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63-445: Power dividers (also power splitters and, when used in reverse, power combiners ) and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port 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

126-782: A "storage function", is equivalent to passivity. For a given system with a known model, it is often easier to construct a storage function satisfying the differential inequality than directly computing the available energy, as taking the supremum on a collection of trajectories might require the use of calculus of variations . In circuit design , informally, passive components refer to ones that are not capable of power gain ; this means they cannot amplify signals. Under this definition, passive components include capacitors , inductors , resistors , diodes , transformers , voltage sources, and current sources. They exclude devices like transistors , vacuum tubes , relays , tunnel diodes, and glow tubes . To give other terminology, systems for which

189-505: A coupled-line hybrid. The Wilkinson power divider consists of two parallel uncoupled 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

252-709: A few authors go so far as to define it as a positive 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. The main line insertion loss from port 1 to port 2 (P 1 – P 2 ) is: Insertion loss: L i 2 , 1 = − 10 log ⁡ ( P 2 P 1 ) d B {\displaystyle L_{i2,1}=-10\log {\left({\frac {P_{2}}{P_{1}}}\right)}\quad {\rm {dB}}} Part of this loss

315-448: 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. 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 ( stripline and microstrip ). An implementation in stripline

378-419: A multi-section filter design in the same way as the multiple sections of a coupled-line coupler except that here the coupling of each section is controlled with the impedance of the branch lines. The main and coupled line are 2 {\displaystyle \scriptstyle {\sqrt {2}}} of the system impedance. The more sections there are in the coupler, the higher is the ratio of impedances of

441-412: A scattering matrix that is no longer all-zeroes on the antidiagonal. This terminology defines the power difference in dB between the two output ports of a 3 dB hybrid. In an ideal hybrid circuit, the difference should be 0 dB . However, in a practical device the amplitude balance is frequency dependent and departs from the ideal 0 dB difference. The phase difference between the two output ports of

504-488: A value in dB from the nominal coupling factor. It can be shown that coupled-line directional couplers have τ   {\displaystyle \tau \ } purely real and κ   {\displaystyle \kappa \ } purely imaginary at all frequencies. This leads to a simplification of the S-matrix and the result that the coupled port is always in quadrature phase (90°) with

567-443: 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. Branch line couplers can be used as crossovers as an alternative to air bridges , 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

630-511: Is calculated from the addition of the isolation and (negative) coupling measurements as: Note that if the positive definition of coupling is used, the formula results in: The S-matrix for an ideal (infinite isolation and perfectly matched) symmetrical directional coupler is given by, In general, τ   {\displaystyle \tau \ } and κ   {\displaystyle \kappa \ } are complex , frequency dependent, numbers. The zeroes on

693-411: Is defined as: C 3 , 1 = 10 log ⁡ ( P 3 P 1 ) d B {\displaystyle C_{3,1}=10\log {\left({\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}} where P 1 is the input power at port 1 and P 3 is the output power from the coupled port (see figure 1). The coupling factor represents

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756-431: Is designed for high power operation (large connectors), while the coupled port may use a small connector, such as an SMA connector . The internal load power rating may also limit operation on the coupled line. 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

819-481: Is due to some power going to the coupled port and is called coupling loss and is given by: Coupling loss: L c 2 , 1 = − 10 log ⁡ ( 1 − P 3 P 1 ) d B {\displaystyle L_{c2,1}=-10\log {\left(1-{\frac {P_{3}}{P_{1}}}\right)}\quad {\rm {dB}}} The insertion loss of an ideal directional coupler will consist entirely of

882-489: Is frequently used in control systems to design stable control systems or to show stability in control systems. This is especially important in the design of large, complex control systems (e.g. stability of airplanes). Passivity is also used in some areas of circuit design, especially filter design. A passive filter is a kind of electronic filter that is made only from passive components – in contrast to an active filter, it does not require an external power source (beyond

945-419: Is much wider: for instance a coupler specified as 2–4 GHz might have a main line which could operate at 1–5 GHz . The coupled response is periodic with frequency. For example, a λ/4 coupled-line coupler will have responses at n λ/4 where n 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

1008-419: Is not clear how this definition would be formalized to multiport devices with memory – as a practical matter, circuit designers use this term informally, so it may not be necessary to formalize it. This term is used colloquially in a number of other contexts: Passivity, in most cases, can be used to demonstrate that passive circuits will be stable under specific criteria. This only works if only one of

1071-563: Is one that consumes energy, but does not produce energy. Under this methodology, voltage and current sources are considered active, while resistors , capacitors , inductors , transistors , tunnel diodes , metamaterials and other dissipative and energy-neutral components are considered passive. Circuit designers will sometimes refer to this class of components as dissipative, or thermodynamically passive. While many books give definitions for passivity, many of these contain subtle errors in how initial conditions are treated and, occasionally,

1134-430: Is related to τ   {\displaystyle \tau \ } by; Coupling factor is related to κ   {\displaystyle \kappa \ } by; Non-zero main diagonal entries are related to return loss , and non-zero antidiagonal entries are related to isolation by similar expressions. Some authors define the port numbers with ports 3 and 4 interchanged. This results in

1197-405: 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 backward coupler . The main line is the section between ports 1 and 2 and the coupled line

1260-570: Is shown in the graph of figure 3 and the table below. 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: Isolation: I 4 , 1 = − 10 log ⁡ ( P 4 P 1 ) d B {\displaystyle I_{4,1}=-10\log {\left({\frac {P_{4}}{P_{1}}}\right)}\quad {\rm {dB}}} Isolation can also be defined between

1323-504: Is taken over all T  ≥ 0 and all admissible pairs { v (·),  i (·)} with the fixed initial state  x (e.g., all voltage–current trajectories for a given initial condition of the system). A system is considered passive if E A is finite for all initial states  x . Otherwise, the system is considered active. Roughly speaking, the inner product ⟨ v ( t ) , i ( t ) ⟩ {\displaystyle \langle v(t),i(t)\rangle }

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1386-420: Is the instantaneous power (e.g., the product of voltage and current), and E A is the upper bound on the integral of the instantaneous power (i.e., energy). This upper bound (taken over all T  ≥ 0) is the available energy in the system for the particular initial condition x . If, for all possible initial states of the system, the energy available is finite, then the system is called passive. If

1449-415: Is the output power from the coupled port and P 4 is the power output from the isolated port. 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 measurable, and

1512-402: 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 coupled port, and the diagonal port being the isolated port. On some directional couplers, the main line

1575-486: 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. The term hybrid coupler originally applied to 3 dB coupled-line directional couplers, that is, directional couplers in which

1638-490: Is used for devices with tight coupling (commonly, a power divider will provide half the input power at each of its output ports – a 3 dB divider) and is usually considered a 3-port device. Common properties desired for all directional couplers are wide operational bandwidth , high directivity, and a good impedance match at all ports when the other ports are terminated in matched loads. Some of these, and other, general characteristics are discussed below. The coupling factor

1701-407: The coupling factor in dB marked on it. Directional couplers have four ports . 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,

1764-584: The small signal model is not passive are sometimes called locally active (e.g. transistors and tunnel diodes). Systems that can generate power about a time-variant unperturbed state are often called parametrically active (e.g. certain types of nonlinear capacitors). Formally, for a memoryless two-terminal element, this means that the current–voltage characteristic is monotonically increasing . For this reason, control systems and circuit network theorists refer to these devices as locally passive, incrementally passive, increasing, monotone increasing, or monotonic. It

1827-459: The above definitions of passivity is used – if components from the two are mixed, the systems may be unstable under any criteria. In addition, passive circuits will not necessarily be stable under all stability criteria. For instance, a resonant series LC circuit will have unbounded voltage output for a bounded voltage input, but will be stable in the sense of Lyapunov , and given bounded energy input will have bounded energy output. Passivity

1890-735: The audio frequencies encountered in telephony . Also at microwave frequencies, particularly the higher bands, waveguide 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. 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 received signals on telephone lines. The symbols most often used for directional couplers are shown in figure 1. The symbol may have

1953-473: The available energy is finite, it is known to be non-negative, since any trajectory with voltage v ( t ) = 0 {\displaystyle v(t)=0} gives an integral equal to zero, and the available energy is the supremum over all possible trajectories. Moreover, by definition, for any trajectory { v (·),  i (·)}, the following inequality holds: The existence of a non-negative function E A that satisfies this inequality, known as

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2016-669: The best isolation. Directivity is directly related to isolation. It is defined as: Directivity: D 3 , 4 = − 10 log ⁡ ( P 4 P 3 ) = − 10 log ⁡ ( P 4 P 1 ) + 10 log ⁡ ( P 3 P 1 ) d B {\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}}} where: P 3

2079-481: 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 applies for coupling factors looser than 10 dB ; 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 3 dB hybrids. Branch-line couplers usually do not have such

2142-413: The coupled line a higher impedance 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. The frequency range specified by manufacturers is that of the coupled line. The main line response

2205-434: 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 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

2268-417: 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

2331-427: 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 ( Butterworth filter ), equal-ripple ( Cauer filter ), or a specified-ripple ( Chebychev filter ) response. Ripple is the maximum variation in output of the coupled port in its passband , usually quoted as plus or minus

2394-423: The coupling loss. In a real directional coupler, however, the insertion loss consists of a combination of coupling loss, dielectric loss, conductor loss, and VSWR loss. Depending on the frequency range, coupling loss becomes less significant above 15 dB coupling where the other losses constitute the majority of the total loss. The theoretical insertion loss (dB) vs coupling (dB) for a dissipationless coupler

2457-444: The coupling. It is used for strong couplings in the range 3 dB to 6 dB . 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 three ports of a passive, lossless three-port and poor isolation

2520-406: The definitions do not generalize to all types of nonlinear time-varying systems with memory. Below is a correct, formal definition, taken from Wyatt et al., which also explains the problems with many other definitions. Given an n - port R with a state representation S , and initial state x , define available energy E A as: where the notation sup x → T ≥0 indicates that the supremum

2583-446: 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. 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 distributed-element filters . The sections of

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2646-401: The desire to incorporate a passive filter that leads the designer to use the hybrid format. Passive circuit elements may be divided into energic and non-energic kinds. When current passes through it, an energic passive circuit element converts some of the energy supplied to it into heat . It is dissipative . When current passes through it, a non-energic passive circuit element converts none of

2709-450: 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. 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

2772-421: The energy supplied to it into heat. It is non-dissipative. Resistors are energic. Ideal capacitors, inductors, transformers, and gyrators are non-energic. Insertion loss In telecommunications , insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber and is usually expressed in decibels (dB). If the power transmitted to

2835-428: The form; in this article have the meaning "parameter P at port a due to an input at port b ". A symbol for power dividers is shown in figure 2. Power dividers and directional couplers are in all essentials the same class of device. Directional coupler 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. Power divider

2898-511: 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 30 dB while the isolation between ports 2 and 3 can be a different value such as 25 dB . Isolation can be estimated from the coupling plus return loss . The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some RF power will always be present. Waveguide directional couplers will have

2961-416: The insertion loss is positive and measures how much smaller the signal is after adding the filter. In case the two measurement ports use the same reference impedance, the insertion loss ( I L {\displaystyle IL} ) is defined as: Here S 21 {\displaystyle S_{21}} is one of the scattering parameters . Insertion loss is the extra loss produced by

3024-445: 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 matched load (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. Symbols of

3087-497: 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 2 {\displaystyle \scriptstyle {\sqrt {2}}} of

3150-485: The load before insertion is P T and the power received by the load after insertion is P R , then the insertion loss in decibels is given by, Insertion loss is a figure of merit for an electronic filter and this data is generally specified with a filter. Insertion loss is defined as a ratio of the signal level in a test configuration without the filter installed ( | V 1 | {\displaystyle \left\vert V_{1}\right\vert } ) to

3213-425: The matrix main diagonal are a consequence of perfect matching – power input to any port is not reflected back to that same port. The zeroes on the matrix antidiagonal are a consequence of perfect isolation between the input and isolated port. For a passive lossless directional coupler, we must in addition have, since the power entering the input port must all leave by one of the other two ports. Insertion loss

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3276-422: The minimum track width that can be produced and also puts a limit on how close the lines can be placed to each other. This becomes a problem when very tight coupling is required and 3 dB couplers often use a different design. However, tightly coupled lines can be produced in air stripline which also permits manufacture by printed planar technology. In this design the two lines are printed on opposite sides of

3339-627: The moderately large voltages and currents, and the lack of easy access to a power supply), filters in power distribution networks (due to the large voltages and currents), power supply bypassing (due to low cost, and in some cases, power requirements), as well as a variety of discrete and home brew circuits (for low-cost and simplicity). Passive filters are uncommon in monolithic integrated circuit design, where active devices are inexpensive compared to resistors and capacitors, and inductors are prohibitively expensive. Passive filters are still found, however, in hybrid integrated circuits . Indeed, it may be

3402-588: The output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power equally between two ports is called a hybrid coupler . 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 microwave frequencies where transmission line designs are commonly used to implement many circuit elements. However, lumped component devices are also possible at lower frequencies, such as

3465-475: The output port. Some applications make use of this phase difference. Letting κ = i κ I   {\displaystyle \kappa =i\kappa _{\mathrm {I} }\ } , the ideal case of lossless operation simplifies to, 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

3528-451: The primary property of a directional coupler. Coupling factor is a negative quantity, it cannot exceed 0 dB for a passive device, and in practice does not exceed −3 dB 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

3591-469: The signal level with the filter installed ( | V 2 | {\displaystyle \left\vert V_{2}\right\vert } ). This ratio is described in decibels by the following equation: For passive filters, | V 2 | {\displaystyle \left\vert V_{2}\right\vert } will be smaller than | V 1 | {\displaystyle \left\vert V_{1}\right\vert } . In this case,

3654-438: The signal). Since most filters are linear, in most cases, passive filters are composed of just the four basic linear elements – resistors, capacitors, inductors, and transformers. More complex passive filters may involve nonlinear elements, or more complex linear elements, such as transmission lines. A passive filter has several advantages over an active filter : They are commonly used in speaker crossover design (due to

3717-482: The system impedance – for a 50 Ω system the Wilkinson lines are approximately 70 Ω Passivity (engineering) An electronic circuit consisting entirely of passive components is called a passive circuit , and has the same properties as a passive component. If a component is not passive, then it is an active component . In control systems and circuit network theory, a passive component or circuit

3780-451: The transmission strip. This leads to transmission modes 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 which rises noticeably with frequency. A variation of this design sometimes encountered has

3843-506: 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. Consequently: I 3 , 2 = − 10 log ⁡ ( P 3 P 2 ) d B {\displaystyle I_{3,2}=-10\log {\left({\frac {P_{3}}{P_{2}}}\right)}\quad {\rm {dB}}} The isolation between

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3906-414: The two outputs are each half the input power. This synonymously meant a quadrature 3 dB 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 hybrid coupler without qualification means

3969-457: The two paths through it. The design is a 3-branch coupler equivalent to two 3 dB 90° hybrid couplers connected in cascade . The result is effectively a 0 dB coupler. It will cross over the inputs to the diagonally opposite outputs with a phase delay of 90° in both lines. The construction of the Lange coupler is similar to the interdigital filter with paralleled lines interleaved to achieve

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