Coax Electrical vs Physical Length

Formula

Description

The velocity factor (VF) of a cable is the ratio of the signal propagation speed to the speed of light in vacuum. Because electromagnetic waves travel slower in the cable dielectric than in free space, a cable appears electrically longer than its physical length. The electrical length determines the phase delay and is critical for antenna feed lines, delay matching, phasing harnesses, and impedance matching networks where specific electrical lengths (λ/4, λ/2) are required. VF = 1/√(εr) where εr is the dielectric constant of the insulation material.

Variables

• l_electrical — Equivalent free-space length (m)
• l_physical — Actual cable length (m)
• VF — Velocity factor (0 to 1, dimensionless)

Practical Notes

Common velocity factors: solid polyethylene (RG-58) VF = 0.66, foam polyethylene (LMR-400) VF = 0.85, air-spaced (hardline) VF = 0.92-0.95, PTFE (Teflon) VF = 0.70. For a quarter-wave matching section at 100 MHz (λ = 3 m): physical length = (3/4) × VF = 0.75 × 0.66 = 0.495 m for solid PE coax. VF can be measured with a network analyzer or TDR (time-domain reflectometer).