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refactor: dämpfungsglied

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This commit is contained in:
Matthias Jung
2026-08-09 11:41:06 +02:00
parent 4ad7f18bea
commit c6fd3828a9
6 changed files with 347 additions and 12 deletions
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contents/html/applet_daempfungsglied.html
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<html>
<div class="text-start" id="attenuator-calculator">
<p>Mit diesem Applet können symmetrische T- und Pi-Dämpfungsglieder für ein 50-Ω-System berechnet werden.</p>
<div class="row g-3 align-items-end">
<div class="col-12 col-sm-6">
<label class="form-label" for="attenuator-db">Dämpfung in dB</label>
<input class="form-control" id="attenuator-db" type="number" min="0.1" max="100" step="0.1" value="6" inputmode="decimal">
</div>
<div class="col-12 col-sm-6">
<label class="form-label" for="attenuator-impedance">Systemimpedanz</label>
<input class="form-control" id="attenuator-impedance" type="text" value="50 Ω" readonly>
</div>
<div class="col-12 col-sm-6">
<span class="form-label d-block">Schaltungsform</span>
<div class="form-check form-check-inline">
<input class="form-check-input" id="attenuator-pi" type="radio" name="attenuator-topology" value="pi" checked>
<label class="form-check-label" for="attenuator-pi">Pi</label>
</div>
<div class="form-check form-check-inline">
<input class="form-check-input" id="attenuator-t" type="radio" name="attenuator-topology" value="t">
<label class="form-check-label" for="attenuator-t">T</label>
</div>
</div>
<div class="col-12 col-sm-6">
<label class="form-label" for="attenuator-series">Normreihe</label>
<select class="form-select" id="attenuator-series">
<option value="E12">E12</option>
<option value="E24" selected>E24</option>
<option value="E48">E48</option>
<option value="E96">E96</option>
</select>
</div>
</div>
<p class="text-danger mt-3" id="attenuator-error" role="alert" hidden></p>
<div class="mt-4" id="attenuator-output">
<p class="mb-1">Die idealen Widerstandswerte betragen:</p>
<div id="attenuator-ideal-result"></div>
<p class="mb-1">Die nächsten Widerstandswerte aus der <span id="attenuator-series-name">E24</span>-Reihe betragen:</p>
<div id="attenuator-standard-result"></div>
<p class="mb-1">Mit diesen Normwerten wird folgende Dämpfung erreicht:</p>
<div id="attenuator-achieved-result"></div>
</div>
</div>
<script>
(function() {
"use strict";
const impedance = 50;
const preferredValues = {
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],
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],
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],
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]
};
const attenuationInput = document.getElementById("attenuator-db");
const seriesSelect = document.getElementById("attenuator-series");
const output = document.getElementById("attenuator-output");
const error = document.getElementById("attenuator-error");
const idealResult = document.getElementById("attenuator-ideal-result");
const standardResult = document.getElementById("attenuator-standard-result");
const achievedResult = document.getElementById("attenuator-achieved-result");
const latexResults = [idealResult, standardResult, achievedResult];
let katexWaitTimer = null;
function decimalLatex(value, maximumFractionDigits, minimumFractionDigits = 0) {
return value.toLocaleString("de-DE", {
maximumFractionDigits: maximumFractionDigits,
minimumFractionDigits: minimumFractionDigits,
useGrouping: false
}).replace(",", "{,}");
}
function resistanceLatex(value) {
if (value >= 1e6) {
return decimalLatex(value / 1e6, 3) + "\\,\\mathrm{M}\\Omega";
}
if (value >= 1e3) {
return decimalLatex(value / 1e3, 3) + "\\,\\mathrm{k}\\Omega";
}
return decimalLatex(value, 2) + "\\,\\Omega";
}
function nearestPreferredValue(value, seriesName) {
const values = preferredValues[seriesName];
const decade = Math.floor(Math.log10(value));
const candidates = [];
for (let exponent = decade - 1; exponent <= decade + 1; exponent += 1) {
values.forEach(function(baseValue) {
candidates.push(baseValue * Math.pow(10, exponent));
});
}
return candidates.reduce(function(nearest, candidate) {
return Math.abs(candidate - value) < Math.abs(nearest - value) ? candidate : nearest;
});
}
function multiplyMatrices(left, right) {
return [
[
left[0][0] * right[0][0] + left[0][1] * right[1][0],
left[0][0] * right[0][1] + left[0][1] * right[1][1]
],
[
left[1][0] * right[0][0] + left[1][1] * right[1][0],
left[1][0] * right[0][1] + left[1][1] * right[1][1]
]
];
}
function achievedAttenuation(topology, symmetricResistance, middleResistance) {
const seriesMatrix = function(resistance) {
return [[1, resistance], [0, 1]];
};
const shuntMatrix = function(resistance) {
return [[1, 0], [1 / resistance, 1]];
};
let matrix;
if (topology === "pi") {
matrix = multiplyMatrices(
multiplyMatrices(shuntMatrix(symmetricResistance), seriesMatrix(middleResistance)),
shuntMatrix(symmetricResistance)
);
} else {
matrix = multiplyMatrices(
multiplyMatrices(seriesMatrix(symmetricResistance), shuntMatrix(middleResistance)),
seriesMatrix(symmetricResistance)
);
}
const denominator = matrix[0][0]
+ matrix[0][1] / impedance
+ matrix[1][0] * impedance
+ matrix[1][1];
const transmission = 2 / denominator;
return -20 * Math.log10(Math.abs(transmission));
}
function katexIsReady() {
return window.katex && typeof window.katex.render === "function";
}
function setLatex(element, latex) {
element.attenuatorLatex = latex;
if (katexIsReady()) {
window.katex.render(latex, element, {
displayMode: true,
throwOnError: false,
strict: false
});
return;
}
element.textContent = "";
}
function renderResultsWhenKatexIsReady() {
if (katexIsReady()) {
katexWaitTimer = null;
latexResults.forEach(function(element) {
setLatex(element, element.attenuatorLatex);
});
return;
}
if (katexWaitTimer === null) {
katexWaitTimer = window.setTimeout(function() {
katexWaitTimer = null;
renderResultsWhenKatexIsReady();
}, 50);
}
}
function networkValuesLatex(topology, symmetricResistance, middleResistance) {
if (topology === "pi") {
return "\\begin{aligned}"
+ "R_1=R_3&=" + resistanceLatex(symmetricResistance) + "\\\\"
+ "R_2&=" + resistanceLatex(middleResistance)
+ "\\end{aligned}";
}
return "\\begin{aligned}"
+ "R_1=R_2&=" + resistanceLatex(symmetricResistance) + "\\\\"
+ "R_3&=" + resistanceLatex(middleResistance)
+ "\\end{aligned}";
}
function calculate() {
const attenuation = attenuationInput.valueAsNumber;
const topology = document.querySelector('input[name="attenuator-topology"]:checked').value;
const seriesName = seriesSelect.value;
if (!Number.isFinite(attenuation) || attenuation <= 0 || attenuation > 100) {
error.textContent = "Bitte eine Dämpfung zwischen 0,1 dB und 100 dB eingeben.";
error.hidden = false;
output.hidden = true;
return;
}
error.hidden = true;
output.hidden = false;
const voltageRatio = Math.pow(10, attenuation / 20);
let symmetricResistance;
let middleResistance;
if (topology === "pi") {
symmetricResistance = impedance * (voltageRatio + 1) / (voltageRatio - 1);
middleResistance = impedance * (voltageRatio * voltageRatio - 1) / (2 * voltageRatio);
} else {
symmetricResistance = impedance * (voltageRatio - 1) / (voltageRatio + 1);
middleResistance = 2 * impedance * voltageRatio / (voltageRatio * voltageRatio - 1);
}
const preferredSymmetricResistance = nearestPreferredValue(symmetricResistance, seriesName);
const preferredMiddleResistance = nearestPreferredValue(middleResistance, seriesName);
const actualAttenuation = achievedAttenuation(
topology,
preferredSymmetricResistance,
preferredMiddleResistance
);
setLatex(
idealResult,
networkValuesLatex(topology, symmetricResistance, middleResistance)
);
setLatex(
standardResult,
networkValuesLatex(topology, preferredSymmetricResistance, preferredMiddleResistance)
);
setLatex(
achievedResult,
"a_\\mathrm{erreicht}=" + decimalLatex(actualAttenuation, 2, 2) + "\\,\\mathrm{dB}"
);
document.getElementById("attenuator-series-name").textContent = seriesName;
if (!katexIsReady()) {
renderResultsWhenKatexIsReady();
}
}
attenuationInput.addEventListener("input", calculate);
seriesSelect.addEventListener("change", calculate);
document.querySelectorAll('input[name="attenuator-topology"]').forEach(function(input) {
input.addEventListener("change", calculate);
});
calculate();
}());
</script>
</html>