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98-415: Microwave circulators rely on the anisotropic and non- reciprocal properties of magnetized microwave ferrite material. Microwave electromagnetic waves propagating in magnetized ferrite interact with electron spins in the ferrite and are consequently influenced by the microwave magnetic permeability of the ferrite. This permeability is mathematically described by a linear vector operator, also known as

196-422: A r = G E / [ 2 ( 1 + ν ) ] = 2 ( 1 + ν ) G E ≡ 2 C 44 C 11 − C 12 . {\displaystyle a_{r}={\frac {G}{E/[2(1+\nu )]}}={\frac {2(1+\nu )G}{E}}\equiv {\frac {2C_{44}}{C_{11}-C_{12}}}.} The latter expression

294-408: A plasma , so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in lightning or a plasma globe ) that is directional. An anisotropic liquid has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform , which contain no structural ordering of

392-502: A tensor . In the case of magnetized ferrite, the permeability tensor is the Polder tensor . The permeability is a function of the direction of microwave propagation relative to the direction of static magnetization of the ferrite material. Hence, microwave signals propagating in different directions in the ferrite experience different magnetic permeabilities. In the CGS system , the Polder tensor

490-431: A circuit pattern on a ferrite substrate. The circuit is typically formed using thick-film or thin-film metallization processes, often including photolithography . The ferrite substrate is sometimes bonded to a ferrous metal carrier, which serves to improve the efficiency of the magnetic circuit, increase the mechanical strength of the circulator, and protect the ferrite from thermal expansion mismatches between it and

588-417: A circulator for this function. A reflection amplifier is a type of microwave amplifier circuit utilizing negative differential resistance diodes such as tunnel diodes and Gunn diodes . Negative differential resistance diodes can amplify signals, and often perform better at microwave frequencies than two-port devices. However, since the diode is a one-port (two terminal) device, a nonreciprocal component

686-425: A considerable size reduction compared with the junction circulators. On the other hand, lumped-element circulators generally have lower RF power handling capacity than equivalent junction devices and are more complex from a mechanical perspective. The discrete lumped-element inductors and capacitors can be less stable when exposed to vibration or mechanical shocks than the simple distributed impedance transformers in

784-544: A difficult quantity to calculate. In remote sensing applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net irradiance of a scene. For example, let the BRDF be γ ( Ω i , Ω v ) {\displaystyle \gamma (\Omega _{i},\Omega _{v})} where 'i' denotes incident direction and 'v' denotes viewing direction (as if from

882-432: A disk, hexagon, or triangle. An RF/microwave signal entering a circulator port is connected via a stripline to the resonator, where energy is coupled into two counter-rotating circular modes formed by the elliptically polarized waves. These circular modes have different phase velocities which can cause them to combine constructively or destructively at a given port. This produces an anti-node at one port (port 2 if

980-429: A generic term, was originally a proprietary brand of Airborne Instruments Laboratory Inc. (AIL). The version as produced by AIL was essentially air insulated ( air stripline ) with just a thin layer of dielectric material - just enough to support the conducting strip. The conductor was printed on both sides of the dielectric. The more familiar version with the space between the two plates completely filled with dielectric

1078-473: A good antenna. This was intended to highlight the drawbacks of microstrip, but the microstrip patch antenna has become the most popular design of antenna in mobile devices. Stripline remained in the ascendent for its performance advantages through the 1950s and 1960s but eventually microstrip won out, especially in mass produced items, because it was easier to assemble and the lack of an upper dielectric meant that components were easier to access and adjust. As

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1176-544: A high aspect ratio . These features are commonly used in MEMS (microelectromechanical systems) and microfluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching of silicon [100] produces pyramid-like structures) Diffusion tensor imaging

1274-400: A purely reactive impedance. This is not the case with microstrip; the differing dielectrics above and below the strip result in longitudinal non-TEM components to the wave. This results in dispersion and discontinuity elements have a resistive component causing them to radiate. In the 1950s Eugene Fubini , at the time working for AIL, jokingly suggested that a microstrip dipole would make

1372-414: A research team significantly extended this concept, presenting an integrated circuit circulator based on N-path filter concepts. It offers the potential for full-duplex communication (transmitting and receiving at the same time with a single shared antenna over a single frequency). The device uses capacitors and a clock and is much smaller than conventional devices. When one port of a three-port circulator

1470-933: A satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene. P ( Ω i ) = ∫ Ω v γ ( Ω i , Ω v ) n ^ ⋅ d Ω ^ v {\displaystyle P(\Omega _{i})=\int _{\Omega _{v}}\gamma (\Omega _{i},\Omega _{v}){\hat {n}}\cdot d{\hat {\Omega }}_{v}} A ( Ω i , Ω v ) = γ ( Ω i , Ω v ) P ( Ω i ) {\displaystyle A(\Omega _{i},\Omega _{v})={\frac {\gamma (\Omega _{i},\Omega _{v})}{P(\Omega _{i})}}} It

1568-471: A stripline center conductor and sandwiched between two parallel ground planes. A stripline circulator is essentially a stripline center conductor sandwich on ferrite, between ground planes. That is, there is one ferrite disk above the stripline circuit and one ferrite disk below the stripline circuit. Stripline circulators do not have to be constructed with disk- or triangle-shaped ferrites; the ferrites can have almost any shape that has three-way symmetry. This

1666-412: A stripline junction circulator. Switching circulators are similar to other junction circulators, and their microwave theory of operation is the same, except that their direction of circulation can be electronically controlled. Junction circulators use permanent magnets to provide the static magnetic bias for the ferrite(s). However, switching circulators typically rely on the remanent magnetization of

1764-432: A stripline of height }}2H_{L}\\Z_{oU}&=Z_{o}{\text{ of a stripline of height }}2H_{U}\\C_{oL}&={\frac {\sqrt {\varepsilon _{r}}}{V_{c}Z_{oL}}}\\C_{oU}&={\frac {\sqrt {\varepsilon _{r}}}{V_{c}Z_{oU}}}\\C_{o}&=C_{oL}/2+C_{oU}/2\\L_{o}&={\frac {\varepsilon _{r}}{C_{o}V_{c}^{2}}}\\Z_{o}&={\sqrt {\frac {L_{o}}{C_{o}}}}\\\end{aligned}}} . Where: V c {\displaystyle V_{c}}

1862-836: A stripline of height  2 H L Z o U = Z o  of a stripline of height  2 H U C o L = ε r V c Z o L C o U = ε r V c Z o U C o = C o L / 2 + C o U / 2 L o = ε r C o V c 2 Z o = L o C o {\displaystyle {\begin{aligned}Z_{oL}&=Z_{o}{\text{ of

1960-446: Is where (neglecting damping) γ = 1.40 ⋅ g {\displaystyle \gamma =1.40\cdot g\,\,} MHz / Oe is the effective gyromagnetic ratio and g {\displaystyle g} , the so-called effective g-factor , is a ferrite material constant typically in the range of 1.5 - 2.6, depending on the particular ferrite material. ω {\displaystyle \omega }

2058-484: 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 . 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

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2156-448: Is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration. In fluorescence spectroscopy , the fluorescence anisotropy , calculated from the polarization properties of fluorescence from samples excited with plane-polarized light,

2254-475: Is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as bilinear and trilinear filtering , do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily. A chemical anisotropic filter , as used to filter particles,

2352-439: Is also true of the resonator (the center junction portion of the center conductor)- it can be any shape that has three-way symmetry, although there are electrical considerations. The ferrites are magnetized through their thicknesses, i.e., the static magnetic bias field is perpendicular to the plane of the device and the direction of signal propagation is transverse to the direction of the static magnetic field. Both ferrites are in

2450-423: Is an MRI technique that involves measuring the fractional anisotropy of the random motion ( Brownian motion ) of water molecules in the brain. Water molecules located in fiber tracts are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in

2548-416: Is called a transversely isotropic material . Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property. When a material is polycrystalline ,

2646-412: Is due to the fact that FDM is designed to extrude and print layers of thermoplastic materials. This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers. Anisotropic etching techniques (such as deep reactive-ion etching ) are used in microfabrication processes to create well defined microscopic features with

2744-563: Is known as the Zener ratio , a r {\displaystyle a_{r}} , where C i j {\displaystyle C_{ij}} refers to elastic constants in Voigt (vector-matrix) notation . For an isotropic material, the ratio is one. Limitation of the Zener ratio to cubic materials is waived in the Tensorial anisotropy index A that takes into consideration all

2842-494: Is known, Z o {\displaystyle Z_{o}} may be calculated using Z o = Z o a / ε r {\displaystyle Z_{o}=Z_{o}^{a}/{\sqrt {\varepsilon _{r}}}} . The accuracy of this Z o {\displaystyle Z_{o}} estimation is quantified and listed in the microstrip metallic enclosure equations. Since microstrip loss calculation are not directly

2940-421: Is light coming through a polarizer . Another is wood , which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions). In the field of computer graphics , an anisotropic surface changes in appearance as it rotates about its geometric normal , as is the case with velvet . Anisotropic filtering (AF)

3038-468: Is like an AC-powered active circulator. The research claimed to be able to achieve positive gain and low noise for receiving path and broadband nonreciprocity. Another study used resonance with nonreciprocity triggered by angular-momentum biasing, which more closely mimics the way that signals passively circulate in a ferrite circulator. In 1964, Mohr presented and experimentally demonstrated a circulator based on transmission lines and switches. In April, 2016

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3136-813: Is needed to separate the outgoing amplified signal from the incoming input signal. By using a 3-port circulator with the signal input connected to one port, the biased diode connected to a second, and the output load connected to the third, the output and input can be uncoupled. + Anisotropic Anisotropy ( / ˌ æ n aɪ ˈ s ɒ t r ə p i , ˌ æ n ɪ -/ ) is the structural property of non-uniformity in different directions, as opposed to isotropy . An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance , refractive index , conductivity , and tensile strength . An example of anisotropy

3234-458: Is of interest because, with knowledge of the anisotropy function as defined, a measurement of the BRDF from a single viewing direction (say, Ω v {\displaystyle \Omega _{v}} ) yields a measure of the total scene reflectance (planar albedo ) for that specific incident geometry (say, Ω i {\displaystyle \Omega _{i}} ). Stripline In electronics , stripline

3332-515: Is somewhat reduced because of radiation and dispersion effects. The performance disadvantages of microstrip circulators are offset by their relative ease of integration with other planar circuitry. The electrical connections of these circulators to adjacent circuitry are typically made using wire bonds or ribbon bonds. Another advantage of microstrip circulators is their smaller size and correspondingly lower mass than stripline circulators. Despite this advantage, microstrip circulators are often

3430-451: Is split equally into two waves. They propagate in each direction around the circulator with different phase velocities. When they arrive at the output port they have different phase relationships and thus combine accordingly. This combination of waves propagating at different phase velocities is how junction circulators fundamentally operate. The geometry of a stripline junction circulator comprises two ferrite disks or triangles separated by

3528-414: Is terminated in a matched load, it can be used as an isolator , since a signal can travel in only one direction between the remaining ports. An isolator is used to shield equipment on its input side from the effects of conditions on its output side; for example, to prevent a microwave source being detuned by a mismatched load. In radar , circulators are used as a type of duplexer , to route signals from

3626-481: Is the shear modulus , E {\displaystyle E} is the Young's modulus , and ν {\displaystyle \nu } is the material's Poisson's ratio . Therefore, for cubic materials, we can think of anisotropy, a r {\displaystyle a_{r}} , as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:

3724-485: Is the frequency of the RF/microwave signal propagating through the ferrite, H 0 {\displaystyle H_{0}} is the internal magnetic bias field, and M {\displaystyle M} is the magnetization of the ferrite material. In junction circulators and differential phase shift circulators, microwave signal propagation is usually orthogonal to the static magnetic bias field in

3822-430: Is the sped of light. The Z o {\displaystyle Z_{o}} of each stripline may be evaluated independently, and the results used to estimate the Z o {\displaystyle Z_{o}} of the asymmetric stripline. Small errors are introduced in the Z o {\displaystyle Z_{o}} estimation due to the slightly differing capacitance paths to

3920-421: Is the speed of light in a vacuum. H L {\displaystyle H_{L}} and H U {\displaystyle H_{U}} are measured from center of the conductor to the lower and upper ground plane, respectively. Co and Lo are the capacitance and inductance per unit length of the associated transmission line. If there is no dielectric in the asymmetric stripline, then

4018-453: Is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic wavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of elasticity wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in

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4116-797: Is this difference in phase shifts that enables the non-reciprocal behavior of the circulator. A differential phase shifter consists of one or more ferrite slabs, usually positioned on the broad wall(s) of the waveguide. Permanent magnets located outside the waveguide provide static magnetic bias field to the ferrite(s). The ferrite-loaded waveguide is another example of a transverse-field device as described in Circulator § Theory of operation . Different microwave propagation constants corresponding to different directions of signal propagation give rise to different phase velocities and hence, different transmission phase shifts. Depending on which circulator port an incident signal enters, phase shift relationships in

4214-466: Is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon. In NMR spectroscopy , the orientation of nuclei with respect to the applied magnetic field determines their chemical shift . In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like

4312-500: The HF through UHF bands. In a junction circulator, the size of the ferrite(s) is proportional to signal wavelength, but in a lumped-element circulator, the ferrite can be smaller because there is no such wavelength proportionality. In a lumped-element circulator, conductors are wrapped around the ferrite, forming what is typically a woven mesh. The conductor strips are insulated from each other by thin dielectric layers. In some circulators,

4410-770: The magnetically soft (low- coercivity ) ferrites used in other circulators, the hexagonal ferrites used for self-biased circulators are magnetically hard (high- coercivity ) materials. These ferrites are essentially ceramic permanent magnets. In addition to their high magnetic remanence , these ferrites have very large magnetic anisotropy fields, enabling circulator operation up to high microwave frequencies. Because of their thin, planar shape, self-biased circulators can be conveniently integrated with other planar circuitry. Integration of self-biased circulators with semiconductor wafers has been demonstrated at K A -band and V-band frequencies. Lumped-element circulators are small-size devices that are typically used at frequencies in

4508-443: The transmitter to the antenna and from the antenna to the receiver , without allowing signals to pass directly from transmitter to receiver. The alternative type of duplexer is a transmit-receive switch ( TR switch ) that alternates between connecting the antenna to the transmitter and to the receiver. The use of chirped pulses and a high dynamic range may lead to temporal overlap of the sent and received pulses, however, requiring

4606-418: The "reverse" circulation, their major shortcomings, especially at low frequencies, are the bulky sizes and the narrow bandwidths. Early work on non-ferrite circulators includes active circulators using transistors that are non-reciprocal in nature. In contrast to ferrite circulators which are passive devices, active circulators require power. Major issues associated with transistor-based active circulators are

4704-486: The 27 components of the fully anisotropic stiffness tensor. It is composed of two major parts A I {\displaystyle A^{I}} and A A {\displaystyle A^{A}} , the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that A T = A I + A A . {\displaystyle A^{T}=A^{I}+A^{A}.} This first component includes

4802-741: The Earth; significant seismic anisotropy has been detected in the Earth's crust , mantle , and inner core . Geological formations with distinct layers of sedimentary material can exhibit electrical anisotropy; electrical conductivity in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and oil exploration industry to identify hydrocarbon -bearing sands in sequences of sand and shale . Sand-bearing hydrocarbon assets have high resistivity (low conductivity), whereas shales have lower resistivity. Formation evaluation instruments measure this conductivity or resistivity, and

4900-422: The central junction, on which the ferrite resonator is located. These pedestals effectively reduce the height of the waveguide, reducing its characteristic impedance in the resonator region to optimize electrical performance. The reduced-height waveguide sections leading from the resonator to the full-height waveguides serve as impedance transformers. The ferrite resonator is magnetized through its height, i.e.,

4998-430: The circulator design prevents detuning or partial demagnetization of the circulator in the presence of external magnetic fields or ferrous materials, and protects nearby devices from the effects of the circulator's static magnetic field. A waveguide junction circulator contains a magnetized ferrite resonator, which is located at the junction of three waveguides . In contrast with a stripline junction circulator,

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5096-423: The complexity of printed circuits increased, this convenience issue became more important until today microstrip is the dominant planar technology. Miniaturisation also leads to favouring microstrip because its disadvantages are not so severe in a miniaturised circuit. However, stripline is still chosen where operation over a wide band is required. Microstrip is similar to stripline transmission line except that

5194-543: The cosmic anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter , the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars. Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy , for example, may occur in

5292-472: The dielectric material is known as an air stripline . To prevent the propagation of unwanted modes, the two ground planes must be shorted together. This is commonly achieved by a row of vias running parallel to the strip on each side. Like coaxial cable , stripline is non- dispersive , and has no cutoff frequency . Good isolation between adjacent traces can be achieved more easily than with microstrip . Stripline provides for enhanced noise immunity against

5390-410: The difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error. Most common rock-forming minerals are anisotropic, including quartz and feldspar . Anisotropy in minerals is most reliably seen in their optical properties . An example of an isotropic mineral is garnet . Igneous rock like granite also shows the anisotropy due to

5488-560: The direction of measurement. Fourth-rank tensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead. In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper,

5586-542: The direction of the static magnetic bias field, which is through the thickness of the ferrite. The plus and minus subscripts of the propagation constants indicate opposite wave polarizations. Microwave circulators fall into two main classes: differential phase shift circulators and junction circulators, both of which are based on cancellation of waves propagating over two different paths in or near magnetized ferrite material. Waveguide circulators may be of either type, while more compact devices based on stripline are usually of

5684-504: The directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with texture will be often be anisotropic. Textured materials are often the result of processing techniques like cold rolling , wire drawing , and heat treatment . Mechanical properties of materials such as Young's modulus , ductility , yield strength , and high-temperature creep rate , are often dependent on

5782-422: The ferrite itself is the resonator, rather than the metal central portion of a stripline center conductor. The ferrite resonator may have any shape that has three-fold Rotational symmetry , such as a cylinder or Triangular prism . The resonator is often just one ferrite, but it is sometimes composed of two or more ferrites, which may be coupled to each other, in various geometrical configurations. The geometry of

5880-489: The ferrite itself. The ferrites that are used in switching circulators have square magnetic hysteresis loops and often sub- Oersted coercivities . Such a ferrite material requires a relatively small magnetic field and low energy level to flip its magnetic polarity. This is distinctly advantageous for a switching circulator, but the absence of permanent magnets would be a disadvantage of a non-switching junction circulator that must retain its magnetic bias despite exposures to

5978-596: The ferrite. This is the so-called transverse field case. The microwave propagation constants for this case, neglecting losses are where μ 0 {\displaystyle \mu _{0}} is the Permeability of Free Space and ϵ {\displaystyle \epsilon } is the Absolute permittivity of the ferrite material. In a circulator, these propagation constants describe waves having Elliptical polarization that would propagate in

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6076-1610: The formula is claimed to be at least 1% for W/(H-T) > .05 and T< 0.025. For thick conductors, Wheeler provides the following more accurate equations Z s t r i p l i n e = 30 E r l n ( 1 + C 2 ( C + C 2 + 6.27 ) ) {\displaystyle {\begin{aligned}Z_{stripline}={\frac {30}{\sqrt {E_{r}}}}ln{\biggr (}1+{\frac {C}{2}}{\big (}C+{\sqrt {C^{2}+6.27}}{\big )}{\biggr )}\\\end{aligned}}} Where: C = 8 ( 1 − T ) π ( W + Δ W ) Δ W = T π ( 1 − T ) { 1 − 1 2 l n [ ( T 2 − T ) 2 + ( .0796 T W + 1.1 T ) M ] } M = 3 1.5 + T ( 1 − T ) {\displaystyle {\begin{aligned}C&={\frac {8(1-T)}{\pi (W+\Delta W)}}\\\Delta W&={\frac {T}{\pi (1-T)}}{\biggr \{}1-{\frac {1}{2}}ln{\biggr [}{\bigg (}{\frac {T}{2-T}}{\biggr )}^{2}+{\biggr (}{\frac {.0796T}{W+1.1T}}{\biggr )}^{M}{\biggr ]}{\biggr \}}\\M&={\frac {3}{1.5+{\frac {T}{(1-T)}}}}\\\end{aligned}}} Where T and W are as defined

6174-420: The ground planes between the asymmetric case being estimated and the symmetric cases used to make the estimation, so only small asymmetric placement of the strip will be expected to produce an acceptable estimation for Z o {\displaystyle Z_{o}} of the asymmetrically placed strip. To summarize: Z o L = Z o  of

6272-452: The heat source in electronics are often anisotropic. Many crystals are anisotropic to light ("optical anisotropy"), and exhibit properties such as birefringence . Crystal optics describes light propagation in these media. An "axis of anisotropy" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such optical axes . Seismic anisotropy

6370-461: The hybrid couplers and the differential phase shifts cause signals to combine at one other port and cancel at each of the remaining two ports. Differential phase shift circulators are often used as 3-port circulators by connecting one circulator port to a reflectionless termination, or they can be used as isolators by terminating two circulator ports. Though ferrite circulators can provide good "forward" signal circulation while suppressing greatly

6468-482: The junction type. Two or more junction circulators can be combined in a single component to give four or more ports. Typically permanent magnets produce a static magnetic bias in the microwave ferrite material. Ferrimagnetic garnet crystal is used in optical circulators . A stripline junction circulator contains a resonator, which is located at the central junction of the striplines . This resonator may have any shape that has three-fold Rotational symmetry , such as

6566-576: The largest components in microwave modules. Self-biased junction circulators are unique in that they do not utilize permanent magnets that are separate from the microwave ferrite. The elimination of external magnets significantly reduces the size and weight of the circulator compared to electrically-equivalent microstrip junction circulators for similar applications. Monolithic ferrites that are used for self-biased circulators are M-type uniaxial (single magnetic axis) hexagonal ferrites that have been optimized to have low microwave losses. In contrast with

6664-402: The magnetizing coil to magnetize the ferrite in the polarity to provide the desired direction of circulation. Differential phase shift circulators are mainly used in high power microwave applications. They are usually built from rectangular waveguide components. These circulators are 4-port devices having circulation in the sequence 1 - 2 - 3 - 4 - 1, with ports numbered as shown in

6762-681: The material. Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of macromolecules in polymeric materials, polymers are in general described as isotropic. However, mechanically gradient polymers can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropic hydrogels , in order to mimic hierarchically ordered biological soft matter. 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This

6860-402: The mesh is in the form of traces on a printed wiring board with metallized vias to make connections between layers. The conductive strips can be thought of as non- reciprocally coupled inductors. Impedance matching circuitry and broad-banding circuitry in lumped-element circulators are often constructed using discrete ceramic capacitors and air-core inductors. This class of circulator offers

6958-1644: The microstrip is not sandwiched, it is on a surface layer, above a ground plane. Stripline is more expensive to fabricate than microstrip, and because of the second groundplane, the strip widths are much narrower for a given impedance and board thickness than for microstrip. An accurate closed form equation for the characteristic impedance of a stripline with a thin centered conductor has been reported as Z s t r i p l i n e = 30 π E r 1 − T W e f f + C f C f = 2 π l n ( 1 1 − T + 1 ) − T π l n ( 1 ( 1 − T ) 2 − 1 ) {\displaystyle {\begin{aligned}Z_{stripline}&={\frac {30\pi }{\sqrt {E_{r}}}}{\frac {1-T}{W_{eff}+C_{f}}}\\C_{f}&={\frac {2}{\pi }}ln{\biggr (}{\frac {1}{1-T}}+1{\biggr )}-{\frac {T}{\pi }}ln{\biggr (}{\frac {1}{(1-T)^{2}}}-1{\biggr )}\\\end{aligned}}} Where: W e f f = { W − ( 0.35 − W ) 2 1 + 12 T , W < 0.35 W , W ≥ 0.35 T = t h W = w h w = width of

7056-484: The modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index A A {\displaystyle A^{A}} covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise. Fiber-reinforced or layered composite materials exhibit anisotropic mechanical properties, due to orientation of

7154-410: The molecules. Liquid crystals are examples of anisotropic liquids. Some materials conduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from

7252-408: The orientation of the minerals during the solidification process. Anisotropy is also a well-known property in medical ultrasound imaging describing a different resulting echogenicity of soft tissues, such as tendons , when the angle of the transducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when

7350-475: The pi system of benzene . This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change. Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal). Physicists from University of California, Berkeley reported about their detection of

7448-411: The potentially demagnetizing effects of stray magnetic fields, nearby ferrous materials, and temperature variations. The magnetization polarity of the ferrite, and hence the direction of circulation of a switching circulator, is controlled using a magnetizing coil that loops through the ferrite. The coil is connected to electronic driver circuitry that sends current pulses of the correct polarity through

7546-402: The power limitation and the signal-to-noise degradation, which are critical when it is used as a duplexer for sustaining the strong transmit power and clean reception of the signal from the antenna. Varactors offer one solution. One study employed a structure similar to a time-varying transmission line with the effective nonreciprocity triggered by a one-direction propagating carrier pump. This

7644-474: The propagation of radiated RF emissions, at the expense of slower propagation speeds when compared to microstrip lines. The effective permittivity of striplines equals the relative permittivity of the dielectric substrate because of wave propagation only in the substrate. Hence striplines have higher effective permittivity in comparison to microstrip lines, which in turn reduces wave propagation speed (see also velocity factor ) according to Stripline , now used as

7742-400: The reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk material. The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto

7840-419: The remaining port (port 3 if signal propagation is from port 1 to port 2) to be nulled, where l {\displaystyle l} is the path length between adjacent ports and m {\displaystyle m} and n {\displaystyle n} are integers. Solving the two preceding equations simultaneously, for proper circulation the necessary conditions are and Each of

7938-444: The resonator is influenced by electrical and thermal performance considerations. Waveguide junction circulators function in much the same way as stripline junction circulators, and their basic theory of operation is the same. The internal geometry of a waveguide junction circulator comprises a junction of three waveguides, the ferrite resonator, and impedance matching structures. Many of these circulators contain pedestals located in

8036-430: The rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual. Radiance fields (see Bidirectional reflectance distribution function (BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene

8134-434: The results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are produced from the coal and shale reservoirs. The hydraulic conductivity of aquifers is often anisotropic for the same reason. When calculating groundwater flow to drains or to wells ,

8232-454: The same as the above expression. The accuracy is claimed to be at least 0.5% for C>0.25. For stripline conductors that are not centered, that is, the distance to the upper ground plane is not the same as to the lower ground plane, strategies exist to estimate the characteristic impedance in at least one of two ways. If the asymmetry of the conductor placement is not large, the lower and upper capacitance per unit length may be estimated for

8330-449: The same static ad RF magnetic fields. The two ferrites can be thought of as one continuous ferrite with an embedded stripline center conductor. For practical manufacturing reasons, the center conductor is not generally embedded in ferrite, so two discrete ferrites are used. The static magnetic bias field is typically provided by permanent magnets that are located external to the circulator ground planes. Magnetic shielding incorporated into

8428-416: The schematic. There are various feasible circulator architectures, the most common of which utilizes a magic tee hybrid coupler , a quadrature hybrid coupler , and two oppositely-magnetized differential phase shifters. A differential phase shifter provides non-reciprocal transmission phase shift. That is, the forward phase shift is different from the phase shift in the reverse transmission direction. It

8526-477: The signal is incident upon port 1) and a node or null at another port (port 3 if the microwave energy is coupled from port 1 to port 2 and not reflected back into port 2). If losses are neglected for simplification, the counter-rotating modes must differ in phase by an integer multiple of 2 π {\displaystyle 2\pi } for signal propagation from port 1 to port 2 (or from port 2 to port 3, or from port 3 to port 1): and similarly, for

8624-480: The static magnetic bias field is perpendicular to the plane of the device and the direction of signal propagation is transverse to the direction of the static magnetic field. The static magnetic bias field is typically provided by permanent magnets that are external to the waveguide junction. The microstrip junction circulator is another widely-used form of circulator that utilizes the microstrip transmission line topology. A microstrip circulator consists primarily of

8722-508: The stiffness is highest along the <111> direction, normal to the close-packed planes, and smallest parallel to <100>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic. For an isotropic material, G = E / [ 2 ( 1 + ν ) ] , {\displaystyle G=E/[2(1+\nu )],} where G {\displaystyle G}

8820-408: 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 . As shown in the diagram, the central conductor need not be equally spaced between the ground planes. In the general case, the dielectric material may be different above and below the central conductor. A stripline that uses air as

8918-532: The stripline conductor t = thickness of the stripline conductor h = thickness of the substrate from the top ground plate to the bottom ground plate E r = dielectric constant of the substrate dielectric material {\displaystyle {\begin{aligned}W_{eff}&={\begin{cases}W-{\frac {(0.35-W)^{2}}{1+12T}},&W<0.35\\W,&W\geq 0.35\end{cases}}\\T&={\frac {t}{h}}\\W&={\frac {w}{h}}\\w&={\text{width of

9016-1155: The stripline conductor}}\\t&={\text{thickness of the stripline conductor}}\\h&={\text{thickness of the substrate from the top ground plate to the bottom ground plate}}\\E_{r}&={\text{dielectric constant of the substrate dielectric material}}\end{aligned}}} Note that when the conductor thickness is small, T<<1 or t<<h, the equations simplify significantly. Z s t r i p l i n e = 30 π E r 1 W e f f + 0.441271 {\displaystyle {\begin{aligned}Z_{stripline}&={\frac {30\pi }{\sqrt {Er}}}{\frac {1}{W_{eff}+0.441271}}\\\end{aligned}}} Where: W e f f = { W − ( 0.35 − W ) 2 , W < 0.35 W , W ≥ 0.35 {\displaystyle {\begin{aligned}W_{eff}&={\begin{cases}W-(0.35-W)^{2},&W<0.35\\W,&W\geq 0.35\end{cases}}\\\end{aligned}}} The accuracy of

9114-435: The stripline looks like a microstrip with a dielectric of air, ε = 1 {\displaystyle \varepsilon =1} , inside a metallic enclosure. This permits the air characteristic impedance, Z o a {\displaystyle Z_{o}^{a}} , to be calculated using microstrip metallic enclosure equations. When Z o a {\displaystyle Z_{o}^{a}}

9212-402: The surface to which the circulator is mounted. A permanent magnet that is bonded to the circuit face of the ferrite substrate provides the static magnetic bias to the ferrite. Microstrip circulators function in the same way as stripline junction circulators, and their basic theory of operation is the same. In comparison with stripline circulators, electrical performance of microstrip circulators

9310-412: The transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners. Anisotropy, in materials science , is a material's directional dependence of a physical property . This is a critical consideration for materials selection in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy

9408-413: The two counter-rotating modes has its own resonant frequency. The two resonant frequencies are known as the split frequencies. The circulator operating frequency is set between the two split frequencies. These circulator types operate based on faraday rotation . Wave cancellation occurs when waves propagate with and against the circulator's direction of circulation. An incident wave arriving at any port

9506-482: The upper ground plane and the lower ground plane using centered stripline equations and standard transmission line equations for homogeneous lines, V c 2 / ε r = 1 / L C {\displaystyle V_{c}^{2}/\varepsilon _{r}=1/LC} , and Z o 2 = L / C {\displaystyle Z_{o}^{2}=L/C} where V c {\displaystyle V_{c}}

9604-414: Was originally produced by Sanders Associates who marketed it under the brand name of triplate . Stripline was initially preferred to its rival, microstrip, made by ITT . Transmission in stripline is purely TEM mode and consequently there is no dispersion (provided that the dielectric of substrate is not itself dispersive). Also, discontinuity elements on the line (gaps, stubs , posts etc) present

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