# Waveguide (electromagnetism)

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In electromagnetics and communications engineering, the term waveguide may refer to any linear structure that conveys electromagnetic waves between its endpoints. However, the original [1] and most common [1] meaning is a hollow metal pipe used to carry radio waves. This type of waveguide is used as a transmission line mostly at microwave frequencies, for such purposes as connecting microwave transmitters and receivers to their antennas, in equipment such as microwave ovens, radar sets, satellite communications, and microwave radio links.

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, is responsible for electromagnetic radiation such as light, and is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 gigahertz (GHz) to as low as 30 hertz (Hz). At 300 GHz, the corresponding wavelength is 1 mm, and at 30 Hz is 10,000 km. Like all other electromagnetic waves, radio waves travel at the speed of light. They are generated by electric charges undergoing acceleration, such as time varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects.

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, distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses.

## Contents

A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe. An optical fibre is a dielectric guide designed to work at optical frequencies. Transmission lines such as microstrip, coplanar waveguide, stripline or coaxial cable may also be considered to be waveguides.

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact. Microstrip was developed by ITT laboratories as a competitor to stripline.

Coplanar waveguide is a type of electrical planar transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. On a smaller scale, coplanar waveguide transmission lines are also built into monolithic microwave integrated circuits. Conventional coplanar waveguide (CPW) consists of a single conducting track printed onto a dielectric substrate, together with a pair of return conductors, one to either side of the track. All three conductors are on the same side of the substrate, and hence are coplanar. The return conductors are separated from the central track by a small gap, which has an unvarying width along the length of the line. Away from the cental conductor, the return conductors usually extend to an indefinite but large distance, so that each is notionally a semi-infinite plane.

The electromagnetic waves in a (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected between opposite walls of the guide. For the particular case of rectangular waveguide, it is possible to base an exact analysis on this view. Propagation in a dielectric waveguide may be viewed in the same way, with the waves confined to the dielectric by total internal reflection at its surface. Some structures, such as non-radiative dielectric waveguides and the Goubau line, use both metal walls and dielectric surfaces to confine the wave.

Total internal reflection (TIR) is the phenomenon that makes the water-to-air surface in a fish-tank look like a perfectly silvered mirror when viewed from below the water level (Fig. 1). Technically, TIR is the total reflection of a wave incident at a sufficiently oblique angle on the interface between two media, of which the second ("external") medium is transparent to such waves but has a higher wave velocity than the first ("internal") medium. TIR occurs not only with electromagnetic waves such as light waves and microwaves, but also with other types of waves, including sound and water waves. In the case of a narrow train of waves, such as a laser beam, we tend to speak of the total internal reflection of a "ray" (Fig. 2).

The non-radiative dielectric (NRD) waveguide has been introduced by Yoneyama in 1981. In Fig. 1 the cross section of NRD guide is shown: it consists of a dielectric rectangular slab of height a and width b, which is placed between two metallic parallel plates of suitable width. The structure is practically the same as the H waveguide, proposed by Tischer in 1953. Due to the dielectric slab, the electromagnetic field is confined in the vicinity of the dielectric region, whereas in the outside region, for suitable frequencies, the electromagnetic field decays exponentially. Therefore, if the metallic plates are sufficiently extended, the field is practically negligible at the end of the plates and therefore the situation does not greatly differ from the ideal case in which the plates are infinitely extended. The polarization of the electric field in the required mode is mainly parallel to the conductive walls. As it is known, if the electric field is parallel to the walls, the conduction losses decrease in the metallic walls at the increasing frequency, whereas, if the field is perpendicular to the walls, losses increase at the increasing frequency. Since the NRD waveguide has been devised for its implementation at millimeter waves, the selected polarization minimizes the ohmic losses in the metallic walls.

A Goubau line or Sommerfeld-Goubau line, or G-line for short, is a single wire transmission line used to conduct radio waves at UHF and microwave frequencies. The dielectric coated transmission line was invented by F. Harms in 1907 and George J. E. Goubau in 1950, based on work on surface waves on wires from 1899 by Arnold Sommerfeld. It is used as a feedline at UHF to link high frequency transmitters and receivers to their antennas, and in scientific research.

## Principle

Depending on the frequency, waveguides can be constructed from either conductive or dielectric materials. Generally, the lower the frequency to be passed the larger the waveguide is. For example, the natural waveguide the earth forms given by the dimensions between the conductive ionosphere and the ground as well as the circumference at the median altitude of the Earth is resonant at 7.83 Hz. This is known as Schumann resonance. On the other hand, waveguides used in extremely high frequency (EHF) communications can be less than a millimeter in width.

Extremely high frequency (EHF) is the International Telecommunication Union (ITU) designation for the band of radio frequencies in the electromagnetic spectrum from 30 to 300 gigahertz (GHz). It lies between the super high frequency band, and the far infrared band, the lower part of which is also referred to as the terahertz gap. Radio waves in this band have wavelengths from ten to one millimetre, so it is also called the millimetre band and radiation in this band is called millimetre waves, sometimes abbreviated MMW or mmW. Millimetre-length electromagnetic waves were first investigated in the 1890s by Indian scientist Jagadish Chandra Bose.

## History

During the 1890s theorists did the first analyses of electromagnetic waves in ducts. [3] Around 1893 J. J. Thomson derived the electromagnetic modes inside a cylindrical metal cavity. [3] In 1897 Lord Rayleigh did a definitive analysis of waveguides; he solved the boundary-value problem of electromagnetic waves propagating through both conducting tubes and dielectric rods of arbitrary shape. [3] [4] [5] [6] He showed that the waves could travel without attenuation only in specific normal modes with either the electric field (TE modes) or magnetic field (TM modes), or both, perpendicular to the direction of propagation. He also showed each mode had a cutoff frequency below which waves would not propagate. Since the cutoff wavelength for a given tube was of the same order as its width, it was clear that a hollow conducting tube could not carry radio wavelengths much larger than its diameter. In 1902 R. H. Weber observed that electromagnetic waves travel at a slower speed in tubes than in free space, and deduced the reason; that the waves travel in a "zigzag" path as they reflect from the walls. [3] [5] [7]

Sir Joseph John Thomson was an English physicist and Nobel Laureate in Physics, credited with the discovery and identification of the electron, the first subatomic particle to be discovered.

A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at the fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. When relating to music, normal modes of vibrating instruments are called "harmonics" or "overtones".

An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them. Electric field is sometimes abbreviated as E-field. The electric field is defined mathematically as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The SI unit for electric field strength is volt per meter (V/m). Newtons per coulomb (N/C) is also used as a unit of electric field strengh. Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

Prior to the 1920s, practical work on radio waves concentrated on the low frequency end of the radio spectrum, as these frequencies were better for long-range communication. [3] These were far below the frequencies that could propagate in even large waveguides, so there was little experimental work on waveguides during this period, although a few experiments were done. In a June 1, 1894 lecture, "The work of Hertz", before the Royal Society, Oliver Lodge demonstrated the transmission of 3 inch radio waves from a spark gap through a short cylindrical copper duct. [3] [8] In his pioneering 1894-1900 research on microwaves, Jagadish Chandra Bose used short lengths of pipe to conduct the waves, so some sources credit him with inventing the waveguide. [9] However, after this, the concept of radio waves being carried by a tube or duct passed out of engineering knowledge. [3]

The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge, commonly known as the Royal Society, is a learned society. Founded on 28 November 1660, it was granted a royal charter by King Charles II as "The Royal Society". It is the oldest national scientific institution in the world. The society is the United Kingdom's and Commonwealth of Nations' Academy of Sciences and fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, fostering international and global co-operation, education and public engagement.

Sir Oliver Joseph Lodge, was a British physicist and writer involved in the development of, and holder of key patents for, radio. He identified electromagnetic radiation independent of Hertz' proof and at his 1894 Royal Institution lectures, Lodge demonstrated an early radio wave detector he named the "coherer". In 1898 he was awarded the "syntonic" patent by the United States Patent Office. Lodge was Principal of the University of Birmingham from 1900 to 1920.

A spark gap consists of an arrangement of two conducting electrodes separated by a gap usually filled with a gas such as air, designed to allow an electric spark to pass between the conductors. When the potential difference between the conductors exceeds the breakdown voltage of the gas within the gap, a spark forms, ionizing the gas and drastically reducing its electrical resistance. An electric current then flows until the path of ionized gas is broken or the current reduces below a minimum value called the "holding current". This usually happens when the voltage drops, but in some cases occurs when the heated gas rises, stretching out and then breaking the filament of ionized gas. Usually, the action of ionizing the gas is violent and disruptive, often leading to sound, light and heat.

During the 1920s the first continuous sources of high frequency radio waves were developed: the Barkhausen-Kurz tube, [10] the first oscillator which could produce power at UHF frequencies; and the split-anode magnetron which by the 1930s had generated radio waves at up to 10 GHz. [3] These made possible the first systematic research on microwaves in the 1930s. It was discovered that transmission lines used to carry lower frequency radio waves, parallel line and coaxial cable, had excessive power losses at microwave frequencies, creating a need for a new transmission method. [3] [10]

The waveguide was developed independently between 1932 and 1936 by George C. Southworth at Bell Telephone Laboratories [2] and Wilmer L. Barrow at the Massachusetts Institute of Technology, who worked without knowledge of one another. [3] [5] [6] [10] Southworth's interest was sparked during his 1920s doctoral work in which he measured the dielectric constant of water with a radio frequency Lecher line in a long tank of water. He found that if he removed the Lecher line, the tank of water still showed resonance peaks, indicating it was acting as a dielectric waveguide. [3] At Bell Labs in 1931 he resumed work in dielectric waveguides. By March 1932 he observed waves in water-filled copper pipes. Rayleigh's previous work had been forgotten, and Sergei A. Schelkunoff, a Bell Labs mathematician, did theoretical analyses of waveguides [3] [11] and rediscovered waveguide modes. In December 1933 it was realized that with a metal sheath the dielectric is superfluous and attention shifted to metal waveguides.

Barrow had become interested in high frequencies in 1930 studying under Arnold Sommerfeld in Germany. [3] At MIT beginning in 1932 he worked on high frequency antennas to generate narrow beams of radio waves to locate aircraft in fog. He invented a horn antenna and hit on the idea of using a hollow pipe as a feedline to feed radio waves to the antenna. [3] By March 1936 he had derived the propagation modes and cutoff frequency in a rectangular waveguide. [10] The source he was using had a large wavelength of 40 cm, so for his first successful waveguide experiments he used a 16-foot section of air duct, 18 inches in diameter. [3]

Barrow and Southworth became aware of each other's work a few weeks before both were scheduled to present papers on waveguides to a combined meeting of the American Physical Society and the Institute of Radio Engineers in May 1936. [3] [10] They amicably worked out credit sharing and patent division arrangements.

The development of centimeter radar during World War 2 and the first high power microwave tubes, the klystron (1938) and cavity magnetron (1940), resulted in the first widespread use of waveguide. [10] Standard waveguide "plumbing" components were manufactured, with flanges on the end which could be bolted together. After the war in the 1950s and 60s waveguides became common in commercial microwave systems, such as airport radar and microwave relay networks which were built to transmit telephone calls and television programs between cities.

## Analysis

Electromagnetic waveguides are analyzed by solving Maxwell's equations, or their reduced form, the electromagnetic wave equation, with boundary conditions determined by the properties of the materials and their interfaces. These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is characterized by a cutoff frequency below which the mode cannot exist in the guide. Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide. The longitudinal mode of a waveguide is a particular standing wave pattern formed by waves confined in the cavity. The transverse modes are classified into different types:

• TE modes (transverse electric) have no electric field in the direction of propagation.
• TM modes (transverse magnetic) have no magnetic field in the direction of propagation.
• TEM modes (transverse electromagnetic) have no electric nor magnetic field in the direction of propagation.
• Hybrid modes have both electric and magnetic field components in the direction of propagation.

In hollow waveguides (single conductor), TEM waves are not possible, since Maxwell's Equations will give that the electric field must then have zero divergence and zero curl and be equal to zero at boundaries, resulting in a zero field (or, equivalently, ${\displaystyle \nabla ^{2}\Phi =0}$ with boundary conditions guaranteeing only the trivial solution). This contrasts with two-conductor transmission lines used at lower frequencies; coaxial cable, parallel wire line and stripline, in which TEM mode is possible. Additionally, the propagating modes (i.e. TE and TM) inside the waveguide can be mathematically expressed as the superposition of TEM waves. [12]

The mode with the lowest cutoff frequency is termed the dominant mode of the guide. It is common to choose the size of the guide such that only this one mode can exist in the frequency band of operation. In rectangular and circular (hollow pipe) waveguides, the dominant modes are designated the TE1,0 mode and TE1,1 modes respectively. [13]

## Hollow metallic waveguides

In the microwave region of the electromagnetic spectrum, a waveguide normally consists of a hollow metallic conductor. These waveguides can take the form of single conductors with or without a dielectric coating, e.g. the Goubau line and helical waveguides. Hollow waveguides must be one-half wavelength or more in diameter in order to support one or more transverse wave modes.

Waveguides may be filled with pressurized gas to inhibit arcing and prevent multipaction, allowing higher power transmission. Conversely, waveguides may be required to be evacuated as part of evacuated systems (e.g. electron beam systems).

A slotted waveguide is generally used for radar and other similar applications. The waveguide serves as a feed path, and each slot is a separate radiator, thus forming an antenna. This structure has the capability of generating a radiation pattern to launch an electromagnetic wave in a specific relatively narrow and controllable direction.

A closed waveguide is an electromagnetic waveguide (a) that is tubular, usually with a circular or rectangular cross section, (b) that has electrically conducting walls, (c) that may be hollow or filled with a dielectric material, (d) that can support a large number of discrete propagating modes, though only a few may be practical, (e) in which each discrete mode defines the propagation constant for that mode, (f) in which the field at any point is describable in terms of the supported modes, (g) in which there is no radiation field, and (h) in which discontinuities and bends may cause mode conversion but not radiation.[ citation needed ]

The dimensions of a hollow metallic waveguide determine which wavelengths it can support, and in which modes. Typically the waveguide is operated so that only a single mode is present. The lowest order mode possible is generally selected. Frequencies below the guide's cutoff frequency will not propagate. It is possible to operate waveguides at higher order modes, or with multiple modes present, but this is usually impractical.

Waveguides are almost exclusively made of metal and mostly rigid structures. There are certain types of "corrugated" waveguides that have the ability to flex and bend but only used where essential since they degrade propagation properties. Due to propagation of energy in mostly air or space within the waveguide, it is one of the lowest loss transmission line types and highly preferred for high frequency applications where most other types of transmission structures introduce large losses. Due to the skin effect at high frequencies, electric current along the walls penetrates typically only a few micrometers into the metal of the inner surface. Since this is where most of the resistive loss occurs, it is important that the conductivity of interior surface be kept as high as possible. For this reason, most waveguide interior surfaces are plated with copper, silver, or gold.

Voltage standing wave ratio (VSWR) measurements may be taken to ensure that a waveguide is contiguous and has no leaks or sharp bends. If such bends or holes in the waveguide surface are present, this may diminish the performance of both transmitter and receiver equipment connected at either end. Poor transmission through the waveguide may also occur as a result of moisture build up which corrodes and degrades conductivity of the inner surfaces, which is crucial for low loss propagation. For this reason, waveguides are nominally fitted with microwave windows at the outer end that will not interfere with propagation but keep the elements out. Moisture can also cause fungus build up or arcing in high power systems such as radio or radar transmitters. Moisture in waveguides can typically be prevented with silica gel, a desiccant, or slight pressurization of the waveguide cavities with dry nitrogen or argon. Desiccant silica gel canisters may be attached with screw-on nibs and higher power systems will have pressurized tanks for maintaining pressure including leakage monitors. Arcing may also occur if there is a hole, tear or bump in the conducting walls, if transmitting at high power (usually 200 watts or more). Waveguide plumbing [14] is crucial for proper waveguide performance. Voltage standing waves occur when impedance mismatches in the waveguide cause energy to reflect back in the opposite direction of propagation. In addition to limiting the effective transfer of energy, these reflections can cause higher voltages in the waveguide and damage equipment.

Short length of rectangular waveguide (WG17 with UBR120 connection-flanges)
Section of the flexible waveguide
Waveguide (ankle piece 900MHz)

### Waveguide in practice

In practice, waveguides act as the equivalent of cables for super high frequency (SHF) systems. For such applications, it is desired to operate waveguides with only one mode propagating through the waveguide. With rectangular waveguides, it is possible to design the waveguide such that the frequency band over which only one mode propagates is as high as 2:1 (i.e. the ratio of the upper band edge to lower band edge is two). The relation between the waveguide dimensions and the lowest frequency is simple: if ${\displaystyle \scriptstyle W}$ is the greater of its two dimensions, then the longest wavelength that will propagate is ${\displaystyle \scriptstyle \lambda \;=\;2W}$ and the lowest frequency is thus ${\displaystyle \scriptstyle f\;=\;c/\lambda \;=\;c/2W}$

With circular waveguides, the highest possible bandwidth allowing only a single mode to propagate is only 1.3601:1. [15]

Because rectangular waveguides have a much larger bandwidth over which only a single mode can propagate, standards exist for rectangular waveguides, but not for circular waveguides. In general (but not always), standard waveguides are designed such that

• one band starts where another band ends, with another band that overlaps the two bands [16]
• the lower edge of the band is approximately 30% higher than the waveguide's cutoff frequency
• the upper edge of the band is approximately 5% lower than the cutoff frequency of the next higher order mode
• the waveguide height is half the waveguide width

The first condition is to allow for applications near band edges. The second condition limits dispersion, a phenomenon in which the velocity of propagation is a function of frequency. It also limits the loss per unit length. The third condition is to avoid evanescent-wave coupling via higher order modes. The fourth condition is that which allows a 2:1 operation bandwidth. Although it is possible to have a 2:1 operating bandwidth when the height is less than half the width, having the height exactly half the width maximizes the power that can propagate inside the waveguide before dielectric breakdown occurs.

Below is a table of standard waveguides. The waveguide name WR stands for waveguide rectangular, and the number is the inner dimension width of the waveguide in hundredths of an inch (0.01 inch = 0.254 mm) rounded to the nearest hundredth of an inch.

Standard sizes of rectangular waveguide
Waveguide nameFrequency band nameRecommended frequency band of operation (GHz)Cutoff frequency of lowest order mode (GHz)Cutoff frequency of next mode (GHz)Inner dimensions of waveguide opening
EIA RCSC * IEC (inch)(mm)
WR2300WG0.0R30.32 — 0.450.2570.51323.000 × 11.500584.20 × 292.10
WR2100WG0R40.35 — 0.500.2810.56221.000 × 10.500533.40 × 266.7
WR1800WG1R50.45 — 0.630.3280.65618.000 × 9.000457.20 × 228.6
WR1500WG2R60.50 — 0.750.3930.78715.000 × 7.500381.00 × 190.5
WR1150WG3R80.63 — 0.970.5131.02611.500 × 5.750202.10 × 146.5
WR975WG4R90.75 — 1.150.6051.2119.750 × 4.875247.7 × 123.8
WR770WG5R120.97 — 1.450.7661.5337.700 × 3.850195,6 × 97.79
WR650WG6R14 L band (part)1.15 — 1.720.9081.8166.500 × 3.250165.1 × 82.55
WR510WG7R181.45 — 2.201.1572.3145.100 × 2.550129.5 × 64.77
WR430WG8R221.72 — 2.601.3722.7454.300 × 2.150109.2 × 54.61
WR340WG9AR26 S band (part)2.20 — 3.301.7363.4713.400 × 1.70086.36 × 43.18
WR284WG10R32 S band (part)2.60 — 3.952.0784.1562.840 × 1.340 72.14 × 34,94
WR229WG11AR40 C band (part)3.30 — 4.902.5775.1542.290 × 1.14558.17 × 29.08
WR187WG12R48 C band (part)3.95 — 5.853.1536.3051.872 × 0.872 47.55 × 22.2
WR159WG13R58 C band (part)4.90 — 7.053.7127.4231.590 × 0.79540.38 × 20.2
WR137WG14R70 C band (part)5.85 — 8.204.3018.6031.372 × 0.622 34.90 × 15.8
WR112WG15R847.05 — 10.005.26010.5201.122 × 0.497 28.50 × 12.6
WR90WG16R100 X band 8.20 — 12.406.55713.1140.900 × 0.400 22.9 × 10.2
WR75WG17R12010.00 — 15.007.86915.7370.750 × 0.37519.1 × 9.53
WR62WG18R140 Ku band 12.40 — 18.009.48818.9760.622 × 0.31115.8 × 7.90
WR51WG19R18015.00 — 22.0011.57223.1430.510 × 0.25513.0 × 6.48
WR42WG20R220 K band 18.00 — 26.5014.05128.1020.420 × 0.170 10.7 × 4.32
WR34WG21R26022.00 — 33.0017.35734.7150.340 × 0.1708.64 × 4.32
WR28WG22R320 Ka band 26.50 — 40.0021.07742.1540.280 × 0.1407.11 × 3.56
WR22WG23R400 Q band 33.00 — 50.0026.34652.6920.224 × 0.1125.68 × 2.84
WR19WG24R500 U band 40.00 — 60.0031.39162.7820.188 × 0.0944.78 × 2.39
WR15WG25R620 V band 50.00 — 75.0039.87579.7500.148 × 0.0743.76 × 1.88
WR12WG26R740 E band 60.00 — 90.0048.37396.7460.122 × 0.0613.10 × 1.55
WR10WG27R900 W band 75.00 — 110.0059.015118.0300.100 × 0.0502.54 × 1.27
WR8WG28R1200 F band 90.00 — 140.0073.768147.5360.080 × 0.0402.03 × 1,02
WR6, WR7, WR6,5WG29R1400 D band 110.00 — 170.0090.791181.5830.0650 × 0.03251.65 × 0.826
WR5WG30R1800140.00 — 220.00115.714231.4290.0510 × 0.02551.30 × 0.648
WR4WG31R2200172.00 — 260.00137.243274.4850.0430 × 0.02151.09 × 0.546
WR3WG32R2600220.00 — 330.00173.571347.1430.0340 × 0.01700.864 × 0.432
For historical reasons the outside rather than the inside dimensions of these waveguides are 2:1 (with wall thickness WG6–WG10: 0.08" (2.0 mm), WG11A–WG15: 0.064" (1.6 mm), WG16–WG17: 0.05" (1.3 mm), WG18–WG28: 0.04" (1.0 mm)) [17]

For the frequencies in the table above, the main advantage of waveguides over coaxial cables is that waveguides support propagation with lower loss. For lower frequencies, the waveguide dimensions become impractically large, and for higher frequencies the dimensions become impractically small (the manufacturing tolerance becomes a significant portion of the waveguide size).

## Dielectric waveguides

Dielectric rod and slab waveguides are used to conduct radio waves, mostly at millimeter wave frequencies and above. [18] [19] These confine the radio waves by total internal reflection from the step in refractive index due to the change in dielectric constant at the material surface. [20] At millimeter wave frequencies and above, metal is not a good conductor, so metal waveguides can have increasing attenuation. At these wavelengths dielectric waveguides can have lower losses than metal waveguides. Optical fiber is a form of dielectric waveguide used at optical wavelengths.

One difference between dielectric and metal waveguides is that at a metal surface the electromagnetic waves are tightly confined; at high frequencies the electric and magnetic fields penetrate a very short distance into the metal. In contrast, the surface of the dielectric waveguide is an interface between two dielectrics, so the fields of the wave penetrate outside the dielectric in the form of an evanescent (non-propagating) wave. [20]

## Related Research Articles

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A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular to the radiation's propagation direction. Transverse modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an optical fiber and in a laser's optical 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. 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 horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are widely used as antennas at UHF and microwave frequencies, above 300 MHz. They are used as feed antennas for larger antenna structures such as parabolic antennas, as standard calibration antennas to measure the gain of other antennas, and as directive antennas for such devices as radar guns, automatic door openers, and microwave radiometers. Their advantages are moderate directivity, low standing wave ratio (SWR), broad bandwidth, and simple construction and adjustment.

A single-wire transmission line is a method of transmitting electrical power or signals using only a single electrical conductor. This is in contrast to the usual use of a pair of wires providing a complete circuit, or an electrical cable likewise containing two conductors for that purpose.

An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber and rectangular waveguides.

A dielectric resonator antenna (DRA) is a radio antenna mostly used at microwave frequencies and higher, that consists of a block of ceramic material of various shapes, the dielectric resonator, mounted on a metal surface, a ground plane. Radio waves are introduced into the inside of the resonator material from the transmitter circuit and bounce back and forth between the resonator walls, forming standing waves. The walls of the resonator are partially transparent to radio waves, allowing the radio power to radiate into space.

A microwave cavity or radio frequency (RF) cavity is a special type of resonator, consisting of a closed metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies.

Metamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space. However, this class of antenna incorporates metamaterials, which are materials engineered with novel, often microscopic, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the antenna's radiated power.

A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capability to determine whether the EM wave is transmitted, reflected, or absorbed. In general, the lattice structure of the tunable metamaterial is adjustable in real time, making it possible to reconfigure a metamaterial device during operation. It encompasses developments beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials. The ongoing research in this domain includes electromagnetic materials that are very meta which mean good and has a band gap metamaterials (EBG), also known as photonic band gap (PBG), and negative refractive index material (NIM).

A waveguide filter is an electronic filter that is constructed with waveguide technology. Waveguides are hollow metal tubes inside which an electromagnetic wave may be transmitted. Filters are devices used to allow signals at some frequencies to pass, while others are rejected. Filters are a basic component of electronic engineering designs and have numerous applications. These include selection of signals and limitation of noise. Waveguide filters are most useful in the microwave band of frequencies, where they are a convenient size and have low loss. Examples of microwave filter use are found in satellite communications, telephone networks, and television broadcasting.

A via fence, also called a picket fence, is a structure used in planar electronic circuit technologies to improve isolation between components which would otherwise be coupled by electromagnetic fields. It consists of a row of via holes which, if spaced close enough together, form a barrier to electromagnetic wave propagation of slab modes in the substrate. Additionally if radiation in the air above the board is also to be suppressed, then a strip pad with via fence allows a shielding can to be electrically attached to the top side, but electrically behave as if it continued through the PCB.

Leaky-Wave Antenna (LWA) belong to the more general class of Traveling wave antenna, that use a traveling wave on a guiding structure as the main radiating mechanism. Traveling-wave antenna fall into two general categories, slow-wave antennas and fast-wave antennas, which are usually referred to as leaky-wave antennas.

Planar transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines. They are used to interconnect components on printed circuits and integrated circuits working at microwave frequencies because the planar type fits in well with the manufacturing methods for these components. Transmission lines are more than simply interconnections. With simple interconnections, the propagation of the electromagnetic wave along the wire is fast enough to be considered instantaneous, and the voltages at each end of the wire can be considered identical. If the wire is longer than a large fraction of a wavelength, these assumptions are no longer true and transmission line theory must be used instead. With transmission lines, the geometry of the line is precisely controlled so that its electrical behaviour is highly predictable. At lower frequencies, these considerations are only necessary for the cables connecting different pieces of equipment, but at microwave frequencies the distance at which transmission line theory becomes necessary is measured in millimetres. Hence, transmission lines are needed within circuits.

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Patents
• Southworth, , "Wave guide electrotherapeutic system"
• Hopper, , "Wave guide frequency converter", September 10, 1957
Websites