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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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 Turn
6 (1.8) 10.5336.0274.46124.67185.81257.24338.44
7 (2.1) 11.5239.4981.72136.94204.23282.91372.40
8 (2.4) 12.5142.9488.94149.12222.52308.38406.08
9 (2.7) 13.5046.3896.12161.25240.71333.71439.58
10 (3.0) 14.4849.80103.28173.32258.83358.94472.94
11 (3.3) 15.4653.22110.42185.37276.90384.09506.20
12 (3.7) 16.4456.63117.54197.39294.93409.19539.38
13 (3.9) 17.4260.04124.65209.39312.93434.25572.51
14 (4.3) 18.4063.44131.76221.38330.91459.27605.59
15 (4.6) 19.3766.84138.85233.35348.87484.27638.63
16 (4.9) 20.3570.23145.95245.32366.81509.24671.64
17 (5.2) 21.3273.63153.03257.27384.74534.09704.63
18 (5.5) 22.3077.02160.12269.22402.66559.13737.59
19 (5.8) 23.2780.41167.20281.16420.57584.06770.54
20 (6.1) 24.2583.80174.27293.10438.47608.97803.47
25 (7.6) 29.12100.74209.63352.73527.89733.42967.96
30 (9.1) 33.98117.66244.95412.31617.22857.751132.29
35 (10.7) 38.84134.57280.25471.85706.51982.001296.52
40 (12.2) 43.71151.48315.55531.38795.761106.211460.70
45 (13.7) 48.57168.38350.83590.89885.001230.401624.85
50 (15.2) 53.43185.28386.11650.39974.221354.561788.98
 
Table C-2. Rectangular-loop quality factor at f = 1 kHz.
Length ft (m)1 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 4.404.94
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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 44.6447.51
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 44.0745.95
 
Table C-5. Rectangular-loop inductance in µH at f = 40 kHz.
Length ft (m)1 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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) 38.58 134.62 283.16484.52 743.73 1071.721488.10
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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 38.8246.64 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 2.303.17 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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) 36.23 126.79 264.76 446.39 669.68934.00 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) 61.73 217.17 455.85773.93 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) 119.75425.01 905.26 1575.59 2483.09 3727.59 5514.46
 
Table C-12. Quadrupole-loop quality factor at f = 20 kHz.
Length ft (m)1 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 Turn
6 (1.8) 17.61 61.14 127.09 213.56 319.54444.65 589.12
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 1612.562548.33 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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) 25.6137.47 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 1173.781725.94
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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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) 31.5641.31 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 34.5471.83 120.84 180.92 251.66 332.81
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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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 Turn2 Turn3 Turn4 Turn5 Turn6 Turn7 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
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United States Department of Transportation - Federal Highway Administration