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