Stripline impedance: stripline versus microstrip, Wheeler's formula, offset strips, and a worked example
A stripline is a trace on an inner layer with a plane above and a plane below. Both planes take field from the strip, so for the same impedance a stripline is narrower than a microstrip, the wave in it is slower, and it neither radiates nor picks up noise, which is why the sensitive high-speed lines of a multilayer board go inside. This calculator gives Z₀ from the width, the dielectric above and below the strip, εr and the copper weight with Wheeler's closed form, an estimate for a strip that is not centred, the delay, the capacitance and inductance per length, the width for a target impedance, the wavelength at a frequency and the delay of a run, with the cross-section and its field drawn to scale.
How to use the stripline calculator
- Type the trace width and the dielectric above and below it: from the strip's faces to each plane, equal for a centred stripline.
- Pick the substrate in the menu row (it fills in εr) and the copper weight; inner layers are usually ½ or 1 oz.
- Add a target Z₀ for the width that gives it, a frequency for the wavelength and a length for the delay. The Width table tab sweeps the width.
Stripline versus microstrip
A microstrip has one plane and air above; a stripline has a plane on each side and laminate all round. The second plane roughly doubles the capacitance, so the same strip has a much lower Z₀ buried than on the surface, and a 50 Ω stripline must be narrow: about 40 % of the plane spacing on FR-4, against about twice the dielectric height for a microstrip. The field is entirely in the laminate, so εeff = εr, the wave runs at c/√εr (0.48 c on FR-4 against 0.55 c on the surface), and the delay does not depend on the width. The planes shield the strip from radiating and from crosstalk with other layers, and the signal is kept away from the solder mask and the outside world.
Wheeler's formula
Z₀ = (30/√εr) · ln{1 + (4/π)·((b−t)/w') · [ (8/π)·((b−t)/w') + √( ((8/π)·((b−t)/w'))² + 6.27 ) ]}
b is the plane spacing, t the copper thickness and w' the strip's width widened by Wheeler's thickness term Δw. Harold Wheeler published the formula in 1978 as a fit to the exact conformal-map solution, and it is within 0.5 % for any width and thickness a board would use; it is the form given in Wadell's handbook and in most impedance tools. The older IPC-2141 expression, (60/√εr) ln(4b / (0.67π w (0.8 + t/w))), is a narrow-strip approximation and drifts for wide strips.
Offset striplines
On a real stack the inner signal layer is rarely exactly centred: a core on one side and a prepreg on the other leave different distances. The strip then couples more to its nearer plane. The usual estimate treats it as two striplines, one twice the distance to each plane, in parallel: Z₀ = 2 ZA ZB / (ZA + ZB). It is within a few percent for moderate offsets. A strip very near one plane and far from the other is practically a microstrip against the near plane, and a field solver is the honest tool.
In the stack-up
Six-layer boards often put signals on layers 3 and 4 between the planes on 2 and 5, with 0.2–0.4 mm of dielectric each side, which makes a 50 Ω stripline 0.15–0.3 mm wide: easily routed. Keep a strip's planes continuous beneath it (a split in a plane under a stripline is a discontinuity), and remember that the fab's finished dielectric thicknesses after pressing differ from the nominal prepreg; for controlled impedance give the fab the target and let them tune the width to their stack.
Your stripline, step by step
- Geometry: planes 0.62 mm apart, strip 0.20 mm (w' = 0.23 mm with the copper), centred.
- Impedance: Z₀ = 55.8 Ω (59.4 Ω for a thin strip); as a microstrip the strip would be 81.8 Ω.
- Wave: 0.48 c, 6.92 ps/mm, C 0.12 pF/mm, L 386 pH/mm.
- For 50.0 Ω: 0.25 mm wide.
- At 2.4 GHz: λ = 60.2 mm, λ/4 = 15.1 mm; 40.0 mm is 239°, 277 ps.
Worked example: a 0.2 mm strip centred in 0.6 mm of FR-4
Planes 0.62 mm apart with ½ oz copper (17 µm), εr 4.3. Wheeler's thickness term makes the strip 0.23 mm wide for the formula, and Z₀ = 55.8 Ω (59.4 Ω for a thin strip). The same strip as a microstrip on 0.3 mm would be 81.8 Ω: the second plane takes a good share of the impedance away. The wave runs at 0.48 c, 6.92 ps/mm, so at 2.4 GHz the wavelength in the laminate is 60.2 mm and a 40 mm run is 239°. For exactly 50 Ω the strip would be 0.25 mm; offset to 0.2 mm above and 0.5 mm below, the same 0.2 mm strip gives 54.8 Ω.
Questions
Which dielectric constant do I use when the core and the prepreg differ?
For a centred strip an average weighted by thickness is close enough; for an offset strip use each side's εr for its half-stripline, or a field solver. Resin-rich prepreg is usually a little lower than the core.
Why is my stripline narrower than the fab's minimum?
Thin dielectrics push the 50 Ω width below 0.1 mm. Use thicker dielectrics, a lower εr, or accept a higher impedance; the calculator flags widths under 0.1 mm.
Is a stripline slower than a microstrip?
Yes, by √(εr / εeff): about 15 % on FR-4. A signal that changes from an outer to an inner layer changes speed, which matters when matching lengths.
What about differential striplines?
A pair of striplines couples to each other as well as to the planes; the differential impedance needs a coupled-line formula, which is next in this suite.