# Transmission line

A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves.

 Contents

## History

Mathematical analysis of the behavior of electrical transmission lines grew out of the work of James Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the flow of current in a submarine cable. This law correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the Telegrapher's equations. [1]

## Electrical transmission lines

Examples of electrical transmission lines include wires, coaxial cables, dielectric slabs, optical fibres, and circular or rectangular closed waveguides.

Electrical transmission lines can be classified into high-frequency and low-frequency types depending on the type of current they are designed to carry. The same mathematical analysis applies to both classes, but at low frequencies a lumped-parameter model of the transmission line simplifies the calculation tasks. One feature that is common to both types of line is electrical resistance, which increases with the length of the line and is specified in ohms per metre. At low frequencies this parameter allows one to calculate the amount of power that will be lost in the line.

#### Low-frequency electrical transmission lines

These structures are most commonly used to transmit mains electrical power, as either direct current or low-frequency alternating current, over long distances. (See Electric power transmission for more information.)

George Westinghouse, with Nikola Tesla's patents, displayed several polyphase systems, including a transmission line, during the World Columbian Exposition.

#### High-frequency electrical transmission lines

High-frequency transmission lines can be defined as transmission lines that are designed to carry electromagnetic waves whose wavelengths are shorter than or comparable to the length of the line. Under these conditions, the electrical behaviour of the line is more complex than that of a low-frequency transmission line. This often occurs with radio, microwave and optical signals, and with the signals found in high-speed digital circuits.

For the purposes of analysis, an electrical transmission line can be modelled as a two-port network (also called a quadrupole network), as follows:

Missing image
Transmissionline4port.png
Image:Transmissionline4port.png

In the simplest case, the network is assumed to be linear (i.e. the complex voltage across either port is proportional to the complex current flowing into it when there are no reflections), and the two ports are assumed to be interchangeable. If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z0. This is the ratio of the complex voltage to the complex current at any point on the line. Typical values of Z0 are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission.

When sending power down a transmission line, it is usually desirable that all the power is absorbed by the load and none of it is reflected back to the source. This can be ensured by making the source and load impedances equal to Z0, in which case the transmission line is said to be matched.

As mentioned above, some of the power that is fed into a transmission line is lost because of its resistance. This effect is called ohmic or resistive loss. At high frequencies, another effect called dielectric loss starts to occur, adding to the losses caused by resistance. Dielectric loss is caused when the insulating material inside the transmission line absorbs energy from the alternating electric field and converts it to heat.

The total loss of power in a transmission line is often specified in decibels per metre, and usually depends on the frequency of the signal. The manufacturer often supplies a chart showing the loss in dB/m at a range of frequencies. A loss of 3 dB corresponds approximately to a halving of the power.

#### Further reading

• Steinmetz, Charles Proteus, "The Natural Period of a Transmission Line and the Frequency of lightning Discharge Therefrom". The Electrical world. August 27, 1898. Pg. 203 - 205.

## Acoustic transmission lines

An acoustic transmission line consists of a duct of constant cross-sectional area. Its length is normally of a similar order or longer than the wavelengths of the sound it will be used with, but the dimensions of its cross-section are normally smaller than one quarter of a wavelength: therefore it can be described as long and narrow. The duct must contain some medium, such as air, that supports sound propagation.

Sound is introduced at one end of the line by forcing the pressure across the whole cross-section to vary with time. A plane wave will travel down the line at the speed of sound, approximately 330 metres per second in air. When the wave reaches the end of the transmission line, behaviour depends on what is present at the end of the line. There are three possible scenarios:

• A low impedance load (e.g. leaving the end open in free air) will cause a reflected wave in which the sign of the pressure variation has been reversed, but the direction of air movement will remain the same.
• A load that matches the line's own impedance (defined below) will completely absorb the wave and the energy associated with it. No reflection will occur.
• A high impedance load (e.g. by plugging the end of the line) will cause a reflected wave in which the direction of air movement is reversed but the sign of the pressure remains the same.

The impedance of a transmission line is the impedance that the line would exhibit at its input if it were infinitely long. It depends on the cross-sectional area of the line and the characteristic impedance of the sound propagating medium within the duct.

Where a transmission line of finite length is mismatched at both ends, there is the potential for a wave to bounce back and forth many times until it is absorbed. This phenomenon is a kind of resonance and will tend to filter any signal fed into the line.

When this resonance effect is combined with some sort of active feedback mechanism and power input, it is possible to set up an oscillation which can be used to generate periodic acoustic signals such as musical notes.

Part of this article was derived from Federal Standard 1037C.

## Reference

Ernst Weber and Frederik Nebeker, The Evolution of Electrical Engineering, IEEE Press, Piscataway, New Jersey USA, 1994 ISBN 0780310557

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