Via Stub Resonant Frequency
fres = c / (4 · lstub · √εr)
Quick answer
This calculator solves fres = c / (4 × lstub × √εr) for Resonant Frequency. With Stub Length 10 mm, Dielectric Constant 0.5, the result is 10.6 GHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fres | Resonant Frequency | GHz | Hz, kHz, MHz, GHz |
| lstub | Stub Length | mm | mm, cm, m, km |
| er | Dielectric Constant | — | — |
Step by step
- 1. What you know: Stub Length 10 mm, Dielectric Constant 0.5
- 2. The relation: fres = c / (4 × lstub × √εr)
- 3. Substitute: lstub = 10 mm, er = 0.5
- 4. Result: Resonant Frequency = 10.6 GHz
Worked examples
Minimum range
Given: Stub Length 0.1 mm, Dielectric Constant 0.025
Result: Resonant Frequency = 4740 GHz
Low range
Given: Stub Length 1 mm, Dielectric Constant 0.25
Result: Resonant Frequency = 149.9 GHz
Typical
Given: Stub Length 10 mm, Dielectric Constant 0.5
Result: Resonant Frequency = 10.6 GHz
High range
Given: Stub Length 10 cm, Dielectric Constant 0.8
Result: Resonant Frequency = 0.8379 GHz
Maximum range
Given: Stub Length 1 m, Dielectric Constant 8
Result: Resonant Frequency = 26.5 MHz
Solving for each variable
Solve for Resonant Frequency
Stub Length 0.1 mm, Dielectric Constant 0.025 → 4740 GHz
Solve for Stub Length
Resonant Frequency 100 MHz, Dielectric Constant 0.025 → 4.74 m
Solve for Dielectric Constant
Resonant Frequency 100 MHz, Stub Length 0.1 mm → 5.62 × 10⁷
How Resonant Frequency changes with Stub Length
| Stub Length (input) | Resonant Frequency (result) |
|---|---|
| 1 mm | 106 GHz |
| 2.5 mm | 42.4 GHz |
| 5 mm | 21.2 GHz |
| 7.5 mm | 14.13 GHz |
| 10 mm | 10.6 GHz |
| 15 mm | 7.066 GHz |
| 2 cm | 5.3 GHz |
| 4 cm | 2.65 GHz |
| 7 cm | 1.514 GHz |
| 10 cm | 1.06 GHz |
The same result in other units
| Unit | Value |
|---|---|
| MHz | 10600 |
| GHz | 10.6 |
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<p><a href="https://vbatpower.com/formulas/via-stub-resonance/">Via Stub Resonant Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Via Stub Resonant Frequency?
Use fres = c / (4 × lstub × √εr). With Stub Length 10 mm, Dielectric Constant 0.5, Resonant Frequency works out to 10.6 GHz.
How do you calculate stub resonance frequency?
Rearrange for Resonant Frequency: with Stub Length 1 mm, Dielectric Constant 0.25, Resonant Frequency is 149.9 GHz.
What is the formula for Via Stub Resonant Frequency?
The formula is 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.
How do you find Stub Length when you know the other values?
Rearrange for Stub Length: with Resonant Frequency 100 MHz, Dielectric Constant 0.025, Stub Length is 4.74 m.
How do you find Dielectric Constant when you know the other values?
Rearrange for Dielectric Constant: with Resonant Frequency 100 MHz, Stub Length 0.1 mm, Dielectric Constant is 5.62 × 10⁷.
What units does Via Stub Resonant Frequency use?
Resonant Frequency is shown in MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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