# Propagation and antennas

## Feeders and transmission lines

To limit EMC problems and to keep human exposure to RF to a minimum, antennas should be as high and as far away from buildings etc. as it is reasonably practical to make. Do keep in mind that there is always a trade off between the advantage to be gained by height, and the subsequent losses in losses in feeders to the antenna system. It may therefore be necessary to transfer power from the transmitter to the antenna over a fairly long distance, say 10 to 25m. How this is done depends on the type of antenna used. The general name for this connection is 'feeder', which can be just a single wire or a transmission line which may be 'balanced' or 'unbalanced', both types consisting of two conductors. In a balanced line, both conductors have equal potential to earth, ie neither is earthed. In the unbalanced line, one conductor is earthed.

Connections of this type are subdivided according to a property known as the 'characteristic impedance' (ZO) which is measured in ohms. The characteristic impedance of a balanced line depends upon the diameter of the conductors and the spacing between them. Balanced or 'twin feeder' is commercially available with impedances of 75 and 300Ω (300Ω ribbon). Open-wire feeders of 300 to 600Ω impedance can be made by spacing apart two lengths of wire of 14swg (2mm) or 16swg (1.6mm) by low-loss spacers tied to the wire at intervals of 30-40mm. The unbalanced line is the familiar coaxial cable, where the characteristic impedance now depends upon the diameter of the conductor (the 'inner') and the internal diameter of the screen (the 'outer') which is earthed. The most common impedance is 50Ω and sometimes 75Ω.

Photo 7.2. A 50 Ohm BNC plug often used on instruments, and lower power transceivers.

The velocity of propagation of an electromagnetic wave in a transmission line is less than in free space. The ratio of the velocities is the 'velocity ratio' or 'velocity factor'. For most solid polythene-insulated coaxial cables the velocity ratio is about 0.66; 300Ω twin feeder has a velocity ratio of about 0.85.This means that the wave will travel about 30% more slowly in co-axial cable, and about 15% more slowly in twin feeder than it would in free space. The wave is compressed inside the feeder, it travels more slowly and has shorter wavelength, however the frequency remains constant. In the same way as a velocity factor of 0.7 reduces the wave's speed by 30%, it will reduce its wavelength by 30% also. We must therefore remember that a half or quarter wavelength may be a much shorter distance inside the feeder than in free space.

Photo 7.3. A 50 Ohm PL259 plug often used on higher power transceivers.

For the optimum transmission of power, a transmission line must be 'matched', ie the characteristic impedance of the feeder must match the output of the radio to which it is connected and also, it must be terminated, at the load end, with an impedance equal to that of the feeder. That is to say, all impedances from radio to antenna must be equal otherwise maximum transfer of power from one to another will not occur - power losses will result. These power losses will result in reduced performance, and may in extreme cases, result in damage to system components.

### Standing waves

In a transmission line which is not correctly terminated, ie the load impedance is not equal to its characteristic impedance, an input wave (the 'incident' or 'forward' wave) is reflected back to the input end. This is the 'reflected' or 'reverse' wave which is smaller in amplitude than the forward wave, It cannot cancel out the forward wave but combines with it to create points of maximum and minimum voltage (and current).

These variations of voltage (and current) in a mismatched transmission line are known as 'standing waves'. The ratio of maximum and minimum voltage (or current) is the 'standing wave ratio'. Generally it is the voltage which is measured, leading to the term 'voltage standing wave ratio' (VSWR) which is usually abbreviated to 'SWR'. In a correctly terminated line, there is no reflection of the forward power at all, and the SWR is then 1 to 1.

### Stubs

A line is completely mismatched when the far end is either a short-circuit or an open-circuit. There is then no load resistance to dissipate power, and 100% reflection of current and voltage occurs. It can be shown that a λ/4 length of a line which is open-circuit is equivalent to a series-tuned circuit at the frequency corresponding to the wavelength and therefore presents a very low resistance at that particular frequency. In a complementary fashion a short-circuit is equivalent to a parallel-tuned circuit and so presents a very high resistance.

These lengths of line are known as 'stubs'. The open-circuit stub is particularly useful as a means of creating a short-circuit at a particular frequency. This may be required to control a spurious emission from a transmitter, or to reduce the effects of a transmitter on a nearby receiver. For example, a coaxial stub (or stubs) may be a very effective method of controlling television interference when operating a transmitter nearby. They will however only be effective on the frequency for which they are cut.

The velocity ratio must be taken into account when calculating the length of the line which is hence somewhat shorter then the free-space length.

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