How do I calculate the characteristic impedance of a differential microstrip pair?
Differential Microstrip Design
Differential signaling uses two traces carrying equal but opposite signals. The differential impedance is the impedance seen between the two traces when driven differentially. It equals twice the odd-mode impedance of one trace, which accounts for the mutual coupling between the traces. Coupling reduces the odd-mode impedance below the uncoupled (single-ended) impedance.
The coupling factor depends on the gap (S) between traces relative to the dielectric height (h) and trace width (W). Tight coupling (S/h < 1) provides strong noise rejection and compact routing but makes the impedance more sensitive to manufacturing tolerances. Loose coupling (S/h > 3) approaches the uncoupled impedance and is less sensitive to gap variations but provides less common-mode rejection.
For PCB design, specify the differential impedance, trace width, and gap to the fabricator. They will adjust the dimensions based on their process capabilities. Typical tolerances are ±10% for differential impedance on FR4. For tighter control (±5%), use controlled-impedance laminates and specify coupon testing to verify impedance on each panel.
Zodd ≈ Z₀ × (1 - 0.48 × e-0.96·S/h)
Zeven ≈ Z₀ × (1 + 0.48 × e-0.96·S/h)
Zcommon = Zeven / 2
Example: Z₀=60Ω, S=h=5mil
Zodd=60×(1-0.48×e⁻⁰·⁹⁶)=49Ω
Zdiff=2×49=98Ω
Frequently Asked Questions
What differential impedance is standard?
100 Ω: PCIe, USB 2.0, LVDS, Ethernet. 90 Ω: USB 3.0/3.1, HDMI. 85 Ω: some HDMI implementations. The standard is set by the protocol specification and must be matched by the PCB design.
Does the pair need to be equal length?
Yes. Length mismatch between the P and N traces causes timing skew, which degrades eye diagram quality. The maximum skew depends on the data rate: for 10 Gbps signals, skew must be less than approximately 5 mil (0.13 mm). Match within each differential pair, but pairs can differ from each other.
What about edge-coupled vs broadside-coupled?
Edge-coupled (both traces on the same layer) is standard for microstrip differential pairs. Broadside-coupled (traces on adjacent layers directly above each other) provides tighter coupling and smaller footprint but is more sensitive to registration and etch tolerances.