264 lines
12 KiB
HTML
264 lines
12 KiB
HTML
<html>
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<div class="text-start" id="attenuator-calculator">
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<p>Mit diesem Applet können symmetrische T- und Pi-Dämpfungsglieder für ein 50-Ω-System berechnet werden.</p>
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<div class="row g-3 align-items-end">
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<div class="col-12 col-sm-6">
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<label class="form-label" for="attenuator-db">Dämpfung in dB</label>
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<input class="form-control" id="attenuator-db" type="number" min="0.1" max="100" step="0.1" value="6" inputmode="decimal">
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</div>
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<div class="col-12 col-sm-6">
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<label class="form-label" for="attenuator-impedance">Systemimpedanz</label>
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<input class="form-control" id="attenuator-impedance" type="text" value="50 Ω" readonly>
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</div>
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<div class="col-12 col-sm-6">
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<span class="form-label d-block">Schaltungsform</span>
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<div class="form-check form-check-inline">
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<input class="form-check-input" id="attenuator-pi" type="radio" name="attenuator-topology" value="pi" checked>
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<label class="form-check-label" for="attenuator-pi">Pi</label>
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</div>
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<div class="form-check form-check-inline">
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<input class="form-check-input" id="attenuator-t" type="radio" name="attenuator-topology" value="t">
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<label class="form-check-label" for="attenuator-t">T</label>
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</div>
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</div>
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<div class="col-12 col-sm-6">
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<label class="form-label" for="attenuator-series">Normreihe</label>
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<select class="form-select" id="attenuator-series">
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<option value="E12">E12</option>
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<option value="E24" selected>E24</option>
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<option value="E48">E48</option>
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<option value="E96">E96</option>
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</select>
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</div>
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</div>
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<p class="text-danger mt-3" id="attenuator-error" role="alert" hidden></p>
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<div class="mt-4" id="attenuator-output">
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<p class="mb-1">Die idealen Widerstandswerte betragen:</p>
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<div id="attenuator-ideal-result"></div>
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<p class="mb-1">Die nächsten Widerstandswerte aus der <span id="attenuator-series-name">E24</span>-Reihe betragen:</p>
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<div id="attenuator-standard-result"></div>
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<p class="mb-1">Mit diesen Normwerten wird folgende Dämpfung erreicht:</p>
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<div id="attenuator-achieved-result"></div>
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</div>
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</div>
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<script>
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(function() {
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"use strict";
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const impedance = 50;
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const preferredValues = {
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E12: [1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2],
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E24: [1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1],
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E48: [1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40, 1.47, 1.54, 1.62, 1.69, 1.78, 1.87, 1.96, 2.05, 2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01, 3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42, 4.64, 4.87, 5.11, 5.36, 5.62, 5.90, 6.19, 6.49, 6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53],
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E96: [1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76]
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};
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const attenuationInput = document.getElementById("attenuator-db");
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const seriesSelect = document.getElementById("attenuator-series");
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const output = document.getElementById("attenuator-output");
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const error = document.getElementById("attenuator-error");
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const idealResult = document.getElementById("attenuator-ideal-result");
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const standardResult = document.getElementById("attenuator-standard-result");
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const achievedResult = document.getElementById("attenuator-achieved-result");
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const latexResults = [idealResult, standardResult, achievedResult];
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let katexWaitTimer = null;
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function decimalLatex(value, maximumFractionDigits, minimumFractionDigits = 0) {
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return value.toLocaleString("de-DE", {
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maximumFractionDigits: maximumFractionDigits,
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minimumFractionDigits: minimumFractionDigits,
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useGrouping: false
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}).replace(",", "{,}");
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}
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function resistanceLatex(value) {
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if (value >= 1e6) {
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return decimalLatex(value / 1e6, 3) + "\\,\\mathrm{M}\\Omega";
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}
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if (value >= 1e3) {
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return decimalLatex(value / 1e3, 3) + "\\,\\mathrm{k}\\Omega";
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}
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return decimalLatex(value, 2) + "\\,\\Omega";
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}
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function nearestPreferredValue(value, seriesName) {
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const values = preferredValues[seriesName];
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const decade = Math.floor(Math.log10(value));
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const candidates = [];
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for (let exponent = decade - 1; exponent <= decade + 1; exponent += 1) {
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values.forEach(function(baseValue) {
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candidates.push(baseValue * Math.pow(10, exponent));
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});
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}
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return candidates.reduce(function(nearest, candidate) {
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return Math.abs(candidate - value) < Math.abs(nearest - value) ? candidate : nearest;
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});
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}
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function multiplyMatrices(left, right) {
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return [
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[
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left[0][0] * right[0][0] + left[0][1] * right[1][0],
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left[0][0] * right[0][1] + left[0][1] * right[1][1]
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],
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[
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left[1][0] * right[0][0] + left[1][1] * right[1][0],
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left[1][0] * right[0][1] + left[1][1] * right[1][1]
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]
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];
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}
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function achievedAttenuation(topology, symmetricResistance, middleResistance) {
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const seriesMatrix = function(resistance) {
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return [[1, resistance], [0, 1]];
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};
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const shuntMatrix = function(resistance) {
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return [[1, 0], [1 / resistance, 1]];
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};
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let matrix;
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if (topology === "pi") {
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matrix = multiplyMatrices(
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multiplyMatrices(shuntMatrix(symmetricResistance), seriesMatrix(middleResistance)),
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shuntMatrix(symmetricResistance)
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);
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} else {
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matrix = multiplyMatrices(
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multiplyMatrices(seriesMatrix(symmetricResistance), shuntMatrix(middleResistance)),
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seriesMatrix(symmetricResistance)
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);
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}
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const denominator = matrix[0][0]
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+ matrix[0][1] / impedance
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+ matrix[1][0] * impedance
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+ matrix[1][1];
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const transmission = 2 / denominator;
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return -20 * Math.log10(Math.abs(transmission));
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}
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function katexIsReady() {
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return window.katex && typeof window.katex.render === "function";
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}
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function setLatex(element, latex) {
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element.attenuatorLatex = latex;
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if (katexIsReady()) {
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window.katex.render(latex, element, {
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displayMode: true,
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throwOnError: false,
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strict: false
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});
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return;
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}
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element.textContent = "";
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}
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function renderResultsWhenKatexIsReady() {
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if (katexIsReady()) {
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katexWaitTimer = null;
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latexResults.forEach(function(element) {
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setLatex(element, element.attenuatorLatex);
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});
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return;
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}
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if (katexWaitTimer === null) {
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katexWaitTimer = window.setTimeout(function() {
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katexWaitTimer = null;
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renderResultsWhenKatexIsReady();
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}, 50);
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}
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}
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function networkValuesLatex(topology, symmetricResistance, middleResistance) {
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if (topology === "pi") {
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return "\\begin{aligned}"
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+ "R_1=R_3&=" + resistanceLatex(symmetricResistance) + "\\\\"
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+ "R_2&=" + resistanceLatex(middleResistance)
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+ "\\end{aligned}";
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}
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return "\\begin{aligned}"
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+ "R_1=R_2&=" + resistanceLatex(symmetricResistance) + "\\\\"
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+ "R_3&=" + resistanceLatex(middleResistance)
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+ "\\end{aligned}";
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}
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function calculate() {
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const attenuation = attenuationInput.valueAsNumber;
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const topology = document.querySelector('input[name="attenuator-topology"]:checked').value;
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const seriesName = seriesSelect.value;
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if (!Number.isFinite(attenuation) || attenuation <= 0 || attenuation > 100) {
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error.textContent = "Bitte eine Dämpfung zwischen 0,1 dB und 100 dB eingeben.";
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error.hidden = false;
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output.hidden = true;
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return;
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}
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error.hidden = true;
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output.hidden = false;
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const voltageRatio = Math.pow(10, attenuation / 20);
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let symmetricResistance;
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let middleResistance;
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if (topology === "pi") {
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symmetricResistance = impedance * (voltageRatio + 1) / (voltageRatio - 1);
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middleResistance = impedance * (voltageRatio * voltageRatio - 1) / (2 * voltageRatio);
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} else {
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symmetricResistance = impedance * (voltageRatio - 1) / (voltageRatio + 1);
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middleResistance = 2 * impedance * voltageRatio / (voltageRatio * voltageRatio - 1);
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}
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const preferredSymmetricResistance = nearestPreferredValue(symmetricResistance, seriesName);
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const preferredMiddleResistance = nearestPreferredValue(middleResistance, seriesName);
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const actualAttenuation = achievedAttenuation(
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topology,
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preferredSymmetricResistance,
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preferredMiddleResistance
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);
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setLatex(
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idealResult,
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networkValuesLatex(topology, symmetricResistance, middleResistance)
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);
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setLatex(
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standardResult,
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networkValuesLatex(topology, preferredSymmetricResistance, preferredMiddleResistance)
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);
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setLatex(
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achievedResult,
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"a_\\mathrm{erreicht}=" + decimalLatex(actualAttenuation, 2, 2) + "\\,\\mathrm{dB}"
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);
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document.getElementById("attenuator-series-name").textContent = seriesName;
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if (!katexIsReady()) {
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renderResultsWhenKatexIsReady();
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}
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}
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attenuationInput.addEventListener("input", calculate);
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seriesSelect.addEventListener("change", calculate);
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document.querySelectorAll('input[name="attenuator-topology"]').forEach(function(input) {
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input.addEventListener("change", calculate);
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});
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calculate();
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}());
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</script>
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</html>
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