Single-ended Z₀ and differential impedance for microstrip and stripline — with cross-section and propagation delay.

Where controlled impedance comes from

A trace over a reference plane is a transmission line, and its characteristic impedance is set by the cross-section: trace width, the height to the plane, the copper thickness and the dielectric constant. For a microstrip (trace on an outer layer) the classic IPC-2141 approximation is:

Z_{0} = \frac{87}{ε _{r} + 1.41} ln (\frac{5.98 H}{0.8 W + T})

A stripline (trace buried between two planes) is fully surrounded by dielectric, so it's slower but better shielded:

Z_{0} = \frac{60}{ε _{r}} ln (\frac{4 b}{0.67 π ( 0.8 W + T )})

where $b$ is the plane-to-plane spacing with the trace centered. The wave doesn't travel through pure $ε_{r}$ ; for microstrip part of the field is in air, giving an effective value that sets the propagation delay:

ε_{eff} = \frac{ε _{r} + 1}{2} + \frac{ε _{r} - 1}{2} \frac{1}{1 + 12 H / W}, t_{p d} = \frac{ε _{eff}}{c}

Differential pairs

USB, Ethernet, HDMI, LVDS and DDR strobes route as coupled pairs. The differential impedance is a little under twice the single-ended value, reduced by the coupling between the two traces — tighter spacing, stronger coupling, lower Z_diff:

Z_{diff} \approx 2 Z_{0} (1 - 0.48 e^{- 0.96 S / H}) (microstrip), 2 Z_{0} (1 - 0.347 e^{- 2.9 S / b}) (stripline)

Targets are 90 Ω (USB, DDR) or 100 Ω (Ethernet, LVDS, PCIe). These closed-form approximations are accurate to a few percent in their valid range ( $0.1 \leq W / H \leq 2$ for microstrip); for sign-off, match them against your fabricator's field-solver stackup — copper roughness, solder mask and etch taper all shift the real number.

PCB Impedance Calculator

Where controlled impedance comes from

Differential pairs

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