What is the formula for Via Stub Resonant Frequency?

The Via Stub Resonant Frequency formula is fres = c / (4 × lstub × √εr), where fres—Quarter-wave resonant frequency (Hz); lstub—Length of the unused via stub (m); εr—Effective dielectric constant; c—Speed of light.

What does fres mean in the Via Stub Resonant Frequency formula?

fres is Quarter-wave resonant frequency (Hz).

Via Stub Resonant Frequency

Q: How do you calculate Via Stub Resonant Frequency?

Use the formula fres = c / (4 × lstub × √εr). An unused length of plated via barrel (the stub left when a signal changes layers but the via continues) acts as a quarter-wave resonator. Enter the values you know in the calculator above and it solves for the remaining variable.

fres = c / (4 · lstub · √εr)

Calculator

Resonant Frequency

Stub Length

Dielectric Constant

Result

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Formula

fres = c / (4 × lstub × √εr)

Description

An unused length of plated via barrel (the stub left when a signal changes layers but the via continues) acts as a quarter-wave resonator. At its resonant frequency the stub presents a near-short that sucks energy out of the signal, creating a deep notch in the channel response. Knowing this frequency tells you whether a via stub will corrupt your highest signalling rate, and whether back-drilling is needed.

Variables

fres — Quarter-wave resonant frequency (Hz)
lstub — Length of the unused via stub (m)
εr — Effective dielectric constant
c — Speed of light

Practical Notes

Keep fres well above the signal’s knee frequency, or back-drill the stub to shorten it. Longer stubs and higher-εr material push the resonance down into the signal band.

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