2004:
to two non-inverted pulses on the coupled line that travel in opposite direction to each other. When the pulse on the main line leaves the coupled line an inverted signal is induced on the coupled line, triggering two inverted impulses that travel in opposite direction to each other. Both impulses on the coupled line that go in the same direction as the pulse on the main line are of opposite polarity. They cancel each other so there is no response on the exit of the coupled line in forward direction. This is the decoupled port. The pulses on the coupled line that travel in the opposite direction to the pulse on the main line are also of opposite polarity to each other but the second impulse is delayed by twice the delay of the parallel line. For a λ/4 coupled-line the total delay length is λ/2 so the second signal is inverted and this gives a maximum response on the coupled port.
2403:λ/4 transmission lines. The input is fed to both lines in parallel and the outputs are terminated with twice the system impedance bridged between them. The design can be realised in planar format but it has a more natural implementation in coax – in planar, the two lines have to be kept apart so that they do not couple but have to be brought together at their outputs so they can be terminated whereas in coax the lines can be run side-by-side relying on the coax outer conductors for screening. The Wilkinson power divider solves the matching problem of the simple T-junction: it has low VSWR at all ports and high isolation between output ports. The input and output impedances at each port are designed to be equal to the characteristic impedance of the microwave system. This is achieved by making the line impedance
1944:
2210:
2222:
1920:
3514:
1854:
1905:
3105:
3312:
2036:
110:
132:. Port 1 is the input port where power is applied. Port 3 is the coupled port where a portion of the power applied to port 1 appears. Port 2 is the transmitted port where the power from port 1 is outputted, less the portion that went to port 3. Directional couplers are frequently symmetrical so there also exists port 4, the isolated port. A portion of the power applied to port 2 will be coupled to port 4. However, the device is not normally used in this mode and port 4 is usually terminated with a
2917:
22:
3065:
3529:
2336:
140:
371:
2631:
2241:
3254:
3358:
2379:
38:
2347:
three ports of a passive, lossless three-port and poor isolation is unavoidable. It is, however, possible with four-ports and this is the fundamental reason why four-port devices are used to implement three-port power dividers: four-port devices can be designed so that power arriving at port 2 is split between port 1 and port 4 (which is terminated with a matching load) and none (in the ideal case) goes to port 3.
3558:
4249:
3027:
2866:
1872:). An implementation in stripline is shown in figure 4 of a quarter-wavelength (λ/4) directional coupler. The power on the coupled line flows in the opposite direction to the power on the main line, hence the port arrangement is not the same as shown in figure 1, but the numbering remains the same. For this reason it is sometimes called a
1435:
1108:
2613:
2851:
3540:
isolated port: a representative example from figure 21 is shown in figure 22. Note that there is an additional fixed 90° phase shift to both ports at each combiner/divider which is not shown in the diagrams for simplicity. Applying in-phase power to both input ports would not get the desired result: the
3127:
is possible. In figure 17 a circuit is shown which is meant for weak coupling and can be understood along these lines: A signal is coming in one line pair. One transformer reduces the voltage of the signal the other reduces the current. Therefore, the impedance is matched. The same argument holds for
3047:. These two junctions split power equally, but because of the different field configurations at the junction, the electric fields at the output arms are in phase for the H-plane tee and are 180° out of phase for the E-plane tee. The combination of these two tees to form a hybrid tee is known as the
2953:
The
Schwinger reversed-phase coupler is another design using parallel waveguides, this time the long side of one is common with the short side-wall of the other. Two off-centre slots are cut between the waveguides spaced λ/4 apart. The Schwinger is a backward coupler. This design has the advantage
2931:
The concept of the Bethe-hole coupler can be extended by providing multiple holes. The holes are spaced λ/4 apart. The design of such couplers has parallels with the multiple section coupled transmission lines. Using multiple holes allows the bandwidth to be extended by designing the sections as a
2856:
The hybrid ring is not symmetric on its ports; choosing a different port as the input does not necessarily produce the same results. With port 1 or port 3 as the input the hybrid ring is a 0° hybrid as stated. However using port 2 or port 4 as the input results in a 180° hybrid. This fact leads to
2649:
directional coupler consisting of a 3λ/2 ring of transmission line with four lines at the intervals shown in figure 12. Power input at port 1 splits and travels both ways round the ring. At ports 2 and 3 the signal arrives in phase and adds whereas at port 4 it is out of phase and cancels. Ports 2
2251:
The branch-line coupler consists of two parallel transmission lines physically coupled together with two or more branch lines between them. The branch lines are spaced λ/4 apart and represent sections of a multi-section filter design in the same way as the multiple sections of a coupled-line coupler
2003:
is an odd integer. This preferred response gets obvious when a short impulse on the main line is followed through the coupler. When the impulse on the main line reaches the coupled line a signal of the same polarity is induced on the coupled line similar to the response of an RC-high-pass. This leads
356:
since more than this would result in more power output from the coupled port than power from the transmitted port – in effect their roles would be reversed. Although a negative quantity, the minus sign is frequently dropped (but still implied) in running text and diagrams and a few authors go so far
72:
enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. Power entering the output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power equally
1123:
The directivity should be as high as possible. The directivity is very high at the design frequency and is a more sensitive function of frequency because it depends on the cancellation of two wave components. Waveguide directional couplers will have the best directivity. Directivity is not directly
3085:
The standard 3 dB hybrid transformer is shown in figure 16. Power at port 1 is split equally between ports 2 and 3 but in antiphase to each other. The hybrid transformer is therefore a 180° hybrid. The centre-tap is usually terminated internally but it is possible to bring it out as port 4;
2346:
The earliest transmission line power dividers were simple T-junctions. These suffer from very poor isolation between the output ports – a large part of the power reflected back from port 2 finds its way into port 3. It can be shown that it is not theoretically possible to simultaneously match all
100:
Directional couplers and power dividers have many applications. These include providing a signal sample for measurement or monitoring, feedback, combining feeds to and from antennas, antenna beam forming, providing taps for cable distributed systems such as cable TV, and separating transmitted and
1975:
other than the usual TEM mode found in conductive circuits. The propagation velocities of even and odd modes are different leading to signal dispersion. A better solution for microstrip is a coupled line much shorter than λ/4, shown in figure 5, but this has the disadvantage of a coupling factor
1954:
Accuracy of coupling factor depends on the dimensional tolerances for the spacing of the two coupled lines. For planar printed technologies this comes down to the resolution of the printing process which determines the minimum track width that can be produced and also puts a limit on how close the
3334:
balanced telecommunication lines if the insertion loss is not an issue. The resistors in the bridge which represent ports are not usually part of the device (with the exception of port 4 which may well be left permanently terminated internally) these being provided by the line terminations. The
3576:
device normally has a very poor match and reflects much of the incident energy. However, since the devices are essentially identical the reflection coefficients from each device are equal. The reflected voltage from the FETs are in phase at the isolated port and are 180° different at the input
3539:
The phases of the inputs to each power combiner are arranged such that the two inputs are 90° out of phase with each other. Since the coupled port of a hybrid combiner is 90° out of phase with the transmitted port, this causes the powers to add at the output of the combiner and to cancel at the
2278:
of the system impedance. The more sections there are in the coupler, the higher is the ratio of impedances of the branch lines. High impedance lines have narrow tracks and this usually limits the design to three sections in planar formats due to manufacturing limitations. A similar limitation
1887:
is the section between ports 3 and 4. Since the directional coupler is a linear device, the notations on figure 1 are arbitrary. Any port can be the input, (an example is seen in figure 20) which will result in the directly connected port being the transmitted port, the adjacent port being the
2927:
One of the most common, and simplest, waveguide directional couplers is the Bethe-hole directional coupler. This consists of two parallel waveguides, one stacked on top of the other, with a hole between them. Some of the power from one guide is launched through the hole into the other. The
1970:
The λ/4 coupled-line design is good for coaxial and stripline implementations but does not work so well in the now popular microstrip format, although designs do exist. The reason for this is that microstrip is not a homogeneous medium – there are two different mediums above and below the
2881:. The drawback is that for a four channel multiplexer, the output consists of only 1/4 the power from each, and is relatively inefficient. The reason for this is that at each combiner half the input power goes to port 4 and is dissipated in the termination load. If the two inputs were
3476:
radar antenna systems. Both in-phase devices (such as the
Wilkinson divider) and quadrature (90°) hybrid couplers may be used for coherent power divider applications. An example of quadrature hybrids being used in a coherent power combiner application is given in the next section.
2365:
coupler with outputs 90° out of phase. Now any matched 4-port with isolated arms and equal power division is called a hybrid or hybrid coupler. Other types can have different phase relationships. If 90°, it is a 90° hybrid, if 180°, a 180° hybrid and so on. In this article
2885:
the phases could be so arranged that cancellation occurred at port 4 and then all the power would go to port 1. However, multiplexer inputs are usually from entirely independent sources and therefore not coherent. Lossless multiplexing can only be done with filter networks.
1980:
than the main line such as shown in figure 6. This design is advantageous where the coupler is being fed to a detector for power monitoring. The higher impedance line results in a higher RF voltage for a given main line power making the work of the detector diode easier.
3086:
in which case the hybrid can be used as a sum and difference hybrid. However, port 4 presents as a different impedance to the other ports and will require an additional transformer for impedance conversion if it is required to use this port at the same system impedance.
361:
quantity. Coupling is not constant, but varies with frequency. While different designs may reduce the variance, a perfectly flat coupler theoretically cannot be built. Directional couplers are specified in terms of the coupling accuracy at the frequency band center.
2962:
The Moreno crossed-guide coupler has two waveguides stacked one on top of the other like the Bethe-hole coupler but at right angles to each other instead of parallel. Two off-centre holes, usually cross-shaped are cut on the diagonal between the waveguides a distance
3509:
Since hybrid circuits are bi-directional, they can be used to coherently combine power as well as splitting it. In figure 21, an example is shown of a signal split up to feed multiple low power amplifiers, then recombined to feed a single antenna with high power.
3456:. Therefore, the isolators are used in figure 20 to effectively increase the isolation (or directivity) of the directional coupler. Consequently, the injection loss will be the isolation of the directional coupler plus the reverse isolation of the isolator.
2650:
and 3 are in phase with each other, hence this is an example of a 0° hybrid. Figure 12 shows a planar implementation but this design can also be implemented in coax or waveguide. It is possible to produce a coupler with a coupling factor different from
1834:
The phase difference between the two output ports of a hybrid coupler should be 0°, 90°, or 180° depending on the type used. However, like amplitude balance, the phase difference is sensitive to the input frequency and typically will vary a few degrees.
2932:
Butterworth, Chebyshev, or some other filter class. The hole size is chosen to give the desired coupling for each section of the filter. Design criteria are to achieve a substantially flat coupling together with high directivity over the desired band.
2857:
another useful application of the hybrid ring: it can be used to produce sum (Σ) and difference (Δ) signals from two input signals as shown in figure 12. With inputs to ports 2 and 3, the Σ signal appears at port 1 and the Δ signal appears at port 4.
2295:, which in some applications cause an unacceptable amount of coupling between the lines being crossed. An ideal branch-line crossover theoretically has no coupling between the two paths through it. The design is a 3-branch coupler equivalent to two
1315:
925:
2287:
hybrids. Branch-line couplers usually do not have such a wide bandwidth as coupled lines. This style of coupler is good for implementing in high-power, air dielectric, solid bar formats as the rigid structure is easy to mechanically support.
2457:
792:
Isolation can also be defined between the two output ports. In this case, one of the output ports is used as the input; the other is considered the output port while the other two ports (input and isolated) are terminated by matched loads.
2940:
The Riblet short-slot coupler is two waveguides side-by-side with the side-wall in common instead of the long side as in the Bethe-hole coupler. A slot is cut in the sidewall to allow coupling. This design is frequently used to produce a
2701:
136:(typically 50 ohms). This termination can be internal to the device and port 4 is not accessible to the user. Effectively, this results in a 3-port device, hence the utility of the second symbol for directional couplers in figure 1.
3544:
sum of the two inputs would appear at both output ports – that is half the total power out of each. This approach allows the use of numerous less expensive and lower-power amplifiers in the circuitry instead of a single high-power
603:
490:
3584:
will occur directly between the antennas. To receive a signal in that position, one would have to either change the hybrid type or line length. To reject a signal from a given direction, or create the difference pattern for a
887:
788:
333:
2012:. The sections of the coupler are treated as being sections of a filter, and by adjusting the coupling factor of each section the coupled port can be made to have any of the classic filter responses such as maximally flat (
2007:
A single λ/4 coupled section is good for bandwidths of less than an octave. To achieve greater bandwidths multiple λ/4 coupling sections are used. The design of such couplers proceeds in much the same way as the design of
1888:
coupled port, and the diagonal port being the isolated port. On some directional couplers, the main line is designed for high power operation (large connectors), while the coupled port may use a small connector, such as an
3276:. The tee circuit has the benefits of simplicity, low cost, and intrinsically wide bandwidth. It has two major drawbacks; first, the circuit will dissipate power since it is resistive: an equal split will result in
1606:
3348:
The coupled output from the directional coupler can be used to monitor frequency and power level on the signal without interrupting the main power flow in the system (except for a power reduction – see figure 3).
80:
Directional couplers are most frequently constructed from two coupled transmission lines set close enough together such that energy passing through one is coupled to the other. This technique is favoured at the
3000:
apart. The Moreno coupler is good for tight coupling applications. It is a compromise between the properties of the Bethe-hole and
Schwinger couplers with both coupling and directivity varying with frequency.
2876:
A typical power divider is shown in figure 13. Ideally, input power would be divided equally between the output ports. Dividers are made up of multiple couplers and, like couplers, may be reversed and used as
3492:
and other devices. Multiport splitters with more than two output ports usually consist internally of a number of cascaded couplers. Domestic broadband internet service can be provided by cable TV companies
3095:
Hybrid transformers are commonly used in telecommunications for 2 to 4 wire conversion. Telephone handsets include such a converter to convert the 2-wire line to the 4 wires from the earpiece and mouthpiece.
3272:. The delta form uses resistors that are equal to the system impedance. This can be advantageous because precision resistors of the value of the system impedance are always available for most system
2198:
607:
The insertion loss of an ideal directional coupler will consist entirely of the coupling loss. In a real directional coupler, however, the insertion loss consists of a combination of coupling loss,
1295:
1207:
694:
Isolation of a directional coupler can be defined as the difference in signal levels in dB between the input port and the isolated port when the two other ports are terminated by matched loads, or:
4253:
1794:
2998:
1703:
2954:
of a substantially flat directivity response and the disadvantage of a strongly frequency-dependent coupling compared to the Bethe-hole coupler, which has little variation in coupling factor.
2135:
3448:, or even injection phase locking. Because of the symmetry of the directional coupler, the reverse injection will happen with the same possible modulation problems of signal generator F
3231:
2283:; low coupling also requires narrow tracks. Coupled lines are a better choice when loose coupling is required, but branch-line couplers are good for tight coupling and can be used for
2209:
2682:
2427:
2276:
3577:
port. Therefore, all of the reflected power from the FETs goes to the load at the isolated port and no power goes to the input port. This results in a good input match (low VSWR).
1864:
The most common form of directional coupler is a pair of coupled transmission lines. They can be realised in a number of technologies including coaxial and the planar technologies (
1430:{\displaystyle \mathbf {S} ={\begin{bmatrix}0&\tau &\kappa &0\\\tau &0&0&\kappa \\\kappa &0&0&\tau \\0&\kappa &\tau &0\end{bmatrix}}}
189:
891:
The isolation between the input and the isolated ports may be different from the isolation between the two output ports. For example, the isolation between ports 1 and 4 can be
3183:
1103:{\displaystyle D_{3,4}=-10\log {\left({\frac {P_{4}}{P_{3}}}\right)}=-10\log {\left({\frac {P_{4}}{P_{1}}}\right)}+10\log {\left({\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}}
3549:. Yet another approach is to have each solid state amplifier (SSA) feed an antenna and let the power be combined in space or be used to feed a lens attached to an antenna.
97:
designs can be used. Many of these waveguide couplers correspond to one of the conducting transmission line designs, but there are also types that are unique to waveguide.
2608:{\displaystyle \mathbf {S} ={\frac {1}{\sqrt {2}}}{\begin{bmatrix}0&-i&-1&0\\-i&0&0&-1\\-1&0&0&-i\\0&-1&-i&0\end{bmatrix}}}
1967:
sides of the dielectric rather than side by side. The coupling of the two lines across their width is much greater than the coupling when they are edge-on to each other.
3326:
A true hybrid divider/coupler with, theoretically, infinite isolation and directivity can be made from a resistive bridge circuit. Like the tee circuit, the bridge has
2846:{\displaystyle \mathbf {S} ={\frac {1}{\sqrt {2}}}{\begin{bmatrix}0&-i&-i&0\\-i&0&0&i\\-i&0&0&-i\\0&i&-i&0\end{bmatrix}}}
2090:
1729:
1536:
1486:
2067:
1635:
1513:
1461:
3268:
A simple tee circuit of resistors can be used as a power divider as shown in figure 18. This circuit can also be implemented as a delta circuit by applying the
2361:
coupled-line directional couplers, that is, directional couplers in which the two outputs are each half the input power. This synonymously meant a quadrature
504:
3128:
every other direction of a signal through the coupler. The relative sign of the induced voltage and current determines the direction of the outgoing signal.
1806:
Some authors define the port numbers with ports 3 and 4 interchanged. This results in a scattering matrix that is no longer all-zeroes on the antidiagonal.
399:
799:
700:
248:
3043:
Coherent power division was first accomplished by means of simple Tee junctions. At microwave frequencies, waveguide tees have two possible forms – the
3330:
insertion loss. It has the disadvantage that it cannot be used with unbalanced circuits without the addition of transformers; however, it is ideal for
3245:
power divider based on this circuit has the two outputs in 180° phase to each other, compared to λ/4 coupled lines which have a 90° phase relationship.
1984:
The frequency range specified by manufacturers is that of the coupled line. The main line response is much wider: for instance a coupler specified as
213:
tends to be used for 4-port devices that are only loosely coupled – that is, only a small fraction of the input power appears at the coupled port.
3608:. More generally, phase-difference couplers, together with fixed phase delays and antenna arrays, are used in beam-forming networks such as the
4409:
1559:
209:
A symbol for power dividers is shown in figure 2. Power dividers and directional couplers are in all essentials the same class of device.
237:
at all ports when the other ports are terminated in matched loads. Some of these, and other, general characteristics are discussed below.
2221:
348:
The coupling factor represents the primary property of a directional coupler. Coupling factor is a negative quantity, it cannot exceed
2092:
purely imaginary at all frequencies. This leads to a simplification of the S-matrix and the result that the coupled port is always in
619:
coupling where the other losses constitute the majority of the total loss. The theoretical insertion loss (dB) vs coupling (dB) for a
3051:. The magic tee is a four-port component which can perform the vector sum (Σ) and difference (Δ) of two coherent microwave signals.
217:
is used for devices with tight coupling (commonly, a power divider will provide half the input power at each of its output ports – a
3299:
at port 2. Isolation can be improved at the expense of insertion loss at both output ports by replacing the output resistors with
2252:
except that here the coupling of each section is controlled with the impedance of the branch lines. The main and coupled line are
1546:
are a consequence of perfect matching – power input to any port is not reflected back to that same port. The zeroes on the matrix
2143:
4550:
1218:
1130:
2316:
1737:
903:. The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some
2966:
1643:
2099:
1976:
which rises noticeably with frequency. A variation of this design sometimes encountered has the coupled line a higher
3572:
circuits. For example, in a balanced microwave amplifier the two input stages are fed through a hybrid coupler. The
4517:
4502:
4487:
4472:
4443:
4428:
4402:
4387:
4372:
4357:
4331:
4316:
4301:
4286:
2307:
coupler. It will cross over the inputs to the diagonally opposite outputs with a phase delay of 90° in both lines.
1995:. The coupled response is periodic with frequency. For example, a λ/4 coupled-line coupler will have responses at
3368:
If isolation is high, directional couplers are good for combining signals to feed a single line to a receiver for
33:
directional coupler. From left to right: input, coupled, isolated (terminated with a load), and transmitted port.
3204:
2661:
2406:
2255:
4545:
230:
64:
used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a
85:
frequencies where transmission line designs are commonly used to implement many circuit elements. However,
1963:
which also permits manufacture by printed planar technology. In this design the two lines are printed on
1822:. However, in a practical device the amplitude balance is frequency dependent and departs from the ideal
1124:
measurable, and is calculated from the addition of the isolation and (negative) coupling measurements as:
156:
4309:
100 Years of
Telephone Switching (1878–1978): Electronics, computers, and telephone switching (1960–1985)
2319:
with paralleled lines interleaved to achieve the coupling. It is used for strong couplings in the range
3137:
4540:
3580:
If phase-matched lines are used for an antenna input to a 180° hybrid coupler as shown in figure 23, a
2009:
1309:
for an ideal (infinite isolation and perfectly matched) symmetrical directional coupler is given by,
120:
The symbols most often used for directional couplers are shown in figure 1. The symbol may have the
3124:
1955:
lines can be placed to each other. This becomes a problem when very tight coupling is required and
1943:
3201:
coupling, that is equal splitting of the signal between the transmitted port and the coupled port,
1977:
3573:
2451:
it is called a hybrid coupler. The S-matrix for an ideal, symmetric hybrid coupler reduces to;
2396:
2390:
2096:
phase (90°) with the output port. Some applications make use of this phase difference. Letting
61:
2072:
1711:
1518:
1468:
2215:
Microstrip directional coupler on the output of a local oscillator on a spectrum analyser PCB.
2049:
1617:
1495:
1443:
1306:
129:
89:
devices are also possible at lower frequencies, such as the audio frequencies encountered in
69:
3417:
86:
3408:
loss. The internal load on the isolated port will dissipate the signal losses from port P
1959:
couplers often use a different design. However, tightly coupled lines can be produced in
8:
4339:"Beam forming networks of optimum size and compactness for multibeam antennas at 900 MHz"
3546:
3044:
2882:
2642:
612:
598:{\displaystyle L_{c2,1}=-10\log {\left(1-{\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}}
2300:
2013:
1919:
234:
133:
3513:
1814:
This terminology defines the power difference in dB between the two output ports of a
1611:
since the power entering the input port must all leave by one of the other two ports.
615:
loss. Depending on the frequency range, coupling loss becomes less significant above
485:{\displaystyle L_{i2,1}=-10\log {\left({\frac {P_{2}}{P_{1}}}\right)}\quad {\rm {dB}}}
4513:
4498:
4483:
4468:
4454:
4439:
4424:
4398:
4383:
4368:
4353:
4327:
4312:
4297:
4282:
3291:
The insertion loss is not such a problem for an unequal split of power: for instance
3273:
1803:, and non-zero antidiagonal entries are related to isolation by similar expressions.
882:{\displaystyle I_{3,2}=-10\log {\left({\frac {P_{3}}{P_{2}}}\right)}\quad {\rm {dB}}}
783:{\displaystyle I_{4,1}=-10\log {\left({\frac {P_{4}}{P_{1}}}\right)}\quad {\rm {dB}}}
65:
2654:
by making each λ/4 section of the ring alternately low and high impedance but for a
328:{\displaystyle C_{3,1}=10\log {\left({\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}}
3541:
3429:
3369:
3090:
2093:
2025:
2021:
1893:
1853:
4260:
Electronic
Warfare and Radar Systems Engineering Handbook (report number TS 92-78)
3269:
3104:
2032:, usually quoted as plus or minus a value in dB from the nominal coupling factor.
1212:
Note that if the positive definition of coupling is used, the formula results in:
3586:
3465:
3335:
device thus consists essentially of two resistors (plus the port 4 termination).
1972:
1904:
904:
3568:
The phase properties of a 90° hybrid coupler can be used to great advantage in
3494:
3485:
3311:
2916:
2447:
directional couplers are described above. When the coupling is designed to be
1950:. Lumped-element equivalent circuit of the couplers depicted in figures 5 and 6
1539:
494:
Part of this loss is due to some power going to the coupled port and is called
382:
4338:
3520:. Splitter and combiner networks used with amplifiers to produce a high power
2292:
2035:
109:
4534:
3626:
3609:
3601:
2357:
1960:
1889:
1543:
495:
3233:
and the isolated port is terminated in twice the characteristic impedance –
1550:
are a consequence of perfect isolation between the input and isolated port.
229:
Common properties desired for all directional couplers are wide operational
21:
3621:
3605:
3581:
3473:
2017:
1547:
895:
while the isolation between ports 2 and 3 can be a different value such as
4458:
3480:
An inexpensive version of the power divider is used in the home to divide
4258:
3528:
3498:
3080:
3064:
2878:
1800:
900:
620:
2335:
4451:
Microwave
Filters, Impedance-Matching Networks, and Coupling Structures
3469:
3441:
3303:. The isolation improvement is greater than the insertion loss added.
1869:
1601:{\displaystyle \tau {\overline {\tau }}+\kappa {\overline {\kappa }}=1}
608:
139:
4263:. Avionics Department of the Naval Air Warfare Center Weapons Division
2630:
2240:
1553:
For a passive lossless directional coupler, we must in addition have,
370:
3593:
3569:
3288:
directivity leading to very poor isolation between the output ports.
3120:
3048:
3038:
1865:
908:
94:
90:
82:
4480:
Radio engineering for wireless communication and sensor applications
4273: (pp. 6–4.1 to 6–4.5 Power Dividers and Directional Couplers).
3253:
2378:
2291:
Branch line couplers can be used as crossovers as an alternative to
3481:
3357:
2029:
37:
4343:
IEEE Antennas and
Propagation Society International Symposium 1997
919:
Directivity is directly related to isolation. It is defined as:
125:
93:. Also at microwave frequencies, particularly the higher bands,
26:
3489:
623:
coupler is shown in the graph of figure 3 and the table below.
2247:. A 3-section branch-line coupler implemented in planar format
2028:
is the maximum variation in output of the coupled port in its
1818:
hybrid. In an ideal hybrid circuit, the difference should be
3420:
in figure 20 are neglected, the isolation measurement (port P
3300:
2928:
Bethe-hole coupler is another example of a backward coupler.
1987:
30:
3026:
2046:
It can be shown that coupled-line directional couplers have
4510:
RF design guide: systems, circuits, and equations, Volume 1
4410:"Angular beamforming technique for MIMO beamforming system"
3557:
1896:
power rating may also limit operation on the coupled line.
4408:
Apinya Innok, Peerapong
Uthansakul, Monthippa Uthansakul,
3464:
Applications of the hybrid include monopulse comparators,
2865:
2193:{\displaystyle \tau ^{2}+{\kappa _{\mathrm {I} }}^{2}=1\ }
1542:, frequency dependent, numbers. The zeroes on the matrix
345:
is the output power from the coupled port (see figure 1).
3597:
4421:
Handbook of
Microwave Technology: Components and devices
2315:
The construction of the Lange coupler is similar to the
1290:{\displaystyle D_{3,4}=I_{4,1}-C_{3,1}\quad {\rm {dB}}}
1202:{\displaystyle D_{3,4}=I_{4,1}+C_{3,1}\quad {\rm {dB}}}
3612:, to create a radio beam in any prescribed direction.
3208:
3018:
discussed above can also be implemented in waveguide.
2970:
2908:
described above can also be implemented in waveguide.
2730:
2665:
2486:
2410:
2259:
2137:, the ideal case of lossless operation simplifies to,
1332:
352:
for a passive device, and in practice does not exceed
3207:
3140:
2969:
2704:
2664:
2460:
2409:
2258:
2146:
2102:
2075:
2052:
1740:
1714:
1646:
1620:
1562:
1521:
1498:
1471:
1446:
1318:
1221:
1133:
928:
899:. Isolation can be estimated from the coupling plus
802:
703:
507:
402:
251:
159:
4449:
Matthaei, George L.; Young, Leo and Jones, E. M. T.
3604:, by delaying the phase to the lower elements of an
221:
divider) and is usually considered a 3-port device.
2948:
2645:, also called the rat-race coupler, is a four-port
2618:
The two output ports have a 90° phase difference (-
2370:without qualification means a coupled-line hybrid.
2342:. Simple T-junction power division in planar format
1789:{\displaystyle C(\mathrm {dB} )=20\log |\kappa |\ }
911:directional couplers will have the best isolation.
4277:Stephen J. Bigelow, Joseph J. Carr, Steve Winder,
3440:. As the injection level increases, it may cause
3225:
3177:
2993:{\displaystyle \scriptstyle {\sqrt {2}}\lambda /4}
2992:
2845:
2676:
2607:
2421:
2270:
2192:
2129:
2084:
2061:
1788:
1723:
1698:{\displaystyle L(\mathrm {dB} )=-20\log |\tau |\ }
1697:
1629:
1600:
1530:
1507:
1480:
1455:
1429:
1289:
1201:
1102:
881:
782:
597:
484:
327:
183:
4414:International Journal of Antennas and Propagation
3436:that will be injected into the signal generator F
2911:
2894:
2130:{\displaystyle \kappa =i\kappa _{\mathrm {I} }\ }
4532:
3592:Phase-difference couplers can be used to create
2899:
3535:. Phase arrangement on a hybrid power combiner.
3306:
3099:
2957:
2444:
2042:. A 5-section planar format directional coupler
1116:is the output power from the coupled port and P
4493:K.R. Reddy, S. B. Badami, V. Balasubramanian,
1991:might have a main line which could operate at
1799:Non-zero main diagonal entries are related to
2433:system the Wilkinson lines are approximately
1883:is the section between ports 1 and 2 and the
1848:
128:marked on it. Directional couplers have four
4296:, Institution of Electrical Engineers, 1993
3733:For instance, Räisänen and Lehto, pp.120–122
2935:
1120:is the power output from the isolated port.
194:in this article have the meaning "parameter
4337:R. Comitangelo, D. Minervini, B. Piovano,
3004:
2860:
116:. Two symbols used for directional couplers
4465:A Handbook for EMC Testing and Measurement
3501:is connected to one port of the splitter.
3428:) determines the amount of power from the
3352:
3295:at port 3 has an insertion loss less than
3226:{\displaystyle \scriptstyle n={\sqrt {2}}}
2695:The S-matrix for this hybrid is given by;
2373:
1928:. Short section directional coupler with
1838:
41:A 3 dB 2.0–4.2 GHz power divider/combiner.
4350:Survey of instrumentation and measurement
3985:Naval Air Warfare Center, pp.6.4.4, 6.4.5
3917:Naval Air Warfare Center, pp.6.4.1, 6.4.3
3372:. In figure 20, one signal enters port P
3054:
2279:applies for coupling factors looser than
377:. Graph of insertion loss due to coupling
4169:Naval Air Warfare Center, pp.6.4.3–6.4.4
4160:Naval Air Warfare Center, pp.6.4.2–6.4.3
3556:
3527:
3524:(voltage gain 100) solid state amplifier
3512:
3356:
3310:
3252:
3193:is the secondary to primary turns ratio.
3111:. Directional coupler using transformers
3103:
3063:
3025:
3015:
3009:
2915:
2905:
2864:
2677:{\displaystyle \scriptstyle {\sqrt {2}}}
2629:
2422:{\displaystyle \scriptstyle {\sqrt {2}}}
2377:
2334:
2271:{\displaystyle \scriptstyle {\sqrt {2}}}
2239:
2034:
1942:
1860:. Single-section λ/4 directional coupler
1852:
369:
138:
108:
36:
20:
3284:. The second problem is that there is
2688:design the ring would be approximately
2227:Microstrip sawtooth directional coupler
1843:
104:
4533:
3318:. 6 dB resistive bridge hybrid for a
3260:. Simple resistive tee circuit for a
2637:. Hybrid ring coupler in planar format
2625:
2235:
3059:
2385:. Wilkinson divider in coaxial format
101:received signals on telephone lines.
4525:Impulsantwort eines Leitungskopplers
4416:, vol. 2012, iss. 11, December 2012.
4294:Principles of Microwave Measurements
2622:to −1) and so this is a 90° hybrid.
1913:. Short section directional coupler
1809:
1463:is the transmission coefficient and,
245:The coupling factor is defined as:
184:{\displaystyle P_{\mathrm {a,b} }\ }
121:
4326:, Prentice Hall Professional, 2003
4279:Understanding telephone electronics
3564:. Phase combination of two antennas
3552:
3396:of loss, and the signal from port P
1971:transmission strip. This leads to
341:is the input power at port 1 and P
13:
4395:Practical Radio-frequency Handbook
3504:
3178:{\displaystyle C_{3,1}=20\log n\ }
2923:. A multi-hole directional coupler
2889:
2168:
2118:
1751:
1748:
1657:
1654:
1282:
1279:
1194:
1191:
1095:
1092:
874:
871:
775:
772:
590:
587:
477:
474:
320:
317:
240:
172:
166:
14:
4562:
4527:, CQ DL, vol. 7, pp. 28-31, 2020.
4307:Robert J. Chapuis, Amos E. Joel,
4225:Naval Air Warfare Center, p.6.4.4
4216:Naval Air Warfare Center, p.6.4.3
4207:Naval Air Warfare Center, p.6.4.5
4151:Naval Air Warfare Center, p.6.4.1
4069:Naval Air Warfare Center, p.6.4.4
3930:Naval Air Warfare Center, p.6.4.4
3830:Naval Air Warfare Center, p.6.4.1
3812:Naval Air Warfare Center, p.6.4.1
3786:Naval Air Warfare Center, p.6.4.1
3777:Naval Air Warfare Center, p.6.4.1
3751:Naval Air Warfare Center, p.6.4.3
3742:Naval Air Warfare Center, p.6.4.3
3711:Naval Air Warfare Center, p.6.4.3
3702:Naval Air Warfare Center, p.6.4.2
3693:Naval Air Warfare Center, p.6.4.2
3682:Naval Air Warfare Center, p.6.4.1
3664:Naval Air Warfare Center, p.6.4.1
3646:Naval Air Warfare Center, p.6-4.1
3497:). The domestic user's internet
3115:For lower frequencies (less than
3071:. 3 dB hybrid transformer for a
2439:
2330:
2299:90° hybrid couplers connected in
4252: This article incorporates
4247:
3970:Räisänen and Lehto, pp. 122, 127
3248:
2949:Schwinger reversed-phase coupler
2706:
2658:coupler the entire ring is made
2462:
2429:of the system impedance – for a
2310:
2220:
2208:
1918:
1903:
1829:
1320:
4478:Antti V. Räisänen, Arto Lehto,
4365:Mobile Antenna Systems Handbook
4242:
4228:
4219:
4210:
4201:
4192:
4183:
4172:
4163:
4154:
4145:
4136:
4127:
4118:
4109:
4100:
4085:
4076:
4063:
4054:
4045:
4036:
4027:
4014:
4003:
3988:
3973:
3964:
3955:
3952:Räisänen and Lehto, pp. 126–127
3942:
3933:
3920:
3911:
3902:
3893:
3880:
3867:
3850:
3839:
3824:
3815:
3806:
3795:
3780:
3771:
3754:
3745:
3736:
3727:
3338:
2684:of the port impedances – for a
2303:. The result is effectively a
1300:
1276:
1188:
1089:
907:power will always be present.
868:
769:
627:Insertion loss due to coupling
584:
471:
314:
233:, high directivity, and a good
4436:Antenna Handbook: Applications
4345:, vol. 4, pp. 2127-2130, 1997.
4073:Räisänen and Lehto, pp.123–124
4024:Räisänen and Lehto, pp.122–123
3908:Räisänen and Lehto, pp.117–118
3801:Räisänen and Lehto, pp.124–126
3724:Räisänen and Lehto, pp.120–122
3714:
3705:
3696:
3687:
3676:
3667:
3658:
3649:
3638:
3364:. Two-tone receiver test setup
2912:Bethe-hole directional coupler
2895:Waveguide directional couplers
1779:
1771:
1755:
1744:
1708:Coupling factor is related to
1688:
1680:
1661:
1650:
914:
73:between two ports is called a
1:
3928:Räisänen and Lehto, p.118-119
3847:Räisänen and Lehto, p.120-122
3632:
3468:, power combiners, dividers,
3343:
2900:Waveguide branch-line coupler
1614:Insertion loss is related to
224:
4551:Distributed element circuits
3307:6 dB resistive bridge hybrid
3100:Cross-connected transformers
3021:
2958:Moreno crossed-guide coupler
1587:
1571:
689:
7:
4497:, Universities Press, 1994
3673:For instance; Morgan, p.149
3615:
3589:, this is a good approach.
3123:implementation by means of
2010:distributed-element filters
1488:is the coupling coefficient
52:and, when used in reverse,
10:
4567:
3459:
3384:. The signal from port P
3280:insertion loss instead of
3131:The coupling is given by;
3088:
3078:
3036:
2388:
2020:), or a specified-ripple (
1849:Coupled transmission lines
611:loss, conductor loss, and
146:. Symbol for power divider
4189:Räisänen and Lehto, p.116
3899:Räisänen and Lehto, p.126
3864:Räisänen and Lehto, p.127
3655:Räisänen and Lehto, p.116
2936:Riblet short-slot coupler
2399:consists of two parallel
2085:{\displaystyle \kappa \ }
1724:{\displaystyle \kappa \ }
1531:{\displaystyle \kappa \ }
1481:{\displaystyle \kappa \ }
3380:, while both exit port P
3005:Waveguide power dividers
2861:Multiple output dividers
385:from port 1 to port 2 (P
202:due to an input at port
16:Radio technology devices
4423:, Academic Press, 1995
4382:, Que Publishing, 1998
4097:Chapuis and Joel, p.512
3370:two-tone receiver tests
3353:Making use of isolation
2397:Wilkinson power divider
2391:Wilkinson power divider
2374:Wilkinson power divider
2062:{\displaystyle \tau \ }
1839:Transmission line types
1630:{\displaystyle \tau \ }
1508:{\displaystyle \tau \ }
1456:{\displaystyle \tau \ }
365:
4495:Oscillations And Waves
4380:How the Internet Works
4254:public domain material
3565:
3536:
3525:
3365:
3323:
3265:
3227:
3179:
3112:
3076:
3055:Discrete element types
3034:
2994:
2924:
2873:
2847:
2678:
2638:
2609:
2423:
2386:
2354:originally applied to
2343:
2272:
2248:
2194:
2131:
2086:
2063:
2043:
1951:
1861:
1790:
1725:
1699:
1631:
1602:
1532:
1509:
1482:
1457:
1431:
1291:
1203:
1104:
883:
784:
599:
486:
378:
329:
185:
147:
117:
42:
34:
4512:, Artech House, 1995
4482:, Artech House, 2003
4434:Y. T. Lo, S. W. Lee,
4367:, Artech House, 2008
4324:Home Networking Basis
4106:Vizmuller, pp.107–108
3803:Vizmuller, pp.102–103
3792:, pp.585–588, 776–778
3560:
3531:
3516:
3444:of signal generator F
3376:and one enters port P
3360:
3314:
3256:
3228:
3180:
3107:
3067:
3029:
3010:Waveguide hybrid ring
2995:
2919:
2868:
2848:
2679:
2633:
2610:
2424:
2381:
2338:
2273:
2243:
2195:
2132:
2087:
2064:
2038:
1946:
1856:
1791:
1726:
1700:
1632:
1603:
1533:
1510:
1483:
1458:
1432:
1292:
1204:
1105:
884:
785:
600:
487:
373:
357:as to define it as a
330:
186:
150:Symbols of the form;
142:
112:
40:
24:
4546:Microwave technology
4419:Thomas Koryu Ishii,
4234:Fujimoto, pp.199–201
4020:Ishii, pp.205–6, 209
3488:signals to multiple
3205:
3138:
2967:
2702:
2662:
2458:
2407:
2256:
2144:
2100:
2073:
2050:
1844:Directional couplers
1738:
1712:
1644:
1618:
1560:
1519:
1496:
1469:
1444:
1316:
1219:
1131:
926:
800:
701:
505:
400:
249:
157:
105:Notation and symbols
58:directional couplers
3045:E-plane and H-plane
2906:branch-line coupler
2643:hybrid ring coupler
2626:Hybrid ring coupler
2317:interdigital filter
2236:Branch-line coupler
628:
211:Directional coupler
4311:, IOS Press, 2003
4236:Lo and Lee, p.27.7
4142:Bryant, pp.114–115
3948:Ishii, pp. 229–230
3566:
3537:
3526:
3366:
3324:
3274:nominal impedances
3266:
3223:
3222:
3175:
3113:
3077:
3060:Hybrid transformer
3035:
2990:
2989:
2925:
2874:
2843:
2837:
2674:
2673:
2639:
2605:
2599:
2419:
2418:
2387:
2344:
2268:
2267:
2249:
2190:
2127:
2082:
2059:
2044:
2014:Butterworth filter
1973:transmission modes
1952:
1862:
1786:
1721:
1695:
1627:
1598:
1528:
1505:
1478:
1453:
1427:
1421:
1287:
1199:
1100:
879:
780:
626:
595:
482:
379:
325:
181:
148:
118:
43:
35:
4541:Radio electronics
4508:Peter Vizmuller,
4453:McGraw-Hill 1964
4438:, Springer, 1993
4363:Kyōhei Fujimoto,
4352:Wiley-IEEE, 2001
4348:Stephen A. Dyer,
4292:Geoff H. Bryant,
4124:Hickman, pp.49–50
4082:Hickman, pp.50–51
4051:Ishii, pp.212–213
4042:Ishii, pp.211–212
4000:Ishii, pp.223–226
3856:Ishii, pp.223–226
3220:
3174:
2976:
2723:
2722:
2671:
2479:
2478:
2416:
2265:
2189:
2126:
2081:
2058:
2016:), equal-ripple (
1810:Amplitude balance
1785:
1720:
1694:
1626:
1590:
1574:
1527:
1504:
1477:
1452:
1082:
1036:
987:
861:
762:
687:
686:
576:
498:and is given by:
464:
307:
180:
66:transmission line
4558:
4378:Preston Gralla,
4322:Walter Y. Chen,
4272:
4270:
4268:
4251:
4250:
4237:
4232:
4226:
4223:
4217:
4214:
4208:
4205:
4199:
4196:
4190:
4187:
4181:
4180:Gralla, pp.61-62
4176:
4170:
4167:
4161:
4158:
4152:
4149:
4143:
4140:
4134:
4131:
4125:
4122:
4116:
4115:Vizmuller, p.108
4113:
4107:
4104:
4098:
4089:
4083:
4080:
4074:
4067:
4061:
4058:
4052:
4049:
4043:
4040:
4034:
4031:
4025:
4018:
4012:
4007:
4001:
3992:
3986:
3977:
3971:
3968:
3962:
3959:
3953:
3946:
3940:
3937:
3931:
3924:
3918:
3915:
3909:
3906:
3900:
3897:
3891:
3884:
3878:
3871:
3865:
3854:
3848:
3843:
3837:
3828:
3822:
3819:
3813:
3810:
3804:
3799:
3793:
3784:
3778:
3775:
3769:
3768:Vizmuller, p.101
3758:
3752:
3749:
3743:
3740:
3734:
3731:
3725:
3718:
3712:
3709:
3703:
3700:
3694:
3691:
3685:
3684:Vizmuller, p.101
3680:
3674:
3671:
3665:
3662:
3656:
3653:
3647:
3642:
3553:Phase difference
3523:
3430:signal generator
3407:
3395:
3392:will experience
3333:
3329:
3321:
3298:
3294:
3287:
3283:
3279:
3263:
3244:
3240:
3236:
3232:
3230:
3229:
3224:
3221:
3216:
3200:
3184:
3182:
3181:
3176:
3172:
3156:
3155:
3118:
3091:Telephone hybrid
3074:
2999:
2997:
2996:
2991:
2985:
2977:
2972:
2944:
2852:
2850:
2849:
2844:
2842:
2841:
2724:
2718:
2714:
2709:
2691:
2687:
2683:
2681:
2680:
2675:
2672:
2667:
2657:
2653:
2648:
2614:
2612:
2611:
2606:
2604:
2603:
2480:
2474:
2470:
2465:
2450:
2436:
2432:
2428:
2426:
2425:
2420:
2417:
2412:
2364:
2360:
2326:
2322:
2306:
2298:
2286:
2282:
2277:
2275:
2274:
2269:
2266:
2261:
2224:
2212:
2199:
2197:
2196:
2191:
2187:
2180:
2179:
2174:
2173:
2172:
2171:
2156:
2155:
2136:
2134:
2133:
2128:
2124:
2123:
2122:
2121:
2091:
2089:
2088:
2083:
2079:
2069:purely real and
2068:
2066:
2065:
2060:
2056:
2022:Chebychev filter
1994:
1990:
1958:
1935:
1931:
1922:
1907:
1874:backward coupler
1825:
1821:
1817:
1795:
1793:
1792:
1787:
1783:
1782:
1774:
1754:
1730:
1728:
1727:
1722:
1718:
1704:
1702:
1701:
1696:
1692:
1691:
1683:
1660:
1636:
1634:
1633:
1628:
1624:
1607:
1605:
1604:
1599:
1591:
1583:
1575:
1567:
1537:
1535:
1534:
1529:
1525:
1514:
1512:
1511:
1506:
1502:
1487:
1485:
1484:
1479:
1475:
1462:
1460:
1459:
1454:
1450:
1436:
1434:
1433:
1428:
1426:
1425:
1323:
1296:
1294:
1293:
1288:
1286:
1285:
1275:
1274:
1256:
1255:
1237:
1236:
1208:
1206:
1205:
1200:
1198:
1197:
1187:
1186:
1168:
1167:
1149:
1148:
1109:
1107:
1106:
1101:
1099:
1098:
1088:
1087:
1083:
1081:
1080:
1071:
1070:
1061:
1042:
1041:
1037:
1035:
1034:
1025:
1024:
1015:
993:
992:
988:
986:
985:
976:
975:
966:
944:
943:
898:
894:
888:
886:
885:
880:
878:
877:
867:
866:
862:
860:
859:
850:
849:
840:
818:
817:
789:
787:
786:
781:
779:
778:
768:
767:
763:
761:
760:
751:
750:
741:
719:
718:
629:
625:
618:
604:
602:
601:
596:
594:
593:
583:
582:
578:
577:
575:
574:
565:
564:
555:
526:
525:
491:
489:
488:
483:
481:
480:
470:
469:
465:
463:
462:
453:
452:
443:
421:
420:
396:Insertion loss:
355:
351:
334:
332:
331:
326:
324:
323:
313:
312:
308:
306:
305:
296:
295:
286:
267:
266:
220:
190:
188:
187:
182:
178:
177:
176:
175:
87:lumped component
4566:
4565:
4561:
4560:
4559:
4557:
4556:
4555:
4531:
4530:
4397:, Newnes, 2006
4266:
4264:
4257:
4248:
4245:
4240:
4235:
4233:
4229:
4224:
4220:
4215:
4211:
4206:
4202:
4197:
4193:
4188:
4184:
4179:
4177:
4173:
4168:
4164:
4159:
4155:
4150:
4146:
4141:
4137:
4132:
4128:
4123:
4119:
4114:
4110:
4105:
4101:
4096:
4090:
4086:
4081:
4077:
4072:
4070:
4068:
4064:
4059:
4055:
4050:
4046:
4041:
4037:
4032:
4028:
4023:
4021:
4019:
4015:
4010:
4008:
4004:
3999:
3993:
3989:
3984:
3978:
3974:
3969:
3965:
3960:
3956:
3951:
3949:
3947:
3943:
3938:
3934:
3929:
3927:
3925:
3921:
3916:
3912:
3907:
3903:
3898:
3894:
3885:
3881:
3872:
3868:
3863:
3857:
3855:
3851:
3846:
3844:
3840:
3831:
3829:
3825:
3820:
3816:
3811:
3807:
3802:
3800:
3796:
3787:
3785:
3781:
3776:
3772:
3767:
3761:
3759:
3755:
3750:
3746:
3741:
3737:
3732:
3728:
3723:
3721:
3719:
3715:
3710:
3706:
3701:
3697:
3692:
3688:
3683:
3681:
3677:
3672:
3668:
3663:
3659:
3654:
3650:
3645:
3643:
3639:
3635:
3618:
3587:monopulse radar
3555:
3521:
3507:
3505:Power combiners
3486:over-the-air TV
3462:
3455:
3451:
3447:
3439:
3435:
3427:
3423:
3415:
3411:
3405:
3403:
3399:
3393:
3391:
3387:
3383:
3379:
3375:
3355:
3346:
3341:
3331:
3327:
3319:
3309:
3296:
3292:
3285:
3281:
3277:
3261:
3251:
3242:
3238:
3234:
3215:
3206:
3203:
3202:
3198:
3145:
3141:
3139:
3136:
3135:
3125:RF transformers
3116:
3102:
3093:
3083:
3072:
3062:
3057:
3041:
3024:
3012:
3007:
2981:
2971:
2968:
2965:
2964:
2960:
2951:
2942:
2938:
2914:
2902:
2897:
2892:
2890:Waveguide types
2872:. Power Divider
2863:
2836:
2835:
2830:
2822:
2817:
2811:
2810:
2802:
2797:
2792:
2783:
2782:
2777:
2772:
2767:
2758:
2757:
2752:
2744:
2736:
2726:
2725:
2713:
2705:
2703:
2700:
2699:
2689:
2685:
2666:
2663:
2660:
2659:
2655:
2651:
2646:
2628:
2598:
2597:
2592:
2584:
2576:
2570:
2569:
2561:
2556:
2551:
2542:
2541:
2533:
2528:
2523:
2514:
2513:
2508:
2500:
2492:
2482:
2481:
2469:
2461:
2459:
2456:
2455:
2448:
2442:
2434:
2430:
2411:
2408:
2405:
2404:
2393:
2376:
2362:
2355:
2333:
2324:
2320:
2313:
2304:
2296:
2284:
2280:
2260:
2257:
2254:
2253:
2238:
2233:
2232:
2231:
2228:
2225:
2216:
2213:
2175:
2167:
2166:
2162:
2161:
2160:
2151:
2147:
2145:
2142:
2141:
2117:
2116:
2112:
2101:
2098:
2097:
2074:
2071:
2070:
2051:
2048:
2047:
1992:
1985:
1956:
1941:
1940:
1939:
1938:
1937:
1933:
1929:
1923:
1915:
1914:
1908:
1851:
1846:
1841:
1832:
1823:
1819:
1815:
1812:
1778:
1770:
1747:
1739:
1736:
1735:
1713:
1710:
1709:
1687:
1679:
1653:
1645:
1642:
1641:
1619:
1616:
1615:
1582:
1566:
1561:
1558:
1557:
1520:
1517:
1516:
1497:
1494:
1493:
1470:
1467:
1466:
1445:
1442:
1441:
1420:
1419:
1414:
1409:
1404:
1398:
1397:
1392:
1387:
1382:
1376:
1375:
1370:
1365:
1360:
1354:
1353:
1348:
1343:
1338:
1328:
1327:
1319:
1317:
1314:
1313:
1303:
1278:
1277:
1264:
1260:
1245:
1241:
1226:
1222:
1220:
1217:
1216:
1190:
1189:
1176:
1172:
1157:
1153:
1138:
1134:
1132:
1129:
1128:
1119:
1115:
1091:
1090:
1076:
1072:
1066:
1062:
1060:
1056:
1055:
1030:
1026:
1020:
1016:
1014:
1010:
1009:
981:
977:
971:
967:
965:
961:
960:
933:
929:
927:
924:
923:
917:
896:
892:
870:
869:
855:
851:
845:
841:
839:
835:
834:
807:
803:
801:
798:
797:
796:Consequently:
771:
770:
756:
752:
746:
742:
740:
736:
735:
708:
704:
702:
699:
698:
692:
635:Insertion loss
621:dissipationless
616:
586:
585:
570:
566:
560:
556:
554:
547:
543:
542:
512:
508:
506:
503:
502:
501:Coupling loss:
473:
472:
458:
454:
448:
444:
442:
438:
437:
407:
403:
401:
398:
397:
392:
388:
368:
353:
349:
344:
340:
316:
315:
301:
297:
291:
287:
285:
281:
280:
256:
252:
250:
247:
246:
243:
241:Coupling factor
235:impedance match
227:
218:
165:
164:
160:
158:
155:
154:
122:coupling factor
107:
62:passive devices
54:power combiners
50:power splitters
17:
12:
11:
5:
4564:
4554:
4553:
4548:
4543:
4529:
4528:
4521:
4506:
4491:
4476:
4461:
4447:
4432:
4417:
4406:
4391:
4376:
4361:
4346:
4335:
4320:
4305:
4290:
4244:
4241:
4239:
4238:
4227:
4218:
4209:
4200:
4191:
4182:
4171:
4162:
4153:
4144:
4135:
4126:
4117:
4108:
4099:
4084:
4075:
4062:
4053:
4044:
4035:
4026:
4013:
4002:
3987:
3972:
3963:
3954:
3950:Morgan, p. 150
3941:
3932:
3919:
3910:
3901:
3892:
3879:
3877:, p. 2127-2128
3866:
3849:
3838:
3823:
3814:
3805:
3794:
3779:
3770:
3753:
3744:
3735:
3726:
3713:
3704:
3695:
3686:
3675:
3666:
3657:
3648:
3636:
3634:
3631:
3630:
3629:
3624:
3617:
3614:
3554:
3551:
3506:
3503:
3495:cable internet
3461:
3458:
3453:
3449:
3445:
3437:
3433:
3425:
3421:
3413:
3409:
3401:
3397:
3389:
3385:
3381:
3377:
3373:
3354:
3351:
3345:
3342:
3340:
3337:
3308:
3305:
3250:
3247:
3219:
3214:
3211:
3195:
3194:
3186:
3185:
3171:
3168:
3165:
3162:
3159:
3154:
3151:
3148:
3144:
3101:
3098:
3089:Main article:
3079:Main article:
3061:
3058:
3056:
3053:
3037:Main article:
3023:
3020:
3011:
3008:
3006:
3003:
2988:
2984:
2980:
2975:
2959:
2956:
2950:
2947:
2937:
2934:
2913:
2910:
2901:
2898:
2896:
2893:
2891:
2888:
2862:
2859:
2854:
2853:
2840:
2834:
2831:
2829:
2826:
2823:
2821:
2818:
2816:
2813:
2812:
2809:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2785:
2784:
2781:
2778:
2776:
2773:
2771:
2768:
2766:
2763:
2760:
2759:
2756:
2753:
2751:
2748:
2745:
2743:
2740:
2737:
2735:
2732:
2731:
2729:
2721:
2717:
2712:
2708:
2670:
2627:
2624:
2616:
2615:
2602:
2596:
2593:
2591:
2588:
2585:
2583:
2580:
2577:
2575:
2572:
2571:
2568:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2544:
2543:
2540:
2537:
2534:
2532:
2529:
2527:
2524:
2522:
2519:
2516:
2515:
2512:
2509:
2507:
2504:
2501:
2499:
2496:
2493:
2491:
2488:
2487:
2485:
2477:
2473:
2468:
2464:
2441:
2440:Hybrid coupler
2438:
2415:
2389:Main article:
2375:
2372:
2368:hybrid coupler
2352:hybrid coupler
2332:
2331:Power dividers
2329:
2312:
2309:
2264:
2237:
2234:
2230:
2229:
2226:
2219:
2217:
2214:
2207:
2204:
2203:
2202:
2201:
2200:
2186:
2183:
2178:
2170:
2165:
2159:
2154:
2150:
2120:
2115:
2111:
2108:
2105:
2078:
2055:
1932:main line and
1924:
1917:
1916:
1909:
1902:
1901:
1900:
1899:
1898:
1850:
1847:
1845:
1842:
1840:
1837:
1831:
1828:
1811:
1808:
1797:
1796:
1781:
1777:
1773:
1769:
1766:
1763:
1760:
1757:
1753:
1750:
1746:
1743:
1717:
1706:
1705:
1690:
1686:
1682:
1678:
1675:
1672:
1669:
1666:
1663:
1659:
1656:
1652:
1649:
1623:
1609:
1608:
1597:
1594:
1589:
1586:
1581:
1578:
1573:
1570:
1565:
1524:
1501:
1490:
1489:
1474:
1464:
1449:
1438:
1437:
1424:
1418:
1415:
1413:
1410:
1408:
1405:
1403:
1400:
1399:
1396:
1393:
1391:
1388:
1386:
1383:
1381:
1378:
1377:
1374:
1371:
1369:
1366:
1364:
1361:
1359:
1356:
1355:
1352:
1349:
1347:
1344:
1342:
1339:
1337:
1334:
1333:
1331:
1326:
1322:
1302:
1299:
1298:
1297:
1284:
1281:
1273:
1270:
1267:
1263:
1259:
1254:
1251:
1248:
1244:
1240:
1235:
1232:
1229:
1225:
1210:
1209:
1196:
1193:
1185:
1182:
1179:
1175:
1171:
1166:
1163:
1160:
1156:
1152:
1147:
1144:
1141:
1137:
1117:
1113:
1097:
1094:
1086:
1079:
1075:
1069:
1065:
1059:
1054:
1051:
1048:
1045:
1040:
1033:
1029:
1023:
1019:
1013:
1008:
1005:
1002:
999:
996:
991:
984:
980:
974:
970:
964:
959:
956:
953:
950:
947:
942:
939:
936:
932:
916:
913:
876:
873:
865:
858:
854:
848:
844:
838:
833:
830:
827:
824:
821:
816:
813:
810:
806:
777:
774:
766:
759:
755:
749:
745:
739:
734:
731:
728:
725:
722:
717:
714:
711:
707:
691:
688:
685:
684:
681:
677:
676:
673:
669:
668:
665:
661:
660:
657:
653:
652:
649:
645:
644:
641:
637:
636:
633:
592:
589:
581:
573:
569:
563:
559:
553:
550:
546:
541:
538:
535:
532:
529:
524:
521:
518:
515:
511:
479:
476:
468:
461:
457:
451:
447:
441:
436:
433:
430:
427:
424:
419:
416:
413:
410:
406:
390:
386:
383:insertion loss
381:The main line
367:
364:
342:
338:
322:
319:
311:
304:
300:
294:
290:
284:
279:
276:
273:
270:
265:
262:
259:
255:
242:
239:
226:
223:
192:
191:
174:
171:
168:
163:
106:
103:
75:hybrid coupler
46:Power dividers
15:
9:
6:
4:
3:
2:
4563:
4552:
4549:
4547:
4544:
4542:
4539:
4538:
4536:
4526:
4522:
4519:
4518:0-89006-754-6
4515:
4511:
4507:
4504:
4503:81-7371-018-X
4500:
4496:
4492:
4489:
4488:1-58053-542-9
4485:
4481:
4477:
4474:
4473:0-86341-756-6
4470:
4466:
4462:
4460:
4456:
4452:
4448:
4445:
4444:0-442-01594-1
4441:
4437:
4433:
4430:
4429:0-12-374696-5
4426:
4422:
4418:
4415:
4411:
4407:
4404:
4403:0-7506-8039-3
4400:
4396:
4393:Ian Hickman,
4392:
4389:
4388:0-7897-1726-3
4385:
4381:
4377:
4374:
4373:1-59693-126-4
4370:
4366:
4362:
4359:
4358:0-471-39484-X
4355:
4351:
4347:
4344:
4340:
4336:
4333:
4332:0-13-016511-5
4329:
4325:
4321:
4318:
4317:1-58603-372-7
4314:
4310:
4306:
4303:
4302:0-86341-296-3
4299:
4295:
4291:
4288:
4287:0-7506-7175-0
4284:
4281:Newnes, 2001
4280:
4276:
4275:
4274:
4262:
4261:
4255:
4231:
4222:
4213:
4204:
4195:
4186:
4175:
4166:
4157:
4148:
4139:
4133:Hickman, p.50
4130:
4121:
4112:
4103:
4094:
4088:
4079:
4066:
4060:Morgan, p.149
4057:
4048:
4039:
4030:
4022:Morgan, p.149
4017:
4011:Morgan, p.149
4006:
3997:
3991:
3982:
3976:
3967:
3961:Ishii, p. 201
3958:
3945:
3936:
3923:
3914:
3905:
3896:
3890:, pp. 2, 5, 7
3889:
3883:
3876:
3870:
3861:
3853:
3842:
3835:
3827:
3821:Franzen, p.30
3818:
3809:
3798:
3791:
3783:
3774:
3765:
3760:Morgan, p.149
3757:
3748:
3739:
3730:
3717:
3708:
3699:
3690:
3679:
3670:
3661:
3652:
3641:
3637:
3628:
3627:Beam splitter
3625:
3623:
3620:
3619:
3613:
3611:
3610:Butler matrix
3607:
3606:antenna array
3603:
3602:radio station
3599:
3595:
3590:
3588:
3583:
3578:
3575:
3571:
3563:
3559:
3550:
3548:
3543:
3534:
3530:
3519:
3515:
3511:
3502:
3500:
3496:
3491:
3487:
3483:
3478:
3475:
3471:
3467:
3457:
3443:
3431:
3419:
3371:
3363:
3359:
3350:
3336:
3317:
3313:
3304:
3302:
3289:
3275:
3271:
3270:Y-Δ transform
3259:
3255:
3249:Resistive tee
3246:
3217:
3212:
3209:
3192:
3188:
3187:
3169:
3166:
3163:
3160:
3157:
3152:
3149:
3146:
3142:
3134:
3133:
3132:
3129:
3126:
3122:
3110:
3106:
3097:
3092:
3087:
3082:
3070:
3066:
3052:
3050:
3046:
3040:
3032:
3028:
3019:
3017:
3002:
2986:
2982:
2978:
2973:
2955:
2946:
2933:
2929:
2922:
2918:
2909:
2907:
2887:
2884:
2880:
2871:
2867:
2858:
2838:
2832:
2827:
2824:
2819:
2814:
2807:
2804:
2799:
2794:
2789:
2786:
2779:
2774:
2769:
2764:
2761:
2754:
2749:
2746:
2741:
2738:
2733:
2727:
2719:
2715:
2710:
2698:
2697:
2696:
2693:
2668:
2644:
2636:
2632:
2623:
2621:
2600:
2594:
2589:
2586:
2581:
2578:
2573:
2566:
2563:
2558:
2553:
2548:
2545:
2538:
2535:
2530:
2525:
2520:
2517:
2510:
2505:
2502:
2497:
2494:
2489:
2483:
2475:
2471:
2466:
2454:
2453:
2452:
2446:
2437:
2413:
2402:
2398:
2392:
2384:
2380:
2371:
2369:
2359:
2353:
2348:
2341:
2337:
2328:
2318:
2311:Lange coupler
2308:
2302:
2294:
2289:
2262:
2246:
2242:
2223:
2218:
2211:
2206:
2205:
2184:
2181:
2176:
2163:
2157:
2152:
2148:
2140:
2139:
2138:
2113:
2109:
2106:
2103:
2095:
2076:
2053:
2041:
2037:
2033:
2031:
2027:
2024:) response.
2023:
2019:
2015:
2011:
2005:
2002:
1998:
1989:
1982:
1979:
1974:
1968:
1966:
1962:
1961:air stripline
1949:
1945:
1927:
1921:
1912:
1906:
1897:
1895:
1894:internal load
1891:
1890:SMA connector
1886:
1882:
1877:
1875:
1871:
1867:
1859:
1855:
1836:
1830:Phase balance
1827:
1807:
1804:
1802:
1775:
1767:
1764:
1761:
1758:
1741:
1734:
1733:
1732:
1715:
1684:
1676:
1673:
1670:
1667:
1664:
1647:
1640:
1639:
1638:
1621:
1612:
1595:
1592:
1584:
1579:
1576:
1568:
1563:
1556:
1555:
1554:
1551:
1549:
1545:
1544:main diagonal
1541:
1522:
1499:
1472:
1465:
1447:
1440:
1439:
1422:
1416:
1411:
1406:
1401:
1394:
1389:
1384:
1379:
1372:
1367:
1362:
1357:
1350:
1345:
1340:
1335:
1329:
1324:
1312:
1311:
1310:
1308:
1271:
1268:
1265:
1261:
1257:
1252:
1249:
1246:
1242:
1238:
1233:
1230:
1227:
1223:
1215:
1214:
1213:
1183:
1180:
1177:
1173:
1169:
1164:
1161:
1158:
1154:
1150:
1145:
1142:
1139:
1135:
1127:
1126:
1125:
1121:
1110:
1084:
1077:
1073:
1067:
1063:
1057:
1052:
1049:
1046:
1043:
1038:
1031:
1027:
1021:
1017:
1011:
1006:
1003:
1000:
997:
994:
989:
982:
978:
972:
968:
962:
957:
954:
951:
948:
945:
940:
937:
934:
930:
922:Directivity:
920:
912:
910:
906:
902:
889:
863:
856:
852:
846:
842:
836:
831:
828:
825:
822:
819:
814:
811:
808:
804:
794:
790:
764:
757:
753:
747:
743:
737:
732:
729:
726:
723:
720:
715:
712:
709:
705:
695:
682:
679:
678:
674:
671:
670:
666:
663:
662:
658:
655:
654:
650:
647:
646:
642:
639:
638:
634:
631:
630:
624:
622:
614:
610:
605:
579:
571:
567:
561:
557:
551:
548:
544:
539:
536:
533:
530:
527:
522:
519:
516:
513:
509:
499:
497:
496:coupling loss
492:
466:
459:
455:
449:
445:
439:
434:
431:
428:
425:
422:
417:
414:
411:
408:
404:
394:
384:
376:
372:
363:
360:
346:
335:
309:
302:
298:
292:
288:
282:
277:
274:
271:
268:
263:
260:
257:
253:
238:
236:
232:
222:
216:
215:Power divider
212:
207:
205:
201:
197:
169:
161:
153:
152:
151:
145:
141:
137:
135:
131:
127:
123:
115:
111:
102:
98:
96:
92:
88:
84:
78:
76:
71:
67:
63:
59:
55:
51:
47:
39:
32:
28:
23:
19:
4524:
4523:A. Franzen,
4509:
4494:
4479:
4467:, IET, 1994
4464:
4450:
4435:
4420:
4413:
4394:
4379:
4364:
4349:
4342:
4323:
4308:
4293:
4278:
4265:. Retrieved
4259:
4246:
4243:Bibliography
4230:
4221:
4212:
4203:
4198:Ishii, p.200
4194:
4185:
4174:
4165:
4156:
4147:
4138:
4129:
4120:
4111:
4102:
4092:
4087:
4078:
4071:Ishii, p.201
4065:
4056:
4047:
4038:
4033:Ishii, p.211
4029:
4016:
4009:Ishii, p.202
4005:
3998:, pp.811–812
3995:
3990:
3980:
3975:
3966:
3957:
3944:
3939:Ishii, p.200
3935:
3922:
3913:
3904:
3895:
3887:
3882:
3874:
3873:Comitangelo
3869:
3862:, pp.809–811
3859:
3852:
3845:Ishii, p.216
3841:
3836:, pp.775–777
3833:
3826:
3817:
3808:
3797:
3789:
3782:
3773:
3766:, pp.775–777
3763:
3756:
3747:
3738:
3729:
3722:Ishii, p.216
3716:
3707:
3698:
3689:
3678:
3669:
3660:
3651:
3644:Ishii, p.200
3640:
3622:Star coupler
3591:
3579:
3567:
3561:
3538:
3532:
3517:
3508:
3479:
3474:phased array
3463:
3367:
3361:
3347:
3339:Applications
3325:
3315:
3290:
3267:
3257:
3196:
3190:
3130:
3119:) a compact
3114:
3108:
3094:
3084:
3068:
3042:
3030:
3013:
2961:
2952:
2939:
2930:
2926:
2920:
2903:
2879:multiplexers
2875:
2869:
2855:
2694:
2640:
2634:
2619:
2617:
2445:Coupled-line
2443:
2400:
2394:
2382:
2367:
2351:
2349:
2345:
2339:
2314:
2290:
2250:
2244:
2045:
2039:
2018:Cauer filter
2006:
2000:
1996:
1983:
1969:
1964:
1953:
1947:
1936:coupled line
1925:
1910:
1885:coupled line
1884:
1880:
1878:
1873:
1863:
1857:
1833:
1826:difference.
1813:
1805:
1798:
1707:
1613:
1610:
1552:
1548:antidiagonal
1492:In general,
1491:
1304:
1301:S-parameters
1211:
1122:
1111:
921:
918:
890:
795:
791:
696:
693:
606:
500:
493:
395:
380:
374:
358:
347:
336:
244:
228:
214:
210:
208:
203:
199:
195:
193:
149:
143:
134:matched load
119:
113:
99:
79:
74:
57:
53:
49:
45:
44:
18:
4463:D. Morgan,
3983:, pp.60, 71
3926:Dyer, p.480
3720:Dyer, p.479
3499:cable modem
3404:will have
3241:system. A
3081:Hybrid coil
3033:. Magic tee
3016:hybrid ring
2293:air bridges
1801:return loss
915:Directivity
901:return loss
697:Isolation:
4535:Categories
4178:Chen, p.76
3633:References
3542:quadrature
3470:modulators
3442:modulation
3416:. If the
3412:and port P
3344:Monitoring
2094:quadrature
1999:λ/4 where
1870:microstrip
609:dielectric
225:Parameters
4459:299575271
3994:Matthaei
3858:Matthaei
3832:Matthaei
3788:Matthaei
3762:Matthaei
3594:beam tilt
3570:microwave
3562:Figure 23
3533:Figure 22
3518:Figure 21
3424:to port P
3418:isolators
3400:to port P
3388:to port P
3362:Figure 20
3316:Figure 19
3258:Figure 18
3167:
3121:broadband
3109:Figure 17
3069:Figure 16
3049:magic tee
3039:Magic tee
3031:Figure 15
3022:Magic tee
2979:λ
2945:coupler.
2921:Figure 14
2870:Figure 13
2825:−
2805:−
2787:−
2762:−
2747:−
2739:−
2635:Figure 12
2587:−
2579:−
2564:−
2546:−
2536:−
2518:−
2503:−
2495:−
2401:uncoupled
2383:Figure 11
2350:The term
2340:Figure 10
2164:κ
2149:τ
2114:κ
2104:κ
2077:κ
2054:τ
1978:impedance
1881:main line
1866:stripline
1776:κ
1768:
1716:κ
1685:τ
1677:
1668:−
1622:τ
1588:¯
1585:κ
1580:κ
1572:¯
1569:τ
1564:τ
1523:κ
1500:τ
1473:κ
1448:τ
1412:τ
1407:κ
1395:τ
1380:κ
1373:κ
1358:τ
1346:κ
1341:τ
1258:−
1053:
1007:
998:−
958:
949:−
909:Waveguide
832:
823:−
733:
724:−
690:Isolation
552:−
540:
531:−
435:
426:−
278:
231:bandwidth
95:waveguide
91:telephony
83:microwave
4091:Bigelow
3616:See also
3482:cable TV
2883:coherent
2245:Figure 9
2040:Figure 8
2030:passband
1965:opposite
1948:Figure 7
1926:Figure 6
1911:Figure 5
1858:Figure 4
1307:S-matrix
1112:where: P
683:0.00435
632:Coupling
375:Figure 3
359:positive
198:at port
144:Figure 2
114:Figure 1
29:1.7–2.2
4095:, p.211
3490:TV sets
3460:Hybrids
3117:600 MHz
2301:cascade
1993:1–5 GHz
1892:. The
1540:complex
675:0.0436
337:where P
4516:
4501:
4486:
4471:
4457:
4442:
4427:
4401:
4386:
4371:
4356:
4330:
4315:
4300:
4285:
4267:9 June
4093:et al.
3996:et al.
3981:et al.
3979:Reddy
3888:et al.
3886:Innok
3875:et al.
3860:et al.
3834:et al.
3790:et al.
3764:et al.
3472:, and
3466:mixers
3406:0.5 dB
3322:system
3301:T pads
3297:0.2 dB
3293:-40 dB
3264:system
3237:for a
3197:For a
3189:where
3173:
3075:system
2188:
2125:
2080:
2057:
2026:Ripple
1784:
1719:
1693:
1625:
1526:
1503:
1476:
1451:
667:0.458
393:) is:
179:
56:) and
48:(also
4256:from
3596:in a
3522:40 dB
3394:10 dB
3332:600 Ω
3320:600 Ω
3235:100 Ω
2281:10 dB
1934:100 Ω
897:25 dB
893:30 dB
659:1.25
651:3.00
617:15 dB
354:−3 dB
130:ports
68:to a
25:A 10
4514:ISBN
4499:ISBN
4484:ISBN
4469:ISBN
4455:OCLC
4440:ISBN
4425:ISBN
4399:ISBN
4384:ISBN
4369:ISBN
4354:ISBN
4328:ISBN
4313:ISBN
4298:ISBN
4283:ISBN
4269:2006
3582:null
3452:by F
3328:6 dB
3286:0 dB
3282:3 dB
3278:6 dB
3262:50 Ω
3243:3 dB
3239:50 Ω
3199:3 dB
3073:50 Ω
3014:The
2943:3 dB
2904:The
2690:70 Ω
2686:50 Ω
2656:3 dB
2652:3 dB
2647:3 dB
2641:The
2449:3 dB
2435:70 Ω
2431:50 Ω
2395:The
2363:3 dB
2325:6 dB
2321:3 dB
2305:0 dB
2297:3 dB
2285:3 dB
1986:2–4
1957:3 dB
1930:50 Ω
1879:The
1868:and
1824:0 dB
1820:0 dB
1816:3 dB
1731:by;
1637:by;
1538:are
1515:and
1305:The
613:VSWR
366:Loss
350:0 dB
219:3 dB
70:port
60:are
3600:FM
3598:VHF
3574:FET
3547:TWT
3484:or
3164:log
2323:to
1988:GHz
1765:log
1674:log
1050:log
1004:log
955:log
829:log
730:log
643:dB
537:log
432:log
389:– P
275:log
206:".
124:in
31:GHz
4537::
4412:,
4341:,
3161:20
2692:.
2358:dB
2356:3
2327:.
1876:.
1762:20
1671:20
1047:10
1001:10
952:10
905:RF
826:10
727:10
680:30
672:20
664:10
640:dB
534:10
429:10
272:10
126:dB
77:.
27:dB
4520:.
4505:.
4490:.
4475:.
4446:.
4431:.
4405:.
4390:.
4375:.
4360:.
4334:.
4319:.
4304:.
4289:.
4271:.
3493:(
3454:1
3450:2
3446:1
3438:1
3434:2
3432:F
3426:3
3422:2
3414:2
3410:3
3402:1
3398:2
3390:1
3386:3
3382:1
3378:2
3374:3
3218:2
3213:=
3210:n
3191:n
3170:n
3158:=
3153:1
3150:,
3147:3
3143:C
2987:4
2983:/
2974:2
2839:]
2833:0
2828:i
2820:i
2815:0
2808:i
2800:0
2795:0
2790:i
2780:i
2775:0
2770:0
2765:i
2755:0
2750:i
2742:i
2734:0
2728:[
2720:2
2716:1
2711:=
2707:S
2669:2
2620:i
2601:]
2595:0
2590:i
2582:1
2574:0
2567:i
2559:0
2554:0
2549:1
2539:1
2531:0
2526:0
2521:i
2511:0
2506:1
2498:i
2490:0
2484:[
2476:2
2472:1
2467:=
2463:S
2414:2
2263:2
2185:1
2182:=
2177:2
2169:I
2158:+
2153:2
2119:I
2110:i
2107:=
2001:n
1997:n
1780:|
1772:|
1759:=
1756:)
1752:B
1749:d
1745:(
1742:C
1689:|
1681:|
1665:=
1662:)
1658:B
1655:d
1651:(
1648:L
1596:1
1593:=
1577:+
1423:]
1417:0
1402:0
1390:0
1385:0
1368:0
1363:0
1351:0
1336:0
1330:[
1325:=
1321:S
1283:B
1280:d
1272:1
1269:,
1266:3
1262:C
1253:1
1250:,
1247:4
1243:I
1239:=
1234:4
1231:,
1228:3
1224:D
1195:B
1192:d
1184:1
1181:,
1178:3
1174:C
1170:+
1165:1
1162:,
1159:4
1155:I
1151:=
1146:4
1143:,
1140:3
1136:D
1118:4
1114:3
1096:B
1093:d
1085:)
1078:1
1074:P
1068:3
1064:P
1058:(
1044:+
1039:)
1032:1
1028:P
1022:4
1018:P
1012:(
995:=
990:)
983:3
979:P
973:4
969:P
963:(
946:=
941:4
938:,
935:3
931:D
875:B
872:d
864:)
857:2
853:P
847:3
843:P
837:(
820:=
815:2
812:,
809:3
805:I
776:B
773:d
765:)
758:1
754:P
748:4
744:P
738:(
721:=
716:1
713:,
710:4
706:I
656:6
648:3
591:B
588:d
580:)
572:1
568:P
562:3
558:P
549:1
545:(
528:=
523:1
520:,
517:2
514:c
510:L
478:B
475:d
467:)
460:1
456:P
450:2
446:P
440:(
423:=
418:1
415:,
412:2
409:i
405:L
391:2
387:1
343:3
339:1
321:B
318:d
310:)
303:1
299:P
293:3
289:P
283:(
269:=
264:1
261:,
258:3
254:C
204:b
200:a
196:P
173:b
170:,
167:a
162:P
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
