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Transmission line

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A transmission line is a specialized structure designed to conduct electromagnetic waves in a contained manner.

Coaxial cable cut
Coaxial cable cut

While ordinary cables can carry low-frequency alternating current (AC), they fail at high frequencies. This is because at high frequencies, energy radiates off the cable as radio waves. This radiation causes significant power losses. Additionally, high-frequency currents tend to reflect from discontinuities like joints or connectors. These reflections travel back toward the source and act as bottlenecks. To prevent this, transmission lines use specialized construction and impedance matching to ensure signals reach their destination with minimal loss.

To understand how they work, engineers use a distributed-element model.

Transmission line element
Transmission line element

Instead of seeing a cable as one single object, they model it as an infinite series of tiny segments. Each segment contains four specific properties. There is resistance from the conductors and inductance from the magnetic fields. There is also capacitance between the conductors and conductance from the insulating material. These properties are expressed as values per unit length. This model allows scientists to use the telegrapher's equations to calculate voltage and current at any point in time or distance.

There are several distinct types of transmission lines used in technology today.

Segments
Segments

Coaxial cable is one of the most common types, often used for cable television. Parallel lines include ladder lines and twisted pairs, which are frequently used in telephone systems. Engineers also use planar transmission lines, such as stripline or microstrip, on flat circuit boards. These planar lines are often arranged in specific patterns to create distributed-element circuits. These circuits act as alternatives to traditional components like discrete capacitors and inductors.

The mathematical study of these lines grew from the work of several great scientists.

Transmission line symbols
Transmission line symbols

James Clerk Maxwell and Lord Kelvin provided early foundations for this field. In 1855, Lord Kelvin created a diffusion model for current in submarine cables. This model was important because it correctly predicted the poor performance of the 1858 trans-Atlantic telegraph cable. Later, in 1885, Oliver Heaviside published papers describing how signals propagate in cables. He developed the modern form of the telegrapher's equations, which remain fundamental to the theory today.

Engineers use specific numbers to measure how well a line performs.

Gaussian pulse in a balanced transmission line
Gaussian pulse in a balanced transmission line

One key value is the characteristic impedance, denoted by the symbol Z0. This is the ratio of voltage to current for a wave at any point on the line. For example, a coaxial cable typically has a characteristic impedance of about 50 ohms. A twisted pair of wires usually has about 100 ohms. Another important measurement is propagation delay, which is the time it takes a signal to travel. This delay is never less than the length of the line divided by the speed of light.

Power loss is a major concern when designing these systems.

Transmission line animation3
Transmission line animation3

One type of loss is ohmic or resistive loss, where energy is lost due to the resistance of the conductors. At high frequencies, dielectric loss also becomes significant. This happens when the insulating material absorbs energy from the electric field and turns it into heat. Total power loss is often measured in decibels per metre (dB/m). A loss of 3 dB/m is a significant amount, as it represents approximately a halving of the power.

Transmission lines are essential for almost all modern high-speed communication. They serve as feed lines to connect radio transmitters to their antennas. They are also used for computer network connections and high-speed computer data buses. In very high-frequency applications, such as microwaves, engineers switch from transmission lines to waveguides. Waveguides act like pipes to confine and guide electromagnetic waves. By mastering the physics of these lines, we can move massive amounts of data across the world with incredible precision.

SmithChartLineLength
SmithChartLineLength
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🖼️ Images & Media (12)
File:Transmission line animation3.gif
Transmission line animation3.gif
File:Coaxial cable cut.jpg
Coaxial cable cut.jpg
File:Transmission line 4 port.svg
Transmission line 4 port.svg
File:Transmission line symbols.svg
Transmission line symbols.svg
File:TransmissionLineDefinitions.svg
TransmissionLineDefinitions.svg
File:Gaussian pulse in a balanced transmission line.png
Gaussian pulse in a balanced transmission line.png
File:Transmission line element.svg
Transmission line element.svg
File:SmithChartLineLength.svg
SmithChartLineLength.svg
File:Transmission line animation open short2.gif
Transmission line animation open short2.gif
File:Solec Kujawski longwave antenna feeder.jpg
Solec Kujawski longwave antenna feeder.jpg
File:Segments.jpg
Segments.jpg
File:PolarSmith.jpg
PolarSmith.jpg
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