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[null,null,"Small Magnetic Loop Antenna Calculator ver. 1.22a"]
[null,null,"by Steve Yates"]
[null,null,"AA5TB"]
[null,null,"aa5tb@yahoo.com"]
[null,null,"Updated April 28, 2009"]
[]
[null,"Input the following parameters:"]
[]
[null,"Design Frequency =",7,"MHz"]
[null,"Loop Diameter =",4.7,"feet",1.43256,"m"]
[null,"Small loop diameter =",0.9400000000000001,"feet",0.286512,"m"]
[null,"Conductor Diameter =",0.4,"inches",10.16,"mm"]
[null,"Added Loss Resistance =",0,"milliohms"]
[null,"RF Power = ",6,"Watts"]
[]
[null,"Calculated Results:"]
[]
[null,"Bandwidth =",8.599297586969506,"kHz (-3 dB points)"]
[null,"Efficiency =",20.07171388587198,"%",-6.974155423407462,"dB"]
[null,"Loop Area =",17.349445429449634,"ft²",1.6118162227099766,"m²"]
[null,"Radiation Resistance =",24.42755809434743,"mΩ"]
[null,"Total Loss Resistance =",97.27384833881933,"mΩ"]
[null,"Loop Circumference =",14.765485471872028,"ft ",4.500519971826594,"m"]
[null,"Wavelength Percentage =",10.508464107829788,"% λ"]
[null,"Loop Inductance =",4.504875013146343,"μH"]
[null,"Distributed Capacitance =",12.107698086935063,"pF"]
[null,"Q (Quality Factor) =",814.0199742136012]
[null,"Tuning Capacitor =",114.75231010697304,"pF"]
[null,"Capacitor Voltage =",983.7244896877345,"V"]
[null,"Minimum Plate Spacing =",13.116326529169793,"mils (1/1000 in)",0.33315469384091273,"mm"]
[]
["Notes:"]
[null,"1. To truly be considered a small loop, the Loop Circumference should be less "]
[null,"    then 10 % λ.  Larger loops will have greater efficiency but smaller nulls. "]
[null,"2. To see the effects of bad joints, etc., input realistic values into the Added  "]
[null,"    Loss Resistance box."]
[null,"3. The sheets are protected to prevent the user that is unfamiliar with Excel from"]
[null,"    accidentally corrupting formulas.  To unlock the sheets use the password aa5tb."]
[null,"4. This application is free to use as you wish.  If you modify it and pass it on all"]
[null,"    that I ask is that you give me credit for my part of the work. Thanks!"]

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[null,null,"Small Loop Equations for a Copper Loop"]
[null,null,"(circular loop assumed, results may vary with other shapes) "]
[]
[null,null,"Radiation Resistance, Ohms: RR = (3.38×10↑-8)(f²A)²"]
[null,null,"Loss Resistance, Ohms: RL = (9.96×10↑-4)(√f)(S/d)"]
[null,null,"Efficiency: η = RR/(RR+RL)"]
[null,null,"Inductance, Henrys: L = (1.9×10↑-8)S[7.353log10(96S/πd)-6.386]"]
[null,null,"Inductive Reactance, Ohms: XL = 2πf(L×10↑6)"]
[null,null,"Tuning Capacitor, Farads: CT = 1/2πf(XL×10↑6)"]
[null,null,"Quality Factor: Q = (f×10↑6)/Δf = XL/2(RR + RL)"]
[null,null,"Bandwidth, Hertz: Δf = (f×10↑6)/Q = [(f1-f2)×10↑6]"]
[null,null,"Distributed Capacity: pF: CD = 0.82S"]
[null,null,"Capacitor Potential, Volts: VC = √(PXLQ)"]
[null,null,"Capacitor Voltage Rating: 75,000V/in"]
[]
[null,"where "]
[null,null,"f = operating frequency, MHz"]
[null,null,"A = area of loop, square feet"]
[null,null,"S = conductor length, feet"]
[null,null,"d = conductor diameter, inches"]
[null,null,"η = decimal value; dB = 10 log10η"]
[null,null,"P = transmitter power, Watts"]
[]
["Ref. ","The American Radio Relay League, The ARRL Antenna Handbook, "]
[null,"Small High Efficiency Loop Antennas for Transmitting,  "]
[null,"Publication No. 15, p. 5-14, Table 4, 1988"]

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[]
["Givens:"]
["π =",3.141592653589793]
["Loop Diameter D=",56.400000000000006,"inches",1.43256,"m"]
["Conductor Diameter d=",0.4,"inches",0.01016,"m"]
["Added Loss Resistance RL=",0,"mΩ",0,"Ω"]
["RF Power P=",6,"Watts"]
["Frequency F=",7,"MHz",7000000,"Hz"]
[null,1128]
["Calculations:"]
["Loop Circumference S= ",14.765485471872028,"ft",4.500519971826594,"m"]
["Loop Area A=",17.349445429449634,"ft²",1.6118162227099766,"m²"]
["Radiation Resistance RR=",0.024427558094347428,"Ω",24.42755809434743,"mΩ"]
["Loss Resistance RL=",0.09727384833881933,"Ω",97.27384833881933,"mΩ"]
["Total Loss Resistance RT=",0.09727384833881933,"Ω",97.27384833881933,"mΩ"]
["Efficiency η=",0.20071713885871978,null,20.07171388587198,"%",-6.974155423407462,"dB"]
["Inductance L=",4.5048750131463425e-06,"H",4.504875013146343,"μH"]
["Inductive Reactance XL=",198.13475145297082,"Ω"]
["Tuning Capacitor CT=",1.1475231010697305e-10,"F",114.75231010697304,"ρF"]
["Quality Factor Q=",814.0199742136012]
["Bandwidth ΔF= ",8599.297586969506,"Hz",8.599297586969506,"kHz"]
["Distributed Capacity CD=",12.107698086935063,"ρF"]
["Capacitor Potential VC=",983.7244896877345,"V"]
["Minimum Plate Spacing PS=",0.013116326529169792,"in",13.116326529169793,"mils",0.33315469384091273,"mm"]
["Wavelength λ=",140.50998117,"ft",42.82757142857143,"m"]
["Circumference % λ=",10.508464107829788,"%"]
[]
[null,"Radiation","Loss","Total Loss",null,"Inductive","Tuning","Quality",null,"Capacitor","Minimum"]
["Frequency","Resistance","Resistance","Resistance","Efficiency","Reactance","Capacitor","Factor","Bandwidth","Potential","Spacing","Wavelength","Circumference"]
["F","RR","RL","RT","η","XL","CT","Q","ΔF","VC","PS","λ","% λ"]
["MHz","mΩ","mΩ","mΩ","dB","Ω","ρF",null,"kHz","V","mils","m"]
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[2,0.16278256122847098,51.995059025267345,51.995059025267345,-25.05711733565265,56.60992898656309,1405.7157988104198,542.6789842586197,3.685420032862149,429.3321704325031,5.724428939100042,149.8965,3.0024183165227964]
[3,0.8240867162191344,63.68068187889914,63.68068187889914,-18.93618907949405,84.91489347984462,624.7625772490755,658.2063258984468,4.557841336308979,579.0933606151594,7.721244808202126,99.931,4.503627474784195]
[4,2.6045209796555358,73.53211764992268,73.53211764992268,-14.658658390901431,113.21985797312618,351.42894970260494,743.5307101221406,5.379737441299386,710.7001114338723,9.476001485784964,74.94825,6.004836633045593]
[5,6.358693797987147,82.2114067973696,82.2114067973696,-11.439192258402384,141.52482246640773,224.91452780966713,798.942428173256,6.25827321679769,823.6632272043013,10.982176362724017,59.958600000000004,7.506045791306991]
[6,13.18538745950615,90.05808397430575,90.05808397430575,-8.937697024437702,169.82978695968924,156.1906443122689,822.472281303351,7.29507867486057,915.4680518095572,12.206240690794095,49.9655,9.00725494956839]
[7,24.42755809434743,97.27384833881933,97.27384833881933,-6.974155423407461,198.13475145297082,114.75231010697304,814.0199742136012,8.599297586969504,983.7244896877345,13.116326529169793,42.82757142857143,10.508464107829788]
[8,41.67233567448857,103.99011805053469,103.99011805053469,-5.434997787719894,226.43971594625236,87.85723742565123,777.2755097676637,10.292360816039718,1027.6362556189858,13.701816741586478,37.474125,12.009673266091186]
[9,66.75102401374987,110.29817647488402,110.29817647488402,-4.236360374195545,254.74468043953388,69.41806413878616,719.417765616761,12.510116416550053,1048.6215202957603,13.981620270610136,33.31033333333333,13.510882424352586]
[10,101.73910076779435,116.26448647461176,116.26448647461176,-3.309757452130419,283.04964493281545,56.228631952416784,649.1857508245547,15.403911726803356,1050.0051321769815,14.00006842902642,29.979300000000002,15.012091582613982]
[11,148.9562174341277,121.9392221425317,121.9392221425317,-2.5974305852387554,311.35460942609694,46.46994376232794,574.6767275090805,19.141196212484854,1036.131983986183,13.815093119815774,27.25390909090909,16.513300740875383]
[12,210.9661993520984,127.36136375779827,127.36136375779827,-2.051245016968399,339.6595739193785,39.04766107806722,501.968522453858,23.905881471089785,1011.4299218164866,13.485732290886489,24.98275,18.01450989913678]
[13,290.57704570289746,132.56191029012342,132.56191029012342,-1.6322170621043486,367.96453841266015,33.27137985350105,434.8034294657678,29.8985682242037,979.7721466451663,13.063628621935552,23.061,19.51571905739818]
[14,390.84092950955886,137.56599558498186,137.56599558498186,-1.3096846320762723,396.26950290594164,28.68807752674326,374.9662278130084,37.336695844996605,944.2065897947659,12.589421197263546,21.413785714285716,21.016928215659576]
[15,515.0541976369591,142.3943335347575,142.3943335347575,-1.0600882846295354,424.5744673992232,24.99050308996302,322.89559354748195,46.45464447254603,906.9505763468422,12.09267435129123,19.9862,22.518137373920975]
[16,666.7573707918172,147.06423529984536,147.06423529984536,-0.8656139034692212,452.8794318925047,21.96430935641281,278.2424480393409,57.50380688764551,869.5180796157252,11.593574394876336,18.7370625,24.01934653218237]
[17,849.7351435226955,151.59034397298797,151.59034397298797,-0.7129169046633209,481.1843963857863,19.45627403197813,240.27371838363428,70.75264042343933,832.8840164673499,11.105120219564665,17.634882352941176,25.520555690443775]
[18,1068.016384219998,155.985177075802,155.985177075802,-0.5920405661544258,509.48936087906776,17.35451603469654,208.1244734441729,86.48670529767514,797.6360258602823,10.635147011470432,16.655166666666666,27.02176484870517]
[19,1325.8741351159729,160.25953497027828,160.25953497027828,-0.4955557517398581,537.7943253723492,15.575798324769197,180.9374002478314,105.00869347064537,764.0959642646043,10.187946190194724,15.778578947368421,28.522974006966567]
[20,1627.8256122847097,164.4228135947392,164.4228135947392,-0.4179033021132943,566.0992898656309,14.057157988104196,157.92991688299247,126.6384507427915,732.4097779085155,9.765463705446873,14.989650000000001,30.024183165227964]
[21,1978.6322056421413,168.4832475705845,168.4832475705845,-0.35490323959215614,594.4042543589125,12.750256678552558,138.41925767650412,151.7129939323799,702.6108267659271,9.368144356879029,14.275857142857143,31.525392323489363]
[22,2383.299478946043,172.44810173919396,172.44810173919396,-0.3033934031443099,622.7092188521939,11.617485940581984,121.82525840154284,180.58652440930413,674.6630781168839,8.99550770822512,13.626954545454545,33.02660148175077]
[23,2847.0771697960345,176.3238239007194,176.3238239007194,-0.2609651265512481,651.0141833454755,10.629230992895423,107.66256025957567,213.63043888745295,648.4898784604308,8.646531712805745,13.034478260869566,34.52781064001216]
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[27,5406.832945113741,191.04204563669742,191.04204563669742,-0.1508024437879256,764.2340413186017,7.713118237642908,68.26108501720492,395.5401528293135,559.4682021392699,7.459576028523599,11.103444444444445,40.532647273057755]
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