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<!DOCTYPE html>
< html lang = "en" >
< head >
< meta charset = "UTF-8" >
< meta name = "viewport" content = "width=device-width, initial-scale=1.0" >
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< title > VK3CPU RF Inductor Calculator< / title >
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< link rel = "stylesheet" href = "inductor.css" >
< / head >
< body >
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< header > Miguel < a href = "mailto:vk3cpu@gmail.com" > VK3CPU< / a > - RF Inductor Calculator< br > < a href = "inductor_imp.html" > [Wire Imperial]< / a > < a href = "inductor_lrg.html" > [Coax Metric]< / a > < / header >
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< section class = "gridLayoutClass" >
< div id = "inductor-container" class = "inductor-container" style = "position: relative;" >
< canvas id = "inductor2D" class = "inductorClass" width = "350" height = "350" >
< / canvas >
< / div >
< div class = "slider_container" >
< div class = "sliders" >
< label for = "conductor_diameter_slider" > & #8960a:< / label >
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< input type = "range" id = "conductor_diameter_slider" min = "0.1" max = "4.0" value = "1.0" step = "0.05" >
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< / div >
< div class = "sliders" >
< label for = "loop_diameter_slider" > & #8960b:< / label >
< input type = "range" id = "loop_diameter_slider" min = "5.0" max = "50.0" value = "10.0" step = "0.1" >
< / div >
< div class = "sliders" >
< label for = "loop_spacing_slider" > c/a:< / label >
< input type = "range" id = "loop_spacing_slider" min = "1.1" max = "4.0" value = "2.0" step = "0.01" >
< / div >
< div class = "sliders" >
< label for = "loop_turns_slider" > N:< / label >
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< input type = "range" id = "loop_turns_slider" min = "2" max = "100" value = "8.0" step = "1.0" >
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< / div >
< div class = "sliders" >
< label for = "frequency_slider" > f:< / label >
< input type = "range" id = "frequency_slider" min = "1.0" max = "30.0" value = "7.0" step = "0.1" >
< / div >
< / div >
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< div id = "notes" class = "notes" >
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< br >
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< b > < u > Notes:< / u > < / b > < br >
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RF Inductor Calculator was developed to help users predict the RF characteristics of a single-layer solenoid-style air-core inductor. < br > < br >
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< u > Inputs via the slider widgets:< / u >
< ul >
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< li > & #8960a : Conductor diameter in millimeters (mm). Estimated equivalent AWG wire size is also displayed where appropriate.< / li >
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< li > & #8960b : Loop diameter in millimeters (mm).< / li >
< li > c/a : 'c' is the inter-winding spacing, and 'a' is the conductor diameter, so 'c/a' is the spacing ratio. (Must be >= 1.1)
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A low-value will increase the resistance due to the proximity effect.< / li >
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< li > N : Number of turns or windings.< / li >
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< li > f : The frequency of interest (MHz) for some of the calculations.< / li >
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< / ul >
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< p > Characteristics on the left are independent of frequency, while the characteristics on the right are dependent on the selected frequency. < br > < br >
Each of the graphic representations attempt to keep the relative geometry correct, without exceeding the drawing boundary. The coil diameter
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relative to the conductor diameter are representative. < / p >
< u > Calculated dimensions:< / u >
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< ul >
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< li > & #8960o : Outer loop diameter (mm) < / li >
< li > & #8960i : Inner loop diameter (mm) - corresponds to the diameter of the winding former.< / li >
< li > c : Distance between windings, measured from the conductor centers (mm).< / li >
< li > & #8467 : Length of the coil (mm). Equal to c x N.< / li >
< / ul >
< u > Calculated parameters:< / u >
< ul >
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< li > L : Inductance is calculated using Nagaoka's equation incorporating his coefficient.< / li >
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< li > C : Capacitance is calculated using Knight's 2016 paper on self-resonance and self-capacitance of solenoid coils.< / li >
< li > Rdc : DC resistance is calculated using conductor length divided by the conductor cross-sectional area, assuming a copper conductor.< / li >
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< li > SRF : Self-resonant frequency (MHz) for the unloaded coil. Currently using a lumped reactances model. (Looking into modifying the model to
use the conductor length and velocity factor as described by Knight (2016).< / li >
< li > Xl : Inductive reactance at the given frequency. (& #937)< / li >
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< li > & #948 : Skin depth due to skin effect (& #956m)< / li >
< li > Rac : AC resistance is calculated using the skin effect and proximity resistance from empirical data collected by Medhurst using the spacing ratio, and length-to-diameter ratio.< / li >
< li > Q : Quality factor of device, based on reactance (X) & #247 resistance (Rac) at the given frequency.< / li >
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< / ul >
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< / div >
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< / section >
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< script src = "https://cdnjs.cloudflare.com/ajax/libs/mathjs/7.5.1/math.min.js" > < / script >
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< script src = "inductor.js" > < / script >
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< script >
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// Define global storage for calculated values, so we don't recalculate the same things multiple times:
var inductor = {
L : 0.0,
C : 0.0,
Rdc : 0.0,
SRF : 0.0,
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f : 0.0,
Xl : 0.0,
Xc : 0.0,
Z : 0.0,
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skin_depth : 0.0,
Rac : 0.0,
Q : 0.0
};
// Solve all the parameters, and re-draw the canvas:
function recalculate() {
// Input variables:
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const loop_diameter_meters = 0.001 * loop_diameter_slider.value;
const cond_diameter_meters = 0.001 * conductor_diameter_slider.value;
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const spacing_ratio = 1.0 * loop_spacing_slider.value;
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const loop_turns = 1.0 * loop_turns_slider.value;
const frequency_hz = 1e6 * frequency_slider.value;
// Frequency independent characteristics:
inductor.L = getInductance(loop_diameter_meters, cond_diameter_meters, spacing_ratio, loop_turns);
inductor.C = multiloopCapacitance(loop_diameter_meters, cond_diameter_meters, spacing_ratio, loop_turns);
inductor.Rdc = dcResistance(loop_diameter_meters, cond_diameter_meters, spacing_ratio, loop_turns);
inductor.SRF = selfResonantFrequency(inductor.L, inductor.C);
// Frequency dependent characteristics:
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inductor.f = frequency_hz;
inductor.Xl = inductiveReactance(frequency_hz, inductor.L);
inductor.Xc = capacitiveReactance(frequency_hz, inductor.C);
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inductor.skin_depth = skinDepth(frequency_hz);
inductor.Rac = acResistance(loop_diameter_meters, cond_diameter_meters, spacing_ratio, loop_turns, frequency_hz);
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inductor.Q = qualityFactor(inductor.Xl, inductor.Rac);
// Calculate impedance:
var Zl = math.complex(inductor.Rac, inductor.Xl);
var Zc = math.complex(0, inductor.Xc);
inductor.Z = math.divide(math.multiply(Zl, Zc), math.add(Zl, Zc)).toPolar();
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// Redraw the canvas:
drawDesign();
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}
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loop_diameter_slider.oninput = function() {
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recalculate();
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}
conductor_diameter_slider.oninput = function() {
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recalculate();
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}
loop_turns_slider.oninput = function() {
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recalculate();
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}
loop_spacing_slider.oninput = function() {
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recalculate();
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}
frequency_slider.oninput = function() {
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recalculate();
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}
window.onresize = function() {
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recalculate();
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}
window.onorientationchange = function() {
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recalculate();
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}
window.onbeforeprint = function() {
console.log("onbeforeprint");
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drawDesign();
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}
const afront_canvas = document.getElementById("inductor2D");
const fctx = afront_canvas.getContext('2d');
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function drawDesign() {
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const win_width = document.getElementById("inductor-container").clientWidth;
const win_height = document.getElementById("inductor-container").clientHeight;
afront_canvas.width = win_width-12;
afront_canvas.height = win_height-12;
fctx.clearRect(0, 0, win_width, win_height);
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const loop_radius = 0.11 * win_height; // 100; // loop_diameter_slider.value * 80;
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var cond_radius = loop_radius * conductor_diameter_slider.value / loop_diameter_slider.value;
const loopx = win_width/2;
const loopy = win_height/4;
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fctx.font = "bold 14px arial";
fctx.textAlign = "center";
fctx.fillText("Wire - Metric", win_width*0.5, 18);
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// Draw loop ends first, then draw the loop after:
fctx.strokeStyle = "grey";
fctx.beginPath();
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fctx.arc(loopx - 0.5*loop_radius, loopy + 1.414*loop_radius, 0.5 * loop_radius, 0.0, -0.40 * Math.PI, true);
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fctx.lineWidth = cond_radius * 2.0;
fctx.stroke();
fctx.strokeStyle = "black";
fctx.beginPath();
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fctx.arc(loopx + 0.5*loop_radius, loopy + 1.414*loop_radius, 0.5 * loop_radius, Math.PI, -0.60 * Math.PI, false);
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fctx.lineWidth = cond_radius * 2.0;
fctx.stroke();
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// Draw loop:
fctx.beginPath();
fctx.arc(loopx, loopy, loop_radius, 0.0, 2.0 * Math.PI, false);
fctx.stroke();
fctx.lineWidth = 1.0;
// Draw loop diameter arrow:
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const y_offset = loopy + loop_radius + 20;
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var arrow_size = 10.0;
fctx.beginPath();
fctx.moveTo(loopx - loop_radius, loopy);
fctx.lineTo(loopx - loop_radius, y_offset);
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fctx.lineTo(loopx - loop_radius - arrow_size, y_offset - arrow_size);
fctx.lineTo(loopx - loop_radius - arrow_size, y_offset + arrow_size);
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fctx.lineTo(loopx - loop_radius, y_offset);
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fctx.lineTo(loopx - loop_radius - 3.0*arrow_size, y_offset);
fctx.stroke();
fctx.beginPath();
fctx.moveTo(loopx + loop_radius, loopy);
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fctx.lineTo(loopx + loop_radius, y_offset);
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fctx.lineTo(loopx + loop_radius + arrow_size, y_offset - arrow_size);
fctx.lineTo(loopx + loop_radius + arrow_size, y_offset + arrow_size);
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fctx.lineTo(loopx + loop_radius, y_offset);
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fctx.lineTo(loopx + loop_radius + 3.0*arrow_size, y_offset);
fctx.stroke();
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// Write conductor diameter symbol:
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fctx.font = "12px arial";
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const cond_dia = 1.0 * conductor_diameter_slider.value;
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fctx.textAlign = "right";
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fctx.fillText("\u2300a = " + cond_dia.toFixed(3).toString() + "mm", loopx - loop_radius - 2.0*arrow_size, loopy - 6);
// Write loop diameter symbol:
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const loop_dia = 1.0 * loop_diameter_slider.value; // Convert from mm to inches
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fctx.fillText("\u2300b = " + loop_dia.toFixed(2).toString() + "mm", loopx - loop_radius - 2.0*arrow_size, y_offset - 2);
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// Draw inner-diameter arrows: (for using a winding former)
const inner_dia_y = loopy + loop_radius + 40;
fctx.beginPath();
fctx.moveTo(loopx - loop_radius + cond_radius, loopy);
fctx.lineTo(loopx - loop_radius + cond_radius, inner_dia_y);
fctx.lineTo(loopx - loop_radius + cond_radius - arrow_size, inner_dia_y - arrow_size);
fctx.lineTo(loopx - loop_radius + cond_radius - arrow_size, inner_dia_y + arrow_size);
fctx.lineTo(loopx - loop_radius + cond_radius, inner_dia_y);
fctx.lineTo(loopx - loop_radius - 3.0*arrow_size, inner_dia_y);
fctx.stroke();
fctx.beginPath();
fctx.moveTo(loopx + loop_radius - cond_radius, loopy);
fctx.lineTo(loopx + loop_radius - cond_radius, inner_dia_y);
fctx.lineTo(loopx + loop_radius - cond_radius + arrow_size, inner_dia_y - arrow_size);
fctx.lineTo(loopx + loop_radius - cond_radius + arrow_size, inner_dia_y + arrow_size);
fctx.lineTo(loopx + loop_radius - cond_radius, inner_dia_y);
fctx.lineTo(loopx + loop_radius + 3.0*arrow_size, inner_dia_y);
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fctx.stroke();
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fctx.textAlign = "left";
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fctx.fillText("\u2300i = " + (loop_dia-0.5*conductor_diameter_slider.value).toFixed(1).toString() + "mm", loopx + loop_radius + 2.0*arrow_size, inner_dia_y - 2);
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// Draw outer-diameter arrows: (for using a winding former)
const outer_dia_y = loopy + loop_radius + 0;
fctx.beginPath();
fctx.moveTo(loopx - loop_radius - cond_radius, loopy);
fctx.lineTo(loopx - loop_radius - cond_radius, outer_dia_y);
fctx.lineTo(loopx - loop_radius - cond_radius - arrow_size, outer_dia_y - arrow_size);
fctx.lineTo(loopx - loop_radius - cond_radius - arrow_size, outer_dia_y + arrow_size);
fctx.lineTo(loopx - loop_radius - cond_radius, outer_dia_y);
fctx.lineTo(loopx - loop_radius - 3.0*arrow_size, outer_dia_y);
fctx.stroke();
fctx.beginPath();
fctx.moveTo(loopx + loop_radius + cond_radius, loopy);
fctx.lineTo(loopx + loop_radius + cond_radius, outer_dia_y);
fctx.lineTo(loopx + loop_radius + cond_radius + arrow_size, outer_dia_y - arrow_size);
fctx.lineTo(loopx + loop_radius + cond_radius + arrow_size, outer_dia_y + arrow_size);
fctx.lineTo(loopx + loop_radius + cond_radius, outer_dia_y);
fctx.lineTo(loopx + loop_radius + 3.0*arrow_size, outer_dia_y);
fctx.stroke();
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fctx.fillText("\u2300o = " + (loop_dia+0.5*conductor_diameter_slider.value).toFixed(1).toString() + "mm", loopx + loop_radius + 2.0*arrow_size, outer_dia_y - 2);
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// Write loop inductance:
fctx.font = "12px arial";
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fctx.textAlign = "left";
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const L = inductor.L * 1.0e+6;
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fctx.fillText("L = " + L.toPrecision(3).toString() + " \u03bcH", 8, 18);
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fctx.fillText("C = " + (inductor.C * 1e12).toFixed(1) + " pF", 8, 32);
fctx.fillText("Rdc = " + inductor.Rdc.toFixed(2) + " \u03A9", 8, 46);
fctx.fillText("SRF = " + (inductor.SRF * 1e-6).toFixed(1) + " MHz", 8, 60);
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// Draw conductor diameter arrow:
fctx.beginPath();
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fctx.moveTo(loopx - loop_radius - cond_radius, loopy);
fctx.lineTo(loopx - loop_radius - cond_radius - arrow_size, loopy - arrow_size);
fctx.lineTo(loopx - loop_radius - cond_radius - arrow_size, loopy + arrow_size);
fctx.lineTo(loopx - loop_radius - cond_radius, loopy);
fctx.lineTo(loopx - loop_radius - 3.0*arrow_size, loopy);
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fctx.stroke();
fctx.beginPath();
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fctx.moveTo(loopx - loop_radius + cond_radius, loopy);
fctx.lineTo(loopx - loop_radius + cond_radius + arrow_size, loopy - arrow_size);
fctx.lineTo(loopx - loop_radius + cond_radius + arrow_size, loopy + arrow_size);
fctx.lineTo(loopx - loop_radius + cond_radius, loopy);
fctx.lineTo(loopx - loop_radius + cond_radius + 2.0*arrow_size, loopy);
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fctx.stroke();
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var awg = "";
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var swg = "";
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switch(cond_dia) {
case 0.100 :
awg = "~38 AWG";
break;
case 0.150 :
awg = "~35 AWG";
break;
case 0.200 :
awg = "~32 AWG";
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swg = "~36 SWG";
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break;
case 0.250 :
awg = "~30 AWG";
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swg = "~33 SWG";
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break;
case 0.300 :
awg = "~29 AWG";
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swg = "~31 SWG";
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break;
case 0.350 :
awg = "~27 AWG";
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swg = "~29 SWG";
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break;
case 0.400 :
awg = "~26 AWG";
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swg = "~27 SWG";
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break;
case 0.450 :
awg = "~25 AWG";
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swg = "~26 SWG";
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break;
case 0.500 :
awg = "~24 AWG";
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swg = "~25 SWG";
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break;
case 0.550 :
awg = "~23 AWG";
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swg = "~24 SWG";
break;
case 0.600 :
swg = "~23 SWG";
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break;
case 0.650 :
awg = "~22 AWG";
break;
case 0.700 :
awg = "~21 AWG";
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swg = "~22 SWG";
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break;
case 0.800 :
awg = "~20 AWG";
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swg = "~21 SWG";
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break;
case 0.900 :
awg = "~19 AWG";
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swg = "~20 SWG";
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break;
case 1.00 :
awg = "~18 AWG";
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swg = "~19 SWG";
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break;
case 1.15 :
awg = "~17 AWG";
break;
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case 1.20 :
swg = "~18 SWG";
break;
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case 1.30 :
awg = "~16 AWG";
break;
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case 1.40 :
swg = "~17 SWG";
break;
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case 1.45 :
awg = "~15 AWG";
break;
case 1.55 :
awg = "~14 AWG";
break;
case 1.80 :
awg = "~13 AWG";
break;
case 2.00 :
awg = "~12 AWG";
break;
case 2.30 :
awg = "~11 AWG";
break;
case 2.60 :
awg = "~10 AWG";
break;
case 2.90 :
awg = "~9 AWG";
break;
case 3.25 :
awg = "~8 AWG";
break;
case 3.65 :
awg = "~7 AWG";
break;
case 4.10 :
awg = "~6 AWG";
break;
case 4.60 :
awg = "~5 AWG";
break;
}
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fctx.textAlign = "center";
fctx.font = "14px courier";
fctx.fillText(awg, loopx, loopy - 6);
fctx.fillText(swg, loopx, loopy + 12);
fctx.font = "12px arial";
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var cond_spacing = 2.0 * cond_radius * loop_spacing_slider.value;
if((cond_spacing * loop_turns_slider.value) > (0.8 * win_width)) {
cond_radius = ((0.8 * win_width) / (loop_turns_slider.value * 2.0*loop_spacing_slider.value));
cond_spacing = 2.0 * cond_radius * loop_spacing_slider.value;
}
var start_x = win_width/2.0 - loop_turns_slider.value * cond_spacing * 0.5;
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var top_y = win_height * 0.56;
var bot_y = top_y + 2.0 * cond_radius * (loop_diameter_slider.value / conductor_diameter_slider.value);
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for (let i = 0; i < loop_turns_slider.value ; i + + ) {
fctx.beginPath();
fctx.moveTo(start_x + ((0.5 + i) * cond_spacing) + cond_radius, top_y);
fctx.lineTo(start_x + (i+1) * cond_spacing + cond_radius, bot_y);
fctx.arc(start_x + (i+1) * cond_spacing, bot_y, cond_radius, 0, Math.PI, false);
fctx.lineTo(start_x + ((0.5 + i) * cond_spacing) - cond_radius, top_y);
fctx.fillStyle = "grey";
fctx.fill();
fctx.beginPath();
fctx.arc(start_x + (i * cond_spacing), bot_y, cond_radius, 0, Math.PI);
fctx.arc(start_x + (cond_spacing * 0.5) + i * cond_spacing, top_y, cond_radius, Math.PI, 0);
fctx.lineTo(start_x + (i * cond_spacing) + cond_radius, bot_y);
fctx.closePath();
fctx.fillStyle = "black";
fctx.fill();
}
// Draw the wire ends:
fctx.fillRect(start_x - cond_radius, bot_y, 2.0 * cond_radius, 30);
fctx.fillStyle = "grey";
fctx.fillRect(start_x + loop_turns_slider.value*cond_spacing - cond_radius, bot_y, 2.0 * cond_radius, 30);
fctx.fillStyle = "black";
// Draw left spacing arrow:
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const dim_y = win_height * 0.92;
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fctx.beginPath();
fctx.moveTo(start_x - 20, dim_y);
fctx.lineTo(start_x, dim_y);
fctx.lineTo(start_x - 7, dim_y + 7)
fctx.lineTo(start_x - 7, dim_y - 7)
fctx.lineTo(start_x, dim_y);
fctx.moveTo(start_x, dim_y - 7);
fctx.lineTo(start_x, dim_y + 7);
fctx.stroke();
// Draw right spacing arrow:
fctx.beginPath();
fctx.moveTo(start_x + cond_spacing + 20, dim_y);
fctx.lineTo(start_x + cond_spacing, dim_y);
fctx.lineTo(start_x + cond_spacing + 7, dim_y + 7)
fctx.lineTo(start_x + cond_spacing + 7, dim_y - 7)
fctx.lineTo(start_x + cond_spacing, dim_y);
fctx.moveTo(start_x + cond_spacing, dim_y - 7);
fctx.lineTo(start_x + cond_spacing, dim_y + 7);
fctx.stroke();
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// Draw right length arrow:
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fctx.beginPath();
fctx.moveTo(start_x + loop_turns_slider.value*cond_spacing + 20, dim_y);
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing, dim_y);
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing + 7, dim_y + 7)
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing + 7, dim_y - 7)
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing, dim_y);
fctx.moveTo(start_x + loop_turns_slider.value*cond_spacing, dim_y - 7);
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing, dim_y + 7);
fctx.stroke();
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// Extended lines:
fctx.strokeStyle = "grey";
fctx.beginPath();
fctx.moveTo(start_x, bot_y + 35);
fctx.lineTo(start_x, dim_y - 12);
fctx.moveTo(start_x + cond_spacing, bot_y + 15);
fctx.lineTo(start_x + cond_spacing, dim_y - 12);
fctx.moveTo(start_x + loop_turns_slider.value*cond_spacing, bot_y + 35);
fctx.lineTo(start_x + loop_turns_slider.value*cond_spacing, dim_y - 12);
fctx.stroke();
fctx.strokeStyle = "black";
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fctx.font = "12px arial";
fctx.textAlign = "right";
var freq = 1.0 * frequency_slider.value;
fctx.fillText("f = " + freq.toFixed(1) + " MHz", win_width-18, 18);
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fctx.fillText("X\u2097 = " + inductor.Xl.toFixed(1) + " \u03A9", win_width-18, 32);
fctx.fillText("|Z| = " + inductor.Z.r.toFixed(1) + " \u03A9", win_width-18, 46);
fctx.fillText("\u03B4 = " + (inductor.skin_depth * 1e6).toFixed(1) + " \u03BCm", win_width-18, 60);
fctx.fillText("Rac = " + inductor.Rac.toFixed(2) + " \u03A9", win_width-18, 74);
fctx.fillText("Q = " + inductor.Q.toFixed(1), win_width-18, 88);
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fctx.textAlign = "center";
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fctx.fillText("N = " + loop_turns_slider.value.toString(), win_width/2, win_height * 0.52);
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// Draw spacing text: (gap is to avoid collision of spacing and length texts)
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fctx.textAlign = "right";
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var gap = ((loop_turns_slider.value*cond_spacing - cond_spacing) < 60 ) ? ( 60 - ( loop_turns_slider . value * cond_spacing - cond_spacing ) ) : 0 ;
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const spc = loop_spacing_slider.value * conductor_diameter_slider.value;
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fctx.fillText("c = " + spc.toFixed(1).toString() + "mm", start_x + cond_spacing + 20 - gap, dim_y + 20);
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// Draw length text:
const sol_len = loop_turns_slider.value*spc;
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fctx.fillText("\u2113 = " + sol_len.toFixed(1).toString() + "mm", start_x + loop_turns_slider.value*cond_spacing + 20, dim_y + 20);
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}
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recalculate();
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< / script >
< / body >
< / html >
