Velocity Factor
In free space — a perfect vacuum — electromagnetic waves travel at the speed of light: 300,000,000 meters per second (3 × 10⁸ m/s). Inside a coaxial cable, a twisted pair or a circuit-board trace, signals travel slower than this because of the dielectric material around the conductors. The fraction of the speed of light at which the signal travels in a particular line is called the velocity factor of that line, usually written as VF or v/c.
Velocity factor matters whenever timing or length matters: working out how long a signal takes to cross a board or a cable, matching the lengths of clock and data traces, building a delay line, locating a fault in a cable with a time-domain reflectometer, or cutting a piece of cable to a specific electrical length for a matching section. If you ignore it and assume the free-space speed, your delays will be wrong and your cut cables too long.
At 14 MHz, one wavelength in free space is 21.4 meters. Inside RG-213 coax (VF = 0.66), one wavelength is only 14.1 meters — 66% as long. Any cable cut to free-space length will be electrically longer than intended.
View LargerWhat Velocity Factor Is
The velocity factor of a transmission line is the ratio of the wave propagation speed in that line to the speed of light in a vacuum:
- VF = velocity factor (dimensionless, between 0 and 1)
- v = wave propagation speed in the cable (m/s)
- c = speed of light in vacuum = 3 × 10⁸ m/s
Velocity factor is also sometimes expressed as a percentage. A cable with VF = 0.66 is said to have a 66% velocity factor, meaning waves travel at 66% of the speed of light inside it.
The wave propagation speed in a cable is:
v = c × VF = c / √εr
For standard RG-213 with solid polyethylene dielectric (εr = 2.26):
v = 3 × 10⁸ / √2.26 = 3 × 10⁸ / 1.503 = 1.996 × 10⁸ m/s
VF = 1.996 × 10⁸ / 3 × 10⁸ = 0.665 (about 66%)
Why Signals Travel Slower in Cable
The speed of an electromagnetic wave in any medium is determined by two properties of that medium: its electric permittivity (ε) and its magnetic permeability (μ). In a vacuum, these take their minimum values (ε₀ and μ₀), and the resulting wave speed is c = 1/√(ε₀μ₀) = 3 × 10⁸ m/s.
When you fill the space between the conductors with a dielectric material (polyethylene, PTFE, foam, or air), the dielectric has a relative permittivity εr greater than 1. This means the electric fields can be established with greater intensity for a given voltage, which increases the effective capacitance per unit length of the line. As you learned in the distributed circuit model from lesson the Characteristic Impedance lesson, increasing capacitance per unit length while keeping inductance per unit length the same slows the wave: v = 1/√(LC), and if C increases, v decreases.
Physically, the reason a dielectric slows the wave is that its molecules polarize under the influence of the electric field — positive and negative charge centers shift in opposite directions. This polarization stores energy in the molecular structure and slightly delays the propagation of the field. A denser dielectric (higher εr) polarizes more strongly and causes more slowing.
Most practical dielectrics used in coaxial cable have εr between 1.0 (air) and 2.3 (solid polyethylene). Materials with higher εr would reduce the cable's VF further, which is generally undesirable for coaxial cable because it would increase delay and dielectric loss.
For most practical transmission lines, the magnetic permeability is essentially the same as in vacuum (μr ≈ 1) because the dielectric materials used are non-magnetic. In ferrite-loaded cables (which exist but are unusual), the permeability would also differ from vacuum, but this is the exception rather than the rule.
Velocity Factor and Dielectric Constant
The relationship between velocity factor and relative dielectric constant is straightforward:
or equivalently:
εr = 1 / VF²- εr = relative dielectric constant of the insulating material
- VF = velocity factor (between 0 and 1)
This formula lets you calculate VF from the published dielectric constant, or determine the effective dielectric constant from a measured VF:
VF = 1/√2.08 = 1/1.442 = 0.694 (about 69%)
εr = 1/0.82² = 1/0.672 = 1.49 — consistent with foam polyethylene dielectric.
Note that this formula is exact for a cable filled uniformly with a single dielectric, but is only approximate for cables where the dielectric is partly air (such as foam-filled or air-spaced cables). For those, an effective dielectric constant must be determined empirically or from detailed modeling of the field distribution. This is why the published VF for foam-dielectric cables can vary slightly between manufacturers even for nominally similar products.
Velocity Factor of Common Cables
| Cable Type | Dielectric | Velocity Factor | Notes |
|---|---|---|---|
| RG-58A/U | Solid polyethylene | 0.659 (66%) | Common thin coax |
| RG-58C/U | Solid polyethylene | 0.659 (66%) | As above |
| RG-8/U (solid PE) | Solid polyethylene | 0.659 (66%) | Standard RG-8 |
| RG-8X | Foam polyethylene | 0.82 (82%) | Mini-8 flexible cable |
| RG-213/U | Solid polyethylene | 0.659 (66%) | Standard low-loss coax |
| LMR-400 | Foam polyethylene | 0.85 (85%) | Low-loss cable |
| LMR-240 | Foam polyethylene | 0.84 (84%) | Flexible low-loss |
| RG-6/U (CATV) | Foam polyethylene | 0.82 (82%) | 75-ohm CATV cable |
| RG-11/U (CATV) | Foam polyethylene | 0.82 (82%) | 75-ohm larger CATV |
| RG-142 | Solid PTFE | 0.694 (69%) | High-temp military |
| Semi-rigid coax (UT-141) | Solid PTFE | 0.695 (70%) | Microwave and test assemblies |
| Cat 5e / Cat 6 twisted pair | Polyethylene / FEP | 0.64–0.70 | Ethernet, 100 Ω differential |
| FR-4 microstrip (outer layer) | Board material + air above | about 0.53–0.57 | Effective value; about 6 ps/mm |
Notice the spread. Foam-dielectric cables carry signals at more than 80% of the speed of light, while a trace on an ordinary FR-4 circuit board carries them at little more than half that speed — and a stripline trace buried inside the board (VF about 0.48) slower still. A microstrip trace is faster than a buried one because part of its field is in the air above the board, which lowers the effective dielectric constant.
How VF Affects Wavelength and Delay
The wavelength of a signal in a transmission line is shortened by the velocity factor:
- λcable = wavelength in the cable (meters)
- λfree space = c / f = wavelength in free space (meters)
- c = 3 × 10⁸ m/s (speed of light)
- f = frequency (Hz)
- VF = velocity factor of the cable
In practical units with f in MHz and length in feet:
λcable (feet) = (984 / fMHz) × VFOr in meters:
λcable (meters) = (300 / fMHz) × VFλfree space = 300 / 14.2 = 21.13 meters = 69.3 feet
λRG-213 = 21.13 × 0.66 = 13.95 meters (45.7 feet)
A quarter-wave section would be 13.95 / 4 = 3.49 meters (11.4 feet)
For timing work it is usually more convenient to think in terms of propagation delay — the time a signal takes to travel a unit length of line:
- Free space or air: 3.33 ns/m
- Solid-polyethylene coax (VF 0.66): about 5.05 ns/m
- FR-4 microstrip (VF about 0.55): about 6.1 ns/m, or 6.1 ps per millimeter
These numbers come up constantly in high-speed design. A 2 m cable between two pieces of equipment delays every signal by about 10 ns; a 150 mm trace across a circuit board, by about 0.9 ns. When two signals must arrive together — the clock and data lines of a fast memory bus, or the two halves of a USB or HDMI differential pair — their traces must be length-matched so that the difference in delay is a small fraction of the bit time.
Cutting Cable to Length: Worked Examples
The most common practical application of velocity factor is cutting a transmission line to a specific electrical length. The general formula is:
For a quarter-wave section (90°):
Physical length = (1/4) × (c / f) × VFFor a half-wave section (180°):
Physical length = (1/2) × (c / f) × VFλfree space at 433 MHz = 300/433 = 0.693 meters
Quarter-wave in LMR-400 = 0.693 × 0.85 / 4 = 0.147 meters = 14.7 cm
If you had used the free-space quarter-wave (17.3 cm), the section would have been 18% too long, ruining the impedance transformation.
Distance travelled in 10 ns = 10 × 10⁻⁹ s × 0.66 × 3 × 10⁸ m/s
Length = 1.98 meters
A coil of coax cut to this length, terminated correctly at both ends, delays a pulse by 10 ns with very little distortion — a simple way to provide a known delay for testing a trigger circuit or comparing two oscilloscope channels.
A data trace is 30 mm longer than its clock trace on an outer layer.
Delay difference = 30 mm × 6.1 ps/mm = 183 ps
At a data rate of 500 Mb/s the bit time is 2 ns, so 183 ps uses up about 9% of it — usually tolerable, but at 2 Gb/s (0.5 ns bit time) the same mismatch would consume more than a third of the bit and the link would be unreliable. This is why fast board layouts add serpentine “wiggles” to the shorter trace to equalize the lengths.
Measuring VF When It Is Not Published
Sometimes you have a reel of cable with no markings, or the manufacturer's published VF does not match what you observe. In these cases you can measure the velocity factor directly using one of two methods.
Method 1: Network analyzer resonance method
One method uses a vector network analyzer (VNA) or an RF impedance analyzer. Cut a piece of cable of known physical length L. Short one end (connect center conductor to outer conductor with a short wire). Connect the other end to the analyzer. Sweep the frequency while observing the impedance. A short-circuited quarter-wave transmission line looks like an open circuit (very high impedance), and a half-wave line looks like a short circuit (nearly zero impedance). Find the first frequency f₁ at which the shorted cable looks like an open circuit — this is the quarter-wave resonance.
- L = physical length of cable (meters)
- f₁ = first quarter-wave resonant frequency (Hz)
- c = 3 × 10⁸ m/s
With L in feet and f₁ in MHz:
VF = L (feet) × f₁ (MHz) / 246VF = 10 × 16.1 / 246 = 161 / 246 = 0.655
This matches solid polyethylene dielectric (VF = 0.659), confirming the cable is likely standard RG-58 or RG-213 type.
Method 2: TDR (Time Domain Reflectometer) method
A TDR sends a fast pulse down the cable and measures the time for the reflection from the far end to return. If the cable is L meters long and the reflected pulse returns after a time delay Δt seconds, then the one-way travel time is Δt/2, and the velocity is:
v = 2L / Δt
VF = v / c = 2L / (Δt × c)
Most modern TDR instruments measure velocity factor directly, asking you to enter the cable length and reporting the VF, or conversely asking for the VF and reporting cable length (for fault location). An oscilloscope with a fast pulse generator can do the same job: send a pulse into the cable through a resistor equal to Z₀ and measure the time until the reflection from the open far end returns. TDR is covered in detail in the Test Equipment: Advanced module.
Frequently Asked Questions
Does velocity factor change with frequency?
For most practical cables over the frequency range of everyday electronics, the velocity factor is essentially constant. The dielectric constant of polyethylene and PTFE varies very slightly with frequency from a few megahertz to a few gigahertz — typically less than 1% — so this effect is negligible for almost all applications. Circuit-board materials such as FR-4 are different: their dielectric constant falls noticeably with frequency (from about 4.6 at 1 MHz to about 4.2 at a few gigahertz), so trace delay and impedance change slightly with frequency. Specialist low-loss board materials are used where this matters.
Why do my cables work fine even though I never considered velocity factor?
Because most connections do not need to be any particular electrical length. If the line is terminated in its characteristic impedance, the signal arrives cleanly regardless of length, and the only effect of velocity factor is a small delay that nothing in the circuit cares about. Velocity factor becomes critical only when timing or length matters for a specific purpose: a quarter-wave matching section, a delay line, length-matched clock and data traces, or locating a fault by TDR. For general connections where you simply want to get a signal from one place to another, you do not need to worry about velocity factor as long as the impedances are matched.
Why does foam dielectric give a higher velocity factor than solid polyethylene?
Foam dielectric is essentially a mixture of solid polyethylene and air bubbles. Air has εr = 1.0, and solid polyethylene has εr = 2.26. By foaming the plastic to, say, 40–50% air content, the effective dielectric constant drops to about 1.4–1.5, raising the velocity factor from 66% to 82–86%. This also reduces dielectric losses (since air has near-zero loss compared to solid plastic), which is why foam-dielectric cables like LMR-400 have lower attenuation than their solid-dielectric equivalents. The tradeoff is that foam dielectric cables must be handled more carefully — the foam structure can be damaged by sharp bends or excessive compression, which would change the effective dielectric constant and alter both the impedance and velocity factor.
Do the two wires of a differential pair need to be the same length?
Yes, very closely. A differential receiver looks at the difference between the two wires, so it expects the two halves of each edge to arrive at the same moment. If one wire is longer, its half of the edge arrives late (this is called intra-pair skew), the differential signal's edges become slower and less clean, and part of the signal is converted into common-mode noise that can radiate. USB, HDMI and Ethernet layout guidelines limit the length difference within a pair to a millimeter or less on the board, and the cables are made with both wires twisted together so that their lengths stay equal. Velocity factor matters here too: if one wire of the pair runs over a different material (for example, part of it in a connector), its delay changes even if its physical length is the same.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.