Stripline

Design a centered trace between two ground planes in a uniform dielectric.

Stripline geometry

Calculate

Target impedance Z₀ (Ω)

Ground-plane separation B

Full distance between the two planes. The trace is centered, B/2 from each. Units apply to all geometry dimensions.

Dielectric relative permittivity εᵣ

Use the material value, not effective permittivity.

Calculated trace width w

0.47 mm

Calculated impedance: 50 Ω
Dielectric εᵣ = effective εᵣ: 4.3

w = 0.47 mm · B = 1 mm.
Cross-section schematic; proportions are illustrative. B is the full separation between the ground planes.

Homogeneous dielectric between two ground planes. Zero-thickness, lossless estimate.

More measurements

Electrical length & phase delay

Frequency

Line length

Electrical length: 183.02 °
One-way phase delay: 207.51 ps
Guided wavelength: 59.01 mm

Frequency changes propagation readings, not the quasi-static impedance. Phase delay equals group delay only in this nondispersive model.

Width sensitivity

Width variation ± (%)

Only width varies; plane separation and material stay fixed. This is not a combined fabrication tolerance.

Width-only sensitivity at fixed geometry and material
Trace	Width (mm)	Z₀ (Ω)
Narrower	0.45	51.37
Nominal	0.47	50
Wider	0.49	48.7

Model range & numerical check

Calculation range: 1 ≤ εr ≤ 20; 0.01 ≤ w/B ≤ 5. These are supported calculation bounds, not manufacturing limits.

Attainable impedance over supported widths: 8.35 Ω to 160.18 Ω.

Width / plane separation: 0.47
Velocity factor: 0.48
Forward residual: 0 Ω

A small residual confirms numerical consistency, not manufacturing accuracy.

Model & assumptions

Stripline surrounds the signal with one uniform dielectric and two ground planes. The signal is centered: B is the full plane separation, with B/2 to each plane. This differs from embedded microstrip, which has one lower ground.

Cohn’s conformal solution for a centered zero-thickness trace gives:

k=\tanh\!\left(\frac{\pi w}{2B}\right),\quad k'=\operatorname{sech}\!\left(\frac{\pi w}{2B}\right),\qquad Z_0=\frac{\eta_0}{4\sqrt{\varepsilon_r}}\frac{K(k')}{K(k)}

K is the complete elliptic integral with modulus k. The implementation uses arithmetic–geometric means and η₀=376.730313668 Ω. Width synthesis solves this relationship for w while keeping B and εᵣ fixed.

The ideal uniform dielectric supports TEM propagation with effective permittivity equal to material permittivity:

\varepsilon_{\mathrm{eff}}=\varepsilon_r,\quad \lambda_g=\frac{c}{f\sqrt{\varepsilon_r}},\quad\tau=\frac{\ell\sqrt{\varepsilon_r}}{c},\quad\theta=360^\circ f\tau

The tool supports 0.01≤w/B≤5 and 1≤εᵣ≤20. Ground planes are infinite, ideal and equipotential. Finite copper, trace offsets, unequal dielectrics, differential coupling, losses and higher modes are excluded. The ideal solution does not predict all behavior of a fabricated stack. Width sensitivity varies only the trace width; it is not a combined tolerance.

Independent example: w=0.2 mm, B=0.8 mm and εr=4.3 give67.47 Ω. Each distance to ground is 0.4 mm. Frequency and length errors affect only their dependent propagation results.

SourcesPolar Instruments, Calculation of PCB Track Impedance (opens in a new tab)NIST SP 330 (2019), The International System of Units (opens in a new tab)

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