What is the difference between phase velocity and group velocity in a dispersive transmission line?
Phase vs Group Velocity
For a non-dispersive transmission line (TEM-mode coax, stripline), the phase velocity is constant with frequency: vp = c/√εr. The group velocity equals the phase velocity, and all frequency components of a signal travel at the same speed. The signal waveform is preserved (no pulse spreading).
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Frequently Asked Questions
Does vp > c violate relativity?
No. Phase velocity greater than the speed of light does not violate special relativity because it does not represent the transfer of information or energy. A steady-state single-frequency wave carries no information. Information travels at the group velocity, which is always ≤ c.
When does dispersion matter practically?
Dispersion matters when the signal bandwidth is significant compared to the transmission line's cutoff bandwidth. Narrowband signals (<1% BW) experience negligible dispersion even in waveguide. Wideband signals (>10% BW) in waveguide can experience significant pulse spreading and phase distortion.
How do I measure group velocity?
Measure the phase of S21 across frequency. The group delay is tg = -dφ/dω. The group velocity is vg = length / tg. The VNA calculates group delay directly from the phase data. Non-constant group delay across frequency indicates dispersion.