Formula & Calculator
Phase Velocity
The speed at which a wave's phase propagates along a transmission line.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| v_p | Phase velocity (speed of propagation) | m/s |
| L | Inductance per unit length (distributed) | H/m |
| C | Capacitance per unit length (distributed) | F/m |
| VF | Velocity factor = v_p / c (ratio to speed of light, optional) | dimensionless |
What it means
The phase velocity v_p is the speed at which the phase of a sinusoidal wave propagates along a transmission line. It is given by v_p = 1/√(LC), where L and C are the distributed inductance and capacitance per unit length. For a lossless line, the phase velocity is constant and independent of frequency. The phase velocity determines the wavelength on the line: λ = v_p / f. In a coaxial cable, the phase velocity is typically about 2/3 of the speed of light due to the dielectric constant. Example: For a line with L=0.5µH/m and C=0.2nF/m, v_p = 1/√(0.5e-6 * 0.2e-9) = 1/√(1e-16) = 1×10⁸ m/s. The wavelength at 100MHz is λ = 1e8 / 1e8 = 1m.
Worked example
Phase Velocity – Practical Example
Real‑World| Parameter | Value |
|---|---|
| L | 0.25 µH/m |
| C | 100 pF/m |
| Formula | vp = 1 / √(LC) |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Phase velocity v_p = 1/√(LC) is the speed of a sinusoidal wave along a transmission line. It determines the time delay of signals. Engineers use it to compute propagation delays, to design phase shifters, and to analyse dispersion. This velocity is less than or equal to the speed of light, depending on the dielectric. It is essential for high‑speed digital and RF design.
- Propagation delay calculation in interconnects
- Phase shifter and delay line design
- Transmission line length determination for matching
- Signal integrity analysis
- Educational understanding of wave speed