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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.
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2077:. 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.
1459:. 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.
1903:
1550:
1865:. 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.
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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.
1569:. 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.
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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
1981:
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
1930:
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,
1725:
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
1466:
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
1974:
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
1953:
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
1942:
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
1691:
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
1868:
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
1826:
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
1576:
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
1002:
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
1989:
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.
1881:
232:. 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.
104:, 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
2009:, 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.
1814:
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
365:
2045:) 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 a circulator for this function.
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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.
236:
1496:
1663:. 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
1914:
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
195:
1480:
1703:
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
1966:
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.
1982:
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.
456:
535:
1561:. 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
2974:
1687:. 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
977:
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.
1931:
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
1810:
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.
1451:
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.
1764:
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
1797:
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
1658:
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
913:
1625:
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
1242:
1446:
1374:
1847:
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.
1985:
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
1939:. Different microwave propagation constants corresponding to different directions of signal propagation give rise to different phase velocities and hence, different transmission phase shifts.
1160:
764:
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
1581:
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.
1823:
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
114:
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1265:
755:
684:
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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
250:
electromagnetic wave propagating in a magnetized ferrite cylinder. The static magnetic field is oriented parallel to the cylinder axis. This is known as
3064:
1618:
1601:
376:
1850:
Junction circulators use permanent magnets to provide the static magnetic bias for the ferrite(s). However, switching circulators typically rely on the
464:
45:
1943:
circulators by connecting one circulator port to a reflectionless termination, or they can be used as isolators by terminating two circulator ports.
1920:
216:
properties of magnetized microwave ferrite material. Microwave electromagnetic waves propagating in magnetized ferrite interact with electron
3093:
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2159:
2102:
1954:
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).
2614:
Tanaka, S.; Shimomura, N.; Ohtake, K. (1965-03-01). "Active circulators - The realization of circulators using transistors".
1171:
52:
for a circulator (with each waveguide or transmission line port drawn as a single line, rather than as a pair of conductors)
1385:
1313:
3083:
2457:
Geiler, Anton; Harris, Vince (September–October 2014). "Atom
Magnetism: Ferrite Circulators - Past, Present, and Future".
1827:
lumped-element inductors and capacitors can be less stable when exposed to vibration or mechanical shocks than the simple
1910:
Differential phase shift circulators are mainly used in high power microwave applications. They are usually built from
991:
89:
1307:
are integers. Solving the two preceding equations simultaneously, for proper circulation the necessary conditions are
1104:
1975:
it is used as a duplexer for sustaining the strong transmit power and clean reception of the signal from the antenna.
1911:
1828:
1573:
1558:
1075:
If losses are neglected for simplification, the counter-rotating modes must differ in phase by an integer multiple of
31:
2900:
2692:
Qin, Shihan; Xu, Qiang; Wang, Y.E. (2014-10-01). "Nonreciprocal
Components With Distributedly Modulated Capacitors".
690:, is a ferrite material constant typically in the range of 1.5 - 2.6, depending on the particular ferrite material.
2941:
1557:
A waveguide junction circulator contains a magnetized ferrite resonator, which is located at the junction of three
946:
2747:(2016-02-01). "Magnetless Microwave Circulators Based on Spatiotemporally Modulated Rings of Coupled Resonators".
3088:
1693:
360:{\displaystyle B={\begin{bmatrix}\mu &j\kappa &0\\-j\kappa &\mu &0\\0&0&1\end{bmatrix}}H}
2037:, without allowing signals to pass directly from transmitter to receiver. The alternative type of duplexer is a
543:
1697:
1578:
1048:, such as a disk, hexagon, or triangle. An RF/microwave signal entering a circulator port is connected via a
852:{\displaystyle \Gamma _{+}=j\omega {\sqrt {\mu _{0}\epsilon }}\,{\sqrt {\frac {\mu ^{2}-\kappa ^{2}}{\mu }}}}
631:
1165:
and similarly, for the remaining port (port 3 if signal propagation is from port 1 to port 2) to be nulled,
1053:
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590:
224:
of the ferrite. This permeability is mathematically described by a linear vector operator, also known as a
65:
1869:
magnetizing coil to magnetize the ferrite in the polarity to provide the desired direction of circulation.
1032:
30:
This article is about radio frequency (RF) or microwave frequency passive circulators. For other uses, see
1851:
1535:
1057:
247:
57:
2504:. 2021 IEEE International Electron Devices Meeting (IEDM). San Francisco, CA, USA. pp. 4.2.1–4.2.4.
1819:
with metallized vias to make connections between layers. The conductive strips can be thought of as non-
1676:
970:
221:
105:
73:
2375:
Palmer, William; Kirkwood, David; et al. (June 2016). "A Bright Future for
Integrated Magnetics".
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1040:
A stripline junction circulator contains a resonator, which is located at the central junction of the
3011:
2950:
2855:
2701:
2658:
2532:
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2184:
2062:
2005:
1816:
1902:
1608:
E-field scatter plot of an electromagnetic wave propagating through a waveguide junction circulator.
1855:
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1753:) materials. These ferrites are essentially ceramic permanent magnets. In addition to their high
1562:
1098:
for signal propagation from port 1 to port 2 (or from port 2 to port 3, or from port 3 to port 1):
1064:
which can cause them to combine constructively or destructively at a given port. This produces an
1045:
1745:) ferrites used in other circulators, the hexagonal ferrites used for self-biased circulators are
1549:
2772:
2725:
2482:
2400:
2254:
1986:
1754:
1016:
687:
663:
85:
1802:
Lumped-element circulators are small-size devices that are typically used at frequencies in the
2649:
Carchon, G.; Nanwelaers, B. (2000-02-01). "Power and noise limitations of active circulators".
2003:
When one port of a three-port circulator is terminated in a matched load, it can be used as an
1671:
The microstrip junction circulator is another widely-used form of circulator that utilizes the
952:
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of the ferrite material. In a circulator, these propagation constants describe waves having
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190:{\displaystyle S={\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}}}
2418:
Zeina, N.; How, H.; et al. (September 1992). "Self-Biasing
Circulators Operating at K
2030:
1490:
junction circulator having triangular ferrites and an irregular triangle-shaped resonator.
81:
3031:
3015:
2954:
2901:"Next Big Future: Novel miniaturized circulator opens way to doubling wireless capacity"
2859:
2705:
2662:
2536:
2234:
2221:
Fay, C.E.; Comstock, R.L. (1965-01-01). "Operation of the
Ferrite Junction Circulator".
2188:
2053:
1854:
of the ferrite itself. The ferrites that are used in switching circulators have square
1639:
1589:
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.
451:{\displaystyle \mu =1+{\frac {\omega _{0}\omega _{m}}{\omega _{0}^{2}-\omega ^{2}}}}
2070:
1705:
1660:
530:{\displaystyle \kappa ={\frac {\omega \omega _{m}}{{\omega _{0}}^{2}-\omega ^{2}}}}
2502:
Monolithically
Integrated Self-Biased Circulator for mmWave T/R MMIC Applications
1884:
High-Power Liquid-Cooled
Differential Phase Shift Circulator. Image courtesy of
2026:
768:
case. The microwave propagation constants for this case, neglecting losses are
206:
2120:
The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science
1843:
Internal construction of a WR-90 (WG 16; R 100) waveguide switching circulator.
1789:
Woven mesh conductor wrapped around the ferrite of a lumped-element circulator.
3023:
2972:, Jachowski, Ronald E., "Ferrite Circulator", published 1976-01-27
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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
710:
is the frequency of the RF/microwave signal propagating through the ferrite,
27:
Electronic circuit in which a signal entering any port exits at the next port
2819:"New Full Duplex Radio Chip Transmits and Receives Wireless Signals at Once"
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High-Power Liquid-Cooled
Waveguide Junction Circulator. Image courtesy of
17:
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2022:
1978:
1730:
1729:
Monolithic ferrites that are used for self-biased circulators are M-type
1664:
1522:
junction circulator having disk ferrites and a triangle-shaped resonator.
2867:
1785:
1761:
fields, enabling circulator operation up to high microwave frequencies.
84:(RF) signal to exit through the port directly after the one it entered.
1859:
1766:
2962:
2790:
Mohr, Richard (1964). "A New Nonreciprocal Transmission Line Device".
2670:
2435:
1647:
986:
1955:
1885:
1774:
1540:
1506:
junction circulator having disk ferrites and a disk-shaped resonator.
1012:
228:. In the case of magnetized ferrite, the permeability tensor is the
225:
2523:
Konishi, Yoshihiro (November 1965). "Lumped Element Y Circulator".
2052:
2018:
1948:
1879:
1792:
1638:
1534:
985:
36:
2095:
Modern Ferrites, Volume 2: Emerging Technologies and Applications
1068:
at one port (port 2 if the signal is incident upon port 1) and a
220:
in the ferrite and are consequently influenced by the microwave
41:
1585:
permanent magnets that are external to the waveguide junction.
908:{\displaystyle \Gamma _{-}=j\omega {\sqrt {\mu _{0}\epsilon }}}
2844:"Magnetic-free non-reciprocity based on staggered commutation"
2570:. International Microwave Symposium Digest. pp. 147–151.
2118:
Polder, D (1949). "On the Theory of Ferromagnetic Resonance".
1807:
3032:"Low Frequency Circulator/Isolator Uses No Ferrite or Magnet"
2175:
Bosma, H. (1964-01-01). "On Stripline Y-Circulation at UHF".
2145:
2143:
2141:
1923:, and two oppositely-magnetized differential phase shifters.
1898:
Schematic diagram of a differential phase shift circulator.
1831:
impedance transformers in a stripline junction circulator.
2500:
Cui, Yongjie; Chen, Hung-Yu; et al. (December 2021).
1044:. This resonator may have any shape that has three-fold
3000:
Ohm, E. A. (1956), "A Broad-Band Microwave Circulator",
2842:
Reiskarimian, Negar; Krishnaswamy, Harish (2016-04-15).
2823:
IEEE Spectrum: Technology, Engineering, and Science News
2057:
Microwave diode reflection amplifier using a circulator
1475:
Internal Construction of Stripline Junction Circulators
1906:
Internal construction of a differential phase shifter.
1237:{\displaystyle -\Gamma _{-}l+2\Gamma _{+}l=(2n-1)\pi }
287:
129:
1441:{\displaystyle \Gamma _{+}l={\frac {2m+4n-2}{3}}\pi }
1388:
1369:{\displaystyle \Gamma _{-}l={\frac {4m+2n-1}{3}}\pi }
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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
2525:
IEEE Transactions on Microwave Theory and Techniques
2223:
IEEE Transactions on Microwave Theory and Techniques
2216:
2214:
2177:
IEEE Transactions on Microwave Theory and Techniques
3067:
what they are, different types, how they work, etc.
3003:
IRE Transactions on Microwave Theory and Techniques
2939:Chait, H. N.; Curry, T. R. (1959), "Y-Circulator",
2568:
New Design Techniques for Miniature VHF Circulators
2327:
Waveguide Junction Circulators: Theory and Practice
2065:is a type of microwave amplifier circuit utilizing
88:have similar behavior. Ports are where an external
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1155:{\displaystyle 2\Gamma _{-}l-\Gamma _{+}l=2m\pi }
1970:Early work on non-ferrite circulators includes
1267:is the path length between adjacent ports and
2299:The Stripline Circulator: Theory and Practice
8:
2422:-Band Utilizing M-Type Hexagonal Ferrites".
1060:waves. These circular modes have different
2591:Principles of Microwave Ferrite Engineering
2152:Microwave Circulator Design, Second Edition
1656:active electronically scanned array (AESA)
1651:Transmit-Receive (T-R) module used in the
579:{\displaystyle \omega _{0}=\gamma H_{0}\ }
2924:
2875:
1683:metallization processes, often including
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1548:
1455:These circulator types operate based on
1036:Rotating modes in a junction circulator.
1031:
234:
2923:For a description of a circulator, see
2085:
1473:
655:{\displaystyle \gamma =1.40\cdot g\,\,}
1926:A differential phase shifter provides
619:{\displaystyle \omega _{m}=\gamma M\ }
1937:Circulator § Theory of operation
7:
2566:Dunn, V. E.; Roberts, R. W. (1965).
2021:, circulators are used as a type of
1873:Differential phase shift circulators
1390:
1318:
1198:
1179:
1128:
1112:
870:
779:
205:Microwave circulators rely on the
25:
2986:(Second ed.), Artech House,
2352:Ferrites at Microwave Frequencies
1757:, these ferrites have very large
2067:negative differential resistance
1721:Self-biased junction circulator.
1713:Self-biased junction circulators
1511:
1495:
1479:
3048:from the original on 2022-10-09
1956:Symphony Microwave Technologies
1643:Microstrip junction circulator.
1635:Microstrip junction circulators
2899:Wang, Brian (April 18, 2016).
2424:IEEE Transactions on Magnetics
1528:Waveguide junction circulators
1228:
1213:
1028:Stripline junction circulators
1:
2982:Linkhart, Douglas K. (2014),
2743:Estep, N. A.; Sounas, D. L.;
2593:. John Wiley & Sons Ltd.
2150:Linkhart, Douglas K. (2014).
3094:Telecommunications equipment
2350:Baden-Fuller, A. J. (1987).
2033:and from the antenna to the
2025:, to route signals from the
2984:Microwave Circulator Design
2817:Nordrum, Amy (2016-04-15).
2093:Harris, Vincent G. (2023).
1572:The internal geometry of a
1518:Internal construction of a
1486:Internal construction of a
662:MHz / Oe is the effective
370:where (neglecting damping)
32:Circulator (disambiguation)
3110:
2942:Journal of Applied Physics
2272:Soohoo, Ronald F. (1985).
1781:Lumped-element circulators
1726:for similar applications.
947:Permeability of Free Space
686:, the so-called effective
246:E-field vector plot of an
76:device that only allows a
29:
3060:Circulators and Isolators
3024:10.1109/TMTT.1956.1125064
2761:10.1109/TMTT.2015.2511737
2714:10.1109/TMTT.2014.2347935
2589:Helszajn, Joseph (1969).
2576:10.1109/GMTT.1965.1122495
2545:10.1109/tmtt.1965.1126116
2329:. John Wiley & Sons.
2325:Helszajn, Joseph (1998).
2301:. John Wiley & Sons.
2297:Helszajn, Joseph (2008).
2243:10.1109/TMTT.1965.1125923
2197:10.1109/TMTT.1964.1125753
2132:10.1080/14786444908561215
1921:quadrature hybrid coupler
1502:Internal construction of
1003:compact devices based on
962:{\displaystyle \epsilon }
761:of the ferrite material.
3030:Wenzel, C. (July 1991),
2471:10.1109/mmm.2014.2332411
2389:10.1109/MMM.2019.2904381
2354:. Peter Peregrinus Ltd.
1917:magic tee hybrid coupler
1579:characteristic impedance
1577:waveguide, reducing its
1565:, such as a cylinder or
938:{\displaystyle \mu _{0}}
2792:Proceedings of the IEEE
2616:Proceedings of the IEEE
2459:IEEE Microwave Magazine
2377:IEEE Microwave Magazine
2039:transmit-receive switch
1962:Non-ferrite circulators
1935:device as described in
1733:(single magnetic axis)
975:Elliptical polarization
703:{\displaystyle \omega }
2804:10.1109/PROC.1964.3007
2628:10.1109/PROC.1965.3683
2510:10.1109/IEDM19574.2021
2058:
1958:
1907:
1899:
1888:
1852:remanent magnetization
1844:
1799:
1790:
1722:
1668:
1644:
1627:
1609:
1554:
1543:
1442:
1370:
1301:
1281:
1261:
1238:
1156:
1092:
1058:elliptically polarized
1037:
999:
963:
939:
909:
853:
751:
731:
704:
680:
656:
620:
580:
531:
452:
361:
255:
248:elliptically polarized
191:
58:electrical engineering
53:
2848:Nature Communications
2056:
1952:
1912:rectangular waveguide
1905:
1897:
1883:
1842:
1835:Switching circulators
1796:
1788:
1720:
1650:
1642:
1624:
1607:
1552:
1538:
1443:
1371:
1302:
1282:
1262:
1239:
1157:
1093:
1091:{\displaystyle 2\pi }
1035:
989:
971:Absolute permittivity
964:
940:
910:
854:
752:
732:
730:{\displaystyle H_{0}}
705:
681:
657:
621:
581:
532:
453:
362:
245:
222:magnetic permeability
192:
40:
3084:Microwave technology
2276:. Harper & Row.
2097:. Wiley-IEEE Press.
2063:reflection amplifier
2049:Reflection amplifier
1886:Microwave Techniques
1858:loops and often sub-
1817:printed wiring board
1541:Microwave Techniques
1386:
1314:
1291:
1271:
1251:
1172:
1105:
1079:
1023:Junction circulators
953:
922:
866:
775:
741:
714:
694:
670:
632:
591:
544:
465:
377:
273:
115:
3016:1956ITMTT...4..210O
2955:1959JAP....30S.152C
2868:10.1038/ncomms11217
2860:2016NatCo...711217R
2706:2014ITMTT..62.2260Q
2663:2000ITMTT..48..316C
2537:1965ITMTT..13..852K
2274:Microwave Magnetics
2235:1965ITMTT..13...15F
2189:1964ITMTT..12...61B
1856:magnetic hysteresis
1759:magnetic anisotropy
1563:Rotational symmetry
1046:Rotational symmetry
1017:optical circulators
1015:crystal is used in
431:
201:Theory of operation
86:Optical circulators
2059:
1987:integrated circuit
1972:active circulators
1959:
1908:
1900:
1889:
1845:
1800:
1791:
1755:magnetic remanence
1735:hexagonal ferrites
1723:
1669:
1645:
1628:
1610:
1555:
1544:
1462:The geometry of a
1438:
1366:
1297:
1277:
1257:
1234:
1152:
1088:
1038:
1000:
959:
935:
905:
849:
747:
727:
700:
676:
664:gyromagnetic ratio
652:
616:
576:
527:
448:
417:
357:
348:
256:
187:
181:
54:
2963:10.1063/1.2185863
2905:nextbigfuture.com
2700:(10): 2260–2272.
2671:10.1109/22.821785
2436:10.1109/20.179764
2308:978-0-470-25878-1
2161:978-1-60807-583-6
2104:978-1-394-15613-9
1747:magnetically hard
1739:magnetically soft
1689:thermal expansion
1632:
1631:
1622:
1605:
1433:
1361:
1300:{\displaystyle n}
1280:{\displaystyle m}
1260:{\displaystyle l}
903:
847:
846:
812:
750:{\displaystyle M}
679:{\displaystyle g}
615:
575:
525:
446:
243:
106:scattering matrix
94:transmission line
16:(Redirected from
3101:
3089:Radio technology
3049:
3047:
3036:
3026:
2996:
2978:
2977:
2973:
2965:
2949:(4): S152–S153,
2927:
2925:Jachowski (1976)
2921:
2915:
2914:
2912:
2911:
2896:
2890:
2889:
2879:
2839:
2833:
2832:
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2814:
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2563:
2557:
2556:
2520:
2514:
2513:
2497:
2491:
2490:
2454:
2448:
2447:
2430:(5): 3219–3221.
2415:
2409:
2408:
2372:
2366:
2365:
2347:
2341:
2340:
2322:
2313:
2312:
2294:
2288:
2287:
2269:
2263:
2262:
2218:
2209:
2208:
2172:
2166:
2165:
2154:. Artech House.
2147:
2136:
2135:
2115:
2109:
2108:
2090:
1933:transverse-field
1685:photolithography
1623:
1606:
1593:
1592:
1567:Triangular prism
1515:
1499:
1483:
1457:faraday rotation
1447:
1445:
1444:
1439:
1434:
1429:
1406:
1398:
1397:
1375:
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1159:
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1153:
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1135:
1120:
1119:
1097:
1095:
1094:
1089:
1062:phase velocities
968:
966:
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960:
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934:
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914:
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911:
906:
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848:
842:
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840:
828:
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813:
808:
807:
798:
787:
786:
766:transverse field
756:
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709:
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393:
366:
364:
363:
358:
353:
352:
252:Faraday Rotation
244:
196:
194:
193:
188:
186:
185:
50:schematic symbol
21:
3109:
3108:
3104:
3103:
3102:
3100:
3099:
3098:
3074:
3073:
3056:
3045:
3034:
3029:
2999:
2994:
2981:
2975:
2968:
2938:
2935:
2933:Further reading
2930:
2922:
2918:
2909:
2907:
2898:
2897:
2893:
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2840:
2836:
2827:
2825:
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2811:
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2691:
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2686:
2648:
2647:
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2588:
2587:
2583:
2565:
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2560:
2522:
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2517:
2499:
2498:
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2344:
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2316:
2309:
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2284:
2271:
2270:
2266:
2220:
2219:
2212:
2174:
2173:
2169:
2162:
2149:
2148:
2139:
2126:(300): 99–115.
2117:
2116:
2112:
2105:
2092:
2091:
2087:
2083:
2069:diodes such as
2051:
2015:
2001:
1996:
1964:
1946:
1891:
1877:
1875:
1837:
1783:
1770:
1715:
1637:
1614:
1597:
1591:
1546:
1532:
1530:
1523:
1516:
1507:
1500:
1491:
1484:
1407:
1389:
1384:
1383:
1335:
1317:
1312:
1311:
1289:
1288:
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1249:
1248:
1197:
1178:
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1103:
1102:
1077:
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1030:
1025:
984:
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82:radio-frequency
72:three- or four-
35:
28:
23:
22:
15:
12:
11:
5:
3107:
3105:
3097:
3096:
3091:
3086:
3076:
3075:
3069:
3068:
3065:RF Circulators
3062:
3055:
3054:External links
3052:
3051:
3050:
3027:
3010:(4): 210–217,
2997:
2993:978-1608075836
2992:
2979:
2966:
2934:
2931:
2929:
2928:
2916:
2891:
2834:
2809:
2782:
2755:(2): 502–518.
2735:
2684:
2657:(2): 316–319.
2641:
2622:(3): 260–267.
2606:
2599:
2581:
2558:
2531:(6): 852–864.
2515:
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2110:
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2084:
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2014:
2011:
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1997:
1995:
1992:
1963:
1960:
1928:non-reciprocal
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1084:
1056:formed by the
1029:
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2600:0-471-36930-6
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2361:0-86341-064-2
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2336:0-471-98252-0
2332:
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2283:0-06-046367-8
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2071:tunnel diodes
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1864:
1861:
1857:
1853:
1848:
1841:
1834:
1832:
1830:
1824:
1822:
1818:
1812:
1809:
1805:
1795:
1787:
1780:
1778:
1777:frequencies.
1776:
1772:
1762:
1760:
1756:
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1748:
1744:
1740:
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1477:
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1468:
1465:
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1453:
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1423:
1420:
1417:
1414:
1411:
1408:
1402:
1399:
1394:
1382:
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1380:
1363:
1358:
1354:
1351:
1348:
1345:
1342:
1339:
1336:
1330:
1327:
1322:
1310:
1309:
1308:
1294:
1274:
1254:
1231:
1225:
1222:
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1191:
1188:
1183:
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1168:
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1149:
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1137:
1132:
1124:
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1116:
1108:
1101:
1100:
1099:
1085:
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1073:
1071:
1067:
1063:
1059:
1055:
1051:
1047:
1043:
1034:
1027:
1022:
1020:
1018:
1014:
1011:
1010:Ferrimagnetic
1006:
997:
993:
988:
981:
979:
976:
972:
956:
948:
930:
926:
900:
895:
891:
885:
882:
879:
874:
862:
861:
843:
837:
833:
829:
824:
820:
809:
804:
800:
794:
791:
788:
783:
771:
770:
769:
767:
762:
760:
759:magnetization
744:
722:
718:
697:
689:
673:
665:
647:
644:
641:
638:
635:
610:
607:
604:
599:
595:
587:
568:
564:
560:
557:
552:
548:
540:
539:
519:
515:
511:
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481:
477:
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468:
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440:
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389:
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354:
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326:
321:
316:
313:
310:
303:
298:
295:
290:
284:
279:
276:
269:
268:
267:
265:
264:Polder tensor
261:
253:
249:
233:
231:
230:Polder tensor
227:
223:
219:
215:
214:
208:
200:
182:
176:
171:
166:
159:
154:
149:
142:
137:
132:
126:
121:
118:
111:
110:
109:
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103:
102:coaxial cable
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2380:
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2004:
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1994:Applications
1984:
1977:
1969:
1965:
1945:
1941:
1932:
1927:
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1863:coercivities
1849:
1846:
1825:
1821:reciprocally
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1670:
1661:phased array
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369:
257:
210:
204:
96:, such as a
61:
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2075:Gunn diodes
2027:transmitter
1829:distributed
207:anisotropic
18:Circulators
3078:Categories
2970:US 3935549
2910:2016-04-19
2828:2016-07-22
2798:(5): 612.
2081:References
1751:coercivity
1743:coercivity
1706:wire bonds
1698:dispersion
1677:thick-film
1673:microstrip
1559:waveguides
1042:striplines
260:CGS system
213:reciprocal
100:line or a
98:microstrip
70:reciprocal
62:circulator
3039:RF Design
2854:: 11217.
2769:0018-9480
2722:0018-9480
2679:0018-9480
2636:0018-9219
2553:0018-9480
2479:1527-3342
2444:0018-9464
2405:148572410
2397:1527-3342
2259:111367080
2251:0018-9480
2205:0018-9480
2043:TR switch
1979:Varactors
1798:resistor.
1700:effects.
1694:radiation
1681:thin-film
1667:function.
1665:duplexing
1574:waveguide
1520:stripline
1504:stripline
1488:stripline
1464:stripline
1436:π
1424:−
1391:Γ
1364:π
1352:−
1323:−
1319:Γ
1232:π
1223:−
1199:Γ
1184:−
1180:Γ
1176:−
1150:π
1129:Γ
1125:−
1117:−
1113:Γ
1086:π
1066:anti-node
1050:stripline
1005:stripline
992:waveguide
957:ϵ
927:μ
901:ϵ
892:μ
886:ω
875:−
871:Γ
844:μ
834:κ
830:−
821:μ
810:ϵ
801:μ
795:ω
780:Γ
698:ω
645:⋅
636:γ
608:γ
596:ω
561:γ
549:ω
516:ω
512:−
496:ω
482:ω
478:ω
469:κ
437:ω
433:−
419:ω
407:ω
397:ω
381:μ
322:μ
317:κ
311:−
299:κ
291:μ
90:waveguide
78:microwave
48:standard
3043:archived
2886:27079524
2777:17421796
2730:13987504
2487:46417910
2035:receiver
2023:duplexer
2013:Duplexer
2006:isolator
1999:Isolator
1806:through
1731:uniaxial
1653:CAPTOR-E
688:g-factor
3012:Bibcode
2951:Bibcode
2877:4835534
2856:Bibcode
2745:Alù, A.
2702:Bibcode
2659:Bibcode
2533:Bibcode
2231:Bibcode
2185:Bibcode
2031:antenna
2029:to the
1860:Oersted
1626:nulled.
969:is the
945:is the
757:is the
258:In the
66:passive
2990:
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1749:(high-
1247:where
1013:garnet
918:where
614:
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262:, the
226:tensor
68:, non-
3046:(PDF)
3035:(PDF)
2773:S2CID
2726:S2CID
2483:S2CID
2401:S2CID
2255:S2CID
2019:radar
1771:-band
1741:(low-
1054:modes
982:Types
218:spins
64:is a
2988:ISBN
2882:PMID
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1773:and
1696:and
1379:and
1287:and
1070:node
949:and
666:and
642:1.40
211:non-
209:and
74:port
60:, a
44:and
42:ANSI
3020:doi
2959:doi
2872:PMC
2864:doi
2800:doi
2757:doi
2710:doi
2667:doi
2624:doi
2572:doi
2541:doi
2506:doi
2467:doi
2432:doi
2385:doi
2239:doi
2193:doi
2128:doi
2017:In
1808:UHF
1679:or
266:is
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