Transmission Line Loss: Four Coaxial Cables Compared

[jimh]

The transmission line that connects a transmitter to its antenna should not contribute excessive loss of power in the line itself. The power loss in the transmission line should be as low as practicable and should not exceed -1 dB. (For those not familiar with comparison of power levels using deciBels, a ratio of -1 dB is a reduction in power by a factor of 0.79 or about 21-percent.) Power loss in a coaxial transmission line is proportional to the length of the transmission line and the line characteristics. Loss can be reduced by using larger diameter coaxial cables.

In recreational boating, there are four types of coaxial cable in common use. The smallest typical cable is referred to as RG-58 and has a diameter of around 0.2-inches. Another common cable is referred to as RG8X and has a diameter of about 0.24-inches and uses foam dielectric insulation. Also useful is RG-8/U-type cable, which has a diameter of around 0.40-inches. A similar size cable, referred to as "RF400-type" also has a diameter of about 0.40-inches, but includes improved gas-injected HDPE foam dielectric insulation, decreasing loss.

All of the cables used in the comparison (below) are products of Belden, and the outer jacket material is designated as non-contaminating (or fire-resistant), which improves durability in sunlight and prevents loss with age. These same types of coaxial cables are available from other manufacturers and may have slightly different rated loss figures, may have contaminating outer jacket material, may have tinned or bare copper conductors, may have different dielectric insulation, and may sell at significantly different prices.

In Table 1 the length of these four cable types that will produce a loss of -1 dB is shown.

Length for 1-dB loss at 150-MHz (using Belden products)
RG-58/U = 16.4-feet (Belden 8262) Solid polyethylene dielectric, 0.195-inch OD
RG-8X   = 26.3-feet (Belden 9258) Foam polyethylene dielectric, 0.242-inch OD
RG-8/U  = 43.5-feet (Belden 9251) Solid polyethylene dielectric, 0.405-inch OD
RF400   = 66.7-feet (Belden 7810A) Gas-injected foam HDPE dielectric, 0.405-inch OD


Table 1. Length of various types of coaxial cable to cause a loss of -1 dB at 150-MHz

For length for -0.5 dB loss, just reduce the feet to half the value shown.

The above is based on the indicated Belden product numbers, and (if necessary) linear interpolation of loss at 100 and 200-MHz, resulting in the following loss figures for 100-feet of cable:

Rated Loss from Belden Specifications for 100-feet at 150-MHz
RG-58/U = -6.1 dB (Belden 8262)
RG-8X   = -3.8 dB (Belden 9258)
RG-8/U  = -2.3 dB (Belden 9251)
RF400   = -1.5 dB (Belden 7810A)


Table 2. Rated loss of various types of coaxial cable for 100-feet at 150-MHz

The executive summary: if cable loss is expected to exceed -1 dB at 150-MHz due to length, move up to a larger-diameter cable.

[jimh]

Method to Calculate Length of a Loss of -1 dB

The loss figures available for coaxial cable are generally given for 100-foot lengths. A LOSS of NdB per 100-feet means a loss of (NdB/100) per foot.


To deduce the length in feet needed to produce a loss of 1 dB, we express the relationship between loss, feet, and loss-per-foot:

LOSS db =Ffeet x (NdB/100feet)
where NdB is the manufacturer's rated loss in 100-feet of cable

Solving this for Ffeet when LOSSdB == -1 produces

-1 dB =Ffeet x (NdB/100feet)
Ffeet = -1dB / (NdB / 100feet)
Ffeet = -1dB x (100feet/NdB)
Ffeet = -100db-feet / Ndb

For example, if cable has specified loss of -4 dB per 100 feet, the length to produce 1 dB loss is then
-100 / -4 = 25-feet

[jimh]

ASIDE

For readers not familiar with the use of the unit deciBel (dB) to compare a ratio of two power levels, the definition of a deciBel (dB) is

(1) dB = 10 × LOG10(P2/P1)
where P2 and P1 are power levels.

For example, if P1 = 10 and P2 =20, then the deciBel ratio is

dB = 10 × LOG10(20/10)
dB = 10 × LOG10(2)
dB = 10 ×(0.301)
dB = 3.01

If a ratio is given in deciBels, the original power ratio (P2/P1) can be found by
(2) (P2/P1) = 10dB/10

For example, if dB = 3.01 then the ratio (P2/P1) would be
(P2/P1) = 103.01/10
(P2/P1) = 100.301
(P2/P1) = 1.999

As in the first example, if the original power (P1) were 10, an increase of 3.01 dB would require P2 to increase by a factor of 1.999 or to 20.

A simpler relationship: if the power is doubled the gain is 3 dB.

Looking at the power ratio when a loss of -1 dB occurs, we can again use the relationship show in equation (2):

(P2/P1) = 10-1/10
(P2/P1) = 10-0.1
(P2/P1) = 0.794

If the initial power (P1) were 25-Watts, then the resulting power (P2) would be 25 × 0.794 = 19.85-Watts

A change in power of 1 dB is often mentioned as the first noticeable change in power, and cited humorously by this definition:

If you ask your son to turn down his music volume, he will turn it down -1 dB.

HISTORY

The choice of the name deciBel comes from the unit Bel, which was adopted by the Bell System for measurement of telephone signal levels. The Bel was named in honor in Alexander Graham Bell but was too large, so a one-tenth unit or the deciBel was created. See more at

https://en.wikipedia.org/wiki/Decibel