Transmission Lines

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In radio science, “The Feeder” is the transmission line between the transceiver and the aerial. Feeders are of three main types, waveguide, parallel wire and coaxial, with differing amounts of loss and convenience of use. Unfortunately, the inevitable loss in power in a particular type of feeder seems to be in inverse proportion to its convenience of use. These competing factors are here examined in the order of lowest loss to greatest convenience. In essence all feeders are waveguides in that they guide the electromagnetic waves generated by the transceiver to the aerial and vice versa. However the term ‘waveguide’ is usually reserved for feeders in the form of metal tubes containing the wave. In these, the signal is best thought of in wave-like form instead of in the form of voltages and currents. Waveguide feeders are capable of extremely low loss at extremely high frequency.

Thoughts on Radio Frequency Feeders

Less suitable types
The lowest loss transmission line of all is probably the single mode optical fibre made of a special glass. A loss of typically 0.1dB per kilometre has been claimed for this when conveying a usable bandwidth of signals, (say 10% of the optical carrier frequency), approaching 0.01dB/km at the single “best” frequency. Optical fibres don’t have much application in amateur radio except perhaps in the evolving field of optical communication.

During the 1950s, attempts were made to develop waveguides for long haul telecommunications, using a microwave wavelength of 8mm in waveguides of circular cross section some four inches in diameter, using the “circular E01 mode”. In this mode the electric field is circular and is a maximum mid way between the centre of the tube and the circumference, and “chases its tail” rather than anchors itself to the metallic walls of the guide. Loss measurements in early trials reached 1dB/km. However, the circular tube-like waveguide needed to be very straight. Even slight bends resulted in conversion of the wanted E01 circular mode into unwanted modes which not only caused additional loss but travelled at different speeds and corrupted the information carried. The different frequencies inherent in the information carried also resulted in “frequency dispersion”. Hence “sideband reversal” was required every few miles to preserve information integrity together with “unwanted mode suppressors” after every bend. The ultimate intention was to lay these straight four inch diameter pipes beside railway tracks. The aim was to back up or replace wireless microwave links and the existing cables in order to improve GPO telephone and other services including trunk television channels. However it all came to naught because the huge railway system of previous years connecting most towns and villages was curtailed, and because optical fibres with an even greater information carrying capacity were invented.

Practical solutions
A waveguide of more practical form, although with higher loss, is single mode rectangular waveguide, as used by radio amateurs in the GHz bands and in high power radar systems. In this the electric field runs between the two broad walls of the waveguide and the current flows on the inside of both the broad and the narrow walls. It has the disadvantage that it can usually only accommodate a single frequency band, (with a bandwidth of about 30%), but it can convey very high power, (Megawatts at a wavelength of 3cm and 10s of Megawatts at 10cm). At a wavelength of 3 cm, a suitably sized rectangular waveguide has a loss of around 3dB per 100 feet. By “suitably sized” is meant the width of the broad wall must be a little over half a wavelength but less than one wavelength.

Also under the heading of waveguide feeders should be included the Goubau Line, a single wire which guides the E-M wave between its launcher and the collector. It is mainly of academic interest. However, if it is straight, and if it is kept well away from other objects it is capable of very low loss, but bends and other nearby obstructions cause it to radiate, as a significant electric field extends to about a wavelength from the wire. It is therefore very inconvenient to use. It has not been extensively tested at high power.

Parallel Wire.
Next in order of increasing loss comes the parallel wire feeder. This carries current in the wires, which are therefore subject to Ohmic loss. But this may be minimised by increasing the spacing between the wires to raise the characteristic impedance well above the loss resistance. Unfortunately, increasing the spacing between the wires is in conflict with the requirement to reduce radiation on transmission from, and reception of interference by, the wires. However, a spacing of a few inches at frequencies of up to about 30 MHz is a satisfactory compromise. The characteristic impedance of a parallel wire transmission line is determined by the ratio of the spacing of the wires to the diameter of the wires, and is usually between 100 and 800Ω. The “twisted pair” and the “ladder-line” are variants of the parallel wire line with usually a lower characteristic impedance. However, the quality of the dielectric separating the wires significantly affects the loss in such lines. Power handling is usually determined by the breakdown voltage between the wires and can be Megawatts for a wire spacing of a foot or so.

Coaxial Cable.
This is the transmission line with probably the highest loss but is the most convenient to use. It is an unbalanced line, (i.e. the outer conductor or braid is usually earthed and the inner conductor is “live”). However, it has the advantage that, in a properly designed system, the signal currents and voltages are entirely confined within the cable. Thus it may be bent or coiled without regard to adjacent obstructions. Its characteristic impedance and its power handling capacity are determined by the ratio of the sizes of its inner to its outer conductor as modified by the necessary dielectric used to maintain the separation between the two conductors. That said, there is an optimum for this ratio which is different for minimum loss and for maximum power handling. For “air filled” coax, these are respectively, 76.653Ω and 29.933Ω These ratios hold good whatever the overall size that the feeder is scaled up to, (to handle higher power for example). Coax is readily available in sizes from a millimetre in diameter to several centimetres. Its loss per unit length is roughly inversely proportional to its diameter, and proportional to the square root of the frequency. In all sizes the loss is mainly due to the Ohmic resistance of the conductors, although efforts are sometimes made to reduce the contribution which the dielectric makes by using foamed plastic or spaced intermittent supports to maintain the spacing between the central and outer conductors. Loss by radiation through the sheath or braid is usually very low, and for a foil wrapped and braided outer conductor, this can be better than -100dB per metre length. The use of foil however, greatly reduces the “bendability” of the feeder. Some coaxial cables are specially designed to leak a controlled amount of their signal to maintain communication in the underground tunnels in which they are installed.

Epilogue
It happens that the optimum impedance for minimum loss is very close to one of the standard coax impedances, 75Ω, (commonly used for domestic television down leads). This is probably no coincidence and has nothing to do with the centre feed point resistance of a resonant half wave dipole being about 72Ω. The other common characteristic impedance and industrial standard, 50Ω may have been derived more obscurely as follows. When having to make a compromise between the above two values it is sometimes difficult to know whether to take the arithmetic mean or the geometric mean. It so happens that in this case the two are quite close. The arithmetic mean of the two “optimum impedances figures” 76.65 and 29.93 is 53.29, and the geometric mean of these two figures is 47.87 Averaging these and rounding to the nearest convenient round figure gives 50?. Very convenient!

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