Homebrew, open source, repurposed, hacked, software defined, open hardware

Tuesday 22 January 2013

Parallel Standard Resistor Cheat Sheet - With Pi Attenuator Applications

Having received the prototype step attenuator PCBs from Mitch at Hackvana, the next step was to figure out the resistor values for the step attenuator stages.

One could just use a single standard value resistor whose value is closest to the required Pi network resistor value required, but in my book, any job worth doing is usually worth overdoing, unless it's boring.

The PCB has been designed to allow a pair of resistors in parallel to be used to achieve each of the required Pi network resistances.

So, how to quickly and easily find a good match across possibilities in one decade versus three possible decades to choose from in parallel = 36 x 12  = 432 possibilities?

A cheat sheet knocked up in an openoffice spreadsheet led to the following table (saved in tab delimited CSV format, converted to three decimal places, saved as html, then cut and pasted the table html into the blog from a text editor).

To use it, find the closest match to what you need by visual inspection, using the most significant figures. Read off the corresponding values at the top and the left side of the table - these are the resistor values in parallel giving the value in shown the table. Multiply the values by by 10, 100, 1000 etc... to get you into the right decade for your needed value, et voila:


Value: 10 12 15 18 22 27 33 39 47 56 68 82
10 5.000 5.455 6.000 6.429 6.875 7.297 7.674 7.959 8.246 8.485 8.718 8.913
12 5.455 6.000 6.667 7.200 7.765 8.308 8.800 9.176 9.559 9.882 10.200 10.468
15 6.000 6.667 7.500 8.182 8.919 9.643 10.313 10.833 11.371 11.831 12.289 12.680
18 6.429 7.200 8.182 9.000 9.900 10.800 11.647 12.316 13.015 13.622 14.233 14.760
22 6.875 7.765 8.919 9.900 11.000 12.122 13.200 14.066 14.986 15.795 16.622 17.346
27 7.297 8.308 9.643 10.800 12.122 13.500 14.850 15.955 17.149 18.217 19.326 20.312
33 7.674 8.800 10.313 11.647 13.200 14.850 16.500 17.875 19.388 20.764 22.218 23.530
39 7.959 9.176 10.833 12.316 14.066 15.955 17.875 19.500 21.314 22.989 24.785 26.430
47 8.246 9.559 11.371 13.015 14.986 17.149 19.388 21.314 23.500 25.553 27.791 29.876
56 8.485 9.882 11.831 13.622 15.795 18.217 20.764 22.989 25.553 28.000 30.710 33.275
68 8.718 10.200 12.289 14.233 16.622 19.326 22.218 24.785 27.791 30.710 34.000 37.173
82 8.913 10.468 12.680 14.760 17.346 20.312 23.530 26.430 29.876 33.275 37.173 41.000
100 9.091 10.714 13.043 15.254 18.033 21.260 24.812 28.058 31.973 35.897 40.476 45.055
120 9.231 10.909 13.333 15.652 18.592 22.041 25.882 29.434 33.772 38.182 43.404 48.713
150 9.375 11.111 13.636 16.071 19.186 22.881 27.049 30.952 35.787 40.777 46.789 53.017
180 9.474 11.250 13.846 16.364 19.604 23.478 27.887 32.055 37.269 42.712 49.355 56.336
220 9.565 11.379 14.043 16.639 20.000 24.049 28.696 33.127 38.727 44.638 51.944 59.735
270 9.643 11.489 14.211 16.875 20.342 24.545 29.406 34.078 40.032 46.380 54.320 62.898
330 9.706 11.579 14.348 17.069 20.625 24.958 30.000 34.878 41.141 47.876 56.382 65.680
390 9.750 11.642 14.444 17.206 20.825 25.252 30.426 35.455 41.945 48.969 57.904 67.754
470 9.792 11.701 14.536 17.336 21.016 25.533 30.835 36.012 42.727 50.038 59.405 69.819
560 9.825 11.748 14.609 17.439 21.168 25.758 31.164 36.461 43.361 50.909 60.637 71.526
680 9.855 11.792 14.676 17.536 21.311 25.969 31.473 36.885 43.961 51.739 61.818 73.176
820 9.880 11.827 14.731 17.613 21.425 26.139 31.723 37.229 44.452 52.420 62.793 74.545
1000 9.901 11.858 14.778 17.682 21.526 26.290 31.946 37.536 44.890 53.030 63.670 75.786
1200 9.917 11.881 14.815 17.734 21.604 26.406 32.117 37.772 45.229 53.503 64.353 76.755
1500 9.934 11.905 14.851 17.787 21.682 26.523 32.290 38.012 45.572 53.985 65.051 77.750
1800 9.945 11.921 14.876 17.822 21.734 26.601 32.406 38.173 45.804 54.310 65.525 78.427
2200 9.955 11.935 14.898 17.854 21.782 26.673 32.512 38.321 46.017 54.610 65.961 79.053
2700 9.963 11.947 14.917 17.881 21.822 26.733 32.602 38.445 46.196 54.862 66.329 79.583
3300 9.970 11.957 14.932 17.902 21.854 26.781 32.673 38.544 46.340 55.066 66.627 80.012
3900 9.974 11.963 14.943 17.917 21.877 26.814 32.723 38.614 46.440 55.207 66.835 80.311
4700 9.979 11.969 14.952 17.931 21.898 26.846 32.770 38.679 46.535 55.341 67.030 80.594
5600 9.982 11.974 14.960 17.942 21.914 26.870 32.807 38.730 46.609 55.446 67.184 80.817
6800 9.985 11.979 14.967 17.952 21.929 26.893 32.841 38.778 46.677 55.543 67.327 81.023
8200 9.988 11.982 14.973 17.961 21.941 26.911 32.868 38.815 46.732 55.620 67.441 81.188
10000 9.990 11.986 14.978 17.968 21.952 26.927 32.891 38.848 46.780 55.688 67.541 81.333
12000 9.992 11.988 14.981 17.973 21.960 26.939 32.909 38.874 46.817 55.740 67.617 81.443
15000 9.993 11.990 14.985 17.978 21.968 26.951 32.928 38.899 46.853 55.792 67.693 81.554
18000 9.994 11.992 14.988 17.982 21.973 26.960 32.940 38.916 46.878 55.826 67.744 81.628
22000 9.995 11.993 14.990 17.985 21.978 26.967 32.951 38.931 46.900 55.858 67.790 81.695
27000 9.996 11.995 14.992 17.988 21.982 26.973 32.960 38.944 46.918 55.884 67.829 81.752
33000 9.997 11.996 14.993 17.990 21.985 26.978 32.967 38.954 46.933 55.905 67.860 81.797
39000 9.997 11.996 14.994 17.992 21.988 26.981 32.972 38.961 46.943 55.920 67.882 81.828
47000 9.998 11.997 14.995 17.993 21.990 26.984 32.977 38.968 46.953 55.933 67.902 81.857
56000 9.998 11.997 14.996 17.994 21.991 26.987 32.981 38.973 46.961 55.944 67.918 81.880
68000 9.999 11.998 14.997 17.995 21.993 26.989 32.984 38.978 46.968 55.954 67.932 81.901
82000 9.999 11.998 14.997 17.996 21.994 26.991 32.987 38.981 46.973 55.962 67.944 81.918


In this case, the target values, closest parallel approximations, and % error are as follows:

Closest Match 8.7179 11.6471 9.6429 43.4030 29.4059 30.4255 57.9039 71.5265 17.6134 17.8539
Desired Value 8.6955 11.6150 9.6248 43.6212 29.2402 30.3980 57.6900 71.1510 17.6150 17.8489
Percent error 1.0026 1.0028 1.0019 0.9950 1.0057 1.0009 1.0037 1.0053 0.9999 1.0003


From this we see at most, around half a percent error... not awful...

The ten values above are suitable for 1dB, 2dB, 3dB, 5dB and 10dB Pi attenuator networks. If you look closely at the table, the ten values are in bold.

Those wanting 20dB attenuator network values can find them, but Jim, VK5TR reckons one is better off using two 10dB stages rather than excessive attenuation in one stage to avoid excessive coupling between adjacent step attenuator sections, and I think that makes good sense, so I have not bothered to calculate them.

Another reason to use parallel resistors is that most AHARS (Adelaide Hills Amateur Radio Society) members have around 12,000 resistors in a box not doing much from that one time, at AHARS, we bought 1.28 million resistors and sorted them into bulk packs...

After some more work in the spreadsheet, we have a sorted list for easy value lookups:

R1 R2 Parallel Value
10 10 5.000000
10 12 5.454550
12 10 5.454550
10 15 6.000000
12 12 6.000000
15 10 6.000000
10 18 6.428570
18 10 6.428570
12 15 6.666670
15 12 6.666670
10 22 6.875000
22 10 6.875000
12 18 7.200000
18 12 7.200000
10 27 7.297300
27 10 7.297300
15 15 7.500000
10 33 7.674420
33 10 7.674420
12 22 7.764710
22 12 7.764710
10 39 7.959180
39 10 7.959180
15 18 8.181820
18 15 8.181820
10 47 8.245610
47 10 8.245610
12 27 8.307690
27 12 8.307690
10 56 8.484850
56 10 8.484850
10 68 8.717950
68 10 8.717950
12 33 8.800000
33 12 8.800000
10 82 8.913040
82 10 8.913040
15 22 8.918920
22 15 8.918920
18 18 9.000000
100 10 9.090910
12 39 9.176470
39 12 9.176470
120 10 9.230770
150 10 9.375000
180 10 9.473680
12 47 9.559320
47 12 9.559320
220 10 9.565220
15 27 9.642860
27 15 9.642860
270 10 9.642860
330 10 9.705880
390 10 9.750000
470 10 9.791670
560 10 9.824560
680 10 9.855070
820 10 9.879520
12 56 9.882350
56 12 9.882350
18 22 9.900000
22 18 9.900000
1000 10 9.900990
1200 10 9.917360
1200 10 9.917360
1500 10 9.933770
1500 10 9.933770
1800 10 9.944750
2200 10 9.954750
2200 10 9.954750
2700 10 9.963100
2700 10 9.963100
3300 10 9.969790
3900 10 9.974420
4700 10 9.978770
4700 10 9.978770
5600 10 9.982170
5600 10 9.982170
6800 10 9.985320
6800 10 9.985320
8200 10 9.987820
10000 10 9.990010
18000 10 9.994450
33000 10 9.996970
39000 10 9.997440
82000 10 9.998780
12 68 10.200000
68 12 10.200000
15 33 10.312500
33 15 10.312500
12 82 10.468090
82 12 10.468090
100 12 10.714290
18 27 10.800000
27 18 10.800000
22 22 11.000000
150 12 11.111110
180 12 11.250000
15 47 11.370970
47 15 11.370970
220 12 11.379310
270 12 11.489360
330 12 11.578950
390 12 11.641790
18 33 11.647060
33 18 11.647060
470 12 11.701240
560 12 11.748250
680 12 11.791910
820 12 11.826920
15 56 11.830990
56 15 11.830990
1000 12 11.857710
1000 12 11.857710
1200 12 11.881190
1200 12 11.881190
1200 12 11.881190
1500 12 11.904760
1500 12 11.904760
1800 12 11.920530
2200 12 11.934900
2200 12 11.934900
2700 12 11.946900
2700 12 11.946900
3300 12 11.956520
3900 12 11.963190
3900 12 11.963190
4700 12 11.969440
4700 12 11.969440
6800 12 11.978860
6800 12 11.978860
8200 12 11.982460
18000 12 11.992010
33000 12 11.995640
56000 12 11.997430
56000 12 11.997430
82000 12 11.998240
22 27 12.122450
27 22 12.122450
15 68 12.289160
68 15 12.289160
18 39 12.315790
39 18 12.315790
15 82 12.680410
82 15 12.680410
18 47 13.015380
47 18 13.015380
100 15 13.043480
22 33 13.200000
33 22 13.200000
120 15 13.333330
27 27 13.500000
18 56 13.621620
22 39 14.065570
39 22 14.065570
270 15 14.210530
18 68 14.232560
68 18 14.232560
330 15 14.347830
390 15 14.444440
390 15 14.444440
470 15 14.536080
560 15 14.608700
680 15 14.676260
820 15 14.730540
18 82 14.760000
82 18 14.760000
1000 15 14.778330
1200 15 14.814810
1200 15 14.814810
27 33 14.850000
33 27 14.850000
1500 15 14.851490
1500 15 14.851490
1500 15 14.851490
1800 15 14.876030
1800 15 14.876030
2200 15 14.898420
2200 15 14.898420
2200 15 14.898420
2700 15 14.917130
3300 15 14.932130
3900 15 14.942530
3900 15 14.942530
4700 15 14.952280
4700 15 14.952280
5600 15 14.959930
5600 15 14.959930
6800 15 14.966980
6800 15 14.966980
8200 15 14.972610
10000 15 14.977530
22 47 14.985510
47 22 14.985510
18000 15 14.987510
27000 15 14.991670
33000 15 14.993180
82000 15 14.997260
100 18 15.254240
120 18 15.652170
22 56 15.794870
56 22 15.794870
27 39 15.954550
150 18 16.071430
180 18 16.363640
22 68 16.622220
68 22 16.622220
220 18 16.638660
270 18 16.875000
330 18 17.068970
27 47 17.148650
47 27 17.148650
390 18 17.205880
470 18 17.336070
22 82 17.346150
82 22 17.346150
560 18 17.439450
560 18 17.439450
680 18 17.535820
820 18 17.613370
1000 18 17.681730
1200 18 17.733990
1200 18 17.733990
1500 18 17.786560
1500 18 17.786560
2200 18 17.853920
33 39 17.875000
39 33 17.875000
2700 18 17.880790
3300 18 17.902350
3900 18 17.917300
3900 18 17.917300
4700 18 17.931330
4700 18 17.931330
5600 18 17.942330
6800 18 17.952480
8200 18 17.960570
10000 18 17.967660
18000 18 17.982020
18000 18 17.982020
22000 18 17.985280
27000 18 17.988010
33000 18 17.990190
56000 18 17.994220
68000 18 17.995240
82000 18 17.996050
100 22 18.032790
27 56 18.216870
56 27 18.216870
150 22 19.186050
27 68 19.326320
68 27 19.326320
33 47 19.387500
39 39 19.500000
180 22 19.603960
220 22 20.000000
82 27 20.311930
270 22 20.342470
330 22 20.625000
33 56 20.764040
56 33 20.764040
390 22 20.825240
470 22 21.016260
560 22 21.168380
100 27 21.259840
680 22 21.310540
39 47 21.313950
47 39 21.313950
820 22 21.425180
1000 22 21.526420
1200 22 21.603930
1200 22 21.603930
1200 22 21.603930
1500 22 21.682000
1500 22 21.682000
1800 22 21.734360
2200 22 21.782180
2200 22 21.782180
2700 22 21.822190
3300 22 21.854300
3900 22 21.876590
3900 22 21.876590
4700 22 21.897500
4700 22 21.897500
6800 22 21.929050
10000 22 21.951710
18000 22 21.973140
27000 22 21.982090
33000 22 21.985340
56000 22 21.991360
56000 22 21.991360
68000 22 21.992880
82000 22 21.994100
82000 22 21.994100
56 39 22.989470
180 27 23.478260
47 47 23.500000
33 82 23.530430
82 33 23.530430
220 27 24.048580
270 27 24.545450
39 68 24.785050
68 39 24.785050
100 33 24.812030
330 27 24.957980
390 27 25.251800
390 27 25.251800
470 27 25.533200
47 56 25.553400
56 47 25.553400
560 27 25.758090
120 33 25.882350
680 27 25.968880
1000 27 26.290170
1000 27 26.290170
1200 27 26.405870
1200 27 26.405870
1200 27 26.405870
39 82 26.429750
82 39 26.429750
1500 27 26.522590
1500 27 26.522590
1500 27 26.522590
1800 27 26.600990
1800 27 26.600990
2200 27 26.672650
2200 27 26.672650
2700 27 26.732670
2700 27 26.732670
3300 27 26.780880
3900 27 26.814360
3900 27 26.814360
4700 27 26.845780
5600 27 26.870450
8200 27 26.911390
33000 27 26.977930
47000 27 26.984500
56000 27 26.986990
68000 27 26.989280
68000 27 26.989280
82000 27 26.991110
82000 27 26.991110
330 33 30.000000
470 33 30.834990
150 39 30.952380
150 39 30.952380
560 33 31.163580
680 33 31.472650
680 33 31.472650
820 33 31.723330
1000 33 31.945790
1000 33 31.945790
100 47 31.972790
1200 33 32.116790
1200 33 32.116790
1500 33 32.289630
1500 33 32.289630
1500 33 32.289630
1800 33 32.405890
1800 33 32.405890
1800 33 32.405890
2200 33 32.512320
2200 33 32.512320
2200 33 32.512320
2700 33 32.601540
2700 33 32.601540
3300 33 32.673270
3300 33 32.673270
3900 33 32.723110
3900 33 32.723110
3900 33 32.723110
4700 33 32.769910
4700 33 32.769910
4700 33 32.769910
5600 33 32.806670
5600 33 32.806670
6800 33 32.840630
6800 33 32.840630
8200 33 32.867730
27000 33 32.959720
33000 33 32.967030
82000 33 32.986720
220 39 33.127410
56 82 33.275360
82 56 33.275360
120 47 33.772460
68 68 34.000000
270 39 34.077670
330 39 34.878050
390 39 35.454550
150 47 35.786800
100 56 35.897440
470 39 36.011790
560 39 36.460770
680 39 36.884560
68 82 37.173330
82 68 37.173330
820 39 37.229340
180 47 37.268720
1000 39 37.536090
1000 39 37.536090
1000 39 37.536090
1200 39 37.772400
1500 39 38.011700
1500 39 38.011700
1800 39 38.172920
1800 39 38.172920
2200 39 38.320680
3900 39 38.613860
4700 39 38.679050
5600 39 38.730270
12000 39 38.873660
12000 39 38.873660
18000 39 38.915680
22000 39 38.930990
27000 39 38.943750
27000 39 38.943750
33000 39 38.953960
33000 39 38.953960
39000 39 38.961040
47000 39 38.967670
56000 39 38.972860
68000 39 38.977650
68000 39 38.977650
82000 39 38.981460
82000 39 38.981460
270 47 40.031550
100 68 40.476190
150 56 40.776700
82 82 41.000000
330 47 41.140580
390 47 41.945080
470 47 42.727270
560 47 43.360790
120 68 43.404260
680 47 43.961490
680 47 43.961490
820 47 44.452130
820 47 44.452130
220 56 44.637680
1000 47 44.890160
100 82 45.054950
1200 47 45.228550
1500 47 45.572070
1800 47 45.804010
2200 47 46.016910
2200 47 46.016910
2200 47 46.016910
2700 47 46.195850
3300 47 46.340010
270 56 46.380370
3900 47 46.440330
4700 47 46.534650
4700 47 46.534650
5600 47 46.608820
6800 47 46.677380
6800 47 46.677380
8200 47 46.732150
10000 47 46.780130
150 68 46.788990
12000 47 46.816630
15000 47 46.853190
18000 47 46.877600
27000 47 46.918330
33000 47 46.933160
39000 47 46.943430
56000 47 46.960590
82000 47 46.973080
330 56 47.875650
120 82 48.712870
390 56 48.968610
390 56 48.968610
180 68 49.354840
470 56 50.038020
560 56 50.909090
560 56 50.909090
680 56 51.739130
1000 56 53.030300
1200 56 53.503180
1200 56 53.503180
1200 56 53.503180
1500 56 53.984580
1800 56 54.310340
1800 56 54.310340
270 68 54.319530
2200 56 54.609930
2200 56 54.609930
2700 56 54.862120
3300 56 55.065550
3300 56 55.065550
3900 56 55.207280
4700 56 55.340620
5600 56 55.445540
5600 56 55.445540
6800 56 55.542590
6800 56 55.542590
8200 56 55.620160
10000 56 55.688150
15000 56 55.791710
18000 56 55.826320
27000 56 55.884090
39000 56 55.919710
47000 56 55.933360
68000 56 55.953920
82000 56 55.961780
82000 56 55.961780
180 82 56.335880
330 68 56.381910
330 68 56.381910
390 68 57.903930
470 68 59.405200
220 82 59.735100
560 68 60.636940
680 68 61.818180
820 68 62.792790
270 82 62.897730
1000 68 63.670410
1000 68 63.670410
1200 68 64.353310
1200 68 64.353310
1800 68 65.524630
1800 68 65.524630
2200 68 65.961200
2200 68 65.961200
2200 68 65.961200
2700 68 66.329480
3300 68 66.627080
3900 68 66.834680
3900 68 66.834680
4700 68 67.030200
4700 68 67.030200
4700 68 67.030200
5600 68 67.184190
5600 68 67.184190
6800 68 67.326730
8200 68 67.440740
15000 68 67.693120
15000 68 67.693120
390 82 67.754240
27000 68 67.829170
33000 68 67.860170
56000 68 67.917530
68000 68 67.932070
82000 68 67.943660
470 82 69.818840
470 82 69.818840
560 82 71.526480
680 82 73.175850
1000 82 75.785580
1000 82 75.785580
1500 82 77.749680
2200 82 79.053460
2700 82 79.583030
3300 82 80.011830
3300 82 80.011830
3900 82 80.311400
4700 82 80.593890
5600 82 80.816610
5600 82 80.816610
6800 82 81.022960
8200 82 81.188120
8200 82 81.188120
12000 82 81.443470
12000 82 81.443470
15000 82 81.554170
15000 82 81.554170
18000 82 81.628140
18000 82 81.628140
22000 82 81.695500
27000 82 81.751720
27000 82 81.751720
33000 82 81.796750
39000 82 81.827950
47000 82 81.857190
68000 82 81.901240
82000 82 81.918080

No comments:

Post a Comment