A browser-based calculator for PCB transmission-line impedance. It covers five structures: microstrip, symmetric stripline, asymmetric stripline, and differential pairs in both microstrip and stripline.
Two things most calculators leave out are available here: an asymmetric structure where the core and the prepreg have different dielectric constants, and the trapezoidal conductor cross-section produced by etching. Both happen on every real board, and both are routinely ignored.
Which structure to pick
| Structure | When to use it |
|---|---|
| Microstrip | Outer-layer routing (L1 / bottom). One side is open to air |
| Stripline (symmetric) | Inner-layer routing with equal distance to the planes above and below |
| Stripline (asymmetric) | Inner-layer routing where the distances or the dielectric constants differ. This is what most real multilayer boards look like |
| Differential pair (microstrip) | Outer-layer differential routing: USB, LVDS, Ethernet |
| Differential pair (stripline) | Inner-layer differential routing, when noise immunity comes first |
What each input means
- Wtop / Wbot — top and bottom width of the conductor. Etching leaves a trapezoid, so the two are entered separately. Enter the same value twice to treat the trace as rectangular.
- T — conductor thickness. Choose the oz unit if you specify copper by weight (1 oz ≈ 35 µm).
- H — substrate height for microstrip: the distance from the trace to the reference plane.
- B — plate separation for symmetric stripline: the distance between the two ground planes.
- H1 / H2 — for asymmetric stripline, the distance from the trace to the upper and lower plane.
- εr — dielectric constant. FR-4 sits around 4.2–4.5, but it varies with material and frequency, so use the value from the laminate datasheet.
- S — edge-to-edge spacing of a differential pair. Enter it as the minimum clearance at the bottom, since a trapezoid is narrower at the base than at the top.
When the core and the prepreg differ
An inner-layer trace normally has core on one side and prepreg on the other. The two have different resin content, so their dielectric constants are different too — core at 4.3 and prepreg at 4.1, for instance.
Most calculators accept a single εr, which forces you to compromise on an average. The “Stripline (asymmetric)” tab here takes εr1 for the upper side and εr2 for the lower side separately.
The solution splits the capacitance above and below the trace and recombines the two halves. The effective dielectric constant εeff that comes out is weighted by each side’s air capacitance, which is not the same as a weighted average on 1/h. Substituting a plain average here costs you accuracy, and the error grows with the asymmetry.
Handling the trapezoidal cross-section
In subtractive etching the etchant attacks from above, so the top of the conductor is eaten away more than the base and the cross-section ends up as a trapezoid with a narrow top. The design specifies a single W; the finished copper has two different widths.
This tool takes Wtop and Wbot separately and works with the equivalent width (Wtop+Wbot)/2. It also reports the etch factor (T divided by the undercut on one side) so you can compare it against the figure your fabricator quotes.
For the asymmetric stripline, Wtop is applied to the upper capacitance and Wbot to the lower one, so the orientation of the trapezoid is reflected in the result.
About the differential calculation
Besides the differential impedance Zdiff, the differential tabs report the even-mode impedance Z0e, the odd-mode impedance Z0o and the common-mode impedance Zcomm:
Z_diff = 2 × Z_0o Z_comm = Z_0e / 2
You need the common-mode impedance when selecting a common-mode choke or designing common-mode termination. Many calculators give only the differential figure, so this is here for when you need both.
The gap S is entered as the minimum clearance at the base, and a trapezoid is converted to the equivalent spacing S+(Wbot−Wtop)/2. The thickness correction widens each trace and narrows the gap by the same amount, so the pitch Wbot+S is preserved — the number you actually specify in the layout does not drift.
Formulas and sources
| Structure | Formula |
|---|---|
| Microstrip | Hammerstad–Jensen closed form plus a thickness correction |
| Stripline | Exact conformal-mapping solution (complete elliptic integrals) plus Wheeler’s thickness correction |
| Asymmetric stripline | Capacitance split above and below the trace, then recombined |
| Differential microstrip | Kirschning–Jansen static closed form (even and odd mode) |
| Differential stripline | Cohn’s conformal mapping for the even and odd mode |
The complete elliptic integrals are evaluated by the arithmetic–geometric mean, converged to the limit of double precision. No series approximation is used.
Accuracy and range of validity
The implementation is verified by a self-consistency check: with the gap S opened wide, the even and odd modes must converge on the single-ended value. The stripline case matches to machine epsilon, and the microstrip case converges to within 0.001 % at large S/H. By the same argument, the asymmetric stripline reduces exactly to the symmetric one when H1=H2, εr1=εr2 and the cross-section is rectangular.
- This is a static (low-frequency) model. Dispersion, conductor loss, dielectric loss and surface roughness are not included, so above a few GHz the result reads low.
- Expect a few percent of error on the absolute value. It will not agree exactly with your fabricator’s coupon measurements or with a field solver.
- Inputs outside the recommended range raise a warning (W/H, T/B, S/H, εr and so on). The calculation still runs, but trust the number less.
- Confirm the final design with a field solver such as uSimmics (Qucs-S).
Related articles
- Microstrip characteristic impedance — where the formula comes from, and what to watch in design
- Stripline characteristic impedance — the conformal-mapping solution explained
- Differential stripline design — how to think about even and odd modes
- Etching and conductor cross-section — why the trapezoid appears, and the etch factor
- VSWR and reflection — what an impedance mismatch actually costs you
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