(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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This calculation is by no means complete and has \ several weaknesses, but it should be a good guide to get an estimate of the \ correct coil dimensions. This calculation considers only a single conductor \ wire wrapped in a thick solenoid coil; at high frequencies, litz wire \ significantly reduces eddy current losses. This calculation can be easily \ modified to include litz wire. Please send all revisions and corrections to \ Tom Kornack . \ \>", "Text"], Cell[CellGroupData[{ Cell["Definitions", "Section"], Cell["First we define the physical constants of our copper wire:", "Text"], Cell[BoxData[ \(\(consts = {\[IndentingNewLine]\[Mu]\_0 \[Rule] 4 \[Pi]\ 10\^\(-7\), \[IndentingNewLine]\ \[Sigma]\_Cu \[Rule] 1/\((1.68\ 10\^\(-8\))\)\ (*\ 1/\((Ohm\ m)\)\ *) \[IndentingNewLine]};\)\)], "Input"], Cell["\<\ We also declare a rough estimate of the parameters for our coil; \ we'll use these values to calculate things along the way but we'll be able to \ change and optimize things later.\ \>", "Text"], Cell[BoxData[ \(\(typical = {\[IndentingNewLine]Ic \[Rule] Icf, \[IndentingNewLine]l \[Rule] 4.0\ *\ 2.54/100\ , (*\ Length\ in\ m\ *) \[IndentingNewLine]h1 \[Rule] 0.406\ *\ 2.54/100\ , \[IndentingNewLine]h2 \[Rule] 0.800\ *\ 2.54/100, \[IndentingNewLine]d \[Rule] 0.0402\ *\ 2.54/100, (*\ Wire\ diameter\ in\ m\ *) \[IndentingNewLine]f \[Rule] 3000, (*\ Typical\ frequency, \ Hz\ *) \[IndentingNewLine]V \[Rule] 5\ (*\ Volts\ from\ supply\ *) \[IndentingNewLine]};\)\)], "Input"], Cell["\<\ We define the dimensions according to the following figure (d is \ the diameter of the wire, h1 in the inner diameter of the coil, h2 is the \ outer diameter of the coil, and l is the length of the coil):\ \>", "Text"], Cell[GraphicsData["PICT", "\<\ 000000000?D1I`0A0_l<0?on0000B00004P000000000m@5W0000000N00402P00 0000m@5W038000000?D1I`0OP0200800PP001Eo200000@000000000000000000 00400000000000000000040000000000000000000000@0000000m@5W00030000 00X02P000000m@5W0000LWAYIVH0000000000000001QL71/000000001001I`3e 04P0001800001El2004CE4U6AR0XEFiSKfe`LVEcLfET:@00000000000000000H ool00000000@`0002h0000300001000000000040000=`00 0400000000002000000000040000;`0003h0000F00000000000000000000;P00 03P0000R00000000004000050000300003`00015000000000040000000002`00 03P0000l00003P000080000000000`0002d00011000070000000000000000P00 00l000100000`000200000000002000 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"Input"], Cell["\<\ Here I provide two possible values for the length of the wire. For \ optimizations, we require an analytic expression so we use the approximation. \ Be sure to adjust the approximation if the geometry changes considerably. \ \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(LengthWireReal := \ Sum[Sum[2 \[Pi]\ h, {zpos, \(-l\)/2, l/2, d}], {h, h1, h2, d}]\ ;\)\ (*\ Length\ in\ meters\ *) \), "\[IndentingNewLine]", \(LengthWireReal /. typical\)}], "Input"], Cell[BoxData[ \(93.66507700230596`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(LengthWireApprox := \(\(2\) \(\[Pi]\)\(\ \)\(\(h1 + h2\)\/2\) \(\(h2 - h1\)\/d\) \(l\/d\) \(1.03\)\(\ \)\( (*\ Length\ in\ meters\ *) \)\)\), "\[IndentingNewLine]", \(LengthWireApprox /. typical\)}], "Input"], Cell[BoxData[ \(96.66566184855874`\)], "Output"] }, Open ]], Cell["Here's where we choose the value used, real or approximate:", "Text"], Cell[BoxData[ \(\(LengthWire := LengthWireApprox;\)\)], "Input"], Cell[BoxData[ \(Pounds := LengthWire\ *\ \(\(3.281/80\)\(\ \)\( (*\ lbs\ for\ 80\ ft/lb\ wire*) \)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(\[Delta] := \@\(2\/\(\[Mu]\_0\ \[Sigma]\_Cu\ \[Omega]\)\) /. consts;\)\ (*\ results\ in\ meters\ *) \[IndentingNewLine] \[Delta]\ 1000 /. typical\)\(\ \)\( (*\ mm\ *) \)\)\)], "Input"], Cell[BoxData[ \(1.191006536922753`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(CoilVolume := \[Pi]\ \((h2\^2 - h1\^2)\) l;\)\[IndentingNewLine] CoilVolume*\ 10\^6 /. typical\)\(\ \)\( (*\ cm\^3\ *) \)\)\)], "Input"], Cell[BoxData[ \(97.84858361577983`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Area := \(\[Pi]\ d\^2\)\/4\[IndentingNewLine] Area*10\^6 /. typical\)\(\ \)\( (*\ mm\^2\ *) \)\)\)], "Input"], Cell[BoxData[ \(0.81885955452072`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(EffArea := \[Pi]\ d\ \[Delta]\[IndentingNewLine] EffArea*10\^6 /. typical\)\(\ \)\( (*\ mm\^2\ *) \)\)\)], "Input"], Cell[BoxData[ \(3.820531524487136`\)], "Output"] }, Open ]], Cell["Consider a resonant circut as follows:", "Text"], Cell[GraphicsData["PICT", "\<\ 000000000C81h00A0_l<0?on0000B00004P000000001oooooooooooooooooooooooooooooooooooooooooooooooooo ooonnO3RgmkPi>goooooooo`bi000000@i3ooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooolLI=0000001OWM7oooooooonooooooooookooooo ome_4@00000XM;Ooooooooono_ooooojkMbiZ:2OYZVTX:>hb=Sfoooooooooooo ooono?K]j^[[kO?oooooooo`bi000000@i3ooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooccY@0000002n/goWooooooooooooooooooooooooo oooH/Hm_LG1lUKcooooooooooogAZghA00000000000000000000=FVhe^[ooooo ooo`bH/00000;8Soooooooo`bi000000@i3ooooooooooooooooooooooooooooo