velocity factor

{{Short description|Ratio of the speed at which a wavefront passes through the medium to the speed of light in vacuum}}

The velocity factor (VF),Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, {{ISBN|0-8306-4129-7}}, p.251 ('velocity factor') also called wave propagation (relative) speed or (relative) velocity of propagation (VoP or {{nobreak| $v_\mathrm{P}$ ),}}[https://web.archive.org/web/20240712045911/www.generalcable.co.nz/getattachment/f81f14ee-7bec-4841-82d5-84b2df58b4f5/Velocity-of-Propagation.aspx Velocity of Propagation], General Cable Australia Pty Ltd, retrieved 2010-02-13 of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

The speed of radio signals in vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in vacuum is 1.0 (unity). In air, the velocity factor is ~0.9997. In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

The use of the terms velocity of propagation and wave propagation speed to mean a ratio of speeds is confined to the computer networking and cable industries. In a general science and engineering context, these terms would be understood to mean a true speed or velocity in units of distance per time,"velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, {{ISBN|1-85296-150-3}} while velocity factor'' is used for the ratio.

Typical velocity factors

Velocity factor is an important characteristic of communication media such as category 5 cables and radio transmission lines. Plenum data cable typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in vacuum) and riser cable around 0.70 (approximately 210,000,000 m/s or 4.76 ns per metre).

style="width:5em;"\| VF (%)	Cable type	Ethernet physical layer
class="wikitable" \|+ Minimum velocity factors allowed for network cable standards
{{center\|74~79%}}	Cat-7 twisted pair
{{center\|77% }}	RG-8/U	Minimum for 10BASE5IEEE 802.3 Clause 8.4.1.3 The minimum required velocity of propagation is 0.77 c.
{{center\|67% }}	Optical fiber (silica glass)	Minimum for 10BASE-FL,IEEE 802.3 clause 15.3.1.3 The propagation delay shall be ≤5 μs/km. (This is equivalent to a velocity of propagation of 0.67c.) 100BASE-FX, ...
{{center\|67% }}	Plastic optical fiber	1000BASE-RHx PMMA
{{center\|63% }}	Plastic optical fiber	polystyrene
{{center\|65% }}	RG-58A/U	Minimum for 10BASE2IEEE 802.3 Clause 10.5.1.3 The minimum required velocity of propagation is 0.65 c.
{{center\|65% }}	Cat-6A twisted pair	10GBASE-T
{{center\|64% }}	Cat-5e twisted pair	100BASE-TX, 1000BASE-T
{{center\|58.5%}}	Cat-3 twisted pair	Minimum for 10BASE-TIEEE 802.3 Clause 14.4.2.4 The maximum propagation delay of twisted pair shall be 5.7 ns/m (minimum velocity of 0.585 × c).

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:{{cite book |editor-first = H. Ward |editor-last= Silver |year= 2011 |title= The ARRL Handbook for Radio Communications |edition= 88th |publisher = ARRL |place= Newington, CT |isbn= 978-0-87259-096-0 |chapter= Chapter 22: Component Data and References |page= 22.48}}{{cite book |first=Kenneth L. |last=Kaiser |year=2005 |title=Transmission Lines, Matching, and Crosstalk |publisher=CRC Press |place=Boca Raton, FL |isbn=978-0-8493-6362-7 |pages=2–24 |url=https://books.google.com/books?id=QWFd-33xXvgC&pg=SA2-PA24 }}

style="width:5em;"\| VF (%)	Transmission line	Center insulation
class="wikitable"
{{center\|95~99%}}	open-wire line ("ladder line")	air insulated
{{center\|93%}}	HJ8-50B 3 inch Heliax coaxial cable	air dielectric{{cite web \|title=HJ8-50B \|website=commscope.com \|url=https://www.commscope.com/globalassets/digizuite/112335-p360-hj8-50b-external.pdf?r=1 \|access-date=22 March 2022 }}
{{center\|86%}}	RG-8 Belden 7810A coaxial cable	gas-injected foamed high-density polyethylene{{cite report \|title = Belden Global Catalog \|id=7810A \|lang=EN \|via=belden.com \|url=https://catalog.belden.com/techdata/EN/7810A_techdata.pdf }}
{{center\|83%}}	RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
{{center\|82%}}	RG-8X Belden 9258 coaxial cable	foamed polyethylene dielectric
{{center\|80%}}	Belden 9085 twin-lead
{{center\|77%}}	RG-8/U generic	foamed polyethylene
{{center\|66%}}	Belden 8723 twin shielded stranded twisted pair	polypropylene insulator{{cite web \|title=8723 multi-conductor, shielded twisted pair cable \|website=Belden.com \|url=http://www.belden.com/techdatas/english/8723.pdf \|archive-url=https://web.archive.org/web/20180119120036/https://catalog.belden.com/techdata/EN/8723_techdata.pdf \|archive-date=2018-01-19 \|access-date=2017-07-06 }}
{{center\|66%}}	RG-213 CXP213	solid polyethylene dielectric

Calculating velocity factor

=Electric wave=

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), $\kappa$ or $\epsilon_\mathrm{r}$ , of the material through which the signal passes:

: $\mathrm{VF} = { \frac{1}{\sqrt{\kappa}} } \$

in the usual case where the relative permeability, $\mu_\mathrm{r}$ , is 1. In the most general case:

: $\mathrm{VF} = { \frac{1}{\sqrt{\mu_\mathrm{r}\epsilon_\mathrm{r}}} } \$

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

: $\mathrm{VF} = { \frac{1}{c_\mathrm{0}\sqrt{L'C'}} } \$

where $L'$ is the distributed inductance (in henries per unit length), $C'$ is the capacitance between the two conductors (in farads per unit length), and $c_\mathrm{0}$ is the speed of light in vacuum.

=Optical wave=

VF equals the reciprocal of the refractive index ${n}$ of the medium, usually optical fiber.

: $\mathrm{VF} = { \frac{1}{n} } \$

References

Category:Electromagnetic radiation

Category:Velocity