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  <title>Simple RF Coil Designer — MRI Loop Coil Calculator | RF Toolbox</title>
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<header><h2><a href="index.html" style="color:white;text-decoration:none;">RF Toolbox</a></h2></header>
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<div class="breadcrumb"><a href="index.html">⌂ Home</a></div>
<h3>Simple RF Coil Designer</h3>
<div class="tool-concept">
  <p>Designs a single-turn loop coil for MRI or NMR. Given the loop dimensions and Larmor frequency, calculates self-inductance using the single-turn loop (Rosa/Neumann) formula and the tuning capacitor required for resonance.</p>
  <details style="margin-top:8px;">
  <summary style="cursor:pointer;font-size:11px;color:#AA77FF;font-weight:bold;letter-spacing:0.05em;text-transform:uppercase;user-select:none;">Equations &amp; Parameters ▸</summary>

<div style="background:#f0eeff;border-left:3px solid #AA77FF;padding:8px 12px 6px;border-radius:0 4px 4px 0;margin:6px 0 10px;font-size:12.5px;line-height:2.0;overflow-x:auto;">\(L = \mu_0\mu_r\!\left(\tfrac{D}{2}\right)\!\left[\ln\!\left(\tfrac{8D}{d}\right)-2\right] \qquad C = \dfrac{1}{4\pi^2 f^2 L}\)</div>
<table style="font-size:12px;border-collapse:collapse;margin-top:6px;"><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">d</td><td style="padding:3px 0;">Wire diameter (mm). Thicker wire → lower resistance → higher Q.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">D</td><td style="padding:3px 0;">Loop diameter (mm). Larger loop → more inductance, more signal sensitivity.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">f</td><td style="padding:3px 0;">Larmor frequency — the resonant frequency of the nucleus in the static B₀ field. ¹H at 3T ≈ 128 MHz, at 7T ≈ 298 MHz.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">L</td><td style="padding:3px 0;">Self-inductance (Rosa formula).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">C</td><td style="padding:3px 0;">Required tuning capacitor for resonance at f.</td></tr></table>

<div style="margin-top:10px;padding-top:8px;border-top:1px solid #e0d8ff;"><div style="font-size:10px;font-weight:bold;color:#AA77FF;letter-spacing:0.07em;text-transform:uppercase;margin-bottom:4px;">Physical constants used</div><table style="font-size:12px;border-collapse:collapse;"><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">µ₀</td><td>4π×10⁻⁷ H/m</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">¹H γ/2π</td><td>42.577 MHz/T (Larmor frequency per Tesla)</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">¹H at 1.5 T</td><td>63.87 MHz</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">¹H at 3 T</td><td>127.74 MHz</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">¹H at 7 T</td><td>297.7 MHz</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">σ_muscle @ 128 MHz</td><td>≈ 0.77 S/m</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">ε_muscle @ 128 MHz</td><td>≈ 58</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">IEC SAR limit (WB normal)</td><td>2 W/kg (over 6 min)</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">IEC SAR limit (head)</td><td>3.2 W/kg (over 10 min)</td></tr></table></div>
<div style="margin-top:8px;padding-top:6px;border-top:1px solid #e0d8ff;font-size:11.5px;color:#666;"><span style="font-weight:bold;color:#AA77FF;">Reference: </span>Neumann mutual inductance formula; H. Wheeler, "Simple inductance formulas for radio coils," <em>Proc. IRE</em> 16, 1398 (1928)</div>
</details>
</div>
<div class="sec-lbl">Inputs</div>
<div class="sec-lbl" style="margin-top:0;margin-bottom:6px;border:none;color:#888;">Loop geometry</div>
<div class="inp-grid"><div class="inp-row"><label>Wire diameter, <span class="var">d</span></label><div class="inp-inline"><input type="text" id="d" placeholder="Enter mm"  data-tip="Conductor (wire or tube) diameter. Thicker wire lowers resistance and raises Q."><span class="inp-units">mm</span></div><span class="inp-hint">Conductor diameter, not radius</span></div><div class="inp-row"><label>Loop diameter, <span class="var">D</span></label><div class="inp-inline"><input type="text" id="D" placeholder="Enter mm"  data-tip="Loop diameter, measured centre-to-centre of the conductor. Larger D → more inductance."><span class="inp-units">mm</span></div><span class="inp-hint">Centre-to-centre of conductor</span></div></div>
<div class="sec-lbl" style="margin-top:8px;margin-bottom:6px;border:none;color:#888;">Field parameters</div>
<div class="inp-grid"><div class="inp-row"><label>Larmor frequency, <span class="var">f</span></label><div class="inp-inline"><input type="text" id="f" placeholder="Enter freq"  data-tip="Larmor frequency. ¹H: 64 MHz at 1.5T, 128 MHz at 3T, 298 MHz at 7T."><select id="f_dropdown"><option value="0">kHz</option><option value="1" selected>MHz</option><option value="2">GHz</option><option value="3">THz</option></select></div><span class="inp-hint">¹H at 3T ≈ 128 MHz</span></div></div>
<div style="display:flex;gap:8px;align-items:center;margin:12px 0 6px;"><button class="calc-btn" id="btn">Calculate</button> <button class="example-btn" onclick="loadExample({&quot;d&quot;: &quot;1.5&quot;, &quot;D&quot;: &quot;80&quot;, &quot;f&quot;: &quot;128&quot;, &quot;f_dropdown&quot;: &quot;1&quot;})" title="3T MRI ¹H coil — 80 mm loop, 1.5 mm wire, 128 MHz">Load Example</button></div>
<div id="error" class="err-msg" style="color:#c0392b;font-size:12px;margin-bottom:6px;min-height:16px;"></div>
<div class="sec-lbl">Results</div>
<div class="res-grid"><div class="res-card"><h4>Coil Parameters</h4><div class="res-row"><span class="res-lbl">Self-inductance, L</span><span class="res-val " id="L">—</span></div><div class="res-row"><span class="res-lbl">Tuning capacitor, C</span><span class="res-val " id="C">—</span></div></div></div>

<div class="sec-lbl">Diagram</div>
<div class="schematic-box"><div id="tool-diagram"></div></div>
<script>

function drawDiagram() {
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  var Cv = document.getElementById('C') ? document.getElementById('C').textContent : '—';
  var Dv = document.getElementById('D') ? (parseFloat(document.getElementById('D').value)||0) : 0;
  var dv = document.getElementById('d') ? (parseFloat(document.getElementById('d').value)||0) : 0;
  var W=560,H=190,cx=200,cy=85,R=65;
  var s='<svg viewBox="0 0 '+W+' '+H+'" width="'+W+'" height="'+H+'" xmlns="http://www.w3.org/2000/svg" style="font-family:monospace;max-width:100%;">';
  s+='<rect width="'+W+'" height="'+H+'" fill="#faf9ff" rx="4"/>';
  // Loop wire — translucent underlay visualises the wire diameter d
  var wireR=Math.max(3,Math.min(10, dv*1.5));
  s+='<circle cx="'+cx+'" cy="'+cy+'" r="'+R+'" fill="none" stroke="#AA77FF" stroke-width="'+(wireR*2)+'" opacity="0.22"/>';
  s+='<circle cx="'+cx+'" cy="'+cy+'" r="'+R+'" fill="none" stroke="#5533aa" stroke-width="'+Math.max(2,wireR)+'" stroke-linecap="round"/>';
  // Tuning capacitor — break the loop at 3 o'clock; plates perpendicular to the wire
  var gx=cx+R;
  s+='<rect x="'+(gx-wireR-4)+'" y="'+(cy-14)+'" width="'+(2*wireR+8)+'" height="28" fill="#faf9ff"/>';
  s+='<line x1="'+gx+'" y1="'+(cy-13)+'" x2="'+gx+'" y2="'+(cy-3.5)+'" stroke="#5533aa" stroke-width="2" stroke-linecap="round"/>';
  s+='<line x1="'+gx+'" y1="'+(cy+3.5)+'" x2="'+gx+'" y2="'+(cy+13)+'" stroke="#5533aa" stroke-width="2" stroke-linecap="round"/>';
  s+='<line x1="'+(gx-9)+'" y1="'+(cy-3.5)+'" x2="'+(gx+9)+'" y2="'+(cy-3.5)+'" stroke="#5533aa" stroke-width="2.8" stroke-linecap="round"/>';
  s+='<line x1="'+(gx-9)+'" y1="'+(cy+3.5)+'" x2="'+(gx+9)+'" y2="'+(cy+3.5)+'" stroke="#5533aa" stroke-width="2.8" stroke-linecap="round"/>';
  s+='<text x="'+(gx+16)+'" y="'+(cy+4)+'" text-anchor="start" font-size="11" fill="#5533aa" font-style="italic">C</text>';
  // L label inside loop
  s+='<text x="'+cx+'" y="'+(cy+4)+'" text-anchor="middle" font-size="14" fill="#AA77FF" font-weight="bold" font-style="italic">L</text>';
  // Wire-diameter callout (cross-section of the conductor)
  if(dv>0){
    var xd=cx-R*0.72, yd=cy-R*0.72;
    s+='<circle cx="'+xd+'" cy="'+yd+'" r="'+wireR+'" fill="#faf9ff" stroke="#AA77FF" stroke-width="1.2" stroke-dasharray="2,2"/>';
    s+='<text x="'+(xd-wireR-4)+'" y="'+(yd+4)+'" text-anchor="end" font-size="9" fill="#888">d'+(dv?' = '+dv+' mm':'')+'</text>';
  }
  // D dimension — double-headed arrow below the loop
  var ddy=cy+R+12;
  s+='<line x1="'+(cx-R)+'" y1="'+ddy+'" x2="'+(cx+R)+'" y2="'+ddy+'" stroke="#888" stroke-width="1" stroke-dasharray="3,3"/>';
  s+='<polygon points="'+(cx-R)+','+ddy+' '+(cx-R+7)+','+(ddy-3)+' '+(cx-R+7)+','+(ddy+3)+'" fill="#888"/>';
  s+='<polygon points="'+(cx+R)+','+ddy+' '+(cx+R-7)+','+(ddy-3)+' '+(cx+R-7)+','+(ddy+3)+'" fill="#888"/>';
  s+='<text x="'+cx+'" y="'+(ddy+14)+'" text-anchor="middle" font-size="9.5" fill="#888">D'+(Dv?' = '+Dv+' mm':'')+'</text>';
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  s+='<text x="'+(rx2+10)+'" y="42" font-size="10" font-weight="bold" fill="#5533aa" letter-spacing="1">RESULTS</text>';
  s+='<line x1="'+rx2+'" y1="47" x2="'+(rx2+210)+'" y2="47" stroke="#e0d8ff" stroke-width="1"/>';
  s+='<text x="'+(rx2+10)+'" y="66" font-size="11" fill="#555">Self-inductance, L</text>';
  s+='<text x="'+(rx2+200)+'" y="66" text-anchor="end" font-size="12" font-weight="bold" fill="#1a1a1a">'+Lv+'</text>';
  s+='<line x1="'+rx2+'" y1="72" x2="'+(rx2+210)+'" y2="72" stroke="#e8e0ff" stroke-width="1" stroke-dasharray="2,2"/>';
  s+='<text x="'+(rx2+10)+'" y="92" font-size="11" fill="#555">Tuning capacitor, C</text>';
  s+='<text x="'+(rx2+200)+'" y="92" text-anchor="end" font-size="12" font-weight="bold" fill="#1a1a1a">'+Cv+'</text>';
  s+='</svg>';
  document.getElementById('tool-diagram').innerHTML=s;
}

</script>
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