match 0.0288 % E
 99.29840 100.01532 100.12988 100.37708 100.72632 100.88873 match 0.1145 %  
 99.17657  99.24255  99.54840 100.58478 100.70288 100.85938 match 0.0665 %  
 99.37653  99.40808  99.92303 100.51794 100.76324 100.91260 match 0.0318 % E
 99.02057  99.03003  99.32312  99.41132 100.49939 100.57019 match 0.0096 % E
 99.15515  99.17395  99.59271 100.11029 100.71936 100.95599 match 0.0190 % E
 99.52563  99.66992  99.80591 100.02863 100.09198 100.32507 match 0.0633 %  
 99.30676  99.31506 100.09460 100.24689 100.73242 100.82416 match 0.0084 % E
 99.19934 100.01331 100.54498 100.61798 100.78265 100.83527 match 0.0522 %  
 99.18921  99.42377  99.48108  99.51813  99.66431  99.88959 match 0.0372 % E
 99.02594  99.15540  99.49268  99.87921  99.97400 100.18768 match 0.0949 %  
 99.48291  99.58972  99.60236  99.99445  99.99982 100.34668 match 0.0054 % E
 99.58240  99.58661 100.08160 100.23151 100.34338 100.41846 match 0.0042 % E
 99.05511  99.46564  99.72253 100.38129 100.52643 100.62439 match 0.0974 %  
 99.16840  99.22900  99.35278  99.90997 100.11090 100.99524 match 0.0611 %  
 99.32300  99.53986  99.57062  99.66498 100.98218 100.99054 match 0.0083 % E
 99.04492  99.06512  99.27325  99.84222 100.26898 100.89508 match 0.0204 % E
 99.29761  99.94519 100.05933 100.22937 100.79749 100.86810 match 0.0701 %  
 99.18311  99.43286  99.82550  99.90851 100.13312 100.62988 match 0.0832 %  
 99.10010  99.46759  99.49872 100.03058 100.60754 100.69696 match 0.0313 % E
 99.26569  99.41144  99.63007 100.12384 100.54102 100.80298 match 0.1468 %  
 99.57629  99.69794 100.39966 100.60931 100.86017 100.94409 match 0.0832 %  
 99.26355  99.39270 100.53357 100.64459 100.70227 100.81403 match 0.0573 %  
 99.37115  99.46027  99.46173  99.75763 100.41339 100.83875 match 0.0015 % E
 99.14642  99.37982  99.48468  99.79327  99.86505 100.30847 match 0.0719 %  
 99.87128  99.95123 100.41431 100.49524 100.55786 100.60425 match 0.0461 % E
 99.25586  99.58447  99.76764 100.08411 100.48505 100.90460 match 0.1839 %  
 99.05054  99.33008  99.72156  99.74835  99.82849 100.02008 match 0.0269 % E
 99.14154  99.44751  99.91742 100.01178 100.64313 100.81879 match 0.0944 %  
 99.79767  99.84686  99.90594 100.03210 100.57373 100.99725 match 0.0493 % E
 99.35724  99.52515  99.70270  99.91742 100.87769 100.95618 match 0.0778 %  
 99.21143  99.28760  99.43787 100.38733 100.45667 100.90710 match 0.0691 %  
 99.83105  99.94586  99.95715 100.37836 100.80487 100.92395 match 0.0113 % E
 99.33551  99.41571  99.54889  99.65857  99.85071 100.47772 match 0.0807 %  
 99.12152  99.72620  99.78070  99.81946  99.97919 100.06830 match 0.0388 % E
 99.40497  99.41486  99.72479  99.77350 100.40662 100.86414 match 0.0099 % E
 99.59039  99.63904  99.73096  99.82458  99.82593 100.25769 match 0.0013 % E
 99.09241  99.50067  99.62549  99.96539  99.98395 100.73029 match 0.0186 % E
 99.17560  99.38324  99.98096 100.09430 100.18475 100.89215 match 0.0904 %  
 99.17334  99.20221  99.24512  99.25317  99.75311 100.86188 match 0.0081 % E
 99.02277  99.47968  99.94104 100.45929 100.67957 100.70776 match 0.0280 % E
 99.30365  99.44415 100.59857 100.62402 100.77094 100.82819 match 0.0253 % E
 99.13940  99.72382  99.75146 100.11267 100.44702 100.65552 match 0.0277 % E
 99.18591  99.42517  99.75305 100.11810 100.81818 100.98950 match 0.1699 %  
 99.16132  99.32977  99.56311 100.68439 100.82605 100.86139 match 0.0350 % E
 99.49506  99.96869 100.49866 100.59027 100.75891 100.84796 match 0.0884 %  
 99.09137  99.12494  99.52094 100.45624 100.67786 100.94250 match 0.0339 % E
 99.67596  99.69336  99.76367  99.76807 100.17163 100.18359 match 0.0044 % E
 99.00824  99.18640  99.90985 100.04565 100.06592 100.14484 match 0.0203 % E
 99.15247  99.62836 100.08545 100.17560 100.69543 100.86200 match 0.0901 %  
 99.22180  99.45465  99.89197 100.12268 100.98254 100.98907 match 0.0065 % E
 99.06464  99.50360  99.73682 100.50214 100.58954 100.66370 match 0.0737 %  
 99.11951  99.17322  99.22620  99.29755 100.33240 100.96600 match 0.0534 %  
 99.31824  99.32349 100.06531 100.12152 100.64246 100.71875 match 0.0053 % E
 99.67078  99.72089  99.77618 100.36884 100.64520 100.65375 match 0.0085 % E
 99.57794  99.92657 100.15912 100.30969 100.51141 100.84589 match 0.1503 %  
 99.28680  99.50806  99.67621  99.70758 100.28271 100.85510 match 0.0315 % E
 99.11908  99.19446  99.82031 100.33258 100.38721 100.54456 match 0.0544 %  
 99.04852  99.06464  99.37604  99.79620 100.13403 100.75366 match 0.0163 % E
 99.29962  99.80615 100.31091 100.40527 100.93024 100.94543 match 0.0151 % E
 99.30560  99.33002  99.38757  99.51117 100.20477 100.63470 match 0.0246 % E
 99.97131 100.10571 100.18494 100.42004 100.52307 100.95038 match 0.0791 %  
 99.28040  99.73236 100.32397 100.32410 100.32562 100.33246 match 0.0001 % E
 99.17670  99.32025  99.65851 100.23712 100.33508 100.61353 match 0.0977 %  
 99.25848  99.29242  99.63702  99.68585  99.85754 100.41534 match 0.0342 % E
 99.53143 100.29480 100.49719 100.64728 100.72137 100.96027 match 0.0736 %  
 99.23242  99.43695  99.83923  99.99164 100.20654 100.93488 match 0.1527 %  
 99.11090  99.25128  99.61285  99.83887 100.08331 100.14056 match 0.0572 %  
 99.26434 100.14868 100.23840 100.65283 100.90070 100.91345 match 0.0126 % E
 99.18774  99.58618 100.18890 100.19659 100.53156 100.94592 match 0.0077 % E
 99.57672  99.99829 100.17432 100.17804 100.34912 100.38086 match 0.0037 % E
 99.40918  99.67816  99.76416  99.98059 100.16412 100.71021 match 0.0863 %  
 99.03699  99.06030  99.31818  99.33417 100.09851 100.21948 match 0.0161 % E
 99.41046  99.51465  99.57758  99.71460 100.07745 100.91656 match 0.0632 %  
 99.17474  99.19495  99.21338  99.78455 100.20483 100.37811 match 0.0186 % E
 99.10297  99.24579  99.33228  99.38611  99.67377 100.71533 match 0.0542 %  
 99.05060  99.37146  99.59180  99.68854 100.00555 100.53253 match 0.0971 %  
 99.67755  99.76947 100.03381 100.14465 100.62555 100.87762 match 0.0922 %  
 99.14825  99.40051  99.59521  99.82147 100.01385 100.61731 match 0.1927 %  
 99.42267  99.43958  99.70013  99.85486 100.04498 100.67114 match 0.0170 % E
 99.54102 100.04004 100.06067 100.31525 100.44867 100.61639 match 0.0206 % E
 99.48425  99.96265 100.32129 100.59387 100.61353 100.61401 match 0.0005 % E
 99.13660  99.21826  99.77203  99.90521 100.34802 100.70337 match 0.0824 %  
 99.64063  99.68420  99.72845 100.75317 100.75397 100.80707 match 0.0008 % E
 99.64679  99.75623  99.87958 100.35364 100.69177 100.78058 match 0.0882 %  
 99.21613  99.24890 100.50702 100.80426 100.83331 100.92981 match 0.0288 % E
 99.00037  99.34113  99.54291  99.74219 100.49347 100.61365 match 0.1196 %  
 99.00806  99.43665  99.54889  99.92151 100.05548 100.14832 match 0.0928 %  
100.18463 100.39410 100.40350 100.47754 100.84387 100.87555 match 0.0094 % E
 99.33569  99.34253 100.59216 100.63599 100.73193 100.82672 match 0.0069 % E
 99.00543  99.07043  99.26111 100.05792 100.10583 100.12518 match 0.0193 % E
 99.60620  99.61725 100.44568 100.52966 100.72784 100.79852 match 0.0111 % E
 99.45081  99.45557  99.81445 100.05145 100.31750 100.97803 match 0.0048 % E
 99.03229  99.55634  99.81830  99.89288 100.59662 100.79517 match 0.0747 %  
 99.14673  99.19220  99.45581 100.02594 100.46735 100.72906 match 0.0459 % E
 99.07220  99.76361  99.87701 100.21002 100.68500 100.84039 match 0.1137 %  
 99.49536 100.28186 100.37360 100.40259 100.91223 100.96936 match 0.0289 % E
 99.19403  99.56250  99.59296 100.92902 100.93567 100.96564 match 0.0066 % E
 99.31683  99.87573 100.38110 100.84381 100.90936 100.93774 match 0.0281 % E
 99.11145  99.29108  99.63586  99.75311  99.80511 100.92480 match 0.0521 %  
 99.01117  99.49811  99.72632 100.00818 100.30414 100.39197 match 0.0876 %  
 99.06537  99.60382 100.29675 100.35071 100.52887 100.97650 match 0.0538 %  
 99.55261  99.89227  99.94666  99.94971 100.11835 100.78760 match 0.0031 % E
100.11414 100.25818 100.28345 100.53113 100.74335 100.76587 match 0.0224 % E
 99.10730  99.68091  99.68488 100.00629 100.02893 100.40369 match 0.0040 % E
 99.64642  99.87372 100.15192 100.29236 100.43445 100.84119 match 0.1402 %  
 99.58386  99.84534 100.26770 100.29639 100.40735 100.88733 match 0.0286 % E
 99.57031  99.70294  99.89105 100.44806 100.79547 100.88043 match 0.0843 %  
 99.59052 100.03827 100.21802 100.22430 100.63672 100.81519 match 0.0063 % E
 99.49811  99.75494 100.15387 100.17609 100.70929 100.78918 match 0.0222 % E
 99.34253  99.45093  99.56665  99.64246 100.57770 100.99530 match 0.0761 %  
 99.05988  99.30200  99.93677 100.04626 100.40991 100.97125 match 0.1096 %  
 99.38208  99.45367 100.52570 100.53137 100.59137 100.97473 match 0.0056 % E
 99.54254  99.75763 100.43042 100.50958 100.64142 100.93475 match 0.0788 %  
 99.69653  99.74078  99.86493  99.97076 100.36597 100.44720 match 0.0444 % E
 99.14941  99.65137  99.82233 100.43787 100.76611 100.76904 match 0.0029 % E
 99.54889  99.85162  99.90283 100.52179 100.53113 100.73553 match 0.0093 % E
 99.45721  99.80334 100.03601 100.20276 100.73730 100.79797 match 0.0602 %  
 99.32257  99.68134  99.82202 100.24402 100.29840 100.63727 match 0.0542 %  
 99.56555  99.70074  99.75769  99.85748 100.59595 100.71344 match 0.0571 %  
 99.33295  99.70923 100.22144 100.35938 100.61676 100.91180 match 0.1376 %  
 99.27911  99.74396  99.84833 100.28461 100.31512 100.77179 match 0.0304 % E
 99.05847  99.65125  99.72729 100.63684 100.67151 100.90540 match 0.0344 % E
 99.29645  99.41907  99.62170  99.87152 100.52515 100.82111 match 0.1235 %  
 99.32068  99.88586 100.27020 100.67194 100.77563 100.97363 match 0.1030 %  
 99.26398  99.67108  99.67609  99.83740 100.18866 100.52332 match 0.0050 % E
 99.47430  99.67938  99.74701  99.78271 100.28601 100.92261 match 0.0358 % E
 99.08490  99.30560  99.39160 100.55267 100.83368 100.86395 match 0.0300 % E
 99.23303  99.30420  99.30945  99.84985 100.27026 100.82532 match 0.0053 % E
 99.08551  99.66046  99.83063 100.57800 100.62311 100.74023 match 0.0448 % E
 99.29034  99.52576 100.49554 100.49884 100.52936 100.73499 match 0.0033 % E
 99.19843  99.23273 100.09924 100.10950 100.19122 100.48236 match 0.0102 % E
 99.40417  99.55200  99.55231  99.63873 100.05273 100.46912 match 0.0003 % E
 99.13531  99.78796 100.27484 100.55524 100.71106 100.88770 match 0.1550 %  
 99.13794  99.49164  99.65350  99.73657  99.82916 100.59259 match 0.0834 %  
 99.06586  99.57831  99.66113 100.14166 100.54846 100.98584 match 0.0832 %  
 99.22821  99.54248  99.99536  99.99762 100.67896 100.96637 match 0.0023 % E
 99.33710  99.41119  99.50110  99.76208  99.86993 100.92279 match 0.0746 %  
 99.36395  99.56787  99.79150  99.87366 100.18951 100.26654 match 0.0769 %  
 99.10535  99.60614  99.67969 100.03668 100.05927 100.07220 match 0.0129 % E
 99.45667  99.64459 100.20288 100.85883 100.95697 100.98975 match 0.0325 % E
 99.28284  99.30841  99.79785 100.52606 100.59741 100.90356 match 0.0258 % E
 99.82715 100.09607 100.63611 100.76874 100.89240 100.99121 match 0.0979 %  
 99.53442  99.59314  99.75085  99.77747 100.09326 100.30847 match 0.0267 % E
 99.16028  99.23157  99.43549 100.05774 100.18671 100.68597 match 0.0719 %  
 99.09381  99.54657  99.76727  99.86908 100.18060 100.47070 match 0.1020 %  
 99.12122  99.21826  99.63873  99.96625 100.60760 100.82971 match 0.0979 %  
 99.35480  99.53998  99.60889  99.75397  99.77478 100.98737 match 0.0209 % E
 99.28925  99.70990 100.16492 100.29004 100.37946 100.56714 match 0.0892 %  
 99.08612  99.47430  99.51599  99.69208  99.71942 100.08612 match 0.0274 % E
 99.11230  99.45941  99.68341 100.02802 100.47638 100.85278 match 0.2252 %  
 99.15338  99.26501  99.67773  99.68579 100.00073 100.28754 match 0.0081 % E
 99.70026 100.35944 100.45294 100.66681 100.81323 100.82709 match 0.0137 % E
 99.09991  99.31354 100.01007 100.34418 100.52686 100.58563 match 0.0585 %  
 99.07349  99.29443  99.68402 100.35767 100.47858 100.57050 match 0.0915 %  
 99.01544  99.06445  99.95544 100.09186 100.20337 100.63013 match 0.0495 % E
 99.16125  99.19543  99.37006 100.11749 100.29773 100.55811 match 0.0345 % E
 99.84167 100.28833 100.31219 100.33893 100.44269 100.73688 match 0.0238 % E
 99.15540  99.92175  99.93793  99.93970 100.51996 100.92975 match 0.0018 % E
 99.92529 100.38135 100.47656 100.52313 100.83960 100.97125 match 0.0463 % E
 99.20093  99.85236 100.14172 100.22101 100.93927 100.94855 match 0.0092 % E
 99.35889  99.47504  99.71838  99.92261 100.17175 100.66846 match 0.1169 %  
 99.16919  99.55597  99.73138  99.83917  99.99390 100.49377 match 0.1081 %  
 99.31989  99.41608 100.14557 100.29883 100.71960 100.78699 match 0.0669 %  
 99.45575  99.88770 100.02142 100.15607 100.26971 100.85101 match 0.1135 %  
 99.97748 100.10083 100.16766 100.41888 100.64764 100.81287 match 0.0668 %  
 99.35419  99.45453  99.50610  99.75317 100.55884 100.57410 match 0.0152 % E

 113 trials (out of 200) matched better than 0.05% (marked Excellent  "E")

syn08 · 2021-11-13 10:56 pm

Sorry, I screwed it above, nothing to do with C(N-1,2)

1. Pull a resistor out of 6 (so 5 left). Since the probability in the [a, b] interval is uniform, any value is possible there. Let's call this value S1 (sample 1).

2. Around S1, consider an interval [a', b'] defined by the desired matching tolerance.

3. Pull another resistor with value S2 (4 left). S2 can also be anywhere in [a, b] with equal probability; the probability to fall in [a', b'] is P2=(b'-a')/(b-a).

4. The probability for S2 to be OUTSIDE of [a', b'] is obviously 1-P2=1-[(b'-a')/(b-a)]

5. Keep pulling resistors. The probability that 5 resistor will all fall OUTSIDE [a', b'] is then P={1-[(b'-a')/(b-a)]}^5 (or in general ^(N-1) where N is the number of resistors to start with.

6. Now the probability to have AT LEAST one resistor in [a', b'] is 1-{1-[(b'-a')/(b-a)]}^5

7. Repeat the above, for 2 matches out of 5, 4, 3, 2, and note all probabilities in step 6. as (P(i), i=1...5

7. We are still not done yet. Since we constraint the problem to matching the FIRST resistor extracted, and considering the problem is symmetrical for all resistors (e.g. S2 may match with S4) we need to add all these probabilities, that is P=SUM((1-P(i)), i=1...5

Plug in some numbers
a=99
b=101
b'-a'=0.1 (meaning 0.05%)

P2=0.05
1-P2=0.95

P(5)=0.95^5=0.77
P(4)=0.95^4=0.82
P(3)=0.95^3=0.86
P(2)=0.95^2=0.90
P(1)=0.95^1=0.95

SUM(1-P(i)) i=1...5=0.23+0.18+0.14+0.10+0.05 = 0.70

So the probability to find 2 resistors matched to 0.05% in 6 resistors of 1% is 70%. Of course, this result assumed an uniform distribution of the six resistor values, which may not be true. Practically, any distribution beyond uniform increases the success probability, so 93% is kind of worst case. Not sure why your simulation rendered more pessimistic results.

Repeat for 2 matches to 0.01% out of 10 resistors gives:

a=99
b=101
b'-a'=0.02 (meaning 0.01%)

P2=0.01
1-P2=0.99

P(9)=0.99^9=0.914
P(8)=0.99^8=0.923
P(7)=0.99^7=0.932
P(6)=0.99^6=0.941
P(5)=0.99^5=0.951
P(4)=0.99^4=0.961
P(3)=0.99^3=0.970
P(2)=0.99^2=0.980
P(1)=0.99^1=0.990

SUM(1-P(i)) i=1...9 = 0.01+0.02+0.03+0.039+0.049+0.059+0.068+0.077+0.086=0.438

So the probability to find 2 resistors matched to 0.01% in 10 resistors of 1% is 43.6%,

Given the prices of 0.01% resistors like Stackpole that costs $3 a pop, and the prices of 10 resistors 1% like Stackpole total cost of $1.4, I'm not convinced it is worth sorting, at least at this level of 0.01%

kodabmx · 2021-11-13 11:23 pm

10 1% "like" Stackpole: 55 cents. ROHM Semicon | ROHM Semicon ESR18EZPF1000 | Chip Resistor - Surface Mount - LCSC.COM

syn08 · 2021-11-13 11:32 pm

I took the lowest price resistors from the same manuacturer, in stock at the same distributor, since the price ratio matters. The same Rohm 10 resistors cost $1.82 at DigiKey. OTOH, Rohm doesn't do any 0.01% thin film.

But even so, 0.01% sorting (which is 10milliohm/100ohm) requires a 5 1/2 digit ohmmeter and Kelvin probes, plus the work. Myself, I'd rather buy two 0.01% resistor rather than going through the sorting process with 44% chances to succeed or 56% chances to fail, and start over. The series converges rather slow, I can calculate how large the 1% sample size for a certain probability of success (say 90%), I would expect something like 30pcs or more.

For 0.1%, a 4 1/2 multimeter is good enough, and chances to get a 0.1% pair out of 6pcs of 1% are 70%, that looks feasible, but then 0.1% resistors from Stackpole are $0.81 a pop, so compared to the cost of 6 x 1% is a flush.

Not worth the trouble IMO, unless one cannot find the needed resistors in 0.01% or 0.1% tolerances in stock, anywhere (which is very possible today).

NickKUK · 2021-11-13 11:37 pm

The is an assumption that all resistors enter your possession pre-sort using the same process thus share the same probabilities. For example those bought through eBay may not share the same sample tolerances (even if 1%) due to fake/preselection and resorting. So I would place a constraint that all resistors are purchased through the the larger resellers.

kodabmx · 2021-11-13 11:47 pm

^^^^

This.

I'm pretty sure when I first bought parts and didn't know any better, I'd say instead of 1% metal film they were carbon. Or they were just an older style. Still, they work as described. Within 1% of the stated value and they handle their 1/2W rating.

syn08 · 2021-11-14 12:11 am

If one cannot tell metal film from carbon when ordering, then chances are high he also doesn't have an at least 4 1/2 DVM, doesn't understand tolerances in general, and doesn't need 0.1% resistors in particular, to start with.

simon7000 · 2021-11-14 12:13 am

Benb,

https://www.atecorp.com/atecorp/media/pdfs/data-sheets/genrad-1658_manual.pdf

Used and working at most a few hundred dollars.

Nice design, allows 4 terminal connection and under 10 seconds per test.

I also have one like what you used. Had a fellow in a court case claim he had measured loudspeaker lines in a stadium with one. Turns out you can’t use one to measure loudspeaker impedance! (Loudspeakers are transducers and any wind or noise will not allow you to settle in on a value.)

kodabmx · 2021-11-14 6:38 am

syn08 said:
If one cannot tell metal film from carbon when ordering, then chances are high he also doesn't have an at least 4 1/2 DVM, doesn't understand tolerances in general, and doesn't need 0.1% resistors in particular, to start with.

The ad said MF. They look like MF. They perform like CF.

Nothing to do at all with a meter (how do you test it before you purchase?) or being able to read a damned ad.

No typical DIY people need 0.1% resistors, either. And also no need for the condescending attitude.

syn08 · 2021-11-14 5:28 pm

Here's a nice, closed form, formula:

P=1-(1-t/T)^[N(N-1)/2]

where:

t=the target tolerance in %
T=the available resistors tolerance in %
N=the number of resistors with tolerance T to sort from
P=the probability of finding at least 2 resistors within t tolerance

Example:
t=0.01%
T=1%
N=25
...
P=95%

Could also be solved for N to find the number of needed resistors to find a matched pair with a given probability. I'll let other to determine the economic feasibility of sorting resistors for a matched pair, and if it's worth the trouble.

For:

t=0.01%
T=1%
N=10
...
P=36.3%

This matches pretty well the Monte Carlo simulation of 5 million bags of ten random resistors per bag, as in https://www.diyaudio.com/forums/par...r-starting-six-1-resistors-2.html#post6846820, which gave P=36.9%

Mark Johnson · 2022-04-23 9:38 pm

If anyone is wondering about practical applications of these ideas, let me introduce you to the Ship Of Theseus amplifier and its interchangeable Front End cards, including "Bon Homme Richard". SOT offers seven different Front Ends, each named for a famous American ship. You can read about the complete Ship Of Theseus project (here) . Post #1 of that thread includes a large .pdf file with schematics and descriptions of all seven Front Ends (link).

The section which covers Bon Homme Richard is attached below. Notice the discussion about resistor matching; the lab methodology should look quite familiar.

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Resistor matching error starting with six 1% resistors

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