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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 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.
1470: 1939: 1022: 2066:. 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 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. 1448:. Wave cancellation occurs when waves propagate with and against the circulator's direction of circulation. An incident wave arriving at any port 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. 1892: 1539: 1854:. 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 the potentially demagnetizing effects of stray magnetic fields, nearby ferrous materials, and temperature variations. 2043: 1783: 1707: 1629: 27: 1456:
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 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.
1558:. 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 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. 1829: 1884: 1775: 976: 1459:
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 the same static ad RF magnetic fields. The
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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 is like an AC-powered active circulator. The research claimed to be able to achieve positive gain and low noise
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transmission phase shift. That is, the forward phase shift is different from the phase shift in the reverse transmission direction. It 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,
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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
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junction circulator comprises two ferrite disks or triangles separated by 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
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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 the power limitation and the signal-to-noise degradation, which are critical when
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E-field animation of microwave signal propagation through a high-power S-band differential phase shift circulator. In this animation, the signal propagating through the upper differential phase shifter is seen to have a higher velocity than the signal in the lower differential phase shifter. Just
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Depending on which circulator port an incident signal enters, phase shift relationships in 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
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mismatches between it and 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
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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 the
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This class of circulator offers 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
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The ferrite resonator is magnetized through its height, 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. The static magnetic bias field is typically provided by
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junction circulator comprises a junction of three waveguides, the ferrite resonator, and impedance matching structures. Many of these circulators contain pedestals located in the central junction, on which the ferrite resonator is located. These pedestals effectively reduce the height of the
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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
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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.
1870: 221:. 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. 93:, connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1. An ideal three-port circulator thus has the following 1998:, 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. 1803:
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, the mesh is in the form of traces on a
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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 the largest components in microwave modules.
225: 1485: 1652:. The top right circulator port connects to receiver and signal processing circuitry, and the lower right circulator port connects to the transmitter power amplifier near the center of the module. In this instance, the circulator performs a 1903:
components. These circulators are 4-port devices having circulation in the sequence 1 - 2 - 3 - 4 - 1, with ports numbered as shown in the schematic. There are various feasible circulator architectures, the most common of which utilizes a
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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
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Though ferrite circulators can provide good "forward" signal circulation while suppressing greatly the "reverse" circulation, their major shortcomings, especially at low frequencies, are the bulky sizes and the narrow bandwidths.
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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.
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are usually of 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.
445: 524: 1550:. In contrast with a stripline junction circulator, 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 2963: 1676:. 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 966:
that would propagate in 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.
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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
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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.
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Each of 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.
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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
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Internal construction of two different lumped-element isolators. One type of isolator is a circulator having one port internally terminated. The termination in each of these isolators is a rectangular film
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airborne radar. The microstrip junction circulator is visible at the left end of the module. The left port of the circulator connects to the antenna port of the module and ultimately to an element of the
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E-field plot of the rotating standing wave pattern in the ferrite of a waveguide junction circulator. The direction of signal propagation is from bottom to upper right, and the upper left ferrite apex is
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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.
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In 1964, Mohr presented and experimentally demonstrated a circulator based on transmission lines and switches. In April, 2016 a research team significantly extended this concept, presenting an
1928:. Different microwave propagation constants corresponding to different directions of signal propagation give rise to different phase velocities and hence, different transmission phase shifts. 1149: 753:
In junction circulators and differential phase shift circulators, microwave signal propagation is usually orthogonal to the static magnetic bias field in the ferrite. This is the so-called
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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.
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coupled inductors. Impedance matching circuitry and broad-banding circuitry in lumped-element circulators are often constructed using discrete ceramic capacitors and air-core inductors.
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basic theory of operation is the same. In comparison with stripline circulators, electrical performance of microstrip circulators is somewhat reduced because of
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transmission line topology. A microstrip circulator consists primarily of a circuit pattern on a ferrite substrate. The circuit is typically formed using
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electromagnetic wave propagating in a magnetized ferrite cylinder. The static magnetic field is oriented parallel to the cylinder axis. This is known as
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Junction circulators use permanent magnets to provide the static magnetic bias for the ferrite(s). However, switching circulators typically rely on the
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circulators by connecting one circulator port to a reflectionless termination, or they can be used as isolators by terminating two circulator ports.
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properties of magnetized microwave ferrite material. Microwave electromagnetic waves propagating in magnetized ferrite interact with electron
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before the signals reach the quadrature hybrid on the right, the upper signal leads the lower signal by about 90°. Animation courtesy of
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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).
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Tanaka, S.; Shimomura, N.; Ohtake, K. (1965-03-01). "Active circulators - The realization of circulators using transistors".
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for a circulator (with each waveguide or transmission line port drawn as a single line, rather than as a pair of conductors)
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Geiler, Anton; Harris, Vince (September–October 2014). "Atom Magnetism: Ferrite Circulators - Past, Present, and Future".
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lumped-element inductors and capacitors can be less stable when exposed to vibration or mechanical shocks than the simple
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Differential phase shift circulators are mainly used in high power microwave applications. They are usually built from
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are integers. Solving the two preceding equations simultaneously, for proper circulation the necessary conditions are
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it is used as a duplexer for sustaining the strong transmit power and clean reception of the signal from the antenna.
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If losses are neglected for simplification, the counter-rotating modes must differ in phase by an integer multiple of
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Qin, Shihan; Xu, Qiang; Wang, Y.E. (2014-10-01). "Nonreciprocal Components With Distributedly Modulated Capacitors".
679:, is a ferrite material constant typically in the range of 1.5 - 2.6, depending on the particular ferrite material. 2930: 1546:
A waveguide junction circulator contains a magnetized ferrite resonator, which is located at the junction of three
935: 2736:(2016-02-01). "Magnetless Microwave Circulators Based on Spatiotemporally Modulated Rings of Coupled Resonators". 3077: 1682: 349:{\displaystyle B={\begin{bmatrix}\mu &j\kappa &0\\-j\kappa &\mu &0\\0&0&1\end{bmatrix}}H} 2026:, without allowing signals to pass directly from transmitter to receiver. The alternative type of duplexer is a 532: 1686: 1567: 1037:, such as a disk, hexagon, or triangle. An RF/microwave signal entering a circulator port is connected via a 841:{\displaystyle \Gamma _{+}=j\omega {\sqrt {\mu _{0}\epsilon }}\,{\sqrt {\frac {\mu ^{2}-\kappa ^{2}}{\mu }}}} 620: 1154:
and similarly, for the remaining port (port 3 if signal propagation is from port 1 to port 2) to be nulled,
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of the ferrite. This permeability is mathematically described by a linear vector operator, also known as a
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magnetizing coil to magnetize the ferrite in the polarity to provide the desired direction of circulation.
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This article is about radio frequency (RF) or microwave frequency passive circulators. For other uses, see
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with metallized vias to make connections between layers. The conductive strips can be thought of as non-
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Palmer, William; Kirkwood, David; et al. (June 2016). "A Bright Future for Integrated Magnetics".
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A stripline junction circulator contains a resonator, which is located at the central junction of the
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E-field scatter plot of an electromagnetic wave propagating through a waveguide junction circulator.
1844: 1747: 1742:) materials. These ferrites are essentially ceramic permanent magnets. In addition to their high 1551: 1087:
for signal propagation from port 1 to port 2 (or from port 2 to port 3, or from port 3 to port 1):
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which can cause them to combine constructively or destructively at a given port. This produces an
1034: 1734:) ferrites used in other circulators, the hexagonal ferrites used for self-biased circulators are 1538: 2761: 2714: 2471: 2389: 2243: 1975: 1743: 1005: 676: 652: 74: 1791:
Lumped-element circulators are small-size devices that are typically used at frequencies in the
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Carchon, G.; Nanwelaers, B. (2000-02-01). "Power and noise limitations of active circulators".
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When one port of a three-port circulator is terminated in a matched load, it can be used as an
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The microstrip junction circulator is another widely-used form of circulator that utilizes the
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of the ferrite material. In a circulator, these propagation constants describe waves having
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Zeina, N.; How, H.; et al. (September 1992). "Self-Biasing Circulators Operating at K
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junction circulator having triangular ferrites and an irregular triangle-shaped resonator.
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Fay, C.E.; Comstock, R.L. (1965-01-01). "Operation of the Ferrite Junction Circulator".
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of the ferrite itself. The ferrites that are used in switching circulators have square
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E-Field Plots Showing Electromagnetic Wave Propagation in Waveguide Junction Circulators
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on port 3. The label on the permanent magnet indicates the direction of circulation.
440:{\displaystyle \mu =1+{\frac {\omega _{0}\omega _{m}}{\omega _{0}^{2}-\omega ^{2}}}} 2059: 1694: 1649: 519:{\displaystyle \kappa ={\frac {\omega \omega _{m}}{{\omega _{0}}^{2}-\omega ^{2}}}} 2491:
Monolithically Integrated Self-Biased Circulator for mmWave T/R MMIC Applications
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High-Power Liquid-Cooled Differential Phase Shift Circulator. Image courtesy of
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case. The microwave propagation constants for this case, neglecting losses are
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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
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Internal construction of a WR-90 (WG 16; R 100) waveguide switching circulator.
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Woven mesh conductor wrapped around the ferrite of a lumped-element circulator.
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Internal construction of a WR-112 (WG 15; R 84) waveguide junction circulator.
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that have been optimized to have low microwave losses. In contrast with the
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to the resonator, where energy is coupled into two counter-rotating circular
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is the frequency of the RF/microwave signal propagating through the ferrite,
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Electronic circuit in which a signal entering any port exits at the next port
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High-Power Liquid-Cooled Waveguide Junction Circulator. Image courtesy of
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Monolithic ferrites that are used for self-biased circulators are M-type
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junction circulator having disk ferrites and a triangle-shaped resonator.
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fields, enabling circulator operation up to high microwave frequencies.
73:(RF) signal to exit through the port directly after the one it entered. 1848: 1755: 2951: 2779:
Mohr, Richard (1964). "A New Nonreciprocal Transmission Line Device".
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junction circulator having disk ferrites and a disk-shaped resonator.
1001: 217:. In the case of magnetized ferrite, the permeability tensor is the 214: 2512:
Konishi, Yoshihiro (November 1965). "Lumped Element Y Circulator".
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Modern Ferrites, Volume 2: Emerging Technologies and Applications
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at one port (port 2 if the signal is incident upon port 1) and a
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in the ferrite and are consequently influenced by the microwave
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permanent magnets that are external to the waveguide junction.
897:{\displaystyle \Gamma _{-}=j\omega {\sqrt {\mu _{0}\epsilon }}} 2833:"Magnetic-free non-reciprocity based on staggered commutation" 2559:. International Microwave Symposium Digest. pp. 147–151. 2107:
Polder, D (1949). "On the Theory of Ferromagnetic Resonance".
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Bosma, H. (1964-01-01). "On Stripline Y-Circulation at UHF".
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Schematic diagram of a differential phase shift circulator.
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impedance transformers in a stripline junction circulator.
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Cui, Yongjie; Chen, Hung-Yu; et al. (December 2021).
1033:. This resonator may have any shape that has three-fold 2989:
Ohm, E. A. (1956), "A Broad-Band Microwave Circulator",
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Reiskarimian, Negar; Krishnaswamy, Harish (2016-04-15).
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IEEE Spectrum: Technology, Engineering, and Science News
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Microwave diode reflection amplifier using a circulator
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Internal Construction of Stripline Junction Circulators
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Internal construction of a differential phase shifter.
1226:{\displaystyle -\Gamma _{-}l+2\Gamma _{+}l=(2n-1)\pi } 276: 118: 1430:{\displaystyle \Gamma _{+}l={\frac {2m+4n-2}{3}}\pi } 1377: 1358:{\displaystyle \Gamma _{-}l={\frac {4m+2n-1}{3}}\pi } 1305: 1282: 1262: 1242: 1163: 1096: 1070: 983:
junction circulator used as an isolator by placing a
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IEEE Transactions on Microwave Theory and Techniques
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IEEE Transactions on Microwave Theory and Techniques
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IEEE Transactions on Microwave Theory and Techniques
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IEEE Transactions on Microwave Theory and Techniques
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IEEE Transactions on Microwave Theory and Techniques
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IEEE Transactions on Microwave Theory and Techniques
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what they are, different types, how they work, etc.
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IRE Transactions on Microwave Theory and Techniques
2928:Chait, H. N.; Curry, T. R. (1959), "Y-Circulator", 2557:
New Design Techniques for Miniature VHF Circulators
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Waveguide Junction Circulators: Theory and Practice
2054:is a type of microwave amplifier circuit utilizing 77:have similar behavior. Ports are where an external 1429: 1357: 1288: 1268: 1248: 1225: 1143: 1079: 950: 926: 896: 840: 738: 718: 691: 667: 643: 607: 567: 518: 439: 348: 178: 1144:{\displaystyle 2\Gamma _{-}l-\Gamma _{+}l=2m\pi } 1959:Early work on non-ferrite circulators includes 1256:is the path length between adjacent ports and 2288:The Stripline Circulator: Theory and Practice 8: 2411:-Band Utilizing M-Type Hexagonal Ferrites". 1049:waves. These circular modes have different 2580:Principles of Microwave Ferrite Engineering 2141:Microwave Circulator Design, Second Edition 1645:active electronically scanned array (AESA) 1640:Transmit-Receive (T-R) module used in the 568:{\displaystyle \omega _{0}=\gamma H_{0}\ } 2913: 2864: 1672:metallization processes, often including 1394: 1382: 1376: 1322: 1310: 1304: 1281: 1261: 1241: 1190: 1171: 1162: 1120: 1104: 1095: 1069: 943: 918: 912: 883: 877: 862: 856: 825: 812: 804: 803: 792: 786: 771: 765: 731: 726:is the internal magnetic bias field, and 710: 704: 684: 660: 640: 639: 622: 587: 581: 556: 540: 534: 507: 494: 487: 482: 473: 463: 455: 428: 415: 410: 398: 388: 381: 367: 271: 263: 113: 105: 1925: 1890: 1882: 1827: 1773: 1705: 1635: 1602: 1585: 1537: 1444:These circulator types operate based on 1025:Rotating modes in a junction circulator. 1020: 223: 2912:For a description of a circulator, see 2074: 1462: 644:{\displaystyle \gamma =1.40\cdot g\,\,} 1915:A differential phase shifter provides 608:{\displaystyle \omega _{m}=\gamma M\ } 1926:Circulator § Theory of operation 7: 2555:Dunn, V. E.; Roberts, R. W. (1965). 2010:, circulators are used as a type of 1862:Differential phase shift circulators 1379: 1307: 1187: 1168: 1117: 1101: 859: 768: 194:Microwave circulators rely on the 14: 2975:(Second ed.), Artech House, 2341:Ferrites at Microwave Frequencies 1746:, these ferrites have very large 2056:negative differential resistance 1710:Self-biased junction circulator. 1702:Self-biased junction circulators 1500: 1484: 1468: 3037:from the original on 2022-10-09 1945:Symphony Microwave Technologies 1632:Microstrip junction circulator. 1624:Microstrip junction circulators 2888:Wang, Brian (April 18, 2016). 2413:IEEE Transactions on Magnetics 1517:Waveguide junction circulators 1217: 1202: 1017:Stripline junction circulators 1: 2971:Linkhart, Douglas K. (2014), 2732:Estep, N. A.; Sounas, D. L.; 2582:. John Wiley & Sons Ltd. 2139:Linkhart, Douglas K. (2014). 3083:Telecommunications equipment 2339:Baden-Fuller, A. J. (1987). 2022:and from the antenna to the 2014:, to route signals from the 2973:Microwave Circulator Design 2806:Nordrum, Amy (2016-04-15). 2082:Harris, Vincent G. (2023). 1561:The internal geometry of a 1507:Internal construction of a 1475:Internal construction of a 651:MHz / Oe is the effective 359:where (neglecting damping) 21:Circulator (disambiguation) 3099: 2931:Journal of Applied Physics 2261:Soohoo, Ronald F. (1985). 1770:Lumped-element circulators 1715:for similar applications. 936:Permeability of Free Space 675:, the so-called effective 235:E-field vector plot of an 65:device that only allows a 18: 3049:Circulators and Isolators 3013:10.1109/TMTT.1956.1125064 2750:10.1109/TMTT.2015.2511737 2703:10.1109/TMTT.2014.2347935 2578:Helszajn, Joseph (1969). 2565:10.1109/GMTT.1965.1122495 2534:10.1109/tmtt.1965.1126116 2318:. John Wiley & Sons. 2314:Helszajn, Joseph (1998). 2290:. John Wiley & Sons. 2286:Helszajn, Joseph (2008). 2232:10.1109/TMTT.1965.1125923 2186:10.1109/TMTT.1964.1125753 2121:10.1080/14786444908561215 1910:quadrature hybrid coupler 1491:Internal construction of 992:compact devices based on 951:{\displaystyle \epsilon } 750:of the ferrite material. 3019:Wenzel, C. (July 1991), 2460:10.1109/mmm.2014.2332411 2378:10.1109/MMM.2019.2904381 2343:. Peter Peregrinus Ltd. 1906:magic tee hybrid coupler 1568:characteristic impedance 1566:waveguide, reducing its 1554:, such as a cylinder or 927:{\displaystyle \mu _{0}} 2781:Proceedings of the IEEE 2605:Proceedings of the IEEE 2448:IEEE Microwave Magazine 2366:IEEE Microwave Magazine 2028:transmit-receive switch 1951:Non-ferrite circulators 1924:device as described in 1722:(single magnetic axis) 964:Elliptical polarization 692:{\displaystyle \omega } 2793:10.1109/PROC.1964.3007 2617:10.1109/PROC.1965.3683 2499:10.1109/IEDM19574.2021 2047: 1947: 1896: 1888: 1877: 1841:remanent magnetization 1833: 1788: 1779: 1711: 1657: 1633: 1616: 1598: 1543: 1532: 1431: 1359: 1290: 1270: 1250: 1227: 1145: 1081: 1047:elliptically polarized 1026: 988: 952: 928: 898: 842: 740: 720: 693: 669: 645: 609: 569: 520: 441: 350: 244: 237:elliptically polarized 180: 47:electrical engineering 42: 2837:Nature Communications 2045: 1941: 1901:rectangular waveguide 1894: 1886: 1872: 1831: 1824:Switching circulators 1785: 1777: 1709: 1639: 1631: 1613: 1596: 1541: 1527: 1432: 1360: 1291: 1271: 1251: 1228: 1146: 1082: 1080:{\displaystyle 2\pi } 1024: 978: 960:Absolute permittivity 953: 929: 899: 843: 741: 721: 719:{\displaystyle H_{0}} 694: 670: 646: 610: 570: 521: 442: 351: 234: 211:magnetic permeability 181: 29: 3073:Microwave technology 2265:. Harper & Row. 2086:. Wiley-IEEE Press. 2052:reflection amplifier 2038:Reflection amplifier 1875:Microwave Techniques 1847:loops and often sub- 1806:printed wiring board 1530:Microwave Techniques 1375: 1303: 1280: 1260: 1240: 1161: 1094: 1068: 1012:Junction circulators 942: 911: 855: 764: 730: 703: 683: 659: 621: 580: 533: 454: 366: 262: 104: 3005:1956ITMTT...4..210O 2944:1959JAP....30S.152C 2857:10.1038/ncomms11217 2849:2016NatCo...711217R 2695:2014ITMTT..62.2260Q 2652:2000ITMTT..48..316C 2526:1965ITMTT..13..852K 2263:Microwave Magnetics 2224:1965ITMTT..13...15F 2178:1964ITMTT..12...61B 1845:magnetic hysteresis 1748:magnetic anisotropy 1552:Rotational symmetry 1035:Rotational symmetry 1006:optical circulators 1004:crystal is used in 420: 190:Theory of operation 75:Optical circulators 2048: 1976:integrated circuit 1961:active circulators 1948: 1897: 1889: 1878: 1834: 1789: 1780: 1744:magnetic remanence 1724:hexagonal ferrites 1712: 1658: 1634: 1617: 1599: 1544: 1533: 1451:The geometry of a 1427: 1355: 1286: 1266: 1246: 1223: 1141: 1077: 1027: 989: 948: 924: 894: 838: 736: 716: 689: 665: 653:gyromagnetic ratio 641: 605: 565: 516: 437: 406: 346: 337: 245: 176: 170: 43: 2952:10.1063/1.2185863 2894:nextbigfuture.com 2689:(10): 2260–2272. 2660:10.1109/22.821785 2425:10.1109/20.179764 2297:978-0-470-25878-1 2150:978-1-60807-583-6 2093:978-1-394-15613-9 1736:magnetically hard 1728:magnetically soft 1678:thermal expansion 1621: 1620: 1611: 1594: 1422: 1350: 1289:{\displaystyle n} 1269:{\displaystyle m} 1249:{\displaystyle l} 892: 836: 835: 801: 739:{\displaystyle M} 668:{\displaystyle g} 604: 564: 514: 435: 232: 95:scattering matrix 83:transmission line 3090: 3078:Radio technology 3038: 3036: 3025: 3015: 2985: 2967: 2966: 2962: 2954: 2938:(4): S152–S153, 2916: 2914:Jachowski (1976) 2910: 2904: 2903: 2901: 2900: 2885: 2879: 2878: 2868: 2828: 2822: 2821: 2819: 2818: 2803: 2797: 2796: 2776: 2770: 2769: 2729: 2723: 2722: 2678: 2672: 2671: 2635: 2629: 2628: 2600: 2594: 2593: 2575: 2569: 2568: 2552: 2546: 2545: 2509: 2503: 2502: 2486: 2480: 2479: 2443: 2437: 2436: 2419:(5): 3219–3221. 2404: 2398: 2397: 2361: 2355: 2354: 2336: 2330: 2329: 2311: 2302: 2301: 2283: 2277: 2276: 2258: 2252: 2251: 2207: 2198: 2197: 2161: 2155: 2154: 2143:. Artech House. 2136: 2125: 2124: 2104: 2098: 2097: 2079: 1922:transverse-field 1674:photolithography 1612: 1595: 1582: 1581: 1556:Triangular prism 1504: 1488: 1472: 1446:faraday rotation 1436: 1434: 1433: 1428: 1423: 1418: 1395: 1387: 1386: 1364: 1362: 1361: 1356: 1351: 1346: 1323: 1315: 1314: 1295: 1293: 1292: 1287: 1275: 1273: 1272: 1267: 1255: 1253: 1252: 1247: 1232: 1230: 1229: 1224: 1195: 1194: 1176: 1175: 1150: 1148: 1147: 1142: 1125: 1124: 1109: 1108: 1086: 1084: 1083: 1078: 1051:phase velocities 957: 955: 954: 949: 933: 931: 930: 925: 923: 922: 903: 901: 900: 895: 893: 888: 887: 878: 867: 866: 847: 845: 844: 839: 837: 831: 830: 829: 817: 816: 806: 805: 802: 797: 796: 787: 776: 775: 755:transverse field 745: 743: 742: 737: 725: 723: 722: 717: 715: 714: 698: 696: 695: 690: 674: 672: 671: 666: 650: 648: 647: 642: 614: 612: 611: 606: 602: 592: 591: 574: 572: 571: 566: 562: 561: 560: 545: 544: 525: 523: 522: 517: 515: 513: 512: 511: 499: 498: 493: 492: 491: 479: 478: 477: 464: 446: 444: 443: 438: 436: 434: 433: 432: 419: 414: 404: 403: 402: 393: 392: 382: 355: 353: 352: 347: 342: 341: 241:Faraday Rotation 233: 185: 183: 182: 177: 175: 174: 39:schematic symbol 3098: 3097: 3093: 3092: 3091: 3089: 3088: 3087: 3063: 3062: 3045: 3034: 3023: 3018: 2988: 2983: 2970: 2964: 2957: 2927: 2924: 2922:Further reading 2919: 2911: 2907: 2898: 2896: 2887: 2886: 2882: 2830: 2829: 2825: 2816: 2814: 2805: 2804: 2800: 2778: 2777: 2773: 2731: 2730: 2726: 2680: 2679: 2675: 2637: 2636: 2632: 2602: 2601: 2597: 2590: 2577: 2576: 2572: 2554: 2553: 2549: 2511: 2510: 2506: 2488: 2487: 2483: 2445: 2444: 2440: 2410: 2406: 2405: 2401: 2363: 2362: 2358: 2351: 2338: 2337: 2333: 2326: 2313: 2312: 2305: 2298: 2285: 2284: 2280: 2273: 2260: 2259: 2255: 2209: 2208: 2201: 2163: 2162: 2158: 2151: 2138: 2137: 2128: 2115:(300): 99–115. 2106: 2105: 2101: 2094: 2081: 2080: 2076: 2072: 2058:diodes such as 2040: 2004: 1990: 1985: 1953: 1935: 1880: 1866: 1864: 1826: 1772: 1759: 1704: 1626: 1603: 1586: 1580: 1535: 1521: 1519: 1512: 1505: 1496: 1489: 1480: 1473: 1396: 1378: 1373: 1372: 1324: 1306: 1301: 1300: 1278: 1277: 1258: 1257: 1238: 1237: 1186: 1167: 1159: 1158: 1116: 1100: 1092: 1091: 1066: 1065: 1019: 1014: 973: 940: 939: 914: 909: 908: 879: 858: 853: 852: 821: 808: 807: 788: 767: 762: 761: 728: 727: 706: 701: 700: 681: 680: 657: 656: 619: 618: 583: 578: 577: 552: 536: 531: 530: 503: 483: 481: 480: 469: 465: 452: 451: 424: 405: 394: 384: 383: 364: 363: 336: 335: 330: 325: 319: 318: 313: 308: 296: 295: 290: 282: 272: 260: 259: 224: 192: 169: 168: 163: 158: 152: 151: 146: 141: 135: 134: 129: 124: 114: 102: 101: 71:radio-frequency 61:three- or four- 24: 17: 12: 11: 5: 3096: 3094: 3086: 3085: 3080: 3075: 3065: 3064: 3058: 3057: 3054:RF Circulators 3051: 3044: 3043:External links 3041: 3040: 3039: 3016: 2999:(4): 210–217, 2986: 2982:978-1608075836 2981: 2968: 2955: 2923: 2920: 2918: 2917: 2905: 2880: 2823: 2798: 2771: 2744:(2): 502–518. 2724: 2673: 2646:(2): 316–319. 2630: 2611:(3): 260–267. 2595: 2588: 2570: 2547: 2520:(6): 852–864. 2504: 2481: 2438: 2408: 2399: 2356: 2349: 2331: 2324: 2303: 2296: 2278: 2271: 2253: 2199: 2156: 2149: 2126: 2099: 2092: 2073: 2071: 2068: 2039: 2036: 2003: 2000: 1989: 1986: 1984: 1981: 1952: 1949: 1917:non-reciprocal 1863: 1860: 1825: 1822: 1771: 1768: 1757: 1703: 1700: 1625: 1622: 1619: 1618: 1600: 1576: 1518: 1515: 1514: 1513: 1506: 1499: 1497: 1490: 1483: 1481: 1474: 1467: 1465: 1438: 1437: 1426: 1421: 1417: 1414: 1411: 1408: 1405: 1402: 1399: 1393: 1390: 1385: 1381: 1366: 1365: 1354: 1349: 1345: 1342: 1339: 1336: 1333: 1330: 1327: 1321: 1318: 1313: 1309: 1285: 1265: 1245: 1234: 1233: 1222: 1219: 1216: 1213: 1210: 1207: 1204: 1201: 1198: 1193: 1189: 1185: 1182: 1179: 1174: 1170: 1166: 1152: 1151: 1140: 1137: 1134: 1131: 1128: 1123: 1119: 1115: 1112: 1107: 1103: 1099: 1076: 1073: 1045:formed by the 1018: 1015: 1013: 1010: 972: 969: 947: 921: 917: 905: 904: 891: 886: 882: 876: 873: 870: 865: 861: 849: 848: 834: 828: 824: 820: 815: 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2838: 2834: 2827: 2824: 2813: 2809: 2802: 2799: 2794: 2790: 2786: 2782: 2775: 2772: 2767: 2763: 2759: 2755: 2751: 2747: 2743: 2739: 2735: 2728: 2725: 2720: 2716: 2712: 2708: 2704: 2700: 2696: 2692: 2688: 2684: 2677: 2674: 2669: 2665: 2661: 2657: 2653: 2649: 2645: 2641: 2634: 2631: 2626: 2622: 2618: 2614: 2610: 2606: 2599: 2596: 2591: 2589:0-471-36930-6 2585: 2581: 2574: 2571: 2566: 2562: 2558: 2551: 2548: 2543: 2539: 2535: 2531: 2527: 2523: 2519: 2515: 2508: 2505: 2500: 2496: 2492: 2485: 2482: 2477: 2473: 2469: 2465: 2461: 2457: 2453: 2449: 2442: 2439: 2434: 2430: 2426: 2422: 2418: 2414: 2403: 2400: 2395: 2391: 2387: 2383: 2379: 2375: 2371: 2367: 2360: 2357: 2352: 2350:0-86341-064-2 2346: 2342: 2335: 2332: 2327: 2325:0-471-98252-0 2321: 2317: 2310: 2308: 2304: 2299: 2293: 2289: 2282: 2279: 2274: 2272:0-06-046367-8 2268: 2264: 2257: 2254: 2249: 2245: 2241: 2237: 2233: 2229: 2225: 2221: 2217: 2213: 2206: 2204: 2200: 2195: 2191: 2187: 2183: 2179: 2175: 2171: 2167: 2160: 2157: 2152: 2146: 2142: 2135: 2133: 2131: 2127: 2122: 2118: 2114: 2110: 2103: 2100: 2095: 2089: 2085: 2078: 2075: 2069: 2067: 2065: 2061: 2060:tunnel diodes 2057: 2053: 2044: 2037: 2035: 2033: 2029: 2025: 2021: 2017: 2013: 2009: 2001: 1999: 1997: 1996: 1987: 1982: 1980: 1977: 1972: 1969: 1965: 1962: 1957: 1950: 1946: 1940: 1936: 1933: 1929: 1927: 1923: 1918: 1913: 1911: 1907: 1902: 1893: 1885: 1881: 1876: 1871: 1867: 1861: 1859: 1855: 1853: 1850: 1846: 1842: 1837: 1830: 1823: 1821: 1819: 1813: 1811: 1807: 1801: 1798: 1794: 1784: 1776: 1769: 1767: 1766:frequencies. 1765: 1761: 1751: 1749: 1745: 1741: 1737: 1733: 1729: 1725: 1721: 1716: 1708: 1701: 1699: 1696: 1690: 1688: 1684: 1679: 1675: 1671: 1667: 1663: 1655: 1651: 1646: 1643: 1638: 1630: 1623: 1601: 1584: 1583: 1579: 1575: 1571: 1569: 1564: 1559: 1557: 1553: 1549: 1540: 1536: 1531: 1526: 1522: 1516: 1510: 1503: 1498: 1494: 1487: 1482: 1478: 1471: 1466: 1463: 1461: 1457: 1454: 1449: 1447: 1442: 1424: 1419: 1415: 1412: 1409: 1406: 1403: 1400: 1397: 1391: 1388: 1383: 1371: 1370: 1369: 1352: 1347: 1343: 1340: 1337: 1334: 1331: 1328: 1325: 1319: 1316: 1311: 1299: 1298: 1297: 1283: 1263: 1243: 1220: 1214: 1211: 1208: 1205: 1199: 1196: 1191: 1183: 1180: 1177: 1172: 1164: 1157: 1156: 1155: 1138: 1135: 1132: 1129: 1126: 1121: 1113: 1110: 1105: 1097: 1090: 1089: 1088: 1074: 1071: 1062: 1060: 1056: 1052: 1048: 1044: 1040: 1036: 1032: 1023: 1016: 1011: 1009: 1007: 1003: 1000: 999:Ferrimagnetic 995: 986: 982: 977: 970: 968: 965: 961: 945: 937: 919: 915: 889: 884: 880: 874: 871: 868: 863: 851: 850: 832: 826: 822: 818: 813: 809: 798: 793: 789: 783: 780: 777: 772: 760: 759: 758: 756: 751: 749: 748:magnetization 733: 711: 707: 686: 678: 662: 654: 636: 633: 630: 627: 624: 599: 596: 593: 588: 584: 576: 557: 553: 549: 546: 541: 537: 529: 528: 508: 504: 500: 495: 488: 484: 474: 470: 466: 460: 457: 450: 449: 429: 425: 421: 416: 411: 407: 399: 395: 389: 385: 378: 375: 372: 369: 362: 361: 360: 343: 338: 332: 327: 322: 315: 310: 305: 302: 299: 292: 287: 284: 279: 273: 268: 265: 258: 257: 256: 254: 253:Polder tensor 250: 242: 238: 222: 220: 219:Polder tensor 216: 212: 208: 204: 203: 197: 189: 171: 165: 160: 155: 148: 143: 138: 131: 126: 121: 115: 110: 107: 100: 99: 98: 96: 92: 91:coaxial cable 88: 84: 80: 76: 72: 68: 64: 60: 56: 52: 48: 40: 36: 32: 28: 22: 3059: 3027: 2996: 2990: 2972: 2935: 2929: 2908: 2897:. Retrieved 2893: 2883: 2840: 2836: 2826: 2815:. Retrieved 2811: 2801: 2784: 2780: 2774: 2741: 2737: 2727: 2686: 2682: 2676: 2643: 2639: 2633: 2608: 2604: 2598: 2579: 2573: 2556: 2550: 2517: 2513: 2507: 2490: 2484: 2454:(6): 66–72. 2451: 2447: 2441: 2416: 2412: 2402: 2372:(6): 36–50. 2369: 2365: 2359: 2340: 2334: 2315: 2287: 2281: 2262: 2256: 2218:(1): 15–27. 2215: 2211: 2172:(1): 61–72. 2169: 2165: 2159: 2140: 2112: 2108: 2102: 2083: 2077: 2049: 2031: 2027: 2005: 1993: 1991: 1983:Applications 1973: 1966: 1958: 1954: 1934: 1930: 1921: 1916: 1914: 1898: 1879: 1865: 1856: 1852:coercivities 1838: 1835: 1814: 1810:reciprocally 1802: 1790: 1752: 1717: 1713: 1691: 1659: 1650:phased array 1577: 1572: 1560: 1545: 1534: 1520: 1458: 1450: 1443: 1439: 1367: 1235: 1153: 1063: 1028: 990: 985:matched load 906: 754: 752: 617: 358: 246: 199: 193: 85:, such as a 50: 44: 2064:Gunn diodes 2016:transmitter 1818:distributed 196:anisotropic 3067:Categories 2959:US 3935549 2899:2016-04-19 2817:2016-07-22 2787:(5): 612. 2070:References 1740:coercivity 1732:coercivity 1695:wire bonds 1687:dispersion 1666:thick-film 1662:microstrip 1548:waveguides 1031:striplines 249:CGS system 202:reciprocal 89:line or a 87:microstrip 59:reciprocal 51:circulator 3028:RF Design 2843:: 11217. 2758:0018-9480 2711:0018-9480 2668:0018-9480 2625:0018-9219 2542:0018-9480 2468:1527-3342 2433:0018-9464 2394:148572410 2386:1527-3342 2248:111367080 2240:0018-9480 2194:0018-9480 2032:TR switch 1968:Varactors 1787:resistor. 1689:effects. 1683:radiation 1670:thin-film 1656:function. 1654:duplexing 1563:waveguide 1509:stripline 1493:stripline 1477:stripline 1453:stripline 1425:π 1413:− 1380:Γ 1353:π 1341:− 1312:− 1308:Γ 1221:π 1212:− 1188:Γ 1173:− 1169:Γ 1165:− 1139:π 1118:Γ 1114:− 1106:− 1102:Γ 1075:π 1055:anti-node 1039:stripline 994:stripline 981:waveguide 946:ϵ 916:μ 890:ϵ 881:μ 875:ω 864:− 860:Γ 833:μ 823:κ 819:− 810:μ 799:ϵ 790:μ 784:ω 769:Γ 687:ω 634:⋅ 625:γ 597:γ 585:ω 550:γ 538:ω 505:ω 501:− 485:ω 471:ω 467:ω 458:κ 426:ω 422:− 408:ω 396:ω 386:ω 370:μ 311:μ 306:κ 300:− 288:κ 280:μ 79:waveguide 67:microwave 37:standard 3032:archived 2875:27079524 2766:17421796 2719:13987504 2476:46417910 2024:receiver 2012:duplexer 2002:Duplexer 1995:isolator 1988:Isolator 1795:through 1720:uniaxial 1642:CAPTOR-E 677:g-factor 3001:Bibcode 2940:Bibcode 2866:4835534 2845:Bibcode 2734:Alù, A. 2691:Bibcode 2648:Bibcode 2522:Bibcode 2220:Bibcode 2174:Bibcode 2020:antenna 2018:to the 1849:Oersted 1615:nulled. 958:is the 934:is the 746:is the 247:In the 55:passive 2979:  2965:  2873:  2863:  2764:  2756:  2717:  2709:  2666:  2623:  2586:  2540:  2474:  2466:  2431:  2392:  2384:  2347:  2322:  2294:  2269:  2246:  2238:  2192:  2147:  2090:  1764:V-band 1738:(high- 1236:where 1002:garnet 907:where 603:  563:  251:, the 215:tensor 57:, non- 3035:(PDF) 3024:(PDF) 2762:S2CID 2715:S2CID 2472:S2CID 2390:S2CID 2244:S2CID 2008:radar 1760:-band 1730:(low- 1043:modes 971:Types 207:spins 53:is a 2977:ISBN 2871:PMID 2754:ISSN 2707:ISSN 2664:ISSN 2621:ISSN 2584:ISBN 2538:ISSN 2464:ISSN 2429:ISSN 2382:ISSN 2345:ISBN 2320:ISBN 2292:ISBN 2267:ISBN 2236:ISSN 2190:ISSN 2145:ISBN 2088:ISBN 2062:and 1908:, a 1762:and 1685:and 1368:and 1276:and 1059:node 938:and 655:and 631:1.40 200:non- 198:and 63:port 49:, a 33:and 31:ANSI 3009:doi 2948:doi 2861:PMC 2853:doi 2789:doi 2746:doi 2699:doi 2656:doi 2613:doi 2561:doi 2530:doi 2495:doi 2456:doi 2421:doi 2374:doi 2228:doi 2182:doi 2117:doi 2006:In 1797:UHF 1668:or 255:is 81:or 69:or 45:In 35:IEC 3069:: 3060:+ 3030:, 3026:, 3007:, 2995:, 2946:, 2936:30 2934:, 2892:. 2869:. 2859:. 2851:. 2839:. 2835:. 2810:. 2785:52 2783:. 2760:. 2752:. 2742:64 2740:. 2713:. 2705:. 2697:. 2687:62 2685:. 2662:. 2654:. 2644:48 2642:. 2619:. 2609:53 2607:. 2536:. 2528:. 2518:13 2516:. 2470:. 2462:. 2452:15 2450:. 2427:. 2417:28 2415:. 2388:. 2380:. 2370:20 2368:. 2306:^ 2242:. 2234:. 2226:. 2216:13 2214:. 2202:^ 2188:. 2180:. 2170:12 2168:. 2129:^ 2113:40 2111:. 2050:A 1793:HF 1008:. 979:A 97:: 3011:: 3003:: 2997:4 2950:: 2942:: 2902:. 2877:. 2855:: 2847:: 2841:7 2820:. 2795:. 2791:: 2768:. 2748:: 2721:. 2701:: 2693:: 2670:. 2658:: 2650:: 2627:. 2615:: 2592:. 2567:. 2563:: 2544:. 2532:: 2524:: 2501:. 2497:: 2478:. 2458:: 2435:. 2423:: 2409:A 2396:. 2376:: 2353:. 2328:. 2300:. 2275:. 2250:. 2230:: 2222:: 2196:. 2184:: 2176:: 2153:. 2123:. 2119:: 2096:. 2030:( 1758:A 1756:K 1420:3 1416:2 1410:n 1407:4 1404:+ 1401:m 1398:2 1392:= 1389:l 1384:+ 1348:3 1344:1 1338:n 1335:2 1332:+ 1329:m 1326:4 1320:= 1317:l 1284:n 1264:m 1244:l 1218:) 1215:1 1209:n 1206:2 1203:( 1200:= 1197:l 1192:+ 1184:2 1181:+ 1178:l 1136:m 1133:2 1130:= 1127:l 1122:+ 1111:l 1098:2 1072:2 920:0 885:0 872:j 869:= 827:2 814:2 794:0 781:j 778:= 773:+ 734:M 712:0 708:H 663:g 637:g 628:= 600:M 594:= 589:m 558:0 554:H 547:= 542:0 509:2 496:2 489:0 475:m 461:= 430:2 417:2 412:0 400:m 390:0 379:+ 376:1 373:= 344:H 339:] 333:1 328:0 323:0 316:0 303:j 293:0 285:j 274:[ 269:= 266:B 243:. 172:) 166:0 161:1 156:0 149:0 144:0 139:1 132:1 127:0 122:0 116:( 111:= 108:S 23:.

Index

Circulator (disambiguation)

ANSI
IEC
schematic symbol
electrical engineering
passive
reciprocal
port
microwave
radio-frequency
Optical circulators
waveguide
transmission line
microstrip
coaxial cable
scattering matrix
anisotropic
reciprocal
spins
magnetic permeability
tensor
Polder tensor
elliptically polarized
Faraday Rotation
CGS system
Polder tensor
gyromagnetic ratio
g-factor
magnetization

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