.. titel: Friis Transmissionsligning
.. slug: rf-friis-transmission-ligning
.. dato: 26-12-2025 15:00:00 UTC
.. tags: netværk, lommeregner, værktøj
.. kategori: Lommeregnere
.. link:
.. beskrivelse: Anvend Friis transmissionsligningen til at finde modtaget signaleffekt fra sendeeffekt, antenneforstærkning og vejtab. Bruges til RF link budget planlægning.
.. type: tekst
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</style>
<div class="calc-container">
<div class="calc-header">
<h2>Friis transmissionsligningsberegner</h2>
<p>Beregn den modtagne effekt i en trådløs transmission ved hjælp af Friis transmissionsligningen. Indtast frekvensen og afstanden for at bestemme frirumsvejtabet og Fresnel-zonens radius.</p>
<div class="form-section">
<div class="form-row">
<div class="form-group">
<label for="frequency">Frekvens:</label>
<input autocomplete="off" id="frequency" type="text" value="2.4"/>
</div>
<div class="form-group">
<label for="freunit">Frekvensenhed:</label>
<select id="freunit">
<option value="ghz">Gigahertz (GHz)</option>
<option value="mhz">Megahertz (MHz)</option>
<option value="khz">Kilohertz (KHz)</option>
<option value="hz">Hertz (Hz)</option>
</select>
</div>
</div>
<div class="form-row">
<div class="form-group">
<label for="distance">Afstand:</label>
<input autocomplete="off" id="distance" type="text" value="1"/>
</div>
<div class="form-group">
<label for="unit">Afstandsenhed:</label>
<select id="unit">
<option value="feet">Miles</option>
<option value="meters">Kilometer</option>
</select>
</div>
</div>
<div class="button-group">
<button class="calc-button" onclick="fresnelZone()" type="button">Beregne</button>
</div>
</div>
<div class="help-text">
<strong>Note:</strong>Friis-transmissionsligningen beregner den effekt, som modtages af en antenne under idealiserede forhold, hvis en anden antenne et stykke væk sender en kendt mængde strøm.</div>
</div>
<div class="result-section" id="resultsSection" style="display: none;">
<div class="section-header">
<h3><span>📡</span>Beregningsresultater</h3>
</div>
<div class="section-content">
<div class="data-row">
<div class="data-label">Fresnel zone radius:</div>
<div class="data-value highlight" id="fnr">-</div>
</div>
<div class="data-row">
<div class="data-label">Midtpunkt:</div>
<div class="data-value" id="center">-</div>
</div>
</div>
</div>
<div class="info-section">
<h4>Om Friis-transmissionsligningen</h4>
<p>Friis transmissionsligningen relaterer den effekt, som modtages af en antenne, til den effekt, der transmitteres af en anden antenne, adskilt af en vis afstand. Ligningen tager højde for antenneforstærkninger og signalets bølgelængde.</p>
<p><strong>Formel:</strong></p>
<p><code>Pr / Pt = Gt × Gr × (λ / 4πR)²</code></p>
<p><strong>Hvor:</strong></p>
<ul style="margin: 10px 0; padding-left: 20px;">
<li><code>Pr</code>= Strøm på modtagerantennen</li>
<li><code>Pt</code>= Udgangseffekt fra sendeantenne</li>
<li><code>Gr</code>= Forstærkning af modtageantennen</li>
<li><code>Gt</code>= Forstærkning af sendeantennen</li>
<li><code>λ</code>= Bølgelængde</li>
<li><code>R</code>= Afstand mellem antenner</li>
</ul>
<p><strong>Fresnel zone:</strong>Fresnel-zonen er et ellipseformet område mellem sende- og modtageantennerne. Denne lommeregner beregner radius ved midtpunktet, hvilket er afgørende for at bestemme, om forhindringer vil forstyrre signalet.</p>
</div>
</div>
<script>
/**
 * Friis Transmission Equation Calculator
 * Calculates Fresnel zone radius based on frequency and distance
 *
 * Equation:
 * Pr / Pt = Gt × Gr × (Lambda / 4 × Pi × R)²
 *
 * Where:
 * - Pr: Power at the receiving antenna
 * - Pt: Output power of transmitting antenna
 * - Gr: Gain of the receiving antenna
 * - Gt: Gain of the transmitting antenna
 * - Lambda: Wavelength
 * - R: Distance between antennas
 *
 * Fresnel Zone Calculation:
 * For Miles: radius = 72.05 × √(d1 × d2 / f)
 * For Kilometers: radius = 17.32 × √(d1 × d2 / f)
 * Where d1 and d2 are distances from each antenna to the center point
 */

'use strict';

function fresnelZone() {
    // Get input values
    const frequency = Number(document.getElementById("frequency").value);
    const freunit = document.getElementById("freunit").value;
    const distance = Number(document.getElementById("distance").value);
    const unit = document.getElementById("unit").value;

    // Validate inputs
    if (isNaN(frequency) || frequency <= 0) {
        alert("Please enter a valid frequency greater than 0");
        return;
    }

    if (isNaN(distance) || distance <= 0) {
        alert("Please enter a valid distance greater than 0");
        return;
    }

    // Convert frequency to GHz
    let sf;
    if (freunit === "ghz") {
        sf = frequency;
    } else if (freunit === "mhz") {
        sf = frequency / 1000;
    } else if (freunit === "khz") {
        sf = frequency / 1000000;
    } else {
        sf = frequency / 1000000000;
    }

    // Calculate center point (halfway)
    const d1 = distance / 2;
    const d2 = d1;

    // Calculate Fresnel zone radius based on unit
    let radius, distunit;
    if (unit === "feet") {
        // For miles: radius in feet
        radius = Math.round(36.03 * Math.sqrt(distance / sf));
        distunit = "Miles";
    } else {
        // For kilometers: radius in meters
        radius = Math.round(8.657 * Math.sqrt(distance / sf));
        distunit = "Kilometers";
    }

    // Display results
    document.getElementById("fnr").innerHTML = radius + " feet";
    document.getElementById("center").innerHTML = "The center of the Fresnel Zone is " + d1 + " " + distunit + " from the first antenna.";

    // Show results section
    document.getElementById("resultsSection").style.display = "block";

    // Scroll to results
    document.getElementById("resultsSection").scrollIntoView({ behavior: 'smooth', block: 'start' });

    console.log(`Calculation complete: Frequency=${sf}GHz, Distance=${distance}${distunit}, Radius=${radius}ft`);
}

// Add enter key support for inputs
document.addEventListener('DOMContentLoaded', function() {
    console.log('Friis Transmission Equation Calculator initialized');

    // Allow Enter key to trigger calculation
    const inputs = document.querySelectorAll('#frequency, #distance');
    inputs.forEach(input => {
        input.addEventListener('keypress', function(e) {
            if (e.key === 'Enter') {
                fresnelZone();
            }
        });
    });

    // Auto-focus first input
    document.getElementById('frequency').focus();
});
</script>