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Coil size, inductance, resistance, and Q

Chuck Agosta - Clark University

The following chart shows the calculated inductance and resistance of small coils in the size range that we often use with our TDO circuits. In addition the frequency of oscillation is calculated assuming 1 pF of capacitance and 1 uH of additional inductance, the absolute minimum one might expect from a real circuit. In most real circuits the parasitic inductance and capacitance will be greater and the resonant frequency lower. See the TDO tests chart for typical real values. The Q is also calculated. It is based on the resistance and does not account for radiation, so it sets an upper limit. The inductance is a good starting point if the actual parasitic values are known. See the detailed way to do that calculation here (coming soon). In this table the three wire diameters are in mm and correspond to #56, #50, and #45 wire respectively. Inductance is in uH, resistance in Ω, and frequency in MHz.

#56 Wire	#50 Wire	#45 Wire

wire	dia	turns	Induc	Resis	Q	MHz	wire	dia	turns	Induc	Resis	Q	MHz	wire	dia	turns	Induc	Resis	Q	MHz
0.0125	1.5	1	4.704	1.68	37.1	2107	0.02504	1.5	1	4.02	0.81	70.2	2246	0.0447	1.5	1	3.493	0.46	113.5	2374
0.0125	1.5	2	17.221	2.69	47.5	1179	0.02504	1.5	2	14.535	1.24	93.7	1277	0.0447	1.5	2	12.523	0.7	152.9	1369
0.0125	1.5	3	36.606	3.56	53	821	0.02504	1.5	3	30.301	1.59	107.4	900	0.0447	1.5	3	25.821	0.9	175.7	972
0.0125	1.5	4	61.673	4.4	56	636	0.02504	1.5	4	50.698	1.91	117	700	0.0447	1.5	4	42.689	1.07	191.6	761
0.0125	1.5	5	91.657	5.21	57.8	523	0.02504	1.5	5	74.894	2.2	123.8	578	0.0447	1.5	5	62.529	1.22	203.2	631
0.0125	1.5	6	127.705	6	59.4	444	0.02504	1.5	6	102.826	2.47	129.1	494	0.0447	1.5	6	85.223	1.36	212.8	542
0.0125	1.5	7	167.045	6.78	60.1	388	0.02504	1.5	7	133.756	2.74	133.1	434	0.0447	1.5	7	109.964	1.5	219.9	478
0.0125	1.5	8	212.191	7.54	60.9	345	0.02504	1.5	8	167.79	2.99	136.4	387	0.0447	1.5	8	136.618	1.63	225.5	429
0.0125	1.5	9	259.725	8.31	61.2	312	0.02504	1.5	9	204.281	3.25	138.9	351	0.0447	1.5	9	165.098	1.76	230.2	391
0.0125	1.5	10	311.007	9.07	61.4	285	0.02504	1.5	10	243.422	3.49	141	322	0.0447	1.5	10	195.482	1.88	234.3	359
0.0125	1.0	1	2.895	1.22	38.1	2550	0.02504	1.0	1	2.448	0.59	70.2	2710	0.0447	1.0	1	2.108	0.34	111.2	2855
0.0125	1.0	2	10.51	1.96	50.1	1483	0.02504	1.0	2	8.755	0.93	95.2	1611	0.0447	1.0	2	7.452	0.53	151.8	1731
0.0125	1.0	3	22.214	2.58	56.4	1045	0.02504	1.0	3	18.086	1.2	109.3	1152	0.0447	1.0	3	15.18	0.69	174.1	1251
0.0125	1.0	4	37.215	3.17	60	814	0.02504	1.0	4	30.029	1.43	119	904	0.0447	1.0	4	24.836	0.82	189	990
0.0125	1.0	5	55.002	3.74	62.1	673	0.02504	1.0	5	44.03	1.65	125.7	750	0.0447	1.0	5	36.022	0.94	199.5	827
0.0125	1.0	6	76.344	4.29	64	572	0.02504	1.0	6	60.056	1.86	130.9	644	0.0447	1.0	6	48.68	1.05	207.9	714
0.0125	1.0	7	99.39	4.83	64.9	502	0.02504	1.0	7	77.615	2.05	134.8	568	0.0447	1.0	7	62.276	1.16	213.8	633
0.0125	1.0	8	125.82	5.36	65.9	447	0.02504	1.0	8	96.793	2.24	137.9	509	0.0447	1.0	8	76.758	1.26	218.2	571
0.0125	1.0	9	153.357	5.89	66.2	405	0.02504	1.0	9	117.158	2.43	140.3	463	0.0447	1.0	9	92.056	1.36	221.7	522
0.0125	1.0	10	182.917	6.42	66.5	371	0.02504	1.0	10	138.86	2.61	142.2	426	0.0447	1.0	10	108.261	1.46	224.7	481
0.0125	0.7	1	1.88	0.91	38.3	2966	0.02504	0.7	1	1.575	0.45	68.9	3136	0.0447	0.7	1	1.345	0.26	106.9	3287
0.0125	0.7	2	6.769	1.49	51.7	1806	0.02504	0.7	2	5.568	0.72	95	1964	0.0447	0.7	2	4.685	0.42	148.2	2111
0.0125	0.7	3	14.22	1.96	58.8	1290	0.02504	0.7	3	11.39	0.94	109.3	1430	0.0447	0.7	3	9.419	0.54	169.7	1559
0.0125	0.7	4	23.682	2.4	62.8	1013	0.02504	0.7	4	18.756	1.12	118.9	1132	0.0447	0.7	4	15.237	0.65	183.5	1249
0.0125	0.7	5	34.793	2.82	65.2	841	0.02504	0.7	5	27.278	1.29	125.3	946	0.0447	0.7	5	21.866	0.75	192.6	1052
0.0125	0.7	6	48.099	3.22	67.3	718	0.02504	0.7	6	36.946	1.46	130.2	817	0.0447	0.7	6	29.285	0.84	199.6	915
0.0125	0.7	7	62.3	3.62	68.3	633	0.02504	0.7	7	47.414	1.61	133.7	723	0.0447	0.7	7	37.124	0.93	204.2	815
0.0125	0.7	8	78.577	4.01	69.4	564	0.02504	0.7	8	58.758	1.76	136.5	651	0.0447	0.7	8	45.384	1.02	207.4	739
0.0125	0.7	9	95.34	4.4	69.8	513	0.02504	0.7	9	70.677	1.91	138.5	594	0.0447	0.7	9	54.001	1.1	209.6	679
0.0125	0.7	10	113.238	4.78	70.1	471	0.02504	0.7	10	83.295	2.05	140.1	548	0.0447	0.7	10	63.076	1.18	211.6	629
0.0125	0.5	1	1.246	0.69	37.9	3358	0.02504	0.5	1	1.036	0.35	66.4	3528	0.0447	0.5	1	0.878	0.2	100.7	3673
0.0125	0.5	2	4.445	1.15	52.4	2157	0.02504	0.5	2	3.611	0.57	93.3	2344	0.0447	0.5	2	3.005	0.33	141.9	2515
0.0125	0.5	3	9.276	1.52	60.2	1570	0.02504	0.5	3	7.305	0.74	107.6	1746	0.0447	0.5	3	5.95	0.44	162.5	1909
0.0125	0.5	4	15.346	1.86	64.6	1245	0.02504	0.5	4	11.918	0.9	116.9	1400	0.0447	0.5	4	9.504	0.53	174.9	1553
0.0125	0.5	5	22.395	2.18	67.2	1041	0.02504	0.5	5	17.172	1.04	122.8	1181	0.0447	0.5	5	13.477	0.61	182.5	1323
0.0125	0.5	6	30.818	2.48	69.6	892	0.02504	0.5	6	23.075	1.17	127.3	1026	0.0447	0.5	6	17.873	0.69	188.2	1159
0.0125	0.5	7	39.686	2.79	70.6	789	0.02504	0.5	7	29.379	1.29	130.3	913	0.0447	0.5	7	22.434	0.77	191.4	1040
0.0125	0.5	8	49.846	3.08	71.8	706	0.02504	0.5	8	36.155	1.41	132.6	826	0.0447	0.5	8	27.192	0.84	193.3	948
0.0125	0.5	9	60.168	3.37	72.2	644	0.02504	0.5	9	43.188	1.53	134.1	757	0.0447	0.5	9	32.09	0.91	194.4	875
0.0125	0.5	10	71.123	3.66	72.4	593	0.02504	0.5	10	50.587	1.65	135.2	701	0.0447	0.5	10	37.227	0.97	195.4	814
0.0125	0.3	1	0.663	0.45	35.9	3903	0.02504	0.3	1	0.544	0.23	60.4	4050	0.0447	0.3	1	0.457	0.14	88.1	4170
0.0125	0.3	2	2.323	0.78	51.8	2761	0.02504	0.3	2	1.85	0.4	87.4	2981	0.0447	0.3	2	1.513	0.24	126.8	3175
0.0125	0.3	3	4.786	1.04	60.5	2092	0.02504	0.3	3	3.663	0.53	101.3	2331	0.0447	0.3	3	2.912	0.32	145.2	2545
0.0125	0.3	4	7.818	1.27	65.4	1695	0.02504	0.3	4	5.871	0.64	109.9	1920	0.0447	0.3	4	4.545	0.39	155.3	2137
0.0125	0.3	5	11.263	1.49	68.1	1437	0.02504	0.3	5	8.312	0.75	114.7	1649	0.0447	0.3	5	6.308	0.46	160.6	1862
0.0125	0.3	6	15.363	1.7	70.6	1244	0.02504	0.3	6	11.009	0.85	118.2	1452	0.0447	0.3	6	8.227	0.52	164.3	1657
0.0125	0.3	7	19.566	1.9	71.7	1110	0.02504	0.3	7	13.814	0.94	120.1	1308	0.0447	0.3	7	10.154	0.58	165.5	1507
0.0125	0.3	8	24.38	2.1	72.9	999	0.02504	0.3	8	16.793	1.04	121.6	1193	0.0447	0.3	8	12.145	0.64	165.9	1388
0.0125	0.3	9	29.142	2.29	73.2	917	0.02504	0.3	9	19.814	1.12	122.1	1103	0.0447	0.3	9	14.145	0.69	165.6	1293
0.0125	0.3	10	34.144	2.49	73.3	849	0.02504	0.3	10	22.971	1.21	122.6	1028	0.0447	0.3	10	16.245	0.75	165.4	1212
0.0125	0.2	1	0.399	0.32	33.3	4255	0.02504	0.2	1	0.325	0.17	54	4372	0.0447	0.2	1	0.272	0.1	76.1	4463
0.0125	0.2	2	1.375	0.57	49.5	3266	0.02504	0.2	2	1.078	0.3	79.6	3491	0.0447	0.2	2	0.872	0.18	110.5	3679
0.0125	0.2	3	2.794	0.77	58.7	2584	0.02504	0.2	3	2.088	0.41	92.6	2864	0.0447	0.2	3	1.63	0.25	126.2	3104
0.0125	0.2	4	4.507	0.95	63.7	2145	0.02504	0.2	4	3.29	0.5	100.4	2430	0.0447	0.2	4	2.491	0.31	134.6	2694
0.0125	0.2	5	6.408	1.12	66.4	1849	0.02504	0.2	5	4.578	0.59	104.2	2131	0.0447	0.2	5	3.392	0.37	138.2	2401
0.0125	0.2	6	8.664	1.28	69	1619	0.02504	0.2	6	5.984	0.67	106.9	1904	0.0447	0.2	6	4.365	0.42	140.7	2173
0.0125	0.2	7	10.912	1.43	69.8	1458	0.02504	0.2	7	7.409	0.75	108	1736	0.0447	0.2	7	5.314	0.48	140.7	2003
0.0125	0.2	8	13.492	1.58	71	1322	0.02504	0.2	8	8.913	0.82	108.8	1599	0.0447	0.2	8	6.296	0.52	140.6	1863
0.0125	0.2	9	15.973	1.72	71.1	1222	0.02504	0.2	9	10.407	0.9	108.7	1490	0.0447	0.2	9	7.259	0.57	139.5	1751
0.0125	0.2	10	18.559	1.87	71	1138	0.02504	0.2	10	11.967	0.97	108.7	1398	0.0447	0.2	10	8.281	0.62	139	1652