Transmission line

In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas (they are then called feed lines or feeders), distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses.

This article covers two-conductor transmission line such as parallel line (ladder line), coaxial cable, stripline, and microstrip. Some sources also refer to waveguide, dielectric waveguide, and even optical fibre as transmission line, however these lines require different analytical techniques and so are not covered by this article; see Waveguide (electromagnetism).

Transmission line animation3
Schematic of a wave moving rightward down a lossless two-wire transmission line. Black dots represent electrons, and the arrows show the electric field.
F-Stecker und Kabel
One of the most common types of transmission line, coaxial cable.

Overview

Ordinary electrical cables suffice to carry low frequency alternating current (AC), such as mains power, which reverses direction 100 to 120 times per second, and audio signals. However, they cannot be used to carry currents in the radio frequency range,[1] above about 30 kHz, because the energy tends to radiate off the cable as radio waves, causing power losses. Radio frequency currents also tend to reflect from discontinuities in the cable such as connectors and joints, and travel back down the cable toward the source.[1][2] These reflections act as bottlenecks, preventing the signal power from reaching the destination. Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. The distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform impedance, called the characteristic impedance,[2][3][4] to prevent reflections. Types of transmission line include parallel line (ladder line, twisted pair), coaxial cable, and planar transmission lines such as stripline and microstrip.[5][6] The higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the transmitted frequency's wavelength is sufficiently short that the length of the cable becomes a significant part of a wavelength.

At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead,[1] which function as "pipes" to confine and guide the electromagnetic waves.[6] Some sources define waveguides as a type of transmission line;[6] however, this article will not include them. At even higher frequencies, in the terahertz, infrared and visible ranges, waveguides in turn become lossy, and optical methods, (such as lenses and mirrors), are used to guide electromagnetic waves.[6]

The theory of sound wave propagation is very similar mathematically to that of electromagnetic waves, so techniques from transmission line theory are also used to build structures to conduct acoustic waves; and these are called acoustic transmission lines.

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. The model 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.[7]

Applicability

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 or less than the length of the wire.

A common rule of thumb is that the cable or wire should be treated as a transmission line if the length is greater than 1/10 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

Transmission line symbols
Variations on the schematic electronic symbol for a transmission line.

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

Transmission line 4 port

Transmission line 4 port

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.

When sending power down a transmission line, it is usually desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source. This can be ensured by making the load impedance equal to Z0, in which case the transmission line is said to be matched.

TransmissionLineDefinitions
A transmission line is drawn as two black wires. At a distance x into the line, there is current I(x) travelling through each wire, and there is a voltage difference V(x) between the wires. If the current and voltage come from a single wave (with no reflection), then V(x) / I(x) = Z0, where Z0 is the characteristic impedance of the line.

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 (see ohmic heating). 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 (see dielectric heating). The transmission line is modelled with a resistance (R) and inductance (L) in series with a capacitance (C) and conductance (G) in parallel. The resistance and conductance contribute to the loss in a transmission line.

The total loss of power in a transmission line is often specified in decibels per metre (dB/m), 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.

High-frequency transmission lines can be defined as those designed to carry electromagnetic waves whose wavelengths are shorter than or 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, metal mesh optical filters, and with the signals found in high-speed digital circuits.

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. They were developed by Oliver Heaviside who created the transmission line model, and are based on Maxwell's Equations.

Transmission line element
Schematic representation of the elementary component of a transmission line.

The transmission line model is an example of the distributed element model. It represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:

  • The distributed resistance of the conductors is represented by a series resistor (expressed in ohms per unit length).
  • The distributed inductance (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (in henries per unit length).
  • The capacitance between the two conductors is represented by a shunt capacitor (in farads per unit length).
  • The conductance of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (in siemens per unit length).

The model consists of an infinite series of the elements shown in the figure, and the values of the components are specified per unit length so the picture of the component can be misleading. , , , and may also be functions of frequency. An alternative notation is to use , , and to emphasize that the values are derivatives with respect to length. These quantities can also be known as the primary line constants to distinguish from the secondary line constants derived from them, these being the propagation constant, attenuation constant and phase constant.

The line voltage and the current can be expressed in the frequency domain as

Special case of a lossless line

When the elements and are negligibly small the transmission line is considered as a lossless structure. In this hypothetical case, the model depends only on the and 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 with equal propagation speed 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.

General case of a line with losses

In the general case the loss terms, and , are both included, and the full form of the Telegrapher's equations become:

where is the (complex) propagation constant. These equations are fundamental to transmission line theory. They are also wave equations, and have solutions similar to the special case, but which are a mixture of sines and cosines with exponential decay factors. Solving for the propagation constant in terms of the primary parameters , , , and gives:

and the characteristic impedance can be expressed as

The solutions for and are:

The constants must be determined from boundary conditions. For a voltage pulse , starting at and moving in the positive  direction, then the transmitted pulse at position can be obtained by computing the Fourier Transform, , of , attenuating each frequency component by , advancing its phase by , and taking the inverse Fourier Transform. The real and imaginary parts of can be computed as

with

the right-hand expressions holding when neither , nor , nor is zero, and with

where atan2 is the everywhere-defined form of two-parameter arctangent function, with arbitrary value zero when both arguments are zero.

Special, low loss case

For small losses and high frequencies, the general equations can be simplified: If and then

Noting that an advance in phase by is equivalent to a time delay by , can be simply computed as

Heaviside condition

The Heaviside condition is a special case where the wave travels down the line without any dispersion distortion. The condition for this to take place is

Input impedance of transmission line

SmithChartLineLength
Looking towards a load through a length of lossless transmission line, the impedance changes as increases, following the blue circle on this impedance Smith chart. (This impedance is characterized by its reflection coefficient, which is the reflected voltage divided by the incident voltage.) The blue circle, centred within the chart, is sometimes called an SWR circle (short for constant standing wave ratio).

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.

The impedance measured at a given distance from the load impedance may be expressed as

,

where is the propagation constant and is the voltage reflection coefficient measured at the load end of the transmission line. Alternatively, the above formula can be rearranged to express the input impedance in terms of the load impedance rather than the load voltage reflection coefficient:

.

Input impedance of lossless transmission line

For a lossless transmission line, the propagation constant is purely imaginary, , so the above formulas can be rewritten as

where is the wavenumber.

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

Special cases of lossless transmission lines

Half wave length

For the special case where where n is an integer (meaning that the length of the line is a multiple of half a wavelength), the expression reduces to the load impedance so that

for all This includes the case when , meaning that the length of the transmission line is negligibly small compared to the wavelength. The physical significance of this is that the transmission line can be ignored (i.e. treated as a wire) in either case.

Quarter wave length

For the case where the length of the line is one quarter wavelength long, or an odd multiple of a quarter wavelength long, the input impedance becomes

Matched load

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

for all and all .

Short

Transmission line animation open short2
Standing waves on a transmission line with an open-circuit load (top), and a short-circuit load (bottom). Black dots represent electrons, and the arrows show the electric field.

For the case of a shorted load (i.e. ), the input impedance is purely imaginary and a periodic function of position and wavelength (frequency)

Open

For the case of an open load (i.e. ), the input impedance is once again imaginary and periodic

Stepped transmission line

Segments
A simple example of stepped transmission line consisting of three segments.

A stepped transmission line[8] is used for broad range impedance matching. It can be considered as multiple transmission line segments connected in series, with the characteristic impedance of each individual element to be . The input impedance can be obtained from the successive application of the chain relation

where is the wave number of the -th transmission line segment and is the length of this segment, and is the front-end impedance that loads the -th segment.

PolarSmith
The impedance transformation circle along a transmission line whose characteristic impedance is smaller than that of the input cable . And as a result, the impedance curve is off-centred towards the axis. Conversely, if , the impedance curve should be off-centred towards the axis.

Because the characteristic impedance of each transmission line segment is often different from that of the input cable , the impedance transformation circle is off-centred along the axis of the Smith Chart whose impedance representation is usually normalized against .

The stepped transmission line is an example of a distributed element circuit. A large variety of other circuits can also be constructed with transmission lines including filters, power dividers and directional couplers.

Practical types

Coaxial cable

Coaxial lines confine virtually all of the electromagnetic wave to the area inside the cable. 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. In radio-frequency applications up to a few gigahertz, the wave propagates in the transverse electric and magnetic mode (TEM) only, which means that the electric and magnetic fields are both perpendicular to the direction of propagation (the electric field is radial, and the magnetic field is circumferential). However, at frequencies for which the wavelength (in the dielectric) is significantly shorter than the circumference of the cable other transverse modes can propagate. These modes are classified into two groups, transverse electric (TE) and transverse magnetic (TM) waveguide modes. When more than one mode can exist, bends and other irregularities in the cable geometry can cause power to be transferred from one mode to another.

The most common use for coaxial cables is for television and other signals with bandwidth of multiple megahertz. In the middle 20th century they carried long distance telephone connections.

Planar lines

Microstrip

Solec Kujawski longwave antenna feeder
A type of transmission line called a cage line, used for high power, low frequency applications. It functions similarly to a large coaxial cable. This example is the antenna feed line for a longwave radio transmitter in Poland, which operates at a frequency of 225 kHz and a power of 1200 kW.

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. Microstrip is an open structure whereas coaxial cable is a closed structure.

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.

Coplanar waveguide

A coplanar waveguide consists of a center strip and two adjacent outer conductors, all three of them flat structures that are deposited onto the same insulating substrate and thus are located in the same plane ("coplanar"). The width of the center conductor, the distance between inner and outer conductors, and the relative permittivity of the substrate determine the characteristic impedance of the coplanar transmission line.

Balanced lines

A balanced line is a transmission line consisting of two conductors of the same type, and equal impedance to ground and other circuits. There are many formats of balanced lines, amongst the most common are twisted pair, star quad and twin-lead.

Twisted pair

Twisted pairs are commonly used for terrestrial telephone communications. In such cables, many pairs are grouped together in a single cable, from two to several thousand.[9] The format is also used for data network distribution inside buildings, but the cable is more expensive because the transmission line parameters are tightly controlled.

Star quad

Star quad is a four-conductor cable in which all four conductors are twisted together around the cable axis. It is sometimes used for two circuits, such as 4-wire telephony and other telecommunications applications. In this configuration each pair uses two non-adjacent conductors. Other times it is used for a single, balanced line, such as audio applications and 2-wire telephony. In this configuration two non-adjacent conductors are terminated together at both ends of the cable, and the other two conductors are also terminated together.

When used for two circuits, crosstalk is reduced relative to cables with two separate twisted pairs.

When used for a single, balanced line, magnetic interference picked up by the cable arrives as a virtually perfect common mode signal, which is easily removed by coupling transformers.

The combined benefits of twisting, balanced signalling, and quadrupole pattern give outstanding noise immunity, especially advantageous for low signal level applications such as microphone cables, even when installed very close to a power cable.[10][11][12][13][14] The disadvantage is that star quad, in combining two conductors, typically has double the capacitance of similar two-conductor twisted and shielded audio cable. High capacitance causes increasing distortion and greater loss of high frequencies as distance increases.[15][16]

Twin-lead

Twin-lead consists of a pair of conductors held apart by a continuous insulator. By holding the conductors a known distance apart, the geometry is fixed and the line characteristics are reliably consistent. It is lower loss than coaxial cable because the characteristic impedance of twin-lead is generally higher than coaxial cable, leading to lower resistive losses due to the reduced current. However, it is more susceptible to interference.

Lecher lines

Lecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are a convenient practical format that fills the gap between lumped components (used at HF/VHF) and resonant cavities (used at UHF/SHF).

Single-wire line

Unbalanced lines were formerly much used for telegraph transmission, but this form of communication has now fallen into disuse. Cables are similar to twisted pair in that many cores are bundled into the same cable but only one conductor is provided per circuit and there is no twisting. All the circuits on the same route use a common path for the return current (earth return). There is a power transmission version of single-wire earth return in use in many locations.

General applications

Signal transfer

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.

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, although with half the voltage. A Blumlein transmission line is a related pulse forming device that overcomes this limitation. These are sometimes used as the pulsed power sources for radar transmitters and other devices.

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.

See also

References

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

  1. ^ a b c Jackman, Shawn M.; Matt Swartz; Marcus Burton; Thomas W. Head (2011). CWDP Certified Wireless Design Professional Official Study Guide: Exam PW0-250. John Wiley & Sons. pp. Ch. 7. ISBN 978-1118041611.
  2. ^ a b Oklobdzija, Vojin G.; Ram K. Krishnamurthy (2006). High-Performance Energy-Efficient Microprocessor Design. Springer Science & Business Media. p. 297. ISBN 978-0387340470.
  3. ^ Guru, Bhag Singh; Hüseyin R. Hızıroğlu (2004). Electromagnetic Field Theory Fundamentals, 2nd Ed. Cambridge Univ. Press. pp. 422–423. ISBN 978-1139451925.
  4. ^ Schmitt, Ron Schmitt (2002). Electromagnetics Explained: A Handbook for Wireless/ RF, EMC, and High-Speed Electronics. Newnes. p. 153. ISBN 978-0080505237.
  5. ^ Carr, Joseph J. (1997). Microwave & Wireless Communications Technology. USA: Newnes. pp. 46–47. ISBN 978-0750697071.
  6. ^ a b c d Raisanen, Antti V.; Arto Lehto (2003). Radio Engineering for Wireless Communication and Sensor Applications. Artech House. pp. 35–37. ISBN 978-1580536691.
  7. ^ Ernst Weber and Frederik Nebeker, The Evolution of Electrical Engineering, IEEE Press, Piscataway, New Jersey USA, 1994 ISBN 0-7803-1066-7
  8. ^ Qian, Chunqi; Brey, William W. (2009). "Journal of Magnetic Resonance – Impedance matching with an adjustable segmented transmission line". Journal of Magnetic Resonance. 199 (1): 104–110. Bibcode:2009JMagR.199..104Q. doi:10.1016/j.jmr.2009.04.005. PMID 19406676.
  9. ^ Syed V. Ahamed, Victor B. Lawrence, Design and engineering of intelligent communication systems, pp.130–131, Springer, 1997 ISBN 0-7923-9870-X.
  10. ^ The Importance of Star-Quad Microphone Cable
  11. ^ Evaluating Microphone Cable Performance & Specifications
  12. ^ The Star Quad Story
  13. ^ What's Special About Star-Quad Cable?
  14. ^ How Starquad Works
  15. ^ Lampen, Stephen H. (2002). Audio/Video Cable Installer's Pocket Guide. McGraw-Hill. pp. 32, 110, 112. ISBN 978-0071386210.
  16. ^ Rayburn, Ray (2011). Eargle's The Microphone Book: From Mono to Stereo to Surround – A Guide to Microphone Design and Application (3 ed.). Focal Press. pp. 164–166. ISBN 978-0240820750.
  • Steinmetz, Charles Proteus (August 27, 1898), "The Natural Period of a Transmission Line and the Frequency of lightning Discharge Therefrom", The Electrical World: 203–205
  • Grant, I. S.; Phillips, W. R. (1991-08-26), Electromagnetism (2nd ed.), John Wiley, ISBN 978-0-471-92712-9
  • Ulaby, F. T. (2004), Fundamentals of Applied Electromagnetics (2004 media ed.), Prentice Hall, ISBN 978-0-13-185089-7
  • "Chapter 17", Radio communication handbook, Radio Society of Great Britain, 1982, p. 20, ISBN 978-0-900612-58-9
  • Naredo, J. L.; Soudack, A. C.; Marti, J. R. (Jan 1995), "Simulation of transients on transmission lines with corona via the method of characteristics", IEE Proceedings. Generation, Transmission and Distribution., Morelos: Institution of Electrical Engineers, 142 (1), ISSN 1350-2360

Further reading

External links

Antenna (radio)

In radio engineering, an antenna is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

An antenna is an array of conductors (elements), electrically connected to the receiver or transmitter. Antennas can be designed to transmit and receive radio waves in all horizontal directions equally (omnidirectional antennas), or preferentially in a particular direction (directional or high-gain antennas). An antenna may include parasitic elements, parabolic reflectors or horns, which serve to direct the radio waves into a beam or other desired radiation pattern.

The first antennas were built in 1888 by German physicist Heinrich Hertz in his pioneering experiments to prove the existence of electromagnetic waves predicted by the theory of James Clerk Maxwell. Hertz placed dipole antennas at the focal point of parabolic reflectors for both transmitting and receiving. He published his work in Annalen der Physik und Chemie (vol. 36, 1889).

Balun

A balun (for balanced to unbalanced) is an electrical device that converts between a balanced signal and an unbalanced signal. A balun can take many forms and may include devices that also transform impedances but need not do so. Transformer baluns can also be used to connect lines of differing impedance. Sometimes, in the case of transformer baluns, they use magnetic coupling but need not do so. Common-mode chokes are also used as baluns and work by eliminating, rather than ignoring, common mode signals.

There are two variations of this device - they are:

the unun, which transfers signal from one unbalanced line to another.

the balbal, which transfers signal from one balanced line to another.

Characteristic impedance

The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively and equivalently it can be defined as the input impedance of a transmission line when its length is infinite. Characteristic impedance is determined by the geometry and materials of the transmission line and, for a uniform line, is not dependent on its length. The SI unit of characteristic impedance is the ohm.

The characteristic impedance of a lossless transmission line is purely real, with no reactive component. Energy supplied by a source at one end of such a line is transmitted through the line without being dissipated in the line itself. A transmission line of finite length (lossless or lossy) that is terminated at one end with an impedance equal to the characteristic impedance appears to the source like an infinitely long transmission line and produces no reflections.

Electric power transmission

Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines which facilitate this movement are known as a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is known as the "power grid" in North America, or just "the grid". In the United Kingdom, India, Myanmar, Malaysia and New Zealand, the network is known as the "National Grid".

A wide area synchronous grid, also known as an "interconnection" in North America, directly connects a large number of generators delivering AC power with the same relative frequency to a large number of consumers. For example, there are four major interconnections in North America (the Western Interconnection, the Eastern Interconnection, the Quebec Interconnection and the Electric Reliability Council of Texas (ERCOT) grid). In Europe one large grid connects most of continental Europe.

Historically, transmission and distribution lines were owned by the same company, but starting in the 1990s, many countries have liberalized the regulation of the electricity market in ways that have led to the separation of the electricity transmission business from the distribution business.

Electrical termination

In electronics, electrical termination is the practice of ending a transmission line with a device that matches the characteristic impedance of the line. This is intended to prevent signals from reflecting off the end of the transmission line. Reflections at the ends of unterminated transmission lines cause distortion which can produce ambiguous digital signal levels and mis-operation of digital systems. Reflections in analog signal systems cause such effects as video ghosting, or power loss in radio transmitter transmission lines.

Feed line

In a radio antenna, the feed line (feedline), or feeder, is the cable or other transmission line that connects the antenna with the radio transmitter or receiver. In a transmitting antenna, it feeds the radio frequency (RF) current from the transmitter to the antenna, where it is radiated as radio waves. In a receiving antenna it transfers the tiny RF voltage induced in the antenna by the radio wave to the receiver. In order to carry RF current efficiently, feed lines are made of specialized types of cable called transmission line. The most widely used types of feed line are coaxial cable, twin-lead, ladder line, and at microwave frequencies, waveguide.

Particularly with a transmitting antenna, the feed line is a critical component that must be adjusted to work correctly with the antenna and transmitter. Each type of transmission line has a specific characteristic impedance. This must be matched to the impedance of the antenna and the transmitter, to transfer power efficiently to the antenna. If these impedances are not matched it can cause a condition called standing waves on the feed line, in which the RF energy is reflected back toward the transmitter, wasting energy and possibly overheating the transmitter. This adjustment is done with a device called an antenna tuner in the transmitter, and sometimes a matching network at the antenna. The degree of mismatch between the feedline and the antenna is measured by an instrument called an SWR meter (standing wave ratio meter), which measures the standing wave ratio (SWR) on the line.

Frequency domain sensor

Frequency domain (FD) sensor is an instrument developed for measuring soil moisture content. The instrument has an oscillating circuit, the sensing part of the sensor is embedded in the soil, and the operating frequency will depend on the value of soil's dielectric constant.

There are two types of sensors:

Capacitance probe, or fringe capacitance sensor. Capacitance probes use capacitance to measure the dielectric permittivity of the soil. The volume of water in the total volume of soil most heavily influences the dielectric permittivity of the soil because the dielectric constant of water (80) is much greater than the other constituents of the soil (mineral soil: 4, organic matter: 4, air: 1). Thus, when the amount of water changes in the soil, the probe will measure a change in capacitance (from the change in dielectric permittivity) that can be directly correlated with a change in water content. Circuitry inside some commercial probes change the capacitance measurement into a proportional millivolt output. Other configuration are like the neutron probe where an access tube made of PVC is installed in the soil. The probe consists of sensing head at fixed depth. The sensing head consists of an oscillator circuit, the frequency is determined by an annular electrode, fringe-effect capacitor, and the dielectric constant of the soil.

Electrical impedance sensor, which consists of soil probes and using electrical impedance measurement. The most common configuration is based on the standing wave principle (Gaskin & Miller, 1996). The device comprises a 100 MHz sinusoidal oscillator, a fixed impedance coaxial transmission line, and probe wires which is buried in the soil. The oscillator signal is propagated along the transmission line into the soil probe, and if the probe's impedance differs from that of the transmission line, a proportion of the incident signal is reflected back along the line towards the signal source.Compared to time domain reflectometer (TDR), FD sensors are cheaper to build and have a faster response time. However, because of the complex electrical field around the probe, the sensor needs to be calibrated for different soil types. Some commercial sensors have been able to remove the soil type sensitivity by using a high frequency.

Impedance matching

In electronics, impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to maximize the power transfer or minimize signal reflection from the load.

In the case of a complex source impedance ZS and load impedance ZL, maximum power transfer is obtained when

where the asterisk indicates the complex conjugate of the variable. Where ZS represents the characteristic impedance of a transmission line, minimum reflection is obtained when

The concept of impedance matching found first applications in electrical engineering, but is relevant in other applications in which a form of energy, not necessarily electrical, is transferred between a source and a load. An alternative to impedance matching is impedance bridging, in which the load impedance is chosen to be much larger than the source impedance and maximizing voltage transfer, rather than power, is the goal.

Overhead power line

An overhead power line is a structure used in electric power transmission and distribution to transmit electrical energy along large distances. It consists of one or more conductors (commonly multiples of three) suspended by towers or poles. Since most of the insulation is provided by air, overhead power lines are generally the lowest-cost method of power transmission for large quantities of electric energy.

Patch antenna

A patch antenna is a type of radio antenna with a low profile, which can be mounted on a flat surface. It consists of a flat rectangular sheet or "patch" of metal, mounted over a larger sheet of metal called a ground plane. They are the original type of microstrip antenna described by Howell in 1972; the two metal sheets together form a resonant piece of microstrip transmission line with a length of approximately one-half wavelength of the radio waves. The radiation mechanism arises from discontinuities at each truncated edge of the microstrip transmission line. The radiation at the edges causes the antenna to act slightly larger electrically than its physical dimensions, so in order for the antenna to be resonant, a length of microstrip transmission line slightly shorter than one-half the wavelength at the frequency is used. The patch antenna is mainly practical at microwave frequencies, at which wavelengths are short enough that the patches are conveniently small. It is widely used in portable wireless devices because of the ease of fabricating it on printed circuit boards. Multiple patch antennas on the same substrate (see image) called microstrip antennas, can be used to make high gain array antennas, and phased arrays in which the beam can be electronically steered.

A variant of the patch antenna commonly used in mobile phones is the shorted patch antenna, or planar inverted-F antenna (PIFA). In this antenna, one corner of the patch (or sometimes one edge) is grounded with a ground pin. This variant has better matching than the standard patch .

Another variant of patch antenna with the partially etched ground plane, also known as printed monopole antenna, is a very versatile antenna for dual-band operations.

RF connector

A coaxial RF connector (radio frequency connector) is an electrical connector designed to work at radio frequencies in the multi-megahertz range.

RF connectors are typically used with coaxial cables and are designed to maintain the shielding that the coaxial design offers. Better models also minimize the change in transmission line impedance at the connection. Mechanically, they may provide a fastening mechanism (thread, bayonet, braces, blind mate) and springs for a low ohmic electric contact while sparing the gold surface, thus allowing very high mating cycles and reducing the insertion force. Research activity in the area of radio-frequency (RF) circuit design has surged in the 2000s in direct response to the enormous market demand for inexpensive, high-data-rate wireless transceivers.

Radio-frequency engineering

Radio-frequency engineering, or RF engineering, is a subset of electrical and electronic engineering involving the application of transmission line, waveguide, antenna and electromagnetic field principles to the design and application of devices that produce or utilize signals within the radio band, the frequency range of about 20 kHz up to 300 GHz.It is incorporated into almost everything that transmits or receives a radio wave, which includes, but is not limited to, mobile phones, radios, Wi-Fi, and two-way radios.

RF engineering is a highly specialized field that typically includes the following areas of expertise:

Design of antenna systems to provide radiative coverage of a specified geographical area by an electromagnetic field or to provide specified sensitivity to an electromagnetic field impinging on the antenna.

Design of coupling and transmission line structures to transport RF energy without radiation.

Application of circuit elements and transmission line structures in the design of oscillators, amplifiers, mixers, detectors, combiners, filters, impedance transforming networks and other devices.

Verification and measurement of performance of radio frequency devices and systems.To produce quality results, the RF engineer needs an in-depth knowledge of mathematics, physics and general electronics theory as well as specialized training in areas such as wave propagation, impedance transformations, filters and microstrip printed circuit board design to name a few.

Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.

A cavity resonator is one in which waves exist in a hollow space inside the device. In electronics and radio, microwave cavities consisting of hollow metal boxes are used in microwave transmitters, receivers and test equipment to control frequency, in place of the tuned circuits which are used at lower frequencies. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators.

Standing wave ratio

In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line.

The SWR is usually thought of in terms of the maximum and minimum AC voltages along the transmission line, thus called the voltage standing wave ratio or VSWR (sometimes pronounced "vizwar"). For example, the VSWR value 1.2:1 denotes an AC voltage due to standing waves along the transmission line reaching a peak value 1.2 times that of the minimum AC voltage along that line. The SWR can as well be defined as the ratio of the maximum amplitude to minimum amplitude of the transmission line's currents, electric field strength, or the magnetic field strength. Neglecting transmission line loss, these ratios are identical.

The power standing wave ratio (PSWR) is defined as the square of the VSWR, however, this deprecated terminology has no physical relation to actual powers involved in transmission.

SWR is usually measured using a dedicated instrument called an SWR meter. Since SWR is a measure of the load impedance relative to the characteristic impedance of the transmission line in use (which together determine the reflection coefficient as described below), a given SWR meter can only interpret the impedance it sees in terms of SWR if it has been designed for that particular characteristic impedance. In practice most transmission lines used in these applications are coaxial cables with an impedance of either 50 or 75 ohms, so most SWR meters correspond to one of these.

Checking the SWR is a standard procedure in a radio station. Although the same information could be obtained by measuring the load's impedance with an impedance analyzer (or "impedance bridge"), the SWR meter is simpler and more robust for this purpose. By measuring the magnitude of the impedance mismatch at the transmitter output it reveals problems due to either the antenna or the transmission line.

Star network

A star network is an implementation of a spoke–hub distribution paradigm in computer networks. In a star network, every host is connected to a central hub. In its simplest form, one central hub acts as a conduit to transmit messages. The star network is one of the most common computer network topologies.

The hub and hosts, and the transmission lines between them, form a graph with the topology of a star. Data on a star network passes through the hub before continuing to its destination. The hub manages and controls all functions of the network. It also acts as a repeater for the data flow.

The star topology reduces the impact of a transmission line failure by independently connecting each host to the hub. Each host may thus communicate with all others by transmitting to, and receiving from, the hub. The failure of a transmission line linking any host to the hub will result in the isolation of that host from all others, but the rest of the network will be unaffected.The star configuration is commonly used with twisted pair cable and optical fibre cable. However, it can also be used with coaxial cable.

Stripline

Stripline is a transverse electromagnetic (TEM) transmission line medium invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s. Stripline is the earliest form of planar transmission line.

Telegrapher's equations

The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver Heaviside who in the 1880s developed the transmission line model. The model demonstrates that the electromagnetic waves can be reflected on the wire, and that wave patterns can appear along the line. The theory applies to transmission lines of all frequencies including high-frequency transmission lines (such as telegraph wires and radio frequency conductors), audio frequency (such as telephone lines), low frequency (such as power lines) and direct current.

Twin-lead

Twin-lead cable is a two-conductor flat cable used as a balanced transmission line to carry radio frequency (RF) signals. It is constructed of two stranded copper or copper-clad steel wires, held a precise distance apart by a plastic (usually polyethylene) ribbon. The uniform spacing of the wires is the key to the cable's function as a transmission line; any abrupt changes in spacing would reflect some of the signal back toward the source. The plastic also covers and insulates the wires.

Twin lead can have significantly lower signal loss than miniature flexible coaxial cable at shortwave and VHF radio frequencies; for example, type RG-58 coaxial cable loses 6.6 dB per 100 m at 30 MHz, while 300 ohm twin-lead loses only 0.55 dB. However, twin-lead is more vulnerable to interference. Proximity to metal objects will inject signals into twin-lead that would be blocked out by coaxial cable. Twin lead therefore requires careful installation around rain gutters, and standoffs from metal support masts. Twin-lead is also susceptible to significant degradation when wet or ice covered, whereas coax is less or not affected in these conditions. For these reasons, coax has largely replaced twin-lead in most uses, except where maximum signal is required.

Wind power in North Dakota

North Dakota is a leading U.S. state in wind power generation. Data from 2017 indicates that the state generates 26.8% of its electricity from wind, enough to power over one million homes .

As of the end of 2017, 2996 megawatts (MW) of generation capacity had been installed for wind power in North Dakota. Additional capacity had been limited by transmission line constraints until the completion of a transmission line from Fargo to central Minnesota in 2015. Additional wind farms are once again planned for the state.Very favorable wind conditions in the state enable wind farms to achieve capacity factors in excess of 40 percent. The Thunder Spirit wind farm, completed in 2015, is expected to have a capacity factor greater than 45 percent.

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