How is velocity factor calculated from the dielectric constant?

Velocity factor (VF) is the inverse square root of the effective dielectric constant: VF = 1/sqrt(Er_eff). For solid polyethylene dielectric (Er = 2.25), VF = 1/sqrt(2.25) = 0.667 or 66.7%. For foam polyethylene (Er_eff = 1.45-1.55 due to air content), VF = 0.80-0.83 or 80-83%. For air-spaced dielectric (Er = 1.0), VF = 1.0 or 100%. PTFE (Teflon) has Er = 2.1, giving VF = 0.69 or 69%. The effective dielectric constant may differ from the bulk material constant in cables where the dielectric is not homogeneous (e.g., foam or helical-spacer designs where air gaps modify the effective Er).

Why does velocity factor matter for antenna and cable measurements?

Velocity factor directly affects the electrical length of a cable. A quarter-wavelength matching section at 1 GHz in free space is 75 mm, but in a cable with VF = 0.66, it is only 49.5 mm (75 * 0.66). Cutting phasing harnesses, delay lines, or matching stubs to the wrong velocity factor causes impedance mismatch and phase errors. In distance-to-fault (DTF) measurements on cable analyzers, incorrect VF entry causes the displayed fault distance to be wrong by the VF error percentage. A VF error of 5% on a 100-meter cable run shows the fault at 95 or 105 meters instead of the correct location. Cable velocity factor must also be known for accurate TDR measurements and for calculating group delay through cable assemblies.

What velocity factors do common cables have?

RG-58 (solid PE): 66%. RG-213 (solid PE): 66%. LMR-400 (foam PE): 85%. RG-402 semi-rigid (PTFE): 69.5%. LDF4-50A 1/2-inch foam (foam PE): 88%. LDF5-50A 7/8-inch foam: 88%. RG-316 (PTFE): 69.5%. Air-dielectric hardline: 92-95%. Heliax with helical spacer: 88-92%. Open-wire transmission line: 95-97%. The velocity factor is frequency-independent for most practical purposes, though very slight dispersion exists due to the frequency dependence of the dielectric constant at microwave frequencies.

What is Cable Velocity Factor? | Signal Propagation Speed

Definition & Physics

Cable velocity factor (VF, also called velocity of propagation or VoP) is the ratio of the electromagnetic wave propagation speed within a transmission line to the speed of light in vacuum (c = 3 × 10⁸ m/s). It is determined by the effective dielectric constant (ε_r,eff) of the insulating material between the conductors: VF = 1/√ε_r,eff. Since all real dielectric materials have ε_r > 1, signals always travel slower than light in cable, with typical velocity factors ranging from 66% (solid polyethylene) to 95% (air-spaced dielectric).

Velocity factor is critical for any application requiring precise electrical length: phasing harnesses in antenna arrays, delay lines, quarter-wave matching transformers, stub tuners, and cable length measurement via TDR or DTF. An incorrect velocity factor entry in a cable analyzer causes proportional errors in distance-to-fault readings. In phased array feeds, a 2% velocity factor error across a 16-element array at 10 GHz produces 7.2 degrees of phase error, shifting the beam by 0.5 degrees and degrading sidelobe levels by 3-5 dB.

Key Formulas

Velocity Factor:

VF = 1 / √ε_r,eff = v_p / c

Solid PE (ε_r = 2.25): VF = 1/1.5 = 0.667 (66.7%)

Electrical Length:

L_elec = L_phys / VF

1 m cable at VF = 0.66: electrical length = 1.52 m

Wavelength in Cable:

λ_cable = VF × λ₀ = VF × c / f

1 GHz, VF = 0.85: λ_cable = 255 mm

Velocity Factor by Cable Type

Cable	Dielectric	ε_r,eff	VF	λ/4 at 1 GHz
RG-58	Solid PE	2.25	66%	49.5 mm
RG-316	Solid PTFE	2.07	69.5%	52.1 mm
LMR-400	Foam PE	1.38	85%	63.8 mm
LDF4-50A (1/2")	Foam PE	1.29	88%	66.0 mm
LDF5-50A (7/8")	Foam PE	1.29	88%	66.0 mm
Air-dielectric hardline	Air + spacers	1.07-1.15	92-97%	69-73 mm
Open-wire line	Air	~1.0	95-97%	71-73 mm

Practical Application

An amateur radio operator builds a quarter-wave vertical antenna for 146 MHz using RG-213 coaxial cable as a matching section. The free-space quarter wavelength is λ/4 = 300/(4 × 146) = 513 mm. With RG-213's velocity factor of 66%, the cable quarter-wave section must be cut to 513 × 0.66 = 339 mm. Using the wrong velocity factor (e.g., 85% for foam cable) would produce a 436 mm section that is electrically 33% too long, presenting a reactive impedance rather than the intended quarter-wave transformation. The operator verifies the cut length by measuring the cable's first resonance on a VNA: the cable appears as a short circuit at the input when it is exactly λ/2 electrically, confirming the velocity factor and physical length are correct.

Frequently Asked Questions

How is VF calculated from dielectric constant?

VF = 1/√ε_r,eff. Solid PE (ε_r = 2.25): VF = 66.7%. Foam PE (ε_r ~1.4): VF = 83-85%. PTFE (ε_r = 2.07): VF = 69.5%. Air (ε_r = 1): VF = 100%.

Why does VF matter for measurements?

Incorrect VF causes proportional errors in DTF fault distance and TDR readings. Also critical for cutting matching stubs and phasing harnesses: λ/4 at 1 GHz is 49.5 mm in solid PE cable vs. 66 mm in foam cable. Wrong VF = wrong impedance match.

Common cable velocity factors?

RG-58/213: 66%. RG-316/402: 69.5%. LMR-400: 85%. 1/2" and 7/8" foam: 88%. Air-dielectric hardline: 92-95%. Open-wire: 95-97%. VF is essentially frequency-independent for practical use.

Cable Velocity Factor