Sail Away

## Transmission Lines

A transmission line is used to connect a radio antenna with the transceiver. It allows to carry the power of the transmitter over an appreciable distance without much loss due to conductor resistance, insulator losses or radiation.
In modern HF installations, coaxial types of transmission lines are used. Coaxial or concentric lines are made of two cylindrical conductors with a common axis. The space between the two conductors is filled with an insulating material. Current flows along the center conductor and returns along the inside of the shield or braid. Due to the skin effect at high frequencies, the current does not penetrate more than a few micro metes into the conductors, hence with any practical thickness of the shield conductor, there is no current on the outside. The combined electromagnetic field is thus completely inside the cable and cannot radiate.

### Characteristic Impedance

A transmission line can be considered as a long ladder network of series inductances (along the conductors) and shunt capacitances (between inner and outer conductors). It differs from conventional L-C circuits in the fact that the network elements are uniformly distributed along the line. If the inductance and capacitance per unit length are L and C, then the characteristic impedance of the transmission line is:

`  Z0 = L/C           `
Notice, that in this model there are no dissipative elements (resistors) so no energy is lost while electromagnetic signals are send along the line.
For the geometric topology of coaxial transmission lines the inductance and capacitance per unit length can be expressed as a function of the dimensions of the conductors. Thus also the characteristic impedance can be calculated from the physical dimensions:
`  Z0 = 158 * log(D/d)      for air-core coax  `
With D and d the diameter of the outer conductor and inner connector respectively.

### Velocity Factor

If the medium between the conductors of a transmission line is air, the travelling waves will propagate along the line with the same speed as waves in free space. If a dielectric material is used between the conductors for insulation or support purposes, the waves will travel considerably slower. The ratio pf the velocity on the line to the velocity in free space is known as velocity factor. It is approximately 0.66 for solid polythene cables such as the popular RG-xxx cables.
It is important to make proper allowances for this factor, because it means that a cable has two different lengths: a physical- and an electrical length.

### Standing Waves

If a transmission line is terminated by a resistive load equal in value to its characteristic impedance, on one end and a generator with source impedance also equal in value to the characteristic line impedance, there is no reflection at the line ends and the line carries a pure travelling wave.This is the situation of optimal power transfer from generator to load.
If the line is not correctly terminated, the voltage to current ration is not the same for the load as for the transmission line and the power fed into the line cannot be completely absorbed by the load. In this case some of the power is reflected at the end of the line and will start travelling back to the generator. The two travelling waves will interact along the line an result in a standing wave.

To obtain maximum efficiency of a transmission line, the characteristic impedance (Z0) of the line must be equal in value to the load (Z) it feeds.
Standing Wave Ratio (SWR) is a figure which represents the amount of mismatch of a transmission line system. The SWR figure is 1 for an optimal system and greater than one if the system is not perfectly matched:

`  SWR = Z0/Z  or  Z/Z0    (whichever is greater)`
If the line system is mismatched, there is a standing wave along the line. Voltage and current amplitudes along the line are not constant but vary with the distance along the line. The SWR can also me expressed in the voltage or current ratios:
```  SWR = Imax/Imin
SWR = Vmax/Vmin```
A simple SWR meter measuring the power ratio of the forward and backward waves can be used to measure the efficiency of a transmission line system.

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