GENERACIÓN Y CARACTERÍSTICAS DE LAS VENTAJAS

Electromagnetic waves travels through a vacuum at the speed of light, 299,792,458 meters per second (983,571,056 feet per second). This is known as the free-space value of the speed of light. Since radio waves are part of the electromagnetic spectrum, they travel at the speed of light, too. But what happens when radio waves travel through coaxial cable? Their velocity is somewhat slower than it is in a vacuum! Indeed, radio waves travel through trunk and feeder-type coaxial cable at approximately 87% of the free space value of the speed of light, or 260,819,438 meters per second (855,706,819 feet per second). Looking at this another way, radio waves travel 1 foot in a vacuum in 1.02 nanosecond (ns), and through 1 foot of coaxial cable in 1.17 ns.

Why do radio waves travel more slowly through coaxial cable than they do through a vacuum? First, the conductors used in coaxial cable are not perfect. The loss in those conductors slows down the waves slightly, but the effect is almost negligible at frequencies used in cable networks. Of more importance is the effect of the dielectric material which separates the coaxial cable’s center conductor and shield. Indeed, the presence of a dielectric other than a vacuum or air reduces the velocity of an electromagnetic wave, often by 10% to 20% or more.

The ratio of the velocity of an electromagnetic wave–specifically what is known as a transverse electromagnetic (TEM) mode wave–in a vacuum to its velocity in a dielectric material, νTEM(vacuum)/νTEM(dielectric), equals what is called index of refraction.10 Velocity factor is the reciprocal of index of refraction.

The dielectric’s magnetic permeability (represented by the symbol µ and expressed in henrys/meter) and electric permittivity (represented by the symbol ε and expressed in farads/meter) are two key properties that determine the velocity of electromagnetic waves in coaxial cable. The ratio of ε(dielectric)/ε(vacuum) is the dielectric constant εr. The velocity of an electromagnetic wave in a dielectric is equal to the ratio of its velocity in a vacuum to the square root of the dielectric constant: νTEM(dielectric) = νTEM(vacuum)/√εr. A little number crunching with the latter equation and the ratio that defines index of refraction is 1/√εr = velocity factor.

The dielectric constant εr of the coaxial cable in the example in the first paragraph is approximately 1.32, so the velocity factor is 1/√1.32 = 0.87. Velocity of propagation is velocity factor expressed as a percentage. So, a velocity factor of 0.87 is 87% velocity of propagation, which means that radios waves travel through the coaxial cable at 87% the free-space value of the speed of light.

One application for understanding velocity of propagation is calculating propagation or transit delay in a cable network–that is, the time it takes for electromagnetic waves to travel from one point to another.

The Data-Over-Cable Service Interface Specification (DOCSIS®) Radio Frequency Interface Specification includes assumed downstream and upstream RF channel transmission characteristics for cable networks. Among those assumed characteristics is the previously mentioned transit delay. For instance, the transit delay from the headend to the most distant customer is assumed to be less than or equal to 0.800 millisecond (ms). Note that 0.800 ms (800 microseconds) is a one-way specification. The same assumed transit delay also applies in the upstream direction. The approximate downstream or upstream transit delay can be calculated if one knows the length of the optical fiber link between the headend or hub and node, as well as the length of distribution network coaxial cable from the node to the most distant customer. The calculation is done using the reciprocal of the fiber’s index of refraction–its velocity factor, which is then converted to velocity of propagation–and the velocity of propagation of the coaxial cable. The approximate index of refraction for single mode optical fiber at 1310 nm is 1.46, making its velocity factor 0.68 and its velocity of propagation 68%. In other words, light propagates through the optical fiber at a velocity that is 68% of the speed of light in a vacuum. A typical velocity of propagation for commonly used hardline distribution-type coaxial cables is the previously discussed 87%.

10 _{The ratio ν}

TEM(vacuum)/νTEM(dielectric) is called the index of refraction because the difference in the velocity of

Since the speed of light in a vacuum is 299,792,458 meters per second, 68% of that value is 203,858,871 meters per second. Thus, light will propagate through 203,858,871 meters of optical fiber in one second. For coaxial cable with a velocity of propagation of 87%, RF will propagate through 260,819,438 meters of coax in one second.

Example: Assume a cable system with an optical fiber link from headend to node that is 30 kilometers (km) long. The coaxial cable distribution network connected to the node has a coax run that extends an additional 2 km beyond the node. What is the approximate transit delay from the headend to the most distant customer, excluding delay through active and passive devices?

Solution: Light propagates through 30 km (30,000 meters) of optical fiber in 1.47 x 10-4 _{second (30,000}

meters/203,858,871.44 meters per second = 0.00014716 second). RF propagates through 2 km (2,000 meters) of coax in 7.6681 x 10-6 _{second (2,000 meters/260,819,438.46 meters per second = 0.00000076681 second).} Combining these two numbers yields 1.55 x 10-4 _{second, or 0.155 ms. This is well within the DOCSIS one-way} transit delay specification of 0.800 ms.

Table I-2 summarizes transit delay in ns-per-foot and ns-per-meter for several values of velocity of propagation. The velocity factor of a vacuum is 1.0 and its velocity of propagation is 100%, because electromagnetic signals travel at the free-space value of the speed of light.

The dielectric constant of dry air at a pressure of one atmosphere and a temperature of 23° C is 1.00068, so the velocity factor is 1/√1.00068 = 0.999660173 and the velocity of propagation is 99.966%. The values for a vacuum and air are usually considered to be the same in all but the most critical applications because of the negligible difference between them.

Table I-2 - Velocity of propagation versus transit delay

Velocity of Propagation ns/foot ns/meter Velocity of Propagation ns/foot ns/meter

100% 1.02 3.34 81% 1.26 4.12 99% 1.03 3.37 80% 1.27 4.17 98% 1.04 3.40 79% 1.29 4.22 97% 1.05 3.44 78% 1.30 4.28 96% 1.06 3.47 77% 1.32 4.33 95% 1.07 3.51 76% 1.34 4.39 94% 1.08 3.55 75% 1.36 4.45 93% 1.09 3.59 74% 1.37 4.51 92% 1.11 3.63 73% 1.39 4.57 91% 1.12 3.67 72% 1.41 4.63 90% 1.13 3.71 71% 1.43 4.70 89% 1.14 3.75 70% 1.45 4.77 88% 1.16 3.79 69% 1.47 4.83 87% 1.17 3.83 68% 1.50 4.91 86% 1.18 3.88 67% 1.52 4.98 85% 1.20 3.92 66% 1.54 5.05 84% 1.21 3.97 65% 1.56 5.13 83% 1.22 4.02 64% 1.59 5.21 82% 1.24 4.07 63% 1.61 5.29

Typical published velocities of propagation for modern foam dielectric coaxial cables used by the cable industry are 84-85% for drop-type cables and 87-88% for hardline trunk and feeder cables. Published values for disc-and-air dielectric designs are as high as 93%. As previously noted, the typical velocity of propagation for single mode optical fiber at 1310 nm is about 68%.