Transmission lines, coax, losses SWR

The antenna needs to be connected to our radio through some type of cable, or transmission line. The most commonly found transmission lines, and transmission line connections on radios, are for coaxial cables. These cables come in a wide variety of sizes and impedances, with the most commonly used value being 50 W for radio work and 75 W for television and video work. Cable designations are typically RG-58 or RG-59 for lower power applications at 50 W and 75 W respectively, while RG-8 or RG-11 style cables would be used for higher power applications at those impedances. Mil-qualified versions of the 50 W cables are designated RG-223 for the smaller diameter variety and RG-213 for the larger. Most solid state transmitters are designed to match the 50 W standard, while older vacuum tube output stages could match a wide range of impedances. The presence of a dielectric means the velocity of light is slower in the cables than it would be in vaccuum. This needs to be understood when making matching stubs or phasing lines out of these cables, and most have a velocity factor (VF) specified that indicates the correction that needs be applied. For example, a half wavelength in free space would be 1 meter for a 2 meter radio, but the typical

Coaxial cable - The field is constrained within outer shield. The shield can also be doubled (2 braids, or braid and foil) or even solid (semi-rigid). This style of line is inherently unbalanced. Dielectric and copper losses are the major frequency dependent loss factors. VF=66% for sold polyethylene, 70% for teflon, 78% for foam, ~88% for air.

75 W twin lead - Conductors are ~#12 stranded, and field is constrained mostly within the dielectric, so little weather effects. Very popular before coax, it is not easy to find. Although this appears to be lamp cord it is not, using thicker conductors and a better dielectric material. VF=67%.

300 W twin lead - #20 conductors and thin ribbing between conductors leads to higher losses and sensitivity to weather and collection of dirt as path is partly in air and surface of dielectric. Frequently used in TV and FM radio applications. VF=82%.

450 W window line - #18 conductors with larger spacing and large portions of dielectric removed improve loss situation. VF=95%.

600 W ladder line - The classic “open wire” line used from the earliest days of wireless. Wide spaced with an occasional high quality insulator, these lines, typically constructed from #12 or #14 solid wire, are very low loss and have VF~100%. Homemade versions using plastic clothespins or hair rollers exist because of limited availability of commercial products.

Losses are mainly due to resistive (“copper”) losses and dielectric losses. For this reason, many of the parallel lines provide generally low losses for cables with equivalent conductor sizes. All of these losses increase with frequency as dielectric losses go up and skin depth in conductors decreases, increasing the effective resistance of the conductors.

Losses may also be due to energy lost as radiation. The ideal is to limit radiation to the antenna. This is aided by closely spaced lines that have opposing fields in the adjacent wires. This tends to cancel the possibility of radiation. Again, this effect is influenced by frequency. Higher frequencies mean wires are spaced at a larger fraction of a wavelength so cancellation only occurs at some distance from the wires. Also, as frequency increases, small variations in construction can lead to slight mismatches in the phase of the currents in adjacent wires (so they are no longer exactly 180° apart), leading to imperfect cancellation.

The losses tend to be the limiting factor in the power handling capability of many transmission lines, as the voltage handling capability is quite high for most cables. The losses become an issue of temperature rise in the portions of the cable closest to the transmitter, where the majority of power is lost. For example, the loss in RG-58 coax at 2 meters is approximately 6 dB/100 feet of cable. This means that if a 1000 watt transmitter is connected to a matched load through 100 ft of coax, that only 250 W reaches the load. The other 750 W must be dissipated in the cable. Since the loss is 3 dB for 50 ft, that means that 500 W is dissipated in the first half of the cable, and worse yet 200 W is dissipated in the first 16 ft!

Transmission line losses are of great concern at VHF and UHF frequencies since they not only mean that transmit power is lost on the way to the antenna, but also that receive power is lost on the way from the antenna to the receiver. A good rule of thumb is that the cable loss acts as an increase of an equivalent amount in the noise figure of the receiver. While RG-8 foam is only 2.2 dB/100 ft at 2 meters, the loss of ½” diameter hardline is only 1 dB/100 ft at 2 meters. This means 800 W would reach the antenna and the receiver noise figure would be about 5 dB better. This is why many people invest a lot of time and money in the VHF/UHF “plumbing”.

To this point, we have only considered matched, or so called “flat” transmission lines, where the impedance of the load (antenna) is equal to the impedance of the cable. As we noticed in looking at antennas, the impedance, Zo, of an antenna varies with frequency, and is typically only “real” at one frequency (the resonant frequency). At other frequencies the impedance contains a reactive component as well as a difference in the real component. So even if we could design an antenna and cable combination that had the same impedance, this condition would only exist over a small range of frequencies. The mismatch that results (or may even exist at resonance if the cable is not well matched to the antenna) produces a reflection of some fraction of the incident energy back toward the source, which generates a variation in the magnitude of the voltage measured down the length of the line. The resulting peaks or troughs in amplitude repeat at multiples of ½ l, and this used to be a way of measuring wavelength in the early days of wireless. The ratio of the voltage maximum to the voltage minimum is the VSWR (or SWR). Another measure of this effect is the reflection coefficient, r, which can be determined from a measurement of forward and reflected power. Some useful equations are:

The reflected power not only can cause excess dissipation in the final stages of the transmitter, but in many solid state radios will result in the transmitter output being restricted to protect the final stage. The SWR also increases the losses on the line, although this effect is typically small except when losses are already high and SWR is also high. An antenna tuner (actually more appropriately called a transmatch) can match the transmitter to the impedance at the end of the transmission line to keep the transmitter happy. This does NOT reduce the SWR on the transmission line itself or eliminate the related losses. A network that matches the antenna to the transmission line is needed to do that.