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  <title>Differential Pair Impedance Calculator | RF Toolbox</title>
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<h3>Differential Pair Impedance Calculator</h3>
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  <p>Edge-coupled differential pairs carry balanced signals. The differential impedance Z_diff = 2·Z_odd is what high-speed differential lines (USB, HDMI, LVDS) must be controlled to. Odd-mode signals travel in opposite directions; even-mode in the same direction.</p>
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  <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;">\(Z_{diff}=2Z_{odd},\quad Z_{odd}\approx Z_0\!\left(1-0.347\,e^{-2.655s/h}\right),\quad Z_{even}\approx Z_0\!\left(1+0.347\,e^{-2.655s/h}\right)\)</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;">w</td><td style="padding:3px 0;">Trace width (mm).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">s</td><td style="padding:3px 0;">Edge-to-edge spacing between the two traces (mm).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">h</td><td style="padding:3px 0;">Substrate height (mm). Trace to nearest ground plane.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">t</td><td style="padding:3px 0;">Trace thickness (mm). Standard 1 oz = 0.035 mm.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">εᵣ</td><td style="padding:3px 0;">Substrate dielectric constant.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Z_odd</td><td style="padding:3px 0;">Odd-mode impedance — the impedance each trace sees when signals are opposite.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Z_diff</td><td style="padding:3px 0;">Differential impedance = 2·Z_odd. The target specification, typically 100 Ω.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Z_even</td><td style="padding:3px 0;">Even-mode impedance — both traces driven together. Z_cm = Z_even/2.</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;">c</td><td>Speed of light = 2.998×10⁸ m/s</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">µ₀</td><td>Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">ε₀</td><td>Permittivity of free space = 8.854×10⁻¹² F/m</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>M. Kirschning &amp; R. Jansen, "Accurate wide-range design equations for the frequency-dependent characteristic of parallel coupled microstrip lines," <em>IEEE Trans. MTT</em> 32 (1984)</div>
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<div class="sec-lbl">Inputs</div>
<div class="inp-grid"><div class="inp-row"><label>Trace width, <span class="var">w</span></label><div class="inp-inline"><input type="text" id="dp2-w" value="0.2" ><span class='inp-units'>mm</span></div></div><div class="inp-row"><label>Edge spacing, <span class="var">s</span></label><div class="inp-inline"><input type="text" id="dp2-s" value="0.2" ><span class='inp-units'>mm</span></div><span class="inp-hint">trace edge to trace edge</span></div><div class="inp-row"><label>Substrate height, <span class="var">h</span></label><div class="inp-inline"><input type="text" id="dp2-h" value="0.2" ><span class='inp-units'>mm</span></div><span class="inp-hint">trace to nearest ground</span></div><div class="inp-row"><label>Trace thickness, <span class="var">t</span></label><div class="inp-inline"><input type="text" id="dp2-t" value="0.035" ><span class='inp-units'>mm</span></div><span class="inp-hint">1 oz Cu = 0.035 mm</span></div><div class="inp-row"><label>Dielectric constant, <span class="var">εᵣ</span></label><div class="inp-inline"><input type="text" id="dp2-er" value="4.4" ></div><span class="inp-hint">FR4≈4.4, Rogers4003≈3.55, PTFE≈2.1</span></div></div>
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<div class="sec-lbl">Results</div>
<div class="res-grid"><div class="res-card"><h4>Differential</h4><div class="res-row"><span class="res-lbl">Differential impedance, Z_diff</span><span class="res-val" id="dp2-zdiff">—</span></div><div class="res-row"><span class="res-lbl">Odd-mode impedance, Z_odd</span><span class="res-val" id="dp2-zodd">—</span></div></div><div class="res-card"><h4>Common-mode</h4><div class="res-row"><span class="res-lbl">Even-mode impedance, Z_even</span><span class="res-val" id="dp2-zeven">—</span></div><div class="res-row"><span class="res-lbl">Common-mode impedance, Z_cm</span><span class="res-val" id="dp2-zcm">—</span></div><div class="res-row"><span class="res-lbl">Single-trace Z₀</span><span class="res-val" id="dp2-z0single">—</span></div></div></div>
<div class="sec-lbl">Diagram</div><div class="schematic-box"><div id="tool-diagram"></div></div>

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