NationMaster - Encyclopedia: 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, as well as electric power transmission. Components of transmission lines include wires, coaxial cables, dielectric slabs, optical fibres, electric power lines, and waveguides. A transmission medium is any material substance, such as fiber-optic cable, twisted-wire pair, coaxial cable, dielectric-slab waveguide, water, or air, that can be used for the propagation of signals, usually in the form of modulated radio, light, or acoustic waves, from one point to another. ... Look up path in Wiktionary, the free dictionary. ... In communications, transmission is the act of transmitting electrical messages (and the associated phenonomena of radiant energy that pass through media). ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... A wave is a disturbance that propagates through space, often transferring energy. ... Transmission lines in Lund, Sweden Electric power transmission is one process in the delivery of electricity to consumers. ... A wire is a single, usually cylindrical, elongated strand of drawn metal. ... Radio-grade flexible coaxial cable. ... A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of electric current and has a relative permittivity greater than unity. ... Fiber Optic strands An optical fiber in American English or fibre in British English is a transparent thin fiber for transmitting light. ... A waveguide is a structure which guides waves, such as electromagnetic waves, light, or sound waves. ...

History

Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the 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] James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematical physicist, born in Edinburgh. ... William Thomson, Archbishop of York, has the same name as this man. ... Oliver Heaviside (May 18, 1850 â€“ February 3, 1925) was a self-taught English engineer, mathematician and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and magnetic... 1855 was a common year starting on Monday (see link for calendar). ... 1858 (MDCCCLVIII) is a common year starting on Friday of the Gregorian calendar (or a common year starting on Sunday of the 12-day-slower Julian calendar). ... A submarine communications cable is a cable laid beneath the sea to carry telecommunications between countries. ... It has been suggested that Electrical telegraph be merged into this article or section. ... 1885 (MDCCCLXXXV) is a common year starting on Thursday. ...

Transmission line vs wire

In many electric circuits, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to the length of the wire. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ... The wavelength is the distance between repeating units of a wave pattern. ...

A common rule of thumb (justified in the input impedance section) is that the cable or wire should be treated as a transmission line if the length is greater than 1/100 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behaviour in systems which have not been carefully designed using transmission line theory.

The four terminal model

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

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 of a given wave to the complex current of the same wave 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. Wikibooks Algebra has more about this subject: Complex numbers In mathematics, a complex number is an expression of the form where a and b are real numbers, and i is a specific imaginary number, called the imaginary unit, with the property i 2 = âˆ’1. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The ohm (symbol: Î©) is the SI unit of electric resistance. ... Radio-grade flexible coaxial cable. ...

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. Impedance matching is the practice of attempting to make the output impedance of a source equal to the input impedance of the load to which it is ultimately connected, usually in order to maximise the power transfer and minimise reflections from the load. ...

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 becomes significant, 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. In physics, heat is defined as energy in transit. ...

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. The decibel (dB) is a measure of the ratio between two quantities, and is used in a wide variety of measurements in acoustics, physics and electronics. ... The metre, or meter, is a measure of length, approximately equal to 3. ...

High-frequency transmission lines can be defined as transmission lines that are designed to carry electromagnetic waves whose wavelengths are comparable to the length of the line. Under these conditions, the approximations useful for calculations at lower frequencies are no longer accurate. This often occurs with radio, microwave and optical signals, and with the signals found in high-speed digital circuits. The wavelength is the distance between repeating units of a wave pattern. ... Microwave image of 3C353 galaxy at 8. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of wavelengths that are studied in the field of optics. ... Digital circuits are electric circuits based on a number of discrete voltage levels. ...

Telegrapher's equations

The Telegrapher's Equations (or just Telegraph Equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver Heaviside who developed the transmission line model. They come from Maxwell's Equations. The Telegraphers Equations (or just Telegraph Equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time. ... International danger high voltage symbol. ... Look up current in Wiktionary, the free dictionary. ... Oliver Heaviside (May 18, 1850 â€“ February 3, 1925) was a self-taught English engineer, mathematician and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and magnetic... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line: Image File history File links Transmission_line_element. ... Image File history File links Transmission_line_element. ...

It should be repeated for clarity that the model consists of an infinite series of the elements shown in the figure, and that the values of the components are specified per unit length so the picture of the component can be misleading. An alternative notation is to use

R'

L'

C'

and

G'

to emphasize that the values are derivatives with respect to length. Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... Inductance is a physical characteristic of an inductor, which is an electrical device that produces at any time a voltage proportional to the instantaneous rate of change in current flowing through it. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... The henry (symbol H) is the SI unit of inductance. ... In electricity, a shunt is a device which allows electrical current to pass around another point in the circuit. ... A capacitor is a device that stores energy in the electric field created between a pair of conductors on which electric charges of equal magnitude, but opposite sign, have been placed. ... The farad (symbol: F) is the SI unit of capacitance. ... The siemens (symbol: S) is an SI derived unit of measurement for electric conductance, being the inverse of the ohm (Ω), named after Werner von Siemens. ...

When the elements R and G are very small, their effects can be neglected, and the transmission line is considered as an idealized, lossless, structure. In this case, the model depends only on the

L

and

C

elements which greatly simplifies the analysis. For a lossless transmission line, the second order steady-state Telegrapher's equations are:

These are wave equations which have plane waves in the forward and reverse directions as solutions. The physical significance of this is that electromagnetic waves propagate down transmission lines and in general, there is a reflected component that interferes with the original signal. These equations are fundamental to transmission line theory. The wave equation is an important partial differential equation that describes a variety of waves, such as sound waves, light waves and water waves. ... In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant amplitude and phase) are infinite parallel planes normal to the propagation direction. ...

Input Impedance of a Transmission line

The characteristic impedance of a transmission line is the ratio of the amplitude of a single voltage wave to its current wave. Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line. To meet Wikipedias quality standards, this article or section may require cleanup. ...

For a lossless transmission line, it can be shown that the impedance measured at a given position

l

from the load impedance

Z L

For the special case where $beta lapprox npi$ where n is an integer, the expression reduceds to the load impedance so that

Z i n = Z L

. This occurs when either the length of the transmission line is at least 100 times smaller than the wavelength (i.e. n=0), or when the length of the line is an exact multiple of half a wavelength. The physical significance of this is that the transmission line can be ignored (i.e. treated as a wire) in either case.

Another special case is when the load impedance is equal to the characteristic impedance of the line (i.e. the line is matched), in which case the impedance reduces to the characteristic impedance of the line so that

Z i n = Z 0

It should be noted that in calculating

β

, the wavelength is generally different inside the transmission line to what it would be in free-space and the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation.

Practical types of electrical transmission line

Coaxial cable

Coaxial lines confine the electromagnetic wave to the area inside the cable, between the center conductor and the shield. The transmission of energy in the line occurs totally through the dielectric inside the cable between the conductors. Coaxial lines can therefore be bent and twisted (subject to limits) without negative effects, and they can be strapped to conductive supports without inducing unwanted currents in them. Radio-grade flexible coaxial cable. ...

In radio-frequency applications up to a few GHz, the wave propagates in the transverse electric magnetic (TEM) mode, which means that the electric and magnetic fields are both perpendicular to the direction of propagation. However, above a certain frequency called the cutoff frequency, the cable behaves as a waveguide, and propagation switches to either a transverse electric (TE) or a transverse magnetic (TM) mode or a mixture of modes. This effect enables coaxial cables to be used at microwave frequencies, although they are not as efficient as the more expensive, purpose-built waveguides. A waveguide is a structure which guides waves, such as electromagnetic waves, light, or sound waves. ...

Microstrip

A microstrip circuit uses a thin flat conductor which is parallel to a ground plane. Microstrip can be made by having a strip of copper on one side of a printed circuit board (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the dielectric constant of the insulating layer determine the characteristic impedance. A microstrip is a thin, flat electrical conductor separated from a ground plane by a layer of insulation or an air gap. ... Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ... In telecommunication, a ground plane is an electrically conductive surface that serves as the near-field reflection point for an antenna, or as a reference ground in a circuit. ... Close-up photo of one side of a motherboard PCB, showing conductive traces, vias and solder points for through-hole components on the opposite side. ... The dielectric constant Îµr (represented as or K in some cases) is defined as the ratio: where Îµs is the static permittivity of the material in question, and Îµ0 is the vacuum permittivity. ...

Stripline

A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes, The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line. Stripline, according to David Pozars fine textbook Microwave Engineering was invented at by R. Barrett in the 1950s. ...

Balanced lines

Lecher lines

Lecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are used at frequencies between HF/VHF where lumped components are used, and UHF/SHF where resonant cavities are more practical. It has been suggested that this article or section be merged with Lecher wire system. ... This article is about the radio frequency. ... HF or Hf might be an acronym or abbreviation for: High frequency Radio hafnium, a chemical element the chemical formula for Hydrofluoric acid Historisk-filosofisk fakultet, abbr. ... Very high frequency (VHF) is the radio frequency range from 30 MHz (wavelength 10 m) to 300 MHz (wavelength 1 m). ... This article is about the radio frequency. ... Microwave Slang for small waves, like at a beach, often used by surfers. ...

General applications of transmission lines

Transferring signals from one point to another

Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss. One familiar example is the down lead from a TV or radio aerial to the receiver. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... A Yagi-Uda antenna An antenna or aerial is an electronic component designed to transmit or receive radio signals (and other electromagnetic waves). ...

Pulse generation

Transmission lines are also used as pulse generators. By charging the transmission line and then discharging it into a resistive load, a rectangular pulse equal in length to twice the electrical length of the line can be obtained. These are sometimes used as the pulsed energy sources for radar transmitters and other devices. Electrical resistance is a measure of the degree to which a body opposes the passage of an electric current. ... In telecommunication, the term electrical length has the following meanings: 1. ... This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll[1]. Radar is a system that uses radio waves to detect, determine the distance of, and map, objects such... In communications and information processing, a transmitter (sometimes abbreviated XMTR) is an object (source) which sends information to an observer (receiver). ...

Stub filters

If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it will function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it is 'working backwards'. One method recommended in the RSGB's radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the feeder delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics. The Radio Society of Great Britain (RSGB) is the UKs recognised national society for radio amateurs. ...

Acoustic transmission lines

A duct for sound propagation also behaves like a transmission line (e.g. air conditioning duct, car muffler, ...). The duct contains some medium, such as air, that supports sound propagation. Its length is normally of a similar order 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. Sound is introduced at one end of the tube 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. 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:

Since a transmission line behaves like a four terminal model, one cannot really define or measure the impedance of a transmission line component. One can however measure its input or output impedance. It depends on the cross-sectional area and length of the line, the sound frequency, as well as the characteristic impedance of the sound propagating medium within the duct. Only in the exceptional case of a closed end tube (to be compared with electrical short circuit), the input impedance could be regarded as a component impedance. The acoustic impedance Z (or sound impedance) is the ratio of sound pressure p to particle velocity v in a medium or acoustic component. ...

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 attenuate any signal fed into the line. The Tacoma Narrows Bridge (shown twisting) in Washington collapsed spectacularly, under moderate wind, in part because of resonance. ...

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 (e.g. in an organ pipe).

The application of transmission line theory is however seldom used in acoustics. An equivalent four terminal model which splits the downstream and upstream waves is used. This eases the introduction of physically measurable acoustic characteristics, reflection coefficients, material constants of insulation material, the influence of air velocity on wavelength (Mach number), etc. This approach also circumvents unpractical theoretical concepts, such as acoustic impedance of a tube, which is not measurable because of its inherent interaction with the sound source and the load of the acoustic component. Mach number (Ma) (pronounced in British English with a Germanic ch, as mack or mark and as mock in American English) is defined as a ratio of the speed of an object or flow relative to the speed of sound in the medium through which it is travelling: Vo/Vs...

"Transmission line" is also the name of a type of audio speaker design in which sound from the back of the bass speaker chassis is channeled along an acoustic transmission line within the speaker. At the other, open end of the transmission line, low frequencies are in phase with the front of the speaker chassis, which improves irradiation of bass frequencies. The disadvantage of this design, that the transmission line causes certain frequencies to be suppressed, can be alleviated by judiciously tuned Helmholtz resonators. Closeup of a loudspeaker driver Wall-mounted loudspeaker. ... A Sony 9 inch woofer Woofer is the term for a loudspeaker driver that is designed to produce low frequency sounds, typically from around 40 hertz up to a few hundred hertz. ... A brass, spherical Helmholtz resonator based on his original design, from around 1890-1900. ...

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