calculator:inductance_of_straight_round_magnetic_wire
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| calculator:inductance_of_straight_round_magnetic_wire [2025/01/11 18:44] – created stan_zurek | calculator:inductance_of_straight_round_magnetic_wire [2025/02/08 16:32] (current) – stan_zurek | ||
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| ==== Calculator of inductance of a straight round magnetic wire ==== | ==== Calculator of inductance of a straight round magnetic wire ==== | ||
| - | {{page> | + | <box 100% # |
| + | |< 100% 10% 90% >| | ||
| + | | | ||
| + | | {{/ | ||
| + | </ | ||
| - | {{page> | ||
| - | <WRAP lo right>//[[https://www.e-magnetica.pl/doku.php/ | + | <box 30% right #f0f0f0> |
| + | Definition of the dimensions of a **straight round wire** | ||
| + | [[/file/inductance_of_straight_round_wire_png|{{/inductance_of_straight_round_wire.png}}]] | ||
| + | {{page> | ||
| + | </box> | ||
| - | [[/ | + | [[/ |
| < | < | ||
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| var d = frm.d.value | var d = frm.d.value | ||
| var l = frm.l.value | var l = frm.l.value | ||
| - | var result1a | + | var ur = frm.ur.value |
| - | var result1b | + | var result1 |
| - | var result2 | + | var result2 |
| - | var result3a | + | |
| - | var result3b | + | var result_avg = " |
| - | var result3c | + | |
| - | var result4 | + | |
| - | var result_avg | + | |
| var d_unit | var d_unit | ||
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| var result1_unit | var result1_unit | ||
| - | var result2_unit | ||
| - | var result3a_unit | ||
| - | var result3b_unit | ||
| - | var result4a_unit | ||
| - | var result4b_unit | ||
| - | var result4c_unit | ||
| - | |||
| - | |||
| - | var result_avg_unit = getSelectedValue(frm.result_avg_unit) | ||
| const pi = 3.14159265358979 | const pi = 3.14159265358979 | ||
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| // calculate inductance | // calculate inductance | ||
| // Rosa (1) | // Rosa (1) | ||
| - | result1 = result1_unit | + | result1 = result1_unit * mu0 * l * (Math.log(2*l/ |
| - | + | ||
| - | // Grover (2) | + | |
| - | result2 = result2_unit | + | |
| - | + | ||
| - | // Paul (3a,b) | + | |
| - | result3a = result3a_unit * mu0 * l * (Math.asinh(l/ | + | |
| - | result3b = result3b_unit * mu0 * l * (Math.log(2*l/ | + | |
| - | + | ||
| - | // King & Prasad (4a) | + | |
| - | result4a = result4a_unit * mu0 * l * (Math.log(2*l/ | + | |
| - | + | ||
| - | // Meinke & Gundlach (4b) | + | |
| - | result4b = result4b_unit * mu0 * l * (Math.log(10*l/ | + | |
| - | + | ||
| - | // Aebischer & Aebischer (4c) | + | |
| - | result4c = result4c_unit * mu0 * l * (Math.log((l+Math.sqrt(l*l+r*r))/ | + | |
| - | + | ||
| - | + | ||
| - | + | ||
| - | // average of all | + | |
| - | sum = result1/ | + | |
| - | result_avg = result_avg_unit * sum / 7 | + | |
| // format number to x digits precision, result will equal 1.234e+2 | // format number to x digits precision, result will equal 1.234e+2 | ||
| result1 | result1 | ||
| - | result2 | ||
| - | result3a = result3a.toPrecision(5) | ||
| - | result3b = result3b.toPrecision(5) | ||
| - | result4a = result4a.toPrecision(5) | ||
| - | result4b = result4b.toPrecision(5) | ||
| - | result4c = result4c.toPrecision(5) | ||
| - | result_avg = result_avg.toPrecision(5) | ||
| // display result | // display result | ||
| frm.result1.value = result1 | frm.result1.value = result1 | ||
| - | frm.result2.value = result2 | ||
| - | frm.result3a.value = result3a | ||
| - | frm.result3b.value = result3b | ||
| - | frm.result4a.value = result4a | ||
| - | frm.result4b.value | ||
| - | frm.result4c.value | ||
| - | frm.result_avg.value = result_avg | ||
| } | } | ||
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| - | //Note: Several assumptions are made for all these equations: 1) The return path is **not** considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than it radius (r << l), and for r ≈ l the calculation | + | //Note: Several assumptions are made for all these equations: 1) The return path is **not** considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than it radius (r << l), otherwise |
| </ | </ | ||
| - | <WRAP lo> | ||
| - | ^ [1] Source: Edward B. Rosa, The self and mutual inductance of linear conductors, Department of Commerce and Labor, Bulletin of the Bureau of Standards, Volume 4, 1907-8, Washington, 1908 ^^^ | ||
| - | | **(1)** \\ //Rosa [1], eq. (9), p. 305// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{r}{l} | ||
| - | ^ //[2] Source: F.W. Grover, Inductance Calculations: | ||
| - | | **(2)** \\ //Grover [2], eq. (7), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - \frac{3}{4} \right) $$ | (H) | | ||
| - | ^ //[3] Source: C.R. Paul. Inductance: Loop and Partial, Wiley-IEEE Press, 2009, New Jersey, ISBN 9780470461884// | ||
| - | | **(3a)** \\ //Paul [3], full eq. (5.18b), p. 208// | ||
| - | | **(3b)** \\ //Paul, [3] simplified eq. (5.18c), p. 208 (for r << l) \\ and for high-frequency (skin depth δ ≈ 0) // | $$ L ≈ \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 \right) $$ | (H) | | ||
| - | ^ //[4] Source: Aebischer H.A., Aebischer B., Improved formulae for the inductance of straight wires. Advanced electromagnetics. 2014 Sep 8; | ||
| - | | **(4a)** \\ //King & Prasad [4] eq. (28), p. 34// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 + \frac{r}{l} \right) $$ | (H) | | ||
| - | | **(4b)** \\ //Meinke & Gundlach [4], eq. (29), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{10⋅l}{4⋅r} \right) - 1 \right) $$ | (H) | | ||
| - | | **(4c)** \\ //Aebischer & Aebischer [4], eq. (34), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{0.905415⋅r}{l} | ||
| - | | where: $μ_0$ - [[/ | ||
| - | </ | ||
| + | ^ Inductance of a straight round magnetic wire or conductor | ||
| + | | // Sources: [1] Edward B. Rosa, The self and mutual inductance of linear conductors, Department of Commerce and Labor, Bulletin of the Bureau of Standards, Volume 4, 1907-8, Washington, 1908, \\ [2] F.W. Grover, Inductance Calculations: | ||
| + | | **(1)** \\ //[1] Rosa, eq. (11), p. 305// \\ and //[2] Grover, eq. (8), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 + \frac{μ_r}{4} \right) $$ | (H) | | ||
| + | | where: $μ_0$ - [[/magnetic permeability of vacuum]] (H/m), $l$ - wire length (m), $r$ - wire radius (m), $μ_r$ - [[/relative magnetic permeability]] of the wire (unitless) | ||
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| + | <box 100% # | ||
| + | {{page> | ||
| - | {{tag> | + | {{tag> |
calculator/inductance_of_straight_round_magnetic_wire.1736617479.txt.gz · Last modified: 2025/01/11 18:44 by stan_zurek