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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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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.
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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.
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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.
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.
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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
1970:
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
1919:
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,
1714:
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
1455:
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
1963:
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
1942:
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
1931:
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
1680:
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
1857:
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
1815:
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
1565:
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
991:
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
1978:
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
354:
2034:) 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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1501:
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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:
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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
184:
1469:
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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
1955:
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.
1971:
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.
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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.
1920:
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.
1440:
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.
1753:
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
1786:
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
1647:
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
902:
1614:
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
1231:
1435:
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1836:
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.
1974:
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.
1812:
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
103:
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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
3053:
1607:
1590:
365:
1839:
Junction circulators use permanent magnets to provide the static magnetic bias for the ferrite(s). However, switching circulators typically rely on the
453:
34:
1932:
circulators by connecting one circulator port to a reflectionless termination, or they can be used as isolators by terminating two circulator ports.
1909:
205:
properties of magnetized microwave ferrite material. Microwave electromagnetic waves propagating in magnetized ferrite interact with electron
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2148:
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1943:
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).
2603:
Tanaka, S.; Shimomura, N.; Ohtake, K. (1965-03-01). "Active circulators - The realization of circulators using transistors".
1160:
41:
for a circulator (with each waveguide or transmission line port drawn as a single line, rather than as a pair of conductors)
1374:
1302:
3072:
2446:
Geiler, Anton; Harris, Vince (September–October 2014). "Atom
Magnetism: Ferrite Circulators - Past, Present, and Future".
1816:
lumped-element inductors and capacitors can be less stable when exposed to vibration or mechanical shocks than the simple
1899:
Differential phase shift circulators are mainly used in high power microwave applications. They are usually built from
980:
78:
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are integers. Solving the two preceding equations simultaneously, for proper circulation the necessary conditions are
1093:
1964:
it is used as a duplexer for sustaining the strong transmit power and clean reception of the signal from the antenna.
1900:
1817:
1562:
1547:
1064:
If losses are neglected for simplification, the counter-rotating modes must differ in phase by an integer multiple of
20:
2889:
2681:
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,
1042:
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579:
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of the ferrite. This permeability is mathematically described by a linear vector operator, also known as a
54:
1858:
magnetizing coil to magnetize the ferrite in the polarity to provide the desired direction of circulation.
1021:
19:
This article is about radio frequency (RF) or microwave frequency passive circulators. For other uses, see
1840:
1524:
1046:
236:
46:
2493:. 2021 IEEE International Electron Devices Meeting (IEDM). San Francisco, CA, USA. pp. 4.2.1–4.2.4.
1808:
with metallized vias to make connections between layers. The conductive strips can be thought of as non-
1665:
959:
210:
94:
62:
2364:
Palmer, William; Kirkwood, David; et al. (June 2016). "A Bright Future for
Integrated Magnetics".
2958:
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A stripline junction circulator contains a resonator, which is located at the central junction of the
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1994:
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E-field scatter plot of an electromagnetic wave propagating through a waveguide junction circulator.
1844:
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1742:) materials. These ferrites are essentially ceramic permanent magnets. In addition to their high
1551:
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for signal propagation from port 1 to port 2 (or from port 2 to port 3, or from port 3 to port 1):
1053:
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
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2714:
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2243:
1975:
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1005:
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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".
1992:
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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179:{\displaystyle S={\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}}}
2407:
Zeina, N.; How, H.; et al. (September 1992). "Self-Biasing
Circulators Operating at K
2019:
1479:
junction circulator having triangular ferrites and an irregular triangle-shaped resonator.
70:
3020:
3004:
2943:
2890:"Next Big Future: Novel miniaturized circulator opens way to doubling wireless capacity"
2848:
2694:
2651:
2525:
2223:
2210:
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
1628:
1578:
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
1873:
High-Power Liquid-Cooled
Differential Phase Shift Circulator. Image courtesy of
2015:
757:
case. The microwave propagation constants for this case, neglecting losses are
195:
2109:
The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science
1832:
Internal construction of a WR-90 (WG 16; R 100) waveguide switching circulator.
1778:
Woven mesh conductor wrapped around the ferrite of a lumped-element circulator.
3012:
2961:, 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
699:
is the frequency of the RF/microwave signal propagating through the ferrite,
16:
Electronic circuit in which a signal entering any port exits at the next port
2808:"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
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2011:
1967:
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Monolithic ferrites that are used for self-biased circulators are M-type
1653:
1511:
junction circulator having disk ferrites and a triangle-shaped resonator.
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1774:
1750:
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".
2659:
2424:
1636:
975:
1944:
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1529:
1495:
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".
2041:
2007:
1937:
1868:
1781:
1627:
1523:
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25:
2084:
Modern Ferrites, Volume 2: Emerging Technologies and Applications
1057:
at one port (port 2 if the signal is incident upon port 1) and a
209:
in the ferrite and are consequently influenced by the microwave
30:
1574:
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".
1796:
3021:"Low Frequency Circulator/Isolator Uses No Ferrite or Magnet"
2164:
Bosma, H. (1964-01-01). "On Stripline Y-Circulation at UHF".
2134:
2132:
2130:
1912:, and two oppositely-magnetized differential phase shifters.
1887:
Schematic diagram of a differential phase shift circulator.
1820:
impedance transformers in a stripline junction circulator.
2489:
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",
2831:
Reiskarimian, Negar; Krishnaswamy, Harish (2016-04-15).
2812:
IEEE Spectrum: Technology, Engineering, and Science News
2046:
Microwave diode reflection amplifier using a circulator
1464:
Internal Construction of Stripline Junction Circulators
1895:
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 }
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1358:{\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
2514:
IEEE Transactions on Microwave Theory and Techniques
2212:
IEEE Transactions on Microwave Theory and Techniques
2205:
2203:
2166:
IEEE Transactions on Microwave Theory and Techniques
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what they are, different types, how they work, etc.
2992:
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
2316:
Waveguide Junction Circulators: Theory and Practice
2054:is a type of microwave amplifier circuit utilizing
77:have similar behavior. Ports are where an external
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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}\ }
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1672:metallization processes, often including
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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:
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2776:
2770:
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2635:
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2600:
2594:
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2575:
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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:
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1247:
1232:
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1195:
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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:
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831:
830:
829:
817:
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806:
805:
802:
797:
796:
787:
776:
775:
755:transverse field
745:
743:
742:
737:
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723:
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717:
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419:
414:
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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:
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2829:
2825:
2816:
2814:
2805:
2804:
2800:
2778:
2777:
2773:
2731:
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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:
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879:
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821:
808:
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788:
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728:
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657:
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451:
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158:
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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:
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2073:
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2068:
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2003:
2000:
1989:
1986:
1984:
1981:
1952:
1949:
1917:non-reciprocal
1863:
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1073:
1045:formed by the
1018:
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969:
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2589:0-471-36930-6
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2350:0-86341-064-2
2346:
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2325:0-471-98252-0
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2272:0-06-046367-8
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2110:
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2100:
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2061:
2060:tunnel diodes
2057:
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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
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2032:TR switch
1968:Varactors
1787:resistor.
1689:effects.
1683:radiation
1670:thin-film
1656:function.
1654:duplexing
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1493:stripline
1477:stripline
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311:μ
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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
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2522:Bibcode
2220:Bibcode
2174:Bibcode
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2018:to the
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958:is the
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1760:-band
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