Differential Pair Impedance

Differential Pair Impedance

High-speed protocols like USB, Ethernet, PCIe, and HDMI use differential signaling: two traces carry the same signal with opposite polarity. This rejects common-mode noise and allows higher speeds.

For a differential microstrip pair, the differential impedance depends on how closely the two traces are spaced:

Zdiff = 2 × Z₀ × (1 - 0.347 × e^(-2.9 × S/H))

Where:

• Z₀ = single-ended microstrip impedance of each trace
• S = spacing between traces (edge-to-edge), same units as H
• H = dielectric height to ground plane

When S is large compared to H, the traces don't interact and Zdiff ≈ 2×Z₀. When the traces are close, mutual coupling reduces Zdiff.

Common targets:

• 90 Ω differential: USB 2.0, USB 3.0
• 100 Ω differential: Ethernet, HDMI, PCIe

Your Task

Implement diffPairImpedance(z0, S, H) returning differential impedance in ohms.

Then find the spacing S needed to achieve 90Ω differential for Z₀=45Ω, H=0.2mm.