841:
895:
556:
283:
1355:, invented in 1952, became a commercial rival of stripline; however, planar formats did not start to become widely used in microwave applications until better dielectric materials became available for the substrates in the 1960s. Another structure which had to wait for better materials was the dielectric resonator. Its advantages (compact size and high quality) were first pointed out by R. D. Richtmeyer in 1939, but materials with good temperature stability were not developed until the 1970s. Dielectric resonator filters are now common in waveguide and transmission line filters.
224:). A common rule of thumb amongst engineers is to change from the lumped to the distributed model when distances involved are more than one-tenth of a wavelength (a 36° phase change). The lumped model completely fails at one-quarter wavelength (a 90° phase change), with not only the value, but the nature of the component not being as predicted. Due to this dependence on wavelength, the distributed-element model is used mostly at higher frequencies; at low frequencies, distributed-element components are too bulky. Distributed designs are feasible above
1181:
940:
488:
152:
1014:
599:
1258:
705:
20:
413:
381:, used for telephone lines and Internet connections. It is not often used for distributed-element circuits because the frequencies used are lower than the point where distributed-element designs become advantageous. However, designers frequently begin with a lumped-element design and convert it to an open-wire distributed-element design. Open wire is a pair of parallel uninsulated conductors used, for instance, for
427:, a centre conductor surrounded by an insulated shielding conductor, is widely used for interconnecting units of microwave equipment and for longer-distance transmissions. Although coaxial distributed-element devices were commonly manufactured during the second half of the 20th century, they have been replaced in many applications by planar forms due to cost and size considerations. Air-
579:. The coupling can be direct or indirect. In indirect coupling, the two lines are run closely together for a distance with no screening between them. The strength of the coupling depends on the distance between the lines and the cross-section presented to the other line. In direct coupling, branch lines directly connect the two main lines together at intervals.
716:-like curves as a circuit component is an emerging field in distributed-element circuits. Fractals have been used to make resonators for filters and antennae. One of the benefits of using fractals is their space-filling property, making them smaller than other designs. Other advantages include the ability to produce
298:, a particularly simple form to model. The cross-sectional dimensions of the line are unvarying along its length, and are small compared to the signal wavelength; thus, only distribution along the length of the line need be considered. Such an element of a distributed circuit is entirely characterised by its length and
1226:), with all their inputs connected via one transmission line and all their outputs via another transmission line. The lengths of the two lines must be equal between each transistor for the circuit to work correctly, and each transistor adds to the output of the amplifier. This is different from a conventional
1235:
amplifier, the overall bandwidth is the same as the bandwidth of a single stage. Distributed amplifiers are used when a single large transistor (or a complex, multi-transistor amplifier) would be too large to treat as a lumped component; the linking transmission lines separate the individual transistors.
1291:
was the first to investigate the possibility of distributed-element circuits, and filed a patent in 1927 for a coaxial filter designed by this method. Mason and Sykes published the definitive paper on the method in 1937. Mason was also the first to suggest a distributed-element acoustic filter in his
1171:
for an ideal three-port circulator, showing that circulators are non-reciprocal by definition. It follows that it is impossible to build a circulator from standard passive components (lumped or distributed). The presence of a ferrite, or some other non-reciprocal material or system, is essential for
879:
Impedance matching for narrow-band applications is frequently achieved with a single matching stub. However, for wide-band applications the impedance-matching network assumes a filter-like design. The designer prescribes a required frequency response, and designs a filter with that response. The only
627:
as a distributed-element circuit. The quarter-wave transformers are alternated with a distributed-element resonator to achieve this. However, this is now a dated design; more compact inverters, such as the impedance step, are used instead. An impedance step is the discontinuity formed at the junction
614:
Cascaded lines are lengths of transmission line where the output of one line is connected to the input of the next. Multiple cascaded lines of different characteristic impedances can be used to construct a filter or a wide-band impedance matching network. This is called a stepped impedance structure.
506:
over conducting lines, but their relative expense and bulk means that microstrip is often preferred. Waveguide mostly finds uses in high-end products, such as high-power military radars and the upper microwave bands (where planar formats are too lossy). Waveguide becomes bulkier with lower frequency,
73:
Conventional circuits consist of individual components manufactured separately then connected together with a conducting medium. Distributed-element circuits are built by forming the medium itself into specific patterns. A major advantage of distributed-element circuits is that they can be produced
1382:
in 1957, should be considered the first fractal antenna. However, its self-similar nature, and hence its relation to fractals was missed at the time. It is still not usually classed as a fractal antenna. Cohen was the first to explicitly identify the class of fractal antennae after being inspired
776:
A taper is a transmission line with a gradual change in cross-section. It can be considered the limiting case of the stepped impedance structure with an infinite number of steps. Tapers are a simple way of joining two transmission lines of different characteristic impedances. Using tapers greatly
662:
A dielectric resonator is a piece of dielectric material exposed to electromagnetic waves. It is most often in the form of a cylinder or thick disc. Although cavity resonators can be filled with dielectric, the essential difference is that in cavity resonators the electromagnetic field is entirely
358:
and resistive losses in lumped components are greater with increasing frequency as a proportion of the nominal value of the lumped-element impedance. In some cases, designers may choose a distributed-element design (even if lumped components are available at that frequency) to benefit from improved
1339:
and was responsible for many filter designs. Matthaei first described the interdigital filter and the combline filter. The group's work was published in a landmark 1964 book covering the state of distributed-element circuit design at that time, which remained a major reference work for many years.
1311:
which operated in the microwave band and resulted in radar equipment small enough to install in aircraft. A surge in distributed-element filter development followed, filters being an essential component of radars. The signal loss in coaxial components led to the first widespread use of waveguide,
1030:
A circulator is usually a three- or four-port device in which power entering one port is transferred to the next port in rotation, as if round a circle. Power can flow in only one direction around the circle (clockwise or anticlockwise), and no power is transferred to any of the other ports. Most
923:
when the coupling factor is high. A power combiner is simply a power splitter used in reverse. In distributed-element implementations using coupled lines, indirectly coupled lines are more suitable for low-coupling directional couplers; directly coupled branch line couplers are more suitable for
524:
band (below microwave frequencies), where waveguides might otherwise be used. Mechanical circuits can also be implemented, in whole or in part, as distributed-element circuits. The frequency at which the transition to distributed-element design becomes feasible (or necessary) is much lower with
856:
Filters are a large percentage of circuits constructed with distributed elements. A wide range of structures are used for constructing them, including stubs, coupled lines and cascaded lines. Variations include interdigital filters, combline filters and hairpin filters. More-recent developments
981:
Another use for a hybrid coupler is to produce the sum and difference of two signals. In the illustration, two input signals are fed into the ports marked 1 and 2. The sum of the two signals appears at the port marked Σ, and the difference at the port marked Δ. In addition to their uses as
353:
Distributed-element circuits are cheap and easy to manufacture in some formats, but take up more space than lumped-element circuits. This is problematic in mobile devices (especially hand-held ones), where space is at a premium. If the operating frequencies are not too high, the designer may
1234:
is multiplied by the gain of each stage. Although a distributed amplifier has lower gain than a conventional amplifier with the same number of transistors, it has significantly greater bandwidth. In a conventional amplifier, the bandwidth is reduced by each additional stage; in a distributed
1292:
1927 doctoral thesis, and a distributed-element mechanical filter in a patent filed in 1941. Mason's work was concerned with the coaxial form and other conducting wires, although much of it could also be adapted for waveguide. The acoustic work had come first, and Mason's colleagues in the
663:
contained within the cavity walls. A dielectric resonator has some field in the surrounding space. This can lead to undesirable coupling with other components. The major advantage of dielectric resonators is that they are considerably smaller than the equivalent air-filled cavity.
781:
between lines in different media, especially different forms of planar media. Tapers commonly change shape linearly, but a variety of other profiles may be used. The profile that achieves a specified match in the shortest length is known as a
Klopfenstein taper and is based on the
902:
A directional coupler is a four-port device which couples power flowing in one direction from one path to another. Two of the ports are the input and output ports of the main line. A portion of the power entering the input port is coupled to a third port, known as the
313:
Commensurate line circuits are important because a design theory for producing them exists; no general theory exists for circuits consisting of arbitrary lengths of transmission line (or any arbitrary shapes). Although an arbitrary shape can be analysed with
1303:, there was little demand for distributed-element circuits; the frequencies used for radio transmissions were lower than the point at which distributed elements became advantageous. Lower frequencies had a greater range, a primary consideration for
914:
A power divider is often constructed as a directional coupler, with the isolated port permanently terminated in a matched load (making it effectively a three-port device). There is no essential difference between the two devices. The term
547:
A stub is a short length of line that branches to the side of a main line. The end of the stub is often left open- or short-circuited, but may also be terminated with a lumped component. A stub can be used on its own (for instance, for
1166:
1065:; however, circulators are an exception. There are several equivalent ways to define or represent reciprocity. A convenient one for circuits at microwave frequencies (where distributed-element circuits are used) is in terms of their
732:
the manufacturing tolerances become tighter and are eventually greater than the construction method can achieve. However, after a small number of iterations, the performance is close to that of a true fractal. These may be called
519:
in high-end radio transmitters (marine, military, amateur radio), electronic circuits can be implemented as mechanical components; this is done largely because of the high quality of the mechanical resonators. They are used in the
681:
of wire in a cavity; one end is unconnected, and the other is bonded to the cavity wall. Although they are superficially similar to lumped inductors, helical resonators are distributed-element components and are used in the
389:. The designer does not usually intend to implement the circuit in this form; it is an intermediate step in the design process. Distributed-element designs with conductor pairs are limited to a few specialised uses, such as
797:, the taper is itself the antenna. Horn antennae, like other tapers, are often linear, but the best match is obtained with an exponential curve. The Vivaldi antenna is a flat (slot) version of the exponential taper.
208:, respectively. The distributed-element model is used when this assumption no longer holds, and these properties are considered to be distributed in space. The assumption breaks down when there is significant time for
1315:
The wartime work was mostly unpublished until after the war for security reasons, which made it difficult to ascertain who was responsible for each development. An important centre for this research was the
764:. The first three are closed curves, suitable for patch antennae. The latter two are open curves with terminations on opposite sides of the fractal. This makes them suitable for use where a connection in
376:
Several types of transmission line exist, and any of them can be used to construct distributed-element circuits. The oldest (and still most widely used) is a pair of conductors; its most common form is
1320:(Rad Lab), but work was also done elsewhere in the US and Britain. The Rad Lab work was published by Fano and Lawson. Another wartime development was the hybrid ring. This work was carried out at
453:
The majority of modern distributed-element circuits use planar transmission lines, especially those in mass-produced consumer items. There are several forms of planar line, but the kind known as
911:. For power flowing in the reverse direction and entering the output port, a reciprocal situation occurs; some power is coupled to the isolated port, but none is coupled to the coupled port.
927:
Distributed-element designs rely on an element length of one-quarter wavelength (or some other length); this will hold true at only one frequency. Simple designs, therefore, have a limited
2902:
Janković, Nikolina; Zemlyakov, Kiril; Geschke, Riana Helena; Vendik, Irina; Crnojević-Bengin, Vesna, "Fractal-based multi-band microstrip filters", ch. 6 in, Crnojević-Bengin, Vesna (ed),
563:
Departures from constructing with uniform transmission lines in distributed-element circuits are rare. One such departure that is widely used is the radial stub, which is shaped like a
321:
An important difference between distributed-element circuits and lumped-element circuits is that the frequency response of a distributed circuit periodically repeats as shown in the
1307:
purposes. These frequencies require long antennae for efficient operation, and this led to work on higher-frequency systems. A key breakthrough was the 1940 introduction of the
552:), or several of them can be used together in a more complex circuit such as a filter. A stub can be designed as the equivalent of a lumped capacitor, inductor, or resonator.
777:
reduces the mismatch effects that a direct join would cause. If the change in cross-section is not too great, no other matching circuitry may be needed. Tapers can provide
363:. Distributed-element designs tend to have greater power-handling capability; with a lumped component, all the energy passed by a circuit is concentrated in a small volume.
502:
are possible. These sometimes exist simultaneously, and this situation has no analogy in conducting lines. Waveguides have the advantages of lower loss and higher quality
931:
over which they will work successfully. Like impedance matching networks, a wide-band design requires multiple sections and the design begins to resemble a filter.
1324:, and was published after the war by W. A. Tyrrell. Tyrrell describes hybrid rings implemented in waveguide, and analyses them in terms of the well-known waveguide
310:
consisting of capacitors and inductors can be directly converted into a distributed circuit with a one-to-one correspondence between the elements of each circuit.
1079:
640:
is an empty (or sometimes dielectric-filled) space surrounded by conducting walls. Apertures in the walls couple the resonator to the rest of the circuit.
970:. Each of its four ports is connected to a ring of transmission line at a different point. Waves travel in opposite directions around the ring, setting up
274:
integrated circuits. This choice is particularly significant for hand-held devices, because lumped-element designs generally result in a smaller product.
1348:
498:
Many distributed-element designs can be directly implemented in waveguide. However, there is an additional complication with waveguides in that multiple
962:(a lumped device used in telephones), it now has a broader meaning. A widely used distributed-element hybrid which does not use coupled lines is the
525:
mechanical circuits. This is because the speed at which signals travel through mechanical media is much lower than the speed of electrical signals.
461:
and hence is cheap to make. It also lends itself to integration with lumped circuits on the same board. Other forms of printed planar lines include
242:
There is no clear-cut demarcation in the frequency at which these models should be used. Although the changeover is usually somewhere in the 100-to-
3261:
Ramadan, Ali; Al-Husseini, Mohammed; Kabalan Karim Y; El-Hajj, Ali, "Fractal-shaped reconfigurable antennas", ch. 10 in, Nasimuddin, Nasimuddin,
648:. Cavity resonators can be used in many media, but are most naturally formed in waveguide from the already existing metal walls of the guide.
345:). There is no equivalent in lumped circuits for a fixed delay, although an approximation could be constructed for a limited frequency range.
978:
results in a null; no power will leave a port set at that point. At other points, constructive interference maximises the power transferred.
1058:
is used to reflect back more power than it received. The circulator is used to direct the input and output power flows to separate ports.
431:
coaxial line is used for low-loss and high-power applications. Distributed-element circuits in other media still commonly transition to
148:
in the field soon led to broader applications. They can now be found in domestic products such as satellite dishes and mobile phones.
623:; in this role, it is called an impedance inverter. This structure can be used in filters to implement a lumped-element prototype in
533:
There are several structures that are repeatedly used in distributed-element circuits. Some of the common ones are described below.
567:. They are often used in pairs, one on either side of the main transmission line. Such pairs are called butterfly or bowtie stubs.
872:; the structure can become quite complex. For simple, narrow-band requirements, a single resonator may suffice (such as a stub or
1213:
889:
583:
470:
355:
122:
3258:, interview no. 005 for the IEEE History Centre, 3 March 1973, Engineering and Technology History Wiki, retrieved 15 April 2018.
212:
to travel from one terminal of a component to the other; "significant", in this context, implies enough time for a noticeable
3437:
805:
Resistive elements are generally not useful in a distributed-element circuit. However, distributed resistors may be used in
105:
A phenomenon commonly used in distributed-element circuits is that a length of transmission line can be made to behave as a
1374:
which overcame some practical limitations of
Richards theory, published by Kuroda in 1955. According to Nathan Cohen, the
246:
range, the technological scale is also significant; miniaturised circuits can use the lumped model at a higher frequency.
1196:
Distributed elements are usually passive, but most applications will require active components in some role. A microwave
813:. In planar media they can be implemented as a meandering line of high-resistance material, or as a deposited patch of
616:
3103:"The use of coaxial and balanced transmission lines in filters and wide band transformers for high radio frequencies"
3239:
Penn, Stuart; Alford, Neil, "Ceramic dielectrics for microwave applications", ch. 10 in, Nalwa, Hari Singh (ed),
1208:, and some passive components) are discrete. The active components may be packaged, or they may be placed on the
50:
or other distributed components. These circuits perform the same functions as conventional circuits composed of
3419:
3404:
3389:
3363:
3348:
3322:
3307:
3270:
3248:
3222:
3207:
3192:
3177:
3162:
3068:
3053:
3038:
3023:
3008:
2982:
2967:
2952:
2926:
2911:
2896:
2881:
2866:
2851:
2836:
2821:
2806:
2759:
2744:
2718:
2703:
2673:
2658:
2632:
2617:
2602:
2587:
2572:
2546:
2531:
2502:
2487:
2472:
2457:
2442:
2416:
1244:
778:
3447:
1270:
928:
263:
1252:
1062:
482:
87:
3102:
1332:
919:
is usually used when the coupling factor (the proportion of power reaching the coupled port) is low, and
1039:
to protect a transmitter (or other equipment) from damage due to reflections from the antenna, and as a
132:
Distributed-element circuits were studied during the 1920s and 1930s but did not become important until
3442:
1278:
835:
118:
2666:
A History of
Engineering and Science in the Bell System: Volume 5: Communications Sciences (1925–1980)
1371:
1197:
840:
303:
259:
173:
24:
821:
material. In waveguide, a card of microwave absorbent material can be inserted into the waveguide.
1363:
1317:
1185:
991:
806:
729:
448:
318:
to determine its behaviour, finding useful structures is a matter of trial and error or guesswork.
299:
255:
306:, where all the elements are the same length. With commensurate circuits, a lumped circuit design
1209:
987:
880:
difference from a standard filter design is that the filter's source and load impedances differ.
251:
95:
51:
3132:
907:. None of the power entering the input port is coupled to the fourth port, usually known as the
1367:
1351:. Although stripline was another wartime invention, its details were not published until 1951.
1277:, an effect which was not well understood at the time. Heaviside's analysis, now known as the
810:
315:
644:
occurs due to electromagnetic waves reflected back and forth from the cavity walls setting up
1269:
in 1881. Heaviside used it to find a correct description of the behaviour of signals on the
1219:
789:
Tapers can be used to match a transmission line to an antenna. In some designs, such as the
458:
436:
270:
can use lumped designs at higher frequencies than printed circuits, and this is done in some
247:
185:
160:
75:
16:
Electrical circuits composed of lengths of transmission lines or other distributed components
1375:
1248:
1227:
1047:
1036:
898:
Microstrip sawtooth directional coupler, a variant of the coupled-lines directional coupler
862:
657:
603:
209:
177:
79:
1161:{\displaystyle ={\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}}}
894:
868:
As with lumped-element filters, the more elements used, the closer the filter comes to an
8:
2593:
Cohen, Nathan, "Fractal antenna and fractal resonator primer", ch. 8 in, Frame, Michael,
1274:
1212:
in chip form without individual packaging to reduce size and eliminate packaging-induced
1051:
947:
A directional coupler which splits power equally between the output and coupled ports (a
555:
417:
342:
282:
753:
31:. The distributed-element circuitry is centre and left of centre, and is constructed in
1231:
959:
765:
576:
549:
542:
338:
267:
181:
114:
110:
70:
frequencies, where conventional components are difficult (or impossible) to implement.
43:
1200:
uses distributed elements for many passive components, but active components (such as
3415:
3400:
3385:
3359:
3344:
3318:
3303:
3266:
3244:
3218:
3203:
3188:
3173:
3158:
3143:
3128:
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3019:
3004:
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2787:
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2714:
2699:
2684:
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2654:
2628:
2613:
2598:
2583:
2568:
2542:
2527:
2498:
2483:
2468:
2453:
2438:
2412:
1384:
975:
721:
672:
575:
Coupled lines are two transmission lines between which there is some electromagnetic
516:
432:
334:
330:
326:
295:
294:
The overwhelming majority of distributed-element circuits are composed of lengths of
145:
47:
2827:
Hilty, Kurt, "Attenuation measurement", pp. 422–439 in, Dyer, Stephen A (ed),
2679:
Fano, R M; Lawson, A W, "Design of microwave filters", ch. 10 in, Ragan, G L (ed),
1359:
1312:
extending the filter technology from the coaxial domain into the waveguide domain.
1308:
1273:. Transmission of early transatlantic telegraph had been difficult and slow due to
1266:
1073:. From the definition of a circulator, it is clear that this will not be the case,
1070:
1032:
967:
869:
783:
749:
637:
492:
322:
307:
287:
2958:
Lacomme, Philippe; Marchais, Jean-Claude; Hardange, Jean-Philippe; Normant, Eric,
3014:
Magnusson, Philip C; Weisshaar, Andreas; Tripathi, Vijai K; Alexander, Gerald C,
1288:
873:
794:
699:
624:
564:
521:
398:
271:
156:
3329:
2423:
151:
3255:
2554:"The introduction of the loading coil: George A. Campbell and Michael I. Pupin"
1265:
Distributed-element modelling was first used in electrical network analysis by
983:
745:
620:
499:
386:
382:
354:
miniaturise components rather than switching to distributed elements. However,
163:(left), and as a distributed-element design printed on the board itself (right)
99:
28:
3123:
Matthaei, G L, "Comb-line band-pass filters of narrow or moderate bandwidth",
3094:
3085:
3076:
2639:
619:. This has the useful property of transforming any impedance network into its
3431:
3370:
3334:
Transactions of the IRE Professional Group on
Microwave Theory and Techniques
3277:
3241:
Handbook of Low and High
Dielectric Constant Materials and Their Applications
2725:
1379:
999:
995:
971:
939:
757:
645:
628:
of two cascaded transmission lines with different characteristic impedances.
424:
213:
83:
3113:
2989:
1180:
3229:
1336:
1304:
1300:
1282:
1066:
1002:
790:
378:
337:; distributed forms are an irrational function. Another difference is that
141:
133:
3147:
2933:
586:. Another property of coupled lines is that they act as a pair of coupled
1296:
radio department asked him to assist with coaxial and waveguide filters.
761:
725:
390:
325:
example; the equivalent lumped circuit does not. This is a result of the
189:
63:
3200:
A Practical Design of Lumped, Semi-lumped & Microwave Cavity
Filters
2791:
2781:
2774:
2688:
2625:
Filter Design for
Satellite Communications: Helical Resonator Technology
487:
341:
lengths of line introduce a fixed delay at all frequencies (assuming an
3140:
Microwave
Filters, Impedance-Matching Networks, and Coupling Structures
2553:
1352:
1205:
1055:
1025:
818:
728:
rejection. In practice, a true fractal cannot be made because at each
598:
454:
428:
221:
193:
126:
32:
2726:"Microstrip—a new transmission technique for the kilomegacycle range"
1344:
1325:
1321:
1293:
883:
845:
814:
717:
641:
587:
503:
462:
401:
394:
232:
217:
201:
106:
67:
55:
3288:
2780:
Heaviside, Oliver, "Electromagnetic induction and its propagation",
1328:. Other researchers soon published coaxial versions of this device.
1043:
connecting the antenna, transmitter and receiver of a radio system.
1013:
704:
117:, and cascaded lines. Circuits built from these components include
2524:
Stripline-like
Transmission Lines for Microwave Integrated Circuits
1069:. A reciprocal circuit will have an S-parameter matrix, , which is
1040:
849:
607:
412:
360:
205:
197:
59:
457:
is the most common. It can be manufactured by the same process as
2990:"A History of microwave filter research, design, and development"
2580:
Microwave
Electronics: Measurement and Materials Characterization
1257:
1189:
1061:
Passive circuits, both lumped and distributed, are nearly always
982:
couplers and power dividers, directional couplers can be used in
950:
858:
744:
Fractals that have been used as a circuit component include the
713:
466:
290:
constructed from lumped (top) and distributed components (bottom)
2945:
Distributed Power Amplifiers for RF and Microwave Communications
2874:
Data and Computer Communications: Networking and Internetworking
2578:
Chen, L F; Ong, C K; Neo, C P; Varadan, V V; Varadan, Vijay K,
3382:
Microwave Circuit Design Using Linear and Nonlinear Techniques
2623:
Doumanis, Efstratios; Goussetis, George; Kosmopoulos, Savvas,
2409:
Asymmetric Passive Components in Microwave Integrated Circuits
216:
change. The amount of phase change is dependent on the wave's
140:. After the war their use was limited to military, space, and
19:
2508:
Barrett, R M, "Etched sheets serve as microwave components",
1201:
678:
590:. This property is used in many distributed-element filters.
137:
91:
1387:
in 1987, but he could not get a paper published until 1995.
615:
A single, cascaded line one-quarter wavelength long forms a
420:. One has the cover removed, showing its internal structure.
3031:
Microwave Resonators and Filters for Wireless Communication
3061:
Integrated Microwave Front-ends with Avionics Applications
1285:. It remains the standard analysis of transmission lines.
1184:
Microstrip circuit with discrete transistors in miniature
861:
filters. Many filters are constructed in conjunction with
741:
where it is necessary to distinguish from a true fractal.
2515:
Barrett, R M; Barnes, M H, "Microwave printed circuits",
1223:
687:
683:
227:
27:
with distributed elements. The circuitry on the right is
2889:
Handbook of Microwave Technology: Components and devices
109:. Distributed-element components which do this include
3380:
Vendelin, George D; Pavio, Anthony M; Rohde, Ulrich L,
2640:"Broadband logarithmically periodic antenna structures"
2465:
Control Components Using Si, GaAs, and GaN Technologies
943:
Hybrid ring, used to produce sum and difference signals
708:
Three-iteration Hilbert fractal resonator in microstrip
277:
3377:, vol. 35, iss. 11, pp. 1294–1306, November 1947.
2732:, vol. 40, iss. 12, pp. 1644–1650, December 1952.
2450:
Fundamentals of RF and Microwave Transistor Amplifiers
1343:
Planar formats began to be used with the invention of
1100:
469:
and many variations. Planar lines can also be used in
196:
are assumed to be "lumped" at one point in space in a
1188:
packages, capacitors and resistors in chip form, and
1082:
3185:
Radio-Frequency and Microwave Communication Circuits
2932:
Johnson, Robert A; Börner, Manfred; Konno, Masashi,
2769:, vol. 1, pp. 139–140, Copley Publishers, 1925
507:
which militates against its use on the lower bands.
3120:, vol. 10, iss. 6, pp. 479–491, November 1962.
3118:
IRE Transactions on Microwave Theory and Techniques
2428:
IRE Transactions on Microwave Theory and Techniques
1222:consist of a number of amplifying devices (usually
172:Distributed-element circuits are designed with the
159:as conventional discrete components connected on a
3092:Mason, Warren P, "Electromechanical wave filter",
2994:IEEE Transactions: Microwave Theory and Techniques
1160:
884:Power dividers, combiners and directional couplers
582:Coupled lines are a common method of constructing
2799:Ridge Waveguides and Passive Microwave Components
2430:, vol. 6, iss. 4, pp. 369–373, October 1958.
2424:"An analysis of a broad-band coaxial hybrid ring"
829:
3429:
3341:Basic Microwave Techniques and Laboratory Manual
3336:, vol. 1, iss. 2, pp. 17–23, November 1953.
2844:Microstrip Filters for RF/Microwave Applications
3295:, vol. 10, iss. 6, pp. 391–397, June 1939.
3089:, filed 25 November 1941, issued 28 March 1944.
2940:, vol. 18, iss. 3, pp. 155–170, July 1971.
2829:Wiley Survey of Instrumentation and Measurement
2560:, vol. 11, no. 1, pp. 36–57, January 1970.
1046:An unusual application of a circulator is in a
348:
3315:Fundamental of Microwave and Radar Engineering
3236:, vol. 5, iss. 2, pp. 104–109, June 1958.
3215:Radio-Frequency Integrated-Circuit Engineering
3202:, Springer Science & Business Media, 2012
3138:Matthaei, George L; Young, Leo; Jones, E M T,
3083:Mason, Warren P, "Wave transmission network",
3080:, filed 25 June 1927, issued 11 November 1930.
2565:Microwave Ring Circuits and Related Structures
2437:, Springer Science & Business Media, 2013
515:In a few specialist applications, such as the
473:, where they are integral to the device chip.
3098:, filed 20 August 1958, issued 25 April 1961.
1035:materials. Uses of circulators include as an
1031:distributed-element circulators are based on
958:. Although "hybrid" originally referred to a
3230:"Synthesis of a class of strip-line filters"
3046:Passive RF and Microwave Integrated Circuits
2996:, pp. 1055–1067, vol. 32, iss. 9, 1984.
2694:Garg, Ramesh; Bahl, Inder; Bozzi, Maurizio,
2595:Benoit Mandelbrot: A Life In Many Dimensions
1358:Important theoretical developments included
724:designs, good in-band performance, and good
2938:IEEE Transactions on Sonics and Ultrasonics
2814:Microwave Mixer Technology and Applications
3284:, vol. 36, iss. 2, pp. 217–220, 1948.
1017:A coaxial ferrite circulator operating at
974:. At some points on the ring, destructive
3412:Passive Microwave Components and Antennas
2934:"Mechanical filters—a review of progress"
2904:Advances in Multi-Band Microstrip Filters
1245:Distributed-element filter § History
800:
254:are larger than equivalent designs using
2921:, John Wiley & Sons Australia, 1983
2651:Foundations of Microstrip Circuit Design
2644:1958 IRE International Convention Record
1331:George Matthaei led a research group at
1256:
1179:
1012:
938:
893:
839:
703:
597:
554:
486:
471:monolithic microwave integrated circuits
411:
281:
150:
18:
3016:Transmission Lines and Wave Propagation
2752:The Cable Television Technical Handbook
2512:, vol. 25, pp. 114–118, June 1952.
1281:, identified the problem and suggested
1253:Planar transmission line § History
890:Power dividers and directional couplers
651:
584:power dividers and directional couplers
262:are smaller than PCB technologies, and
3430:
3127:, vol. 6, pp. 82–91, August 1963
2943:Kumar, Narendra; Grebennikov, Andrei,
2859:Theory and Design of Microwave Filters
231:, and are the technology of choice at
3278:"Resistor-transmission-line circuits"
848:hairpin filter (left), followed by a
528:
302:. A further simplification occurs in
3397:The Resource Handbook of Electronics
2649:Edwards, Terry C; Steer, Michael B,
2120:Kumar & Grebennikov, pp. 153–154
1588:Edwards & Steer, pp. 78, 345–347
1175:
666:
371:
286:Frequency response of a fifth-order
278:Construction with transmission lines
167:
144:infrastructure, but improvements in
123:power dividers, directional couplers
2977:, Cambridge University Press, 2004
2906:, Cambridge University Press, 2015
2713:, Cambridge University Press, 2017
2668:, AT&T Bell Laboratories, 1984
2646:, New York, 1957, pp. 119–128.
1366:, which was published in 1948, and
631:
13:
3356:CRC Handbook of Electrical Filters
3234:IRE Transactions on Circuit Theory
3109:, vol. 16, pp. 275–302, 1937.
2872:Hura, Gurdeep S; Singhal, Mukesh,
2842:Hong, Jia-Shen G; Lancaster, M J,
2495:Automated Electronic Filter Design
1930:Hong & Lancaster, pp. 109, 235
1505:Henderson & Camargo, pp. 24–25
1378:, invented by Raymond DuHamel and
617:quarter-wave impedance transformer
14:
3459:
2919:Mechanical Filters in Electronics
2812:Henderson, Bert; Camargo, Edmar,
2709:Ghione, Giovanni; Pirola, Marco,
2610:Electronics via Waveform Analysis
2539:Radar Imaging of Airborne Targets
2350:Makimoto & Yamashita, pp. 1–2
1644:Bhat & Koul, pp. 10, 602, 622
824:
610:) with stepped impedance matching
593:
90:formats for applications such as
3371:"Hybrid circuits for microwaves"
3339:Sisodia, M L; Raghuvanshi, G S,
3114:"Interdigital band-pass filters"
3074:Mason, Warren P, "Wave filter",
2960:Air and Spaceborne Radar Systems
2739:, Krishna Prakashan Media, 2010
2522:Bhat, Bharathi; Koul, Shiban K,
2026:Ghione & Pirola, pp. 172–173
1603:Edwards & Steer, pp. 347–348
570:
3256:"Oral-History: Warren P. Mason"
2681:Microwave Transmission Circuits
2482:, Technical Publications, 2009
2401:
2389:
2380:
2362:
2353:
2344:
2335:
2326:
2317:
2308:
2299:
2286:
2277:
2268:
2259:
2241:
2232:
2223:
2214:
2205:
2196:
2168:
2159:
2150:
2141:
2132:
2123:
2114:
2105:
2096:
2087:
2065:
2047:
2029:
2020:
2011:
2002:
1993:
1984:
1981:Sisodia & Raghuvansh, p. 70
1975:
1966:
1957:
1948:
1939:
1921:
1912:
1903:
1882:
1861:
1840:
1818:
1805:
1796:
1783:
1770:
1757:
1744:
1731:
1718:
1705:
1683:
1674:
1665:
1656:
1647:
1638:
1606:
1597:
1579:
1551:
1542:
1489:Hura & Singhal, pp. 178–179
1249:Waveguide filter § History
1192:filters as distributed elements
78:for consumer products, such as
3414:, BoD – Books on Demand, 2010
3384:, John Wiley & Sons, 2005
3354:Taylor, John; Huang, Qiuting,
3343:, New Age International, 1987
3265:, BoD – Books on Demand, 2011
3217:, John Wiley & Sons, 2015
3187:, John Wiley & Sons, 2004
3172:, John Wiley & Sons, 2005
2846:, John Wiley & Sons, 2004
2831:, John Wiley & Sons, 2004
2786:, pp. 79–81, 3 June 1887
2696:Microstrip Lines and Slotlines
2653:, John Wiley & Sons, 2016
2582:, John Wiley & Sons, 2004
2567:, John Wiley & Sons, 2004
2526:, New Age International, 1989
2452:, John Wiley & Sons, 2009
2411:, John Wiley & Sons, 2006
2386:Levy & Cohn, pp. 1056–1057
2111:Bhat & Khoul, pp. 9–10, 15
2102:Maloratsky (2004), pp. 285–286
2017:Chang & Hsieh, pp. 197–198
1933:Makimoto & Yamashita, p. 2
1680:Penn & Alford, pp. 524–530
1629:Chang & Hsieh, pp. 227–229
1560:Taylor & Huang pp. 353–358
1539:Ghione & Pirola, pp. 18–19
1533:
1518:
1480:
1458:
1449:
1440:
1431:
1409:
1396:
1089:
1083:
1008:
924:high-coupling power dividers.
830:Filters and impedance matching
439:for interconnection purposes.
264:monolithic integrated circuits
1:
3107:Bell System Technical Journal
2737:Electro Magnetic Field Theory
2563:Chang, Kai; Hsieh, Lung-Hwa,
2519:, vol. 46, 16 September 1951.
2250:Sheingold & Morita (1953)
1999:Bhat & Khoul, pp. 622–627
1390:
1271:transatlantic telegraph cable
510:
3438:Distributed element circuits
3317:, S. Chand Publishing, 2011
3300:Microwave Electronic Devices
2975:Planar Microwave Engineering
2724:Grieg, D D; Englemann, H F,
2480:Antenna And Wave Propagation
2422:Albanese, V J; Peyser, W P,
2305:Levy and Cohn, pp. 1057–1059
2253:Albanese & Peyser (1958)
1632:Bhat & Koul, pp. 602–609
483:Waveguide (electromagnetism)
476:
349:Advantages and disadvantages
220:(and inversely dependent on
40:Distributed-element circuits
7:
3328:Sheingold, L S; Morita, T,
3029:Makimoto, M; Yamashita, S,
3001:Microwave Circulator Design
2314:Barrett & Barnes (1951)
2184:Fagen & Millman, p. 108
1834:Edwards & Steer, p. 493
1333:Stanford Research Institute
693:
66:. They are used mostly at
10:
3464:
3293:Journal of Applied Physics
3198:Natarajan, Dhanasekharan,
2478:Bakshi, U A; Bakshi, A V,
2371:First English publication:
2323:Grieg and Englemann (1952)
1548:Ghione & Pirola, p. 18
1242:
1238:
1023:
934:
887:
836:Distributed-element filter
833:
697:
670:
655:
540:
480:
446:
407:
304:commensurate line circuits
260:Hybrid integrated circuits
2597:, World Scientific, 2015
2041:Maloratsky (2004), p. 117
2038:Chang & Hsieh, p. 227
2008:Maloratsky (2004), p. 117
1972:Maloratsky (2004), p. 160
1283:methods for overcoming it
1198:hybrid integrated circuit
677:A helical resonator is a
442:
174:distributed-element model
136:, when they were used in
25:low-noise block converter
3101:Mason, W P; Sykes, R A,
2664:Fagen, M D; Millman, S,
2638:DuHamell, R; Isbell, D,
2435:Microwave Systems Design
2374:Ozaki & Ishii (1958)
2229:Levy & Cohn, p. 1055
2220:Fano & Lawson (1948)
2211:Levy & Cohn, p. 1055
2187:Levy & Cohn, p. 1055
1891:Maloratsky (2012), p. 69
1364:commensurate line theory
1318:MIT Radiation Laboratory
988:frequency discriminators
771:
449:Planar transmission line
416:A collection of coaxial
366:
329:of lumped forms being a
300:characteristic impedance
256:surface-mount technology
176:, an alternative to the
82:. They are also made in
3289:"Dielectric resonators"
3243:, Academic Press, 1999
2962:, William Andrew, 2001
2891:, Academic Press, 1995
2138:Heaviside (1887), p. 81
1279:telegrapher's equations
536:
266:are smaller than both.
252:through-hole technology
96:satellite communication
46:composed of lengths of
3375:Proceedings of the IRE
3282:Proceedings of the IRE
3254:Polkinghorn, Frank A,
2730:Proceedings of the IRE
2558:Technology and Culture
1563:Johnson (1983), p. 102
1262:
1220:Distributed amplifiers
1193:
1162:
1021:
944:
899:
853:
801:Distributed resistance
709:
611:
560:
495:
459:printed circuit boards
421:
291:
248:Printed circuit boards
164:
36:
3170:Modern Antenna Design
3157:, Artech House, 2008
3095:U.S. patent 2,981,905
3086:U.S. patent 2,345,491
3077:U.S. patent 2,345,491
3063:, Artech House, 2012
3003:, Artech House, 2014
2999:Linkhart, Douglas K,
2947:, Artech House, 2015
2816:, Artech House, 2013
2754:, Artech House, 1985
2711:Microwave Electronics
2698:, Artech House, 2013
2627:, Artech House, 2015
2467:, Artech House, 2014
2332:Bhat & Koul, p. 3
1260:
1183:
1163:
1016:
954:coupler) is called a
942:
897:
863:dielectric resonators
843:
739:finite-order fractals
707:
601:
559:Butterfly stub filter
558:
490:
415:
285:
210:electromagnetic waves
186:electrical resistance
180:in which the passive
161:printed circuit board
154:
76:printed circuit board
22:
3448:Microwave technology
3410:Zhurbenko, Vitaliy,
3228:Ozaki, H; Ishii, J,
3168:Milligan, Thomas A,
3155:Modern Radar Systems
2988:Levy, R; Cohn, S B,
2683:, McGraw-Hill, 1948
1573:(1971), pp. 155, 169
1527:Natarajan, pp. 11–12
1376:log-periodic antenna
1228:multistage amplifier
1172:the device to work.
1080:
1048:reflection amplifier
658:Dielectric resonator
652:Dielectric resonator
604:orthomode transducer
418:directional couplers
178:lumped-element model
80:satellite television
54:components, such as
3395:Whitaker, Jerry C,
3330:"A coaxial magic-T"
3263:Microstrip Antennas
3183:Misra, Devendra K,
3059:Maloratsky, Leo G,
3044:Maloratsky, Leo G,
2917:Johnson, Robert A,
2765:Heaviside, Oliver,
2552:Brittain, James E,
2056:Sharma, pp. 175–176
1963:Bahl (2009), p. 149
1897:Bahl (2014), p. 214
1870:Bakshi & Bakshi
1671:Hunter, pp. 209–210
1455:Hunter, pp. 139–140
1437:Hunter, pp. 137–138
1368:Kuroda's identities
1052:negative resistance
917:directional coupler
316:Maxwell's equations
268:Integrated circuits
182:electrical elements
44:electrical circuits
3399:, CRC Press, 2000
3358:, CRC Press, 1997
3276:Richards, Paul I,
3018:, CRC Press, 2000
2876:, CRC Press, 2001
2541:, CRC Press, 1999
2395:Cohen, pp. 210–211
2190:Polkinghorn (1973)
1909:Hilty, pp. 426–427
1831:, pp. 404–406, 540
1502:Craig, pp. 291–292
1263:
1194:
1158:
1152:
1022:
960:hybrid transformer
945:
900:
854:
710:
612:
565:sector of a circle
561:
550:impedance matching
543:Stub (electronics)
529:Circuit components
517:mechanical filters
496:
433:coaxial connectors
422:
356:parasitic elements
292:
235:frequencies above
165:
48:transmission lines
37:
3443:Radio electronics
3302:, Springer, 2012
3287:Richtmeyer, R D,
3142:McGraw-Hill 1964
3125:Microwave Journal
3048:, Elsevier, 2004
3033:, Springer, 2013
2767:Electrical Papers
2612:, Springer, 2012
2497:, Springer, 2016
2341:Richtmeyer (1939)
2093:Roer, pp. 255–256
1849:Zhurbenko, p. 311
1802:Zhurbenko, p. 310
1474:Nguyen, pp. 27–28
1385:Benoit Mandelbrot
1349:Robert M. Barrett
1176:Active components
730:fractal iteration
673:Helical resonator
667:Helical resonator
372:Paired conductors
339:cascade-connected
335:complex frequency
331:rational function
327:transfer function
296:transmission line
168:Circuit modelling
146:materials science
3455:
3153:Meikle, Hamish,
3097:
3088:
3079:
2887:Ishii, T Koryu,
2608:Craig, Edwin C,
2493:Banerjee, Amal,
2396:
2393:
2387:
2384:
2378:
2366:
2360:
2357:
2351:
2348:
2342:
2339:
2333:
2330:
2324:
2321:
2315:
2312:
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2303:
2297:
2290:
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2275:
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2263:
2257:
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2230:
2227:
2221:
2218:
2212:
2209:
2203:
2200:
2194:
2172:
2166:
2163:
2157:
2154:
2148:
2145:
2139:
2136:
2130:
2129:Heaviside (1925)
2127:
2121:
2118:
2112:
2109:
2103:
2100:
2094:
2091:
2085:
2069:
2063:
2051:
2045:
2033:
2027:
2024:
2018:
2015:
2009:
2006:
2000:
1997:
1991:
1988:
1982:
1979:
1973:
1970:
1964:
1961:
1955:
1952:
1946:
1943:
1937:
1925:
1919:
1916:
1910:
1907:
1901:
1886:
1880:
1876:Milligan, p. 513
1865:
1859:
1844:
1838:
1822:
1816:
1809:
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1794:
1787:
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1768:
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1735:
1729:
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1716:
1709:
1703:
1692:Whitaker, p. 227
1687:
1681:
1678:
1672:
1669:
1663:
1662:Helszajn, p. 189
1660:
1654:
1651:
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1604:
1601:
1595:
1583:
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1484:
1478:
1462:
1456:
1453:
1447:
1444:
1438:
1435:
1429:
1413:
1407:
1400:
1383:by a lecture of
1360:Paul I. Richards
1309:cavity magnetron
1267:Oliver Heaviside
1261:Oliver Heaviside
1167:
1165:
1164:
1159:
1157:
1156:
1020:
968:rat-race coupler
953:
784:Chebychev filter
754:Sierpiński curve
750:Minkowski island
638:cavity resonator
632:Cavity resonator
493:waveguide filter
323:Chebyshev filter
288:Chebyshev filter
245:
238:
230:
3463:
3462:
3458:
3457:
3456:
3454:
3453:
3452:
3428:
3427:
3112:Matthaei, G L,
3093:
3084:
3075:
2973:Lee, Thomas H,
2783:The Electrician
2750:Harrel, Bobby,
2537:Borden, Brett,
2463:Bahl, Inder J,
2448:Bahl, Inder J,
2404:
2399:
2394:
2390:
2385:
2381:
2377:
2367:
2363:
2359:Richards (1948)
2358:
2354:
2349:
2345:
2340:
2336:
2331:
2327:
2322:
2318:
2313:
2309:
2304:
2300:
2291:
2287:
2283:Matthaei (1963)
2282:
2278:
2274:Matthaei (1962)
2273:
2269:
2264:
2260:
2256:
2246:
2242:
2237:
2233:
2228:
2224:
2219:
2215:
2210:
2206:
2201:
2197:
2193:
2173:
2169:
2164:
2160:
2155:
2151:
2147:Brittain, p. 39
2146:
2142:
2137:
2133:
2128:
2124:
2119:
2115:
2110:
2106:
2101:
2097:
2092:
2088:
2084:
2070:
2066:
2062:
2059:Linkhart, p. 29
2052:
2048:
2044:
2034:
2030:
2025:
2021:
2016:
2012:
2007:
2003:
1998:
1994:
1989:
1985:
1980:
1976:
1971:
1967:
1962:
1958:
1953:
1949:
1945:Harrell, p. 150
1944:
1940:
1936:
1926:
1922:
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1908:
1904:
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1887:
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1879:
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1611:
1607:
1602:
1598:
1594:
1591:Banerjee, p. 74
1584:
1580:
1576:
1556:
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1547:
1543:
1538:
1534:
1530:
1523:
1519:
1515:
1485:
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1454:
1450:
1445:
1441:
1436:
1432:
1428:
1414:
1410:
1401:
1397:
1393:
1335:which included
1289:Warren P. Mason
1255:
1241:
1178:
1151:
1150:
1145:
1140:
1134:
1133:
1128:
1123:
1117:
1116:
1111:
1106:
1096:
1095:
1081:
1078:
1077:
1028:
1018:
1011:
984:balanced mixers
948:
937:
892:
886:
874:spurline filter
838:
832:
827:
803:
795:Vivaldi antenna
774:
702:
700:Fractal antenna
696:
675:
669:
660:
654:
634:
625:ladder topology
596:
573:
545:
539:
531:
522:radio frequency
513:
485:
479:
451:
445:
435:at the circuit
410:
387:telegraph poles
383:telephone lines
374:
369:
351:
280:
272:radio frequency
243:
236:
225:
170:
157:low-pass filter
100:microwave links
29:lumped elements
17:
12:
11:
5:
3461:
3451:
3450:
3445:
3440:
3424:
3423:
3408:
3393:
3378:
3369:Tyrrell, W A,
3367:
3352:
3337:
3326:
3311:
3296:
3285:
3274:
3259:
3252:
3237:
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3211:
3196:
3181:
3166:
3151:
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3121:
3110:
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3072:
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2520:
2513:
2506:
2491:
2476:
2461:
2446:
2433:Awang, Zaiki,
2431:
2420:
2407:Ahn, Hee-Ran,
2403:
2400:
2398:
2397:
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2258:
2255:
2254:
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2247:
2240:
2238:Tyrrell (1947)
2231:
2222:
2213:
2204:
2195:
2192:
2191:
2188:
2185:
2182:
2181:(1971), p. 155
2174:
2167:
2158:
2149:
2140:
2131:
2122:
2113:
2104:
2095:
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2035:
2028:
2019:
2010:
2001:
1992:
1983:
1974:
1965:
1956:
1947:
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1934:
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1927:
1920:
1911:
1902:
1899:
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1693:
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1506:
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1500:
1497:
1490:
1486:
1479:
1476:
1475:
1472:
1464:
1457:
1448:
1446:Hunter, p. 137
1439:
1430:
1427:
1426:
1419:
1415:
1408:
1394:
1392:
1389:
1240:
1237:
1177:
1174:
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1129:
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1115:
1112:
1110:
1107:
1105:
1102:
1101:
1099:
1094:
1091:
1088:
1085:
1024:Main article:
1010:
1007:
996:phase shifters
972:standing waves
936:
933:
888:Main article:
885:
882:
870:ideal response
834:Main article:
831:
828:
826:
825:Circuit blocks
823:
802:
799:
773:
770:
746:Koch snowflake
695:
692:
671:Main article:
668:
665:
656:Main article:
653:
650:
646:standing waves
633:
630:
606:(a variety of
595:
594:Cascaded lines
592:
572:
569:
541:Main article:
538:
535:
530:
527:
512:
509:
481:Main article:
478:
475:
447:Main article:
444:
441:
409:
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373:
370:
368:
365:
350:
347:
279:
276:
169:
166:
15:
9:
6:
4:
3:
2:
3460:
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3353:
3350:
3346:
3342:
3338:
3335:
3331:
3327:
3324:
3320:
3316:
3313:Sharma, K K,
3312:
3309:
3305:
3301:
3297:
3294:
3290:
3286:
3283:
3279:
3275:
3272:
3268:
3264:
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3257:
3253:
3250:
3246:
3242:
3238:
3235:
3231:
3227:
3224:
3220:
3216:
3213:Nguyen, Cam,
3212:
3209:
3205:
3201:
3197:
3194:
3190:
3186:
3182:
3179:
3175:
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3017:
3013:
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3006:
3002:
2998:
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2898:
2894:
2890:
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2883:
2879:
2875:
2871:
2868:
2864:
2860:
2857:Hunter, Ian,
2856:
2853:
2849:
2845:
2841:
2838:
2834:
2830:
2826:
2823:
2819:
2815:
2811:
2808:
2804:
2800:
2797:Helszajn, J,
2796:
2793:
2789:
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2772:
2768:
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2761:
2757:
2753:
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2701:
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2663:
2660:
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2641:
2637:
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2622:
2619:
2615:
2611:
2607:
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2600:
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2581:
2577:
2574:
2570:
2566:
2562:
2559:
2555:
2551:
2548:
2544:
2540:
2536:
2533:
2529:
2525:
2521:
2518:
2517:Radio TV News
2514:
2511:
2507:
2504:
2500:
2496:
2492:
2489:
2485:
2481:
2477:
2474:
2470:
2466:
2462:
2459:
2455:
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2447:
2444:
2440:
2436:
2432:
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2421:
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2414:
2410:
2406:
2405:
2392:
2383:
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2370:
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2365:
2356:
2347:
2338:
2329:
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2311:
2302:
2295:
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2235:
2226:
2217:
2208:
2199:
2189:
2186:
2183:
2180:
2176:
2175:
2171:
2162:
2153:
2144:
2135:
2126:
2117:
2108:
2099:
2090:
2080:
2076:
2074:Meikle, p. 91
2073:
2072:
2068:
2058:
2055:
2054:
2050:
2040:
2037:
2036:
2032:
2023:
2014:
2005:
1996:
1990:Ishii, p. 226
1987:
1978:
1969:
1960:
1954:Awang, p. 296
1951:
1942:
1932:
1929:
1928:
1924:
1918:Cohen, p. 220
1915:
1906:
1896:
1894:Hilty, p. 425
1893:
1890:
1889:
1885:
1875:
1873:pp. 3-68–3-70
1872:
1869:
1868:
1864:
1854:
1852:Misra, p. 276
1851:
1848:
1847:
1843:
1833:
1830:
1826:
1825:
1821:
1815:, pp. 180–181
1814:
1808:
1799:
1792:
1786:
1779:
1773:
1766:
1760:
1754:, pp. 191–192
1753:
1747:
1740:
1734:
1727:
1721:
1714:
1708:
1698:
1694:
1691:
1690:
1686:
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1628:
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1614:
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1590:
1587:
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1559:
1558:
1554:
1545:
1536:
1526:
1525:
1521:
1511:
1507:
1504:
1501:
1499:Gupta, p. 5.5
1498:
1495:
1491:
1488:
1487:
1483:
1473:
1470:
1466:
1465:
1461:
1452:
1443:
1434:
1424:
1420:
1418:Nguyen, p. 28
1417:
1416:
1412:
1405:
1399:
1395:
1388:
1386:
1381:
1380:Dwight Isbell
1377:
1373:
1369:
1365:
1361:
1356:
1354:
1350:
1346:
1341:
1338:
1334:
1329:
1327:
1323:
1319:
1313:
1310:
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1302:
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1268:
1259:
1254:
1250:
1246:
1236:
1233:
1229:
1225:
1221:
1217:
1215:
1211:
1207:
1203:
1199:
1191:
1187:
1186:surface-mount
1182:
1173:
1153:
1147:
1142:
1137:
1130:
1125:
1120:
1113:
1108:
1103:
1097:
1092:
1086:
1076:
1075:
1074:
1072:
1068:
1064:
1059:
1057:
1053:
1049:
1044:
1042:
1038:
1034:
1027:
1015:
1006:
1004:
1001:
1000:antenna array
997:
993:
989:
985:
979:
977:
973:
969:
965:
961:
957:
952:
941:
932:
930:
925:
922:
921:power divider
918:
912:
910:
909:isolated port
906:
896:
891:
881:
877:
875:
871:
866:
864:
860:
851:
847:
842:
837:
822:
820:
816:
812:
808:
798:
796:
792:
787:
785:
780:
769:
768:is required.
767:
763:
759:
758:Hilbert curve
755:
751:
747:
742:
740:
736:
731:
727:
723:
719:
715:
706:
701:
691:
689:
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674:
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647:
643:
639:
629:
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618:
609:
605:
600:
591:
589:
585:
580:
578:
571:Coupled lines
568:
566:
557:
553:
551:
544:
534:
526:
523:
518:
508:
505:
501:
494:
489:
484:
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364:
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346:
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328:
324:
319:
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311:
309:
305:
301:
297:
289:
284:
275:
273:
269:
265:
261:
257:
253:
250:(PCBs) using
249:
240:
234:
229:
223:
219:
215:
211:
207:
203:
199:
195:
191:
187:
183:
179:
175:
162:
158:
153:
149:
147:
143:
139:
135:
130:
128:
124:
120:
116:
115:coupled lines
112:
108:
103:
101:
97:
93:
89:
85:
81:
77:
74:cheaply as a
71:
69:
65:
61:
57:
53:
49:
45:
41:
34:
30:
26:
21:
3425:
3411:
3396:
3381:
3374:
3355:
3340:
3333:
3314:
3299:
3292:
3281:
3262:
3240:
3233:
3214:
3199:
3184:
3169:
3154:
3139:
3124:
3117:
3106:
3060:
3045:
3030:
3015:
3000:
2993:
2974:
2959:
2944:
2937:
2918:
2903:
2888:
2873:
2861:, IET, 2001
2858:
2843:
2828:
2813:
2801:, IET, 2000
2798:
2782:
2766:
2751:
2736:
2735:Gupta, S K,
2729:
2710:
2695:
2680:
2665:
2650:
2643:
2624:
2609:
2594:
2579:
2564:
2557:
2538:
2523:
2516:
2509:
2494:
2479:
2464:
2449:
2434:
2427:
2408:
2402:Bibliography
2391:
2382:
2364:
2355:
2346:
2337:
2328:
2319:
2310:
2301:
2293:
2288:
2279:
2270:
2261:
2243:
2234:
2225:
2216:
2207:
2202:Borden, p. 3
2198:
2178:
2170:
2165:Mason (1961)
2161:
2156:Mason (1930)
2152:
2143:
2134:
2125:
2116:
2107:
2098:
2089:
2078:
2067:
2049:
2031:
2022:
2013:
2004:
1995:
1986:
1977:
1968:
1959:
1950:
1941:
1923:
1914:
1905:
1884:
1863:
1842:
1828:
1820:
1812:
1807:
1798:
1790:
1785:
1777:
1772:
1764:
1759:
1751:
1746:
1738:
1733:
1725:
1720:
1712:
1707:
1696:
1685:
1676:
1667:
1658:
1649:
1640:
1623:
1616:
1608:
1599:
1581:
1570:
1566:Mason (1961)
1553:
1544:
1535:
1520:
1509:
1493:
1482:
1468:
1460:
1451:
1442:
1433:
1422:
1411:
1403:
1398:
1357:
1342:
1330:
1314:
1301:World War II
1298:
1287:
1264:
1230:, where the
1218:
1195:
1170:
1067:S-parameters
1060:
1050:, where the
1045:
1029:
980:
976:interference
963:
955:
946:
926:
920:
916:
913:
908:
905:coupled port
904:
901:
878:
867:
855:
811:terminations
804:
791:horn antenna
788:
775:
743:
738:
735:pre-fractals
734:
711:
676:
661:
635:
613:
581:
574:
562:
546:
532:
514:
497:
452:
425:Coaxial line
423:
391:Lecher lines
379:twisted pair
375:
352:
320:
312:
293:
241:
171:
142:broadcasting
134:World War II
131:
104:
72:
64:transformers
39:
38:
3298:Roer, T G,
2510:Electronics
1855:Lee, p. 100
1699:, pp. 12–14
1653:Lee, p. 787
1471:, pp. 45–46
1425:, pp. 35–36
1406:, pp. 35–37
1370:, a set of
1206:transistors
1009:Circulators
992:attenuators
964:hybrid ring
852:stub filter
844:Microstrip
807:attenuators
779:transitions
762:Peano curve
726:out-of-band
712:The use of
190:capacitance
127:circulators
3432:Categories
3420:9533070838
3405:1420036866
3390:0471715824
3364:0849389518
3349:0852268580
3323:8121935377
3308:1461525004
3271:9533072474
3249:0080533531
3223:0471398209
3208:364232861X
3193:0471478733
3178:0471720607
3163:1596932430
3069:1608072061
3054:0080492053
3039:3662043254
3024:0849302692
3009:1608075834
2983:0521835267
2968:0815516134
2953:1608078329
2927:0471089192
2912:1107081971
2897:0123746965
2882:1420041312
2867:0852967772
2852:0471464201
2837:0471221651
2822:1608074897
2807:0852967942
2760:0890061572
2745:8187224754
2719:1107170273
2704:1608075354
2674:0932764061
2659:1118936191
2633:160807756X
2618:1461243386
2603:9814366064
2588:0470020458
2573:047144474X
2547:1420069004
2532:8122400523
2503:3319434705
2488:8184317220
2473:1608077128
2458:0470462310
2443:981445124X
2417:0470036958
1615:Magnusson
1492:Magnusson
1391:References
1372:transforms
1353:Microstrip
1275:dispersion
1243:See also:
1214:parasitics
1063:reciprocal
1056:Gunn diode
1026:Circulator
1005:networks.
819:thick-film
722:multi-band
698:See also:
686:and lower
588:resonators
511:Mechanical
504:resonators
455:microstrip
429:dielectric
402:feed lines
343:ideal line
222:wavelength
194:inductance
56:capacitors
33:microstrip
3148:830829462
3133:0026-2897
2292:Matthaei
2265:Ahn, p. 3
2081:, pp. 6–7
1789:Janković
1776:Janković
1763:Janković
1750:Janković
1737:Janković
1711:Janković
1695:Doumanis
1467:Doumanis
1421:Vendelin
1402:Vendelin
1345:stripline
1337:Leo Young
1326:magic tee
1322:Bell Labs
1305:broadcast
1294:Bell Labs
1210:substrate
1071:symmetric
929:bandwidth
846:band-pass
815:thin-film
809:and line
718:wide-band
642:Resonance
477:Waveguide
463:stripline
397:used for
395:twin-lead
308:prototype
233:microwave
218:frequency
202:capacitor
107:resonator
88:waveguide
68:microwave
60:inductors
2177:Johnson
2077:Lacomme
1793:, p. 196
1780:, p. 196
1767:, p. 196
1741:, p. 191
1728:, p. 237
1724:Ramadan
1715:, p. 197
1626:, p. 433
1619:, p. 199
1569:Johnson
1496:, p. 240
1041:duplexer
1037:isolator
857:include
850:low-pass
786:design.
694:Fractals
608:duplexer
577:coupling
393:and the
206:inductor
198:resistor
2792:6884353
2775:3388033
2689:2205252
1512:, p. 73
1299:Before
1239:History
1190:biasing
1033:ferrite
935:Hybrids
859:fractal
766:cascade
714:fractal
690:bands.
467:finline
408:Coaxial
399:antenna
361:quality
244:500 MHz
119:filters
84:coaxial
52:passive
3418:
3403:
3388:
3362:
3347:
3321:
3306:
3269:
3247:
3221:
3206:
3191:
3176:
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3067:
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3037:
3022:
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2880:
2865:
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2687:
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2296:(1964)
2294:et al.
2179:et al.
2079:et al.
1829:et al.
1813:et al.
1791:et al.
1778:et al.
1765:et al.
1752:et al.
1739:et al.
1726:et al.
1713:et al.
1697:et al.
1624:et al.
1617:et al.
1571:et al.
1510:et al.
1494:et al.
1469:et al.
1423:et al.
1404:et al.
1251:, and
1202:diodes
998:, and
956:hybrid
760:, and
443:Planar
125:, and
98:, and
62:, and
1827:Garg
1811:Garg
1622:Garg
1508:Chen
1054:of a
1019:1 GHz
772:Taper
679:helix
500:modes
437:ports
367:Media
237:1 GHz
214:phase
138:radar
111:stubs
92:radar
3416:ISBN
3401:ISBN
3386:ISBN
3360:ISBN
3345:ISBN
3319:ISBN
3304:ISBN
3267:ISBN
3245:ISBN
3219:ISBN
3204:ISBN
3189:ISBN
3174:ISBN
3159:ISBN
3144:OCLC
3129:ISSN
3065:ISBN
3050:ISBN
3035:ISBN
3020:ISBN
3005:ISBN
2979:ISBN
2964:ISBN
2949:ISBN
2923:ISBN
2908:ISBN
2893:ISBN
2878:ISBN
2863:ISBN
2848:ISBN
2833:ISBN
2818:ISBN
2803:ISBN
2788:OCLC
2771:OCLC
2756:ISBN
2741:ISBN
2715:ISBN
2700:ISBN
2685:OCLC
2670:ISBN
2655:ISBN
2629:ISBN
2614:ISBN
2599:ISBN
2584:ISBN
2569:ISBN
2543:ISBN
2528:ISBN
2499:ISBN
2484:ISBN
2469:ISBN
2454:ISBN
2439:ISBN
2413:ISBN
1232:gain
1224:FETs
1003:feed
793:and
720:and
621:dual
537:Stub
226:300
192:and
86:and
42:are
1347:by
966:or
876:).
817:or
737:or
688:UHF
684:VHF
602:An
385:on
333:of
228:MHz
204:or
184:of
3434::
3373:,
3332:,
3291:,
3280:,
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3116:,
3105:,
2992:,
2936:,
2728:,
2642:,
2556:,
2426:,
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1247:,
1216:.
1204:,
994:,
990:,
986:,
951:dB
949:3
865:.
756:,
752:,
748:,
636:A
491:A
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258:.
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1098:(
1093:=
1090:]
1087:S
1084:[
35:.
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