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Publication Number: FHWA-HRT-06-139
Date: October 2006

Traffic Detector Handbook:Third Edition—Volume II

APPENDIX C. LOOP INDUCTANCE AND QUALITY FACTOR TABLES

ABSTRACT

Detector loops are in fact very short solenoids.

Loop inductance and quality factor values calculated for rectangular, quadrupole, and circular loops at excitation frequencies of 1, 20, 40, and 60 kHz are given in these tables. The frequency f at which the values apply is shown as part of the table title. The appropriate length or diameter of the loop is given in the first column, while the number of turns is stated in the first row.

Rectangular and quadrupole loop inductance and quality factor values for 6– ft (1.8-m) wide loops are displayed for 6–20-ft (1.8–6.1-m) loop lengths in 1-ft (0.3-m) increments and for 20–50-ft (6.1–15.2-m) loop lengths in 5-ft (1.5-m) increments. Circular loop inductance and quality factor values are listed for loop diameters of 4, 5, 6, 7, and 8 feet (1.2, 1.5, 1.8, 2.1, and 2.4 m, respectively). All tables show inductance and quality factor values for 1 through 7 turns of wire.

Inductance values shown in the tables are apparent or measured values that include loop resistance and capacitance effects.

The loop inductance shown in these tables is the apparent loop inductance value expressed in µH that includes loop resistance and capacitance effects. It thus represents the value which the user will actually measure when an appropriate measuring instrument is used.

**Table C-1. Rectangular-loop inductance in µH at f = 1 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	10.53	36.02	74.46	124.67	185.81	257.24	338.44
7 (2.1)	11.52	39.49	81.72	136.94	204.23	282.91	372.40
8 (2.4)	12.51	42.94	88.94	149.12	222.52	308.38	406.08
9 (2.7)	13.50	46.38	96.12	161.25	240.71	333.71	439.58
10 (3.0)	14.48	49.80	103.28	173.32	258.83	358.94	472.94
11 (3.3)	15.46	53.22	110.42	185.37	276.90	384.09	506.20
12 (3.7)	16.44	56.63	117.54	197.39	294.93	409.19	539.38
13 (3.9)	17.42	60.04	124.65	209.39	312.93	434.25	572.51
14 (4.3)	18.40	63.44	131.76	221.38	330.91	459.27	605.59
15 (4.6)	19.37	66.84	138.85	233.35	348.87	484.27	638.63
16 (4.9)	20.35	70.23	145.95	245.32	366.81	509.24	671.64
17 (5.2)	21.32	73.63	153.03	257.27	384.74	534.09	704.63
18 (5.5)	22.30	77.02	160.12	269.22	402.66	559.13	737.59
19 (5.8)	23.27	80.41	167.20	281.16	420.57	584.06	770.54
20 (6.1)	24.25	83.80	174.27	293.10	438.47	608.97	803.47
25 (7.6)	29.12	100.74	209.63	352.73	527.89	733.42	967.96
30 (9.1)	33.98	117.66	244.95	412.31	617.22	857.75	1132.29
35 (10.7)	38.84	134.57	280.25	471.85	706.51	982.00	1296.52
40 (12.2)	43.71	151.48	315.55	531.38	795.76	1106.21	1460.70
45 (13.7)	48.57	168.38	350.83	590.89	885.00	1230.40	1624.85
50 (15.2)	53.43	185.28	386.11	650.39	974.22	1354.56	1788.98

**Table C-2. Rectangular-loop quality factor at f = 1 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	1.07	1.81	2.48	3.09	3.67	4.21	4.72
7 (2.1)	1.08	1.83	2.51	3.14	3.72	4.27	4.79
8 (2.4)	1.09	1.85	2.54	3.17	3.76	4.32	4.85
9 (2.7)	1.09	1.87	2.56	3.20	3.80	4.36	4.90
10 (3.0)	1.10	1.88	2.58	3.22	3.83	4.40	4.94
11 (3.3)	1.11	1.89	2.59	3.24	3.85	4.43	4.97
12 (3.7)	1.11	1.90	2.61	3.26	3.87	4.45	5.00
13 (3.9)	1.11	1.91	2.62	3.28	3.89	4.47	5.03
14 (4.3)	1.12	1.91	2.63	3.29	3.91	4.49	5.05
15 (4.6)	1.12	1.92	2.64	3.30	3.92	4.51	5.07
16 (4.9)	1.12	1.92	2.65	3.31	3.94	4.53	5.09
17 (5.2)	1.13	1.93	2.65	3.32	3.95	4.54	5.11
18 (5.5)	1.13	1.93	2.66	3.33	3.96	4.56	5.12
19 (5.8)	1.13	1.94	2.67	3.34	3.97	4.57	5.14
20 (6.1)	1.13	1.94	2.67	3.35	3.98	4.58	5.15
25 (7.6)	1.14	1.96	2.70	3.38	4.02	4.62	5.20
30 (9.1)	1.15	1.97	2.71	3.40	4.05	4.66	5.23
35 (10.7)	1.15	1.98	2.73	3.42	4.07	4.68	5.26
40 (12.2)	1.15	1.98	2.73	3.43	4.08	4.70	5.28
45 (13.7)	1.16	1.99	2.74	3.44	4.09	4.71	5.30
50 (15.2)	1.16	1.99	2.75	3.45	4.10	4.72	5.31

**Table C-3. Rectangular-loop inductance in µH at f = 20 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	10.50	35.96	74.39	124.62	185.85	257.48	339.07
7 (2.1)	11.49	39.43	81.65	136.90	204.32	283.27	373.23
8 (2.4)	12.48	42.88	88.87	149.10	222.66	308.88	407.26
9 (2.7)	13.46	46.31	96.05	161.24	240.92	334.37	441.10
10 (3.0)	14.44	49.73	103.21	173.34	259.12	359.80	474.86
11 (3.3)	15.42	53.15	110.35	185.42	277.28	385.17	508.58
12 (3.7)	16.40	56.56	117.48	197.47	295.41	410.53	542.29
13 (3.9)	17.37	59.96	124.60	209.51	313.54	435.87	576.01
14 (4.3)	18.35	63.36	131.71	221.54	331.65	461.22	609.76
15 (4.6)	19.32	66.75	138.82	233.57	349.76	486.58	643.54
16 (4.9)	20.30	70.15	145.92	245.59	367.87	511.95	677.38
17 (5.2)	21.27	73.54	153.02	257.61	385.99	537.35	711.28
18 (5.5)	22.24	76.93	160.12	269.62	404.11	562.78	745.24
19 (5.8)	23.21	80.32	167.21	281.65	422.25	588.24	779.28
20 (6.1)	24.19	83.71	174.31	293.67	440.40	613.73	813.41
25 (7.6)	29.04	100.65	209.79	353.85	531.41	741.89	985.51
30 (9.1)	33.90	117.58	245.31	414.22	622.99	871.46	1160.59
35 (10.7)	38.75	134.52	280.89	474.83	715.29	1002.77	1339.33
40 (12.2)	43.60	151.47	316.54	535.75	808.46	1136.14	1522.43
45 (13.7)	48.45	168.43	352.28	597.01	902.63	1271.89	1710.61
50 (15.2)	53.30	185.41	388.13	658.67	997.93	1410.37	1904.64

**Table C-4. Rectangular-loop quality factor at f = 20 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	15.61	24.06	30.40	35.41	39.51	42.95	45.87
7 (2.1)	15.75	24.28	30.67	35.73	39.85	43.30	46.24
8 (2.4)	15.86	24.46	30.90	35.98	40.12	43.59	46.52
9 (2.7)	15.95	24.61	31.08	36.18	40.35	43.81	46.75
10 (3.0)	16.03	24.73	31.23	36.36	40.53	44.00	46.93
11 (3.3)	16.10	24.84	31.36	36.50	40.68	44.16	47.08
12 (3.7)	16.15	24.93	31.48	36.63	40.82	44.29	47.21
13 (3.9)	16.20	25.01	31.58	36.74	40.93	44.40	47.31
14 (4.3)	16.25	25.08	31.66	36.83	41.03	44.49	47.39
15 (4.6)	16.29	25.14	31.74	36.92	41.11	44.57	47.46
16 (4.9)	16.32	25.20	31.81	36.99	41.18	44.64	47.51
17 (5.2)	16.36	25.25	31.87	37.06	41.25	44.69	47.55
18 (5.5)	16.39	25.30	31.93	37.12	41.30	44.74	47.59
19 (5.8)	16.41	25.34	31.98	37.17	41.35	44.78	47.61
20 (6.1)	16.44	25.38	32.02	37.22	41.39	44.81	47.62
25 (7.6)	16.54	25.53	32.20	37.39	41.53	44.88	47.59
30 (9.1)	16.60	25.63	32.31	37.48	41.58	44.85	47.44
35 (10.7)	16.65	25.71	32.38	37.53	41.57	44.74	47.18
40 (12.2)	16.69	25.76	32.43	37.54	41.51	44.57	46.84
45 (13.7)	16.72	25.80	32.46	37.53	41.42	44.34	46.43
50 (15.2)	16.75	25.83	32.47	37.49	41.29	44.07	45.95

**Table C-5. Rectangular-loop inductance in µH at f = 40 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	10.44	35.86	74.28	124.61	186.13	258.43	341.24
7 (2.1)	11.43	39.33	81.55	136.94	204.76	284.58	376.22
8 (2.4)	12.41	42.77	88.78	149.19	223.28	310.63	411.12
9 (2.7)	13.39	46.20	95.97	161.40	241.75	336.65	446.04
10 (3.0)	14.37	49.62	103.14	173.59	260.21	362.21	481.07
11 (3.3)	15.34	53.03	110.30	185.76	278.66	388.76	516.24
12 (3.7)	16.32	56.43	117.45	197.92	297.14	414.92	551.61
13 (3.9)	17.29	59.83	124.60	210.09	315.64	441.17	587.21
14 (4.3)	18.26	63.23	131.74	222.27	334.18	467.54	623.08
15 (4.6)	19.23	66.62	138.88	234.46	352.77	494.04	659.24
16 (4.9)	20.20	70.02	146.03	246.66	371.42	520.68	695.72
17 (5.2)	21.17	73.41	153.18	258.89	390.13	547.49	732.56
18 (5.5)	22.14	76.81	160.33	271.13	408.91	574.47	769.77
19 (5.8)	23.11	80.20	167.48	283.40	427.76	601.63	807.38
20 (6.1)	24.07	83.59	174.64	295.69	446.70	628.99	845.42
25 (7.6)	28.91	100.57	210.56	357.63	542.74	769.19	1043.04
30 (9.1)	33.75	117.57	246.71	420.50	641.54	916.19	1255.80
35 (10.7)	38.58	134.62	283.16	484.52	743.73	1071.72	1488.10
40 (12.2)	43.42	151.72	319.96	549.90	849.98	1237.75	1745.46
45 (13.7)	48.25	168.88	357.16	616.85	961.04	1416.63	2035.03
50 (15.2)	53.09	186.12	394.82	685.62	1077.75	1611.21	2366.36

**Table C-6. Rectangular-loop quality factor at f = 40 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	22.45	33.19	40.64	46.18	50.48	53.89	56.63
7 (2.1)	22.63	33.46	40.95	46.51	50.80	54.19	56.89
8 (2.4)	22.78	33.67	41.19	46.76	51.05	54.41	57.07
9 (2.7)	22.90	33.85	41.39	46.97	51.24	54.57	57.18
10 (3.0)	23.01	33.99	41.56	47.13	51.38	54.68	57.24
11 (3.3)	23.09	34.12	41.70	47.27	51.50	53.76	57.26
12 (3.7)	23.17	34.23	41.82	47.38	51.59	54.80	57.24
13 (3.9)	23.24	34.32	41.92	47.47	51.65	54.82	57.19
14 (4.3)	23.30	34.41	42.01	47.55	51.70	54.82	57.12
15 (4.6)	23.35	34.48	42.08	47.61	51.73	54.80	57.02
16 (4.9)	23.39	34.54	42.15	47.66	51.75	54.76	56.90
17 (5.2)	23.44	34.60	42.21	47.70	51.75	54.71	56.77
18 (5.5)	23.48	34.65	42.25	47.73	51.74	54.64	56.61
19 (5.8)	23.51	34.70	42.30	47.75	51.72	54.56	56.44
20 (6.1)	23.54	34.74	42.33	47.76	51.69	54.46	56.25
25 (7.6)	23.67	34.90	42.45	47.75	51.44	53.83	55.08
30 (9.1)	23.76	35.00	42.48	47.61	51.01	52.96	53.59
35 (10.7)	23.82	35.05	42.45	47.39	50.46	51.89	51.80
40 (12.2)	23.87	35.09	42.28	47.10	49.78	50.64	49.74
45 (13.7)	23.91	35.10	42.27	46.74	49.00	49.21	47.41
50 (15.2)	23.94	35.09	42.14	46.33	48.11	47.61	44.82

**Table C-7. Rectangular-loop inductance in µH at f = 60 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	10.40	35.79	74.25	124.77	186.85	260.30	345.26
7 (2.1)	11.38	39.25	81.53	137.19	205.75	287.11	381.59
8 (2.4)	12.36	42.69	88.78	149.56	224.60	313.94	418.12
9 (2.7)	13.34	46.12	96.00	161.90	243.46	340.88	454.97
10 (3.0)	14.31	49.54	103.21	174.24	262.36	367.98	492.24
11 (3.3)	15.28	52.95	110.41	186.59	281.34	395.31	530.03
12 (3.7)	16.25	56.36	117.61	198.96	300.41	422.89	568.41
13 (3.9)	17.22	59.76	124.81	211.37	319.59	450.76	607.46
14 (4.3)	18.19	63.16	132.02	223.81	338.89	478.96	647.24
15 (4.6)	19.16	66.57	139.24	236.29	358.34	507.52	687.83
16 (4.9)	20.12	69.97	146.47	248.83	377.94	536.47	729.31
17 (5.2)	21.09	73.37	153.70	261.41	397.71	565.85	771.74
18 (5.5)	22.05	76.78	160.96	274.06	417.66	595.69	815.22
19 (5.8)	23.02	80.18	168.23	286.77	437.80	626.02	859.83
20 (6.1)	23.98	83.59	175.51	299.55	458.15	656.87	905.65
25 (7.6)	28.81	100.67	212.62	364.62	563.43	820.32	1156.67
30 (9.1)	33.63	117.83	249.52	432.01	675.89	1003.04	1456.51
35 (10.7)	38.45	135.10	287.53	502.29	797.51	1211.88	1828.33
40 (12.2)	43.28	152.49	326.39	576.05	930.74	1456.41	2312.27
45 (13.7)	48.11	170.04	366.24	653.98	1078.66	1750.56	2979.87
50 (15.2)	52.95	187.75	407.21	736.88	1245.26	2115.67	3977.12

**Table C-8. Rectangular-loop quality factor at f = 60 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	26.56	38.32	46.10	51.65	55.77	58.86	61.17
7 (2.1)	26.77	38.60	46.40	51.94	56.02	59.04	61.24
8 (2.4)	26.93	38.82	46.64	52.16	56.19	59.13	61.21
9 (2.7)	27.07	39.01	46.83	52.33	56.30	59.15	61.10
10 (3.0)	27.18	39.16	46.98	52.46	56.37	59.12	60.93
11 (3.3)	27.28	39.29	47.11	52.55	56.39	59.04	60.71
12 (3.7)	27.37	39.40	47.21	52.61	56.39	58.93	60.44
13 (3.9)	27.44	39.49	47.30	52.66	56.36	58.78	60.12
14 (4.3)	27.51	39.58	47.37	52.68	56.30	58.60	59.77
15 (4.6)	27.56	39.65	47.42	52.69	56.22	58.39	59.37
16 (4.9)	27.62	39.71	47.46	52.68	56.12	58.15	58.94
17 (5.2)	27.66	39.76	47.50	52.66	56.01	57.89	58.48
18 (5.5)	27.71	39.81	47.52	52.63	55.88	57.61	57.99
19 (5.8)	27.74	39.85	47.54	52.59	55.73	57.30	57.46
20 (6.1)	27.78	39.89	47.55	52.53	55.57	56.98	56.91
25 (7.6)	27.92	40.01	47.51	52.14	54.56	55.05	53.70
30 (9.1)	28.01	40.06	47.36	51.56	53.26	52.67	49.83
35 (10.7)	28.08	40.07	47.12	50.82	51.69	49.87	45.34
40 (12.2)	28.13	40.03	46.81	49.95	49.88	46.68	40.25
45 (13.7)	28.16	39.97	46.43	48.94	47.84	43.10	34.59
50 (15.2)	28.19	39.87	45.99	47.81	45.56	39.15	28.35

**Table C-9. Quadrupole-loop inductance in µH at f = 1 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	17.73	61.33	127.13	212.86	316.90	438.00	575.12
7 (2.1)	20.06	69.53	144.29	241.80	360.23	498.17	654.45
8 (2.4)	22.38	77.72	161.44	270.73	403.55	558.32	733.75
9 (2.7)	24.70	85.91	178.59	299.65	446.85	618.46	813.03
10 (3.0)	27.02	94.09	195.74	328.57	490.15	678.59	892.31
11 (3.3)	29.34	102.28	212.88	357.49	533.45	738.71	971.58
12 (3.7)	31.67	110.47	230.03	386.41	576.75	798.84	1050.85
13 (3.9)	33.99	118.65	247.18	415.33	620.05	858.96	1130.11
14 (4.3)	36.31	126.84	264.32	444.24	663.34	919.08	1209.38
15 (4.6)	38.63	135.03	281.47	473.16	706.64	979.20	1288.65
16 (4.9)	40.95	143.21	298.61	502.08	749.93	1039.33	1367.91
17 (5.2)	43.27	151.40	315.76	530.99	793.23	1099.45	1447.18
18 (5.5)	45.60	159.59	332.91	559.91	836.52	1159.57	1526.45
19 (5.8)	47.92	167.77	350.05	588.83	879.82	1219.70	1605.73
20 (6.1)	50.24	175.96	367.20	617.74	923.12	1279.82	1685.00
25 (7.6)	61.85	216.89	452.92	762.33	1139.61	1580.47	2081.42
30 (9.1)	73.45	257.83	538.65	906.92	1356.11	1881.15	2477.90
35 (10.7)	85.06	298.76	624.38	1051.52	1572.63	2181.88	2874.48
40 (12.2)	96.67	339.69	710.11	1196.12	1789.18	2482.66	3271.16
45 (13.7)	108.28	380.63	795.85	1340.73	2005.75	2783.49	3667.95
50 (15.2)	119.89	421.56	881.59	1485.36	2222.35	3084.39	4064.88

**Table C-10. Quadrupole-loop quality factor at f = 1 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	1.20	2.06	2.82	3.52	4.16	4.77	5.33
7 (2.1)	1.22	2.10	2.88	3.59	4.25	4.87	5.45
8 (2.4)	1.24	2.13	2.93	3.66	4.33	4.96	5.55
9 (2.7)	1.25	2.16	2.97	3.71	4.39	5.03	5.63
10 (3.0)	1.26	2.18	3.00	3.75	4.44	5.09	5.70
11 (3.3)	1.28	2.20	3.03	3.79	4.49	5.14	5.76
12 (3.7)	1.28	2.22	3.05	3.82	4.52	5.19	5.81
13 (3.9)	1.29	2.23	3.07	3.84	4.56	5.22	5.85
14 (4.3)	1.30	2.25	3.09	3.87	4.59	5.26	5.89
15 (4.6)	1.30	2.26	3.11	3.89	4.61	5.29	5.93
16 (4.9)	1.31	2.27	3.13	3.91	4.46	5.32	5.96
17 (5.2)	1.31	2.28	3.14	3.93	4.66	5.34	5.98
18 (5.5)	1.32	2.29	3.15	3.94	4.68	5.36	6.01
19 (5.8)	1.32	2.29	3.16	3.96	4.69	5.38	6.03
20 (6.1)	1.33	2.30	3.17	3.97	4.71	5.40	6.05
25 (7.6)	1.34	2.33	3.21	4.02	4.77	5.47	6.13
35 (10.7)	1.35	2.35	3.24	4.06	4.81	5.52	6.19
40 (12.2)	1.36	2.36	3.26	4.08	4.84	5.56	6.23
40 (10.7)	1.36	2.37	3.28	4.10	4.87	5.59	6.26
45 (13.7)	1.37	2.38	3.29	4.12	4.89	5.61	6.29
50 (15.2)	1.37	2.39	3.30	4.13	4.90	5.63	6.31

**Table C-11. Quadrupole-loop inductance in µH at f = 20 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	17.69	61.26	127.08	212.98	317.49	439.56	578.46
7 (2.1)	20.01	69.45	144.26	242.03	361.15	500.51	659.37
8 (2.4)	22.32	77.64	161.44	271.10	404.88	561.64	740.66
9 (2.7)	24.64	85.82	178.63	300.21	448.71	622.98	822.40
10 (3.0)	26.96	94.01	195.83	329.35	492.64	684.58	904.66
11 (3.3)	29.28	102.20	213.05	358.53	536.70	746.45	987.48
12 (3.7)	31.59	110.40	230.27	387.77	580.88	808.63	1070.92
13 (3.9)	33.91	118.59	247.51	417.05	625.20	871.14	1155.04
14 (4.3)	36.23	126.79	264.76	446.39	669.68	934.00	1239.90
15 (4.6)	38.55	134.99	282.03	475.79	714.33	997.25	1325.55
16 (4.9)	40.86	143.19	299.32	505.25	759.15	1060.91	1412.05
17 (5.2)	43.18	151.40	316.62	534.78	804.16	1125.01	1499.47
18 (5.5)	45.50	159.61	333.95	564.38	849.37	1189.58	1587.86
19 (5.8)	47.82	167.82	351.29	594.05	894.79	1254.64	1677.30
20 (6.1)	50.14	176.03	368.66	623.81	940.43	1320.24	1767.86
25 (7.6)	61.73	217.17	455.85	773.93	1172.42	1657.20	2239.86
30 (9.1)	73.32	258.42	543.75	926.67	1411.89	2012.31	2751.56
35 (10.7)	84.92	299.81	632.50	1082.59	1660.59	2390.42	3315.54
40 (12.2)	96.53	341.36	722.23	1242.29	1920.49	2797.33	3948.06
45 (13.7)	108.14	383.08	813.10	1406.39	2193.80	3240.10	4670.95
50 (15.2)	119.75	425.01	905.26	1575.59	2483.09	3727.59	5514.46

**Table C-12. Quadrupole-loop quality factor at f = 20 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	17.26	26.53	33.28	38.48	42.64	46.05	48.87
7 (2.1)	17.51	26.91	33.74	38.98	43.16	46.56	49.37
8 (2.4)	17.71	27.22	34.10	39.38	43.57	46.96	49.73
9 (2.7)	17.88	27.47	34.40	39.70	43.89	47.26	50.00
10 (3.0)	18.02	27.69	34.65	39.97	44.15	47.50	50.20
11 (3.3)	18.14	27.87	34.87	40.18	44.36	47.68	50.33
12 (3.7)	18.25	28.02	35.04	40.37	44.52	47.81	50.42
13 (3.9)	18.34	28.16	35.20	40.52	44.66	47.91	50.46
14 (4.3)	18.42	28.28	35.33	40.65	44.77	47.98	50.47
15 (4.6)	18.49	28.38	35.45	40.76	44.85	48.02	50.44
16 (4.9)	18.55	28.47	35.55	40.85	44.92	48.04	50.39
17 (5.2)	18.61	28.55	35.63	40.93	44.96	48.03	50.31
18 (5.5)	18.66	28.63	35.71	40.99	45.00	48.01	50.21
19 (5.8)	18.71	28.69	35.78	41.04	45.01	47.97	50.08
20 (6.1)	18.75	28.75	35.84	41.09	45.02	47.92	49.94
25 (7.6)	18.91	28.98	36.04	41.18	44.89	47.44	48.95
30 (9.1 )	19.03	29.12	36.14	41.12	44.56	46.68	47.58
35 (10.7)	19.11	29.21	36.15	40.96	44.07	45.68	45.88
40 (12.2)	19.17	29.27	36.12	40.71	43.44	44.48	43.86
45 (13.7)	19.22	29.30	36.04	40.38	42.69	43.08	41.56
50 (15.2)	19.26	29.31	35.92	39.99	41.82	41.49	38.97

**Table C-13. Quadrupole-loop inductance in µH at f = 40 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	17.61	61.14	127.09	213.56	319.54	444.65	589.12
7 (2.1)	19.92	69.33	144.35	242.97	364.23	508.03	675.03
8 (2.4)	22.23	77.52	161.64	272.50	409.28	572.25	762.72
9 (2.7)	24.54	85.72	178.97	302.18	454.75	637.45	852.47
10 (3.0)	26.85	93.92	196.35	332.02	500.67	703.75	944.54
11 (3.3)	29.16	102.14	213.77	362.04	547.11	771.28	1039.25
12 (3.7)	31.47	110.36	231.25	392.26	594.11	840.17	1136.92
13 (3.9)	33.78	118.59	248.78	422.70	641.74	910.56	1237.90
14 (4.3)	36.09	126.83	266.38	453.37	690.03	982.62	1342.58
15 (4.6)	38.40	135.08	284.04	484.29	739.06	1056.49	1451.40
16 (4.9)	40.71	143.34	301.78	515.49	788.88	1132.37	1564.81
17 (5.2)	43.02	151.61	319.59	546.97	839.56	1210.42	1683.35
18 (5.5)	45.33	159.90	337.48	578.76	891.16	1290.86	1807.62
19 (5.8)	47.64	168.20	355.46	610.89	943.75	1373.91	1938.27
20 (6.1)	49.96	176.51	373.53	643.36	997.41	1459.80	2076.06
25 (7.6)	62.53	218.33	465.40	811.78	1284.60	1942.02	2907.06
30 (9.1)	73.11	260.61	560.30	992.54	1612.56	2548.33	4123.51
35 (10.7)	84.72	303.46	658.95	1189.34	1998.78	3357.78	6162.33
40 (12.2)	96.40	346.97	762.14	1406.81	2466.77	4524.99	10461.3
45 (13.7)	107.99	391.24	870.79	1650.98	3058.41	6402.00	26153.2
50 (15.2)	119.66	436.39	985.93	1929.88	3841.27	10005.70	68070.5

**Table C-14. Quadrupole-loop quality factor at f = 40 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	24.62	36.14	43.82	49.33	53.42	56.48	58.74
7 (2.1)	24.95	36.58	44.31	49.79	53.81	56.76	58.85
8 (2.4)	25.21	36.94	44.68	50.14	54.08	56.89	58.80
9 (2.7)	25.43	37.23	44.98	50.40	54.24	56.91	58.61
10 (3.0)	25.6	137.47	45.22	50.58	54.33	56.83	58.31
11 (3.3)	25.77	37.67	45.41	50.72	54.34	56.68	57.90
12 (3.7)	25.90	37.84	45.57	50.80	54.31	56.45	57.41
13 (3.9)	26.02	37.99	45.69	50.85	54.22	56.16	56.84
14 (4.3)	26.12	38.11	45.78	50.86	54.09	55.81	56.18
15 (4.6)	26.21	38.22	45.86	50.85	53.93	55.41	55.46
16 (4.9)	26.29	38.31	45.91	50.81	53.72	54.96	54.67
17 (5.2)	26.36	38.39	45.95	50.75	53.49	54.47	53.82
18 (5.5)	26.42	38.46	45.97	50.66	53.22	53.93	52.90
19 (5.8)	26.48	38.52	45.98	50.56	52.92	53.34	51.92
20 (6.1)	26.54	38.57	45.98	50.44	52.60	52.72	50.88
25 (7.6)	26.74	38.72	45.81	49.59	50.61	49.02	44.85
30 (9.1)	26.88	38.75	45.44	48.40	48.04	44.43	37.50
35 (10.7)	26.97	38.70	44.91	46.91	44.96	39.01	28.93
40 (12.2)	27.04	38.59	44.25	45.14	41.38	32.80	19.22
45 (13.7)	27.08	38.43	43.46	43.11	37.11	25.85	8.45
50 (15.2)	27.11	38.22	42.55	40.83	32.83	18.19	-3.31

**Table C-15. Quadrupole-loop inductance in µH at f = 60 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	17.55	61.08	127.31	214.81	323.36	453.84	698.32
7 (2.1)	19.85	69.28	144.73	244.86	369.89	521.58	703.48
8 (2.4)	22.15	77.50	162.23	275.21	417.28	591.44	803.28
9 (2.7)	24.46	85.73	179.82	305.90	465.67	663.76	908.57
10 (3.0)	26.76	93.97	197.52	336.98	515.20	738.91	1020.35
11 (3.3)	29.06	102.23	215.32	368.49	566.00	817.32	1139.78
12 (3.7)	31.37	110.52	233.25	400.48	618.23	899.44	1268.22
13 (3.9)	33.68	118.82	251.32	432.99	672.04	985.81	1407.32
14 (4.3)	35.98	127.15	269.53	466.07	727.63	1077.63	1559.08
15 (4.6)	38.29	135.50	287.90	499.78	785.18	1173.78	1725.94
16 (4.9)	40.60	143.88	306.43	534.17	844.91	1276.87	1910.97
17 (5.2)	42.90	152.28	325.15	569.29	907.05	1387.23	2118.05
18 (5.5)	45.21	160.72	344.06	605.20	971.87	1505.96	2352.17
19 (5.8)	47.53	169.18	363.18	641.98	1039.65	1634.37	2619.87
20 (6.1)	49.84	177.68	382.51	679.68	1110.73	1774.02	2929.90
25 (7.6)	61.41	220.74	482.97	884.97	1530.25	2725.24	5781.94
30 (9.1)	73.02	264.88	591.16	1127.49	2116.11	4590.35	24158.9
35 (10.7)	84.67	310.38	709.46	1425.35	3027.21	10214.52	-14095.7
40 (12.2)	96.36	357.47	840.85	1808.24	4699.56	-77203.2	-5948.3
45 (13.7)	108.11	406.48	989.27	2329.10	8926.13	-10112.4	-3900.7
50 (15.2)	119.91	457.72	1160.02	3093.03	40376.3	-5506.1	-2956.9

**Table C-16. Quadrupole-loop quality factor at f = 60 kHz.**
Length ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
6 (1.8)	28.99	41.41	49.24	54.51	58.09	60.40	61.66
7 (2.1)	29.35	41.87	49.68	54.85	58.23	60.25	61.11
8 (2.4)	29.64	42.23	50.00	55.05	58.22	59.91	60.32
9 (2.7)	29.88	42.52	50.24	55.15	58.08	59.41	59.32
10 (3.0)	30.08	42.75	50.42	55.17	57.83	58.77	58.14
11 (3.3)	30.25	42.94	50.53	55.12	57.50	58.01	56.79
12 (3.7)	30.40	43.09	50.61	55.01	57.08	57.13	55.28
13 (3.9)	30.52	43.22	50.64	54.84	56.58	56.14	53.62
14 (4.3)	30.63	43.32	50.65	54.63	56.02	55.05	51.82
15 (4.6)	30.73	43.40	50.62	54.38	55.38	55.39	49.88
16 (4.9)	30.82	43.47	50.57	54.09	54.69	52.59	47.81
17 (5.2)	30.89	43.52	50.49	53.76	53.94	51.22	45.61
18 (5.5)	30.96	43.56	50.40	53.39	53.14	49.77	43.28
19 (5.8)	31.03	43.58	50.28	53.00	52.27	48.23	40.83
20 (6.1)	31.08	43.60	50.15	52.57	51.36	46.61	36.26
25 (7.6)	31.29	43.54	49.24	49.97	46.02	37.30	23.69
30 (9.1)	31.42	43.32	47.99	46.69	39.49	26.15	6.52
35 (10.7)	31.50	42.97	46.42	42.78	31.85	13.30	-12.97
40 (12.2)	31.54	42.51	44.57	38.28	23.18	-1.11	-34.45
45 (13.7)	31.56	41.96	42.46	33.21	13.53	-16.91	-57.64
50 (15.2)	31.56	41.31	40.08	27.59	2.97	-33.96	-82.23

**Table C-17. Circular-loop inductance in µH at f = 1 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	5.32	18.10	37.28	62.23	92.52	127.80	167.79
5 (1.5)	6.87	23.49	48.53	81.21	120.99	167.44	220.21
6 (1.8)	8.45	29.02	60.12	100.80	150.42	208.47	274.51
7 (2.1)	10.07	34.68	71.99	120.91	180.66	250.65	330.38
8 (2.4)	11.71	40.46	84.12	141.46	211.58	293.82	387.60

**Table C-18. Circular-loop quality factor at f = 1 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	1.03	1.74	2.37	2.95	3.49	4.00	4.48
5 (1.5)	1.06	1.81	2.47	3.08	3.65	4.19	4.69
6 (1.8)	1.09	1.86	2.55	3.18	3.78	4.34	4.87
7 (2.1)	1.11	1.90	2.61	3.27	3.88	4.46	5.01
8 (2.4)	1.13	1.94	2.67	3.34	3.98	4.57	5.14

**Table C-19. Circular-loop inductance in µH at f = 20 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	5.31	18.07	37.24	62.18	92.47	127.76	167.79
5 (1.5)	6.85	23.45	48.47	81.15	120.94	167.44	220.30
6 (1.8)	8.43	28.98	60.06	100.75	150.40	208.54	274.78
7 (2.1)	10.04	34.63	71.93	120.86	180.69	250.85	330.93
8 (2.4)	11.68	40.40	84.05	141.43	211.68	294.21	388.55

**Table C-20. Circular-loop quality factor at f = 20 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	15.16	23.32	29.46	34.34	38.35	41.72	44.61
5 (1.5)	15.57	23.99	30.31	35.32	39.42	42.86	45.79
6 (1.8)	15.90	24.53	30.99	36.09	40.26	43.75	46.72
7 (2.1)	16.19	24.98	31.55	36.73	40.95	44.47	47.46
8 (2.4)	16.43	25.37	32.03	37.26	41.53	45.07	48.07

**Table C-21. Circular-loop inductance in µH at f = 40 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	5.28	18.02	37.16	62.09	92.40	127.75	167.92
5 (1.5)	6.81	23.38	48.38	81.07	120.92	167.58	220.76
6 (1.8)	8.39	28.90	59.96	100.68	150.48	208.94	275.80
7 (2.1)	9.99	34.54	71.83	120.84	180.92	251.66	332.81
8 (2.4)	11.62	40.30	83.96	141.48	212.16	295.61	391.66

**Table C-22. Circular-loop quality factor at f = 40 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	21.85	32.30	39.59	45.08	49.38	52.86	55.74
5 (1.5)	22.40	33.11	40.56	46.13	50.47	53.97	56.83
6 (1.8)	22.84	33.77	41.33	46.95	51.31	54.80	57.63
7 (2.1)	23.21	34.31	41.95	47.61	51.98	55.44	58.23
8 (2.4)	23.53	34.77	42.48	48.16	52.52	55.95	58.66

**Table C-23. Circular-loop inductance in µH at f = 60 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	5.26	17.98	37.10	62.05	92.40	127.89	168.30
5 (1.5)	6.79	23.33	48.32	81.05	121.04	167.99	221.73
6 (1.8)	8.35	28.84	59.90	100.72	150.79	209.83	277.76
7 (2.1)	9.95	34.48	71.79	120.98	181.53	253.27	336.29
8 (2.4)	11.58	40.23	83.95	141.76	214.20	298.26	397.32

**Table C-24. Circular-loop quality factor at f = 60 kHz.**
Diameter ft (m)	1 Turn	2 Turn	3 Turn	4 Turn	5 Turn	6 Turn	7 Turn
4 (1.2)	25.89	37.38	45.06	50.65	54.92	58.28	60.99
5 (1.5)	26.50	38.25	46.05	51.69	55.95	59.26	61.88
6 (1.8)	27.00	38.94	46.83	52.47	56.70	59.95	62.45
7 (2.1)	27.42	39.51	47.45	53.09	57.27	60.41	62.76
8 (2.4)	27.77	39.99	47.97	53.59	57.70	60.71	62.89

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FHWA-HRT-06-139

Page Owner: Office of Research, Development, and Technology, Office of Operations, RDT

Keywords: Traffic detectors, sensors, detector installation, detector maintenance, signalized intersections, intersection safety, intersection treatments, infrared sensor, inductive loop, magnetometer, video image processor, microwave radar sensor, laser radar sensor, acoustic sensor, ultrasonic sensor, magnetic sensor
Scheduled Update: Archive - No Update needed

This page last modified on 03/08/2016