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Differential Via Calculator

Calculate the stub resonance and insertion loss of a differential via pair: the stub notch that dominates a via transition long before conductor and dielectric loss matter.

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Formula

fres≤c4Lstubεr,αc≤Rs(1/d+1/D)πZdense,Zdense=η0πεrln⁡Ddf_{res} \le \frac{c}{4 L_{stub}\sqrt{\varepsilon_r}},\qquad \alpha_c \le \frac{R_s\left(1/d + 1/D\right)}{\pi Z_{dense}},\qquad Z_{dense} = \frac{\eta_0}{\pi\sqrt{\varepsilon_r}}\ln\frac{D}{d}

Reference: Stub loading from S₂₁ of a shunt admittance; the coaxial conductor loss α_c = R_s(1/a + 1/b)/(2η·ln(b/a)) (Pozar, Microwave Engineering, 4th ed., §2.7); the field solution of openspec fix-calculator-formulas-followup (2026-10-12). A via transition is three-dimensional — see the linked full-wave tool.

f_res— First stub resonance, unloaded upper bound (GHz)
d— Finished barrel diameter (mm)
D— Antipad diameter (mm)
L_stub— Unused barrel below the exit layer (mm)
R_s— Surface resistance of copper, √(πfµ₀/σ) (Ω)
Z_dense— Dense-plane limit: two barrels, each inside its own coaxial wall (Ω)
η₀— Impedance of free space, µ₀·c = 376.730313668 Ω (Ω)

How It Works

A via transition is the least controlled part of an otherwise controlled-impedance channel. The trace is held to a few percent; the via is whatever the drill and the antipad happen to produce. This calculator gives the number that most often decides whether that matters: the insertion loss the pair costs across a band, and the stub resonance behind it.

It does not report the pair's impedance, because the via's own dimensions do not determine it. A field solution of three via geometries, solved in three dimensions with the planes in place and cross-checked full-wave, shows the differential impedance moving with the pitch of the planes the via passes through: for a 0.25 mm barrel in a 0.9 mm antipad at a 0.8 mm pitch it is 85.6 Ω with planes 0.1 mm apart and 96.0 Ω with planes 1.0 mm apart. The planes add capacitance at every hole edge without changing the inductance, so no formula in the barrel, antipad and pitch alone lands within 10 % of every case. For the impedance, simulate your stackup with the linked full-wave tool.

The loss is dominated by something that has nothing to do with the via's own resistance. Below the layer where the signal leaves, the barrel carries no signal but is still connected — an open-circuited stub hanging off the through path. A shunt admittance across a line produces a transmission notch when its length reaches a quarter wavelength, and for a stub in a typical board that happens at a frequency well below where conductor and dielectric loss become interesting. Conductor and dielectric loss through 1.6 mm of barrel amount to a fraction of a decibel even at 20 GHz; the stub can take tens.

That is why backdrilling exists. Removing the stub removes the notch, and what is left is the small loss the via itself costs.

The same planes slow the wave in the barrel, so the stub resonance this calculator gives, c/(4·L·√εr), is an upper bound: in the field solution the stubs resonated 8–27 % lower, and the worst in-band loss here is taken at the unloaded resonance. The conductor loss is an upper bound too, at the dense-plane limit where each barrel sits inside its own coaxial wall; the radial currents in the planes are not modelled.

This is a screening model, not a field solution. A real via transition includes pad capacitance, plane-cavity resonance and the launch discontinuity, none of which are here. Use it to decide whether a geometry deserves a full-wave simulation, then run one.

Worked Example

Take a 0.25 mm finished barrel, 0.9 mm antipad, 0.8 mm pitch, in a 1.6 mm board of FR4 at εr = 4.2 with tan δ = 0.02. The signal enters at the top and leaves at 0.4 mm depth. Band of interest: 0.1 to 20 GHz.

The impedance is not computed here. A field solution of this geometry puts the differential impedance between 85.6 Ω, with planes 0.1 mm apart, and 96.0 Ω, with planes 1.0 mm apart, so it depends on the stackup: simulate it with your plane pitch.

Now the stub. The signal exits at 0.4 mm in a 1.6 mm board, leaving 1.2 mm of unused barrel. Its unloaded quarter-wave resonance lands at 30.48 GHz — above the 20 GHz band edge, so the notch itself is outside the band, but its skirt is not. That is an upper bound: the planes slow the wave, and in the field solution this stub resonates nearer 26.3 GHz.

Across 0.1 to 20 GHz the worst insertion loss, taken at the unloaded resonance, is 2.247 dB, at the top of the band. Of that, dielectric loss through the barrel contributes 0.119 dB and conductor loss at most 0.011 dB, the dense-plane bound with Z_dense = (η₀/(π√εr))·ln(D/d) = 74.95 Ω. The remaining ~2.1 dB is the stub. The via's own material loss is under a sixth of a decibel; everything else is the piece of copper that is not carrying signal.

Set the exit depth to 1.6 mm — a fully backdrilled or bottom-exiting via — and the stub disappears along with almost all of the loss: 0.131 dB remains.

Practical Tips

  • ✓Compare the worst in-band insertion loss with and without the stub before deciding whether backdrilling is worth its cost. If the resonance is far above the band, it may not be.
  • ✓Move the transition to a deeper layer if you can — it shortens the stub for free and moves the resonance up.
  • ✓Get the via's differential impedance from a full-wave simulation of your stackup and compare it with the trace's. The mismatch, not the absolute value, is what the channel sees.
  • ✓Antipad diameter is the most effective impedance knob here, and the one your fabricator is most willing to change.
  • ✓Read the stub resonance as the highest the notch can be. The planes pull it lower, by up to about a quarter in the field solution behind this page.
  • ✓Use the linked full-wave S-parameter tool for any transition that this model puts close to a limit.

Common Mistakes

  • ✗Budgeting via loss from conductor and dielectric loss alone. Those are the small terms. The stub is the large one, and it is resonant rather than gradual.
  • ✗Assuming a via is electrically short because it is physically short. A 1.2 mm stub in FR4 is a quarter wavelength at 30 GHz, and its effect is felt long before that.
  • ✗Taking a closed-form formula's word for differential via impedance. The plane pitch alone moves it by more than 10 %, and the usual two-wire-plus-coax estimate reads about half the solved value. Simulate the stackup.
  • ✗Spacing the vias apart to raise the differential impedance without simulating the result. Once plane copper comes between the barrels the coupling changes in a way no closed form here captures.
  • ✗Enlarging the antipad without limit. It raises the impedance toward the trace value, but it also removes plane copper, which is a return-path problem of its own.
  • ✗Taking this model as a substitute for a full-wave simulation on a channel that is genuinely marginal.

Frequently Asked Questions

Because it is resonant. Conductor and dielectric loss in a 1.6 mm barrel are a small fraction of a decibel even at 20 GHz, while a quarter-wave stub puts a deep notch exactly where it resonates. A via that transitions on an upper layer of a thick board leaves a long stub and can notch inside your band.
It is a screening model. The stub resonance is the unloaded upper bound, since the planes slow the wave, and the conductor loss is the dense-plane upper bound. A real via transition also includes pad capacitance, plane-cavity effects and the launch discontinuity, none of which are here. Use it to decide what to simulate.
It removes the stub, which removes the notch. Set the exit depth equal to the board thickness to see the case with no stub at all — the remaining insertion loss is what the via itself costs, and it is usually small.
Because the via's dimensions do not determine it. In a field solution the default pair is 85.6 Ω with planes 0.1 mm apart and 96.0 Ω with planes 1.0 mm apart, and the common-mode impedance also depends on where the return current flows, which is not an input either. Simulate your stackup for the number.
Plane copper comes between the two barrels and the antipads no longer merge into one opening, which changes how the barrels couple. The stub resonance and the loss do not depend on it. The calculator shows whether the antipads overlap; the impedance needs a full-wave simulation either way.

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Your Via's Loss Isn't in the Barrel

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