PCB Signal Propagation Velocity
vp = c / √(εr_eff)
Quick answer
This calculator solves v_p = c / √(ε_r_eff) for Propagation Velocity. With Effective Dielectric Constant 1.1, the result is 2.86 × 10⁸. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Electromagnetic signals on PCB traces travel slower than the speed of light in vacuum due to the dielectric material surrounding the trace. The propagation velocity is c (speed of light) divided by the square root of the effective relative permittivity. For microstrip traces (outer layer), the effective εr is between 1 and εr_substrate because the electric field partially travels through air. For stripline traces (inner layer, buried between ground planes), the effective εr equals the substrate εr. Standard FR-4 has εr ≈ 4.2-4.5 at low frequencies, giving propagation velocities of about 0.47-0.49 × c.
Variables
- v_p — Propagation velocity (m/s)
- ε_r_eff — Effective relative permittivity of the transmission line
Practical Notes
c = 299,792,458 m/s. For FR-4 microstrip (εr_eff ≈ 3.2-3.5), vp ≈ 160-168 mm/ns ≈ 6.0-6.3 in/ns. For FR-4 stripline (εr_eff ≈ 4.2-4.5), vp ≈ 141-146 mm/ns ≈ 5.5-5.8 in/ns. εr increases with frequency (dispersion) in FR-4, which can cause signal distortion at high data rates. Low-loss laminates (Rogers, Megtron) have more stable εr across frequency.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| vp | Propagation Velocity | — | — |
| er | Effective Dielectric Constant | — | — |
Step by step
- 1. What you know: Effective Dielectric Constant 1.1
- 2. The relation: v_p = c / √(ε_r_eff)
- 3. Substitute: er = 1.1
- 4. Result: Propagation Velocity = 2.86 × 10⁸
Worked examples
Minimum range
Given: Effective Dielectric Constant 0.055
Result: Propagation Velocity = 1.28 × 10⁹
Low range
Given: Effective Dielectric Constant 0.55
Result: Propagation Velocity = 4.04 × 10⁸
Typical
Given: Effective Dielectric Constant 1.1
Result: Propagation Velocity = 2.86 × 10⁸
High range
Given: Effective Dielectric Constant 1.76
Result: Propagation Velocity = 2.26 × 10⁸
Maximum range
Given: Effective Dielectric Constant 17.6
Result: Propagation Velocity = 7.15 × 10⁷
Solving for each variable
Solve for Propagation Velocity
Effective Dielectric Constant 0.055 → 1.28 × 10⁹
Solve for Effective Dielectric Constant
Propagation Velocity 0.025 → 1.44 × 10²⁰
How Propagation Velocity changes with Effective Dielectric Constant
| Effective Dielectric Constant (input) | Propagation Velocity (result) |
|---|---|
| 0.11 | 9.04 × 10⁸ |
| 0.275 | 5.72 × 10⁸ |
| 0.55 | 4.04 × 10⁸ |
| 0.825 | 3.3 × 10⁸ |
| 1.1 | 2.86 × 10⁸ |
| 1.65 | 2.33 × 10⁸ |
| 2.2 | 2.02 × 10⁸ |
| 4.4 | 1.43 × 10⁸ |
| 7.7 | 1.08 × 10⁸ |
| 11 | 9.04 × 10⁷ |
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<p><a href="https://vbatpower.com/formulas/pcb-propagation-vel/">PCB Signal Propagation Velocity</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate PCB Signal Propagation Velocity?
Use v_p = c / √(ε_r_eff). With Effective Dielectric Constant 1.1, Propagation Velocity works out to 2.86 × 10⁸.
How do you calculate pcb signal velocity?
Rearrange for Propagation Velocity: with Effective Dielectric Constant 0.55, Propagation Velocity is 4.04 × 10⁸.
What is the formula for PCB Signal Propagation Velocity?
The formula is v_p = c / √(ε_r_eff). Electromagnetic signals on PCB traces travel slower than the speed of light in vacuum due to the dielectric material surrounding the trace.
How do you find Effective Dielectric Constant when you know the other values?
Rearrange for Effective Dielectric Constant: with Propagation Velocity 0.025, Effective Dielectric Constant is 1.44 × 10²⁰.
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