Distributed element filter is an electronic filter in which capacitance, inductance, and resistance (circuit elements) are not localized in capacitors, inductors and discrete resistors since they are in conventional filters. The goal is to allow a variety of signal frequencies to pass, but to block the other. Conventional filters are built from inductors and capacitors, and the built-in circuits are described by the model of lumped elements, which assume each element is "put together" in one place. The model is conceptually simple, but becomes increasingly unreliable as the signal frequency increases, or is equivalent to the reduced wavelength. Distributed element models apply at all frequencies, and are used in transmission line theory; many components of a distributed element are made of a short length of transmission line. In the display of distributed circuits, elements are distributed along the conductors and mixed together. Filter design usually deals only with inductance and capacitance, but because of mixing these elements they can not be treated as separate capacitors and inductors. There is no precise frequency above that distributing filter elements should be used but they are mainly related to microwaves (wavelengths less than one meter).
Distributed element filters are used in many of the same applications as lumped element filters, such as the selectivity of radio channels, bandlimiting noise, and multiplexing multiple signals into a single channel. Distributed element filters can be constructed to have one possible waveform with a centralized element (low-pass, band-pass, etc.) With the exception of high-pass, which is usually only approached. All filter classes used in lumped element design (Butterworth, Chebyshev, etc.) can be implemented using distributed element approach.
There are many forms of components used to build distributed filter elements, but all have common properties causing discontinuities on the transmission line. This discontinuity presents the reactive impedance to the wavefront moving along the line, and this reactance may be selected based on the design to be used as an approximation for the inductor, capacitor, or resonator being equalized, as required by the filter.
The development of distributed element filters was driven by military needs for radar and electronic counter measures during World War II. The densest elemental analog filter has long been developed but the new military system operates at microwave frequencies and new filter design is required. When the war ended, technology found applications in microwave connections used by telephone companies and other organizations with large fixed communications networks, such as television broadcasters. Currently the technology can be found in some mass-produced consumer goods, such as converters (figure 1 shows examples) used with satellite television antennas.
Video Distributed element filter
General comments
- Symbols? is used to mean the wavelength of the signal transmitted to the line or part of the electrical line length.
Distributed element filters are mostly used at frequencies above the VHF band (Very High Frequency) (30 to 300 MHz). At this frequency, the physical length of the passive component is a significant fraction of the operating frequency wavelength, and it becomes difficult to use conventional united element models. The exact point at which modeling of distributed elements becomes necessary depends on the particular design under consideration. A common general rule is to apply distributed element modeling when component dimensions are greater than 0.1. Increasingly miniaturization of electronics means the design of circuits is getting smaller compared. The frequency beyond which the distributed element approach to filter design becomes necessary to be higher as a result of this progress. On the other hand, the antenna structure dimension is usually proportional to? in all frequency bands and require distributed element model.
The most noticeable difference in behavior between distributed element filters and the lumped element approach is that the former will have multiple passband replicas of the passband prototype-paralyzed element, due to the characteristic of the transmission of the repeating channel in the harmonic interval. These fake passbands are not desirable in most cases.
For clarity of presentation, the diagrams in this article are drawn with components that are implemented in stripline format. This does not imply an industry preference, although the format of the planar transmission channel (ie the format in which conductors are composed of flat strips) is popular because they can be implemented using established printed circuit board manufacturing techniques. The structure shown can also be implemented using stripline microstrip or buried techniques (with adjustments suitable for dimensions) and can be adjusted with coaxial cables, twin leads and waveguides, although some structures are more suitable for some implementations than others. Implementation of open wire, for example, a number of structures shown in the second column of Fig. 3 and the equivalent of open wire can be found for most other stripline structures. Planar transmission lines are also used in the design of integrated circuits.
Maps Distributed element filter
History
The development of distributed element filters began in the years before World War II. Warren P. Mason established the field of distributed element circuits. A major paper on this issue was published by Mason and Sykes in 1937. Mason had filed a patent much earlier, in 1927, and the patent probably contained the first published electrical design that moved away from lumped element analysis. The work of Mason and Sykes is focused on the format of coaxial cables and balanced pairs of cables - planar technology has not been used. Much of the development was done during the war years driven by the need for radar screening and electronic countermeasures. Much of this at the MIT Radiation Laboratory, but other laboratories in the US and UK are also involved.
Some important advances in network theory are needed before filters can advance beyond wartime design. One is the equivalent line theory of Paul Richards. The corresponding channel is the network in which all elements have the same length (or in some cases multiples of the unit length), although they may differ in other dimensions to provide different characteristic impedances. The Richards transform enables the design of a lumped element to be taken "as is" and transformed directly into the design of a distributed element using a very simple transformation equation.
The difficulty with Richards transformation from the standpoint of constructing a practical filter is that the design of the resulting distributed element always includes a series connected element. This is impossible to apply in planar technology and is often uncomfortable in other technologies. This problem is solved by K. Kuroda which uses impedance transformers to remove the series element. He published a series of transformations known as Kuroda's identity in 1955, but his work was written in Japanese and several years before his ideas were incorporated into English literature.
After the war, one of the important research avenues was trying to increase bandwidth of broadband filter design. The approach used at the time (and still used today) is to start with a lumped prototype element filter and through various transformations arriving at the desired filter in the form of a distributed element. This approach seems to stop at a minimum of Q of five (see the Band-pass filter below for explanation of Q ). In 1957, Leo Young at Stanford Research Institute published a method for designing a filter that started with a prototype of distributed elements. This prototype is based on a quarter wave impedance transformer and is capable of producing designs with bandwidth up to an octave, corresponding to Q around 1.3. Some of Young's procedures in the paper are empirical, but then, the right solutions are published. Young's paper specifically discusses cavity resonators directly, but the procedure can be applied to other types of directly related resonators, such as those found in modern planar technology and illustrated in this article. The capacitive gap filter (figure 8) and the parallel-coupled line filter (figure 9) are examples of directly coupled resonators.
The introduction of the printed planar technology greatly simplifies the manufacture of many microwave components including filters, and integrated microwave circuits then becomes possible. It is not known when the planar transmission lines started, but experiments using them were recorded as early as 1936. The inventors of the stripline printed, however, are known; this was Robert M. Barrett who published the idea in 1951. It happened quickly, and Barrett's stripline soon had a fierce commercial competition from rival planar formats, especially the triplate and microstrip . The general term stripline in modern usage usually refers to a form later known as triplate .
The initial stripline is directly coupled with the coupled resonator filter, but the length is reduced and compactness increases with the introduction of parallel-coupled line filters, interdigital filters, and comb-line filters. Much of this work was published by a group at Stanford led by George Matthaei, and also included Leo Young mentioned above, in a landmark book that still today serves as a reference for circuit designers. The hairpin filter was first described in 1972. In the 1970s, most of the commonly used filter topologies have now been described. More recent research has concentrated on new mathematical classes or variants of filters, such as pseudo-elliptic, while still using the same basic topology, or with alternative implementation technologies such as suspended stripline and finline.
Non-military initial applications of distributed element filters are in the microwave connection used by telecommunication companies to provide their network backbone. This link is also used by other industries with large fixed networks, especially television broadcasters. Such applications are part of a large capital investment program. However, mass production manufacturing makes the technology cheap enough to be incorporated in domestic satellite television systems. Applications that appear in superconductor filters for use in mobile base stations operated by mobile phone companies.
Basic components
The simplest structure that can be implemented is a step in line characteristic impedance, which introduces discontinuities in transmission characteristics. This is done in planar technology with changes in transmission line width. Figure 4 (a) shows the step in impedance (narrow lines have higher impedance). The step back in the impedance will be the mirror image of figure 4 (a). The discontinuity can be represented approximately as a series inductor, or more precisely, as a low pass T circuit as shown in FIG. 4 (a). Some discontinuities are often combined together with an impedance transformer to produce a higher filter. These impedance transformers can be short transmission lines (often?/4). This composite structure can implement one filter family (Butterworth, Chebyshev, etc.) by estimating the rational transfer function of the corresponding centralized element filter. This correspondence is incorrect because distributed element circuits can not be rational and are the main reason for the difference of truncated elements and the behavior of distributed elements. Impedance transformers are also used in hybrid mixtures of lumped and distributed element filters (so-called semi-lumped structures).
Another very common component of distributed filter elements is the stub. During a narrow frequency range, a stub can be used as a capacitor or inductor (its impedance is determined by its length) but above the band that functions as a resonator. Short-circuit, nominal nominal-wavelength stubs (Fig. 3 (a)) behave as a shunt LC antiresonator, and nominal open-wavelength nominal circuits (Fig. 3 (b)) behave as LC series resonators. Stubs can also be used together with impedance transformers to build more complex filters and, as expected from their resonant properties, most useful in band-pass applications. While open-circuit stubs are easier to produce in planar technology, they have the disadvantage that the significant deviation crosses from the ideal open circuit (see Figure 4 (b)), often leading to a preference for short-circuits (one can always be used in places else by increasing or decreasing?/4 to or from length).
Helical resonators are similar to stubs, because they require distributed element models to represent them, but are actually built using the same element. They are built in a non-planar format and consist of wire reels, on marks and cores, and connect only to one end. This device is usually inside a shielded can with a hole at the top to fit the core. It will often look very similar to the LC resonator being used for the same purpose. They are most useful in upper VHF and lower UHF bands while stubs are more often applied to higher UHF and SHF bands.
Paired line (figure 3 (c-e)) can also be used as filter element; such as stubs, they can act as resonators and also terminated short circuit or open circuit. The combined lines tend to be preferred in planar technology, where they are easy to apply, whereas stubs tend to be preferred elsewhere. Applying the correct open circuit in planar technology is not feasible because of the dielectric effect of the substrate which will always ensure that the equivalent circuit contains the shunt capacitance. However, open circuits are often used in planar formats in preference for short circuits because they are easier to implement. Many types of elements can be classified as trailers and the more common choices shown in the drawing.
Some common structures are shown in FIGS. 3 and 4, together with lumped elements. These centralized elemental approaches should not be taken as equivalent circuits but rather as guidelines for the behavior of distributed elements over a given frequency range. Figures 3 (a) and 3 (b) show short circuits and open circuits, respectively. When the stub length is?/4, this behaves, respectively, as an anti-resonator and resonator and is therefore useful, respectively, as elements in band-pass and band-stop filters. Figure 3 (c) shows a short-circuit line paired with the main line. It also functions as a resonator, but is commonly used in low-pass filter applications with far-reaching resonance frequencies outside of the attractive band. Figures 3 (d) and 3 (e) show the combined line structure both useful in band-pass filters. Picture structures 3 (c) and 3 (e) have equivalent circuits that involve stubs placed in series with lines. This kind of topology is very easy to implement in open wire circuit but not with planar technology. Therefore both of these structures are useful for implementing equivalent series elements.
Low-pass filter
The low-pass filter can be implemented quite directly from the surface element prototype clamped with the impedance filter shown in Fig. 5. This is also called the cascaded lines design. The filter consists of alternating sections of high impedance and low impedance lines corresponding to the series inductor and shunt capacitor in a centralized element implementation. A low pass filter is commonly used to feed a direct current bias (DC) to the active component. Filters intended for this app are sometimes referred to as chokes . In such a case, every element of the filter is?/4 length (where? Is the wavelength of the main line signal is blocked from transmission to the DC source) and the high impedance part of the line is made as narrow as the manufacturing technology will allow to maximize the inductance. Additional parts can be added as needed for filter performance as will be done for lumped elements. As well as the planar shape shown, this structure is particularly suitable for coaxial implementation with alternating discs of metal and threaded insulators to the central conductor.
A more complex example of a steped impedance design is presented in Figure 6. Again, a narrow line is used to implement the inductor and line width according to the capacitor, but in this case, the lumped elements have a resonator connected in the shunt across the main line. This topology can be used to design elliptical filters or Chebyshev filters with attenuation poles in the stopband. However, calculating the component values ​​for this structure is a process that is involved and has caused designers often choose to implement it as a non-derived filter, which performs better and is easier to calculate. The purpose of combining a resonator is to increase stopband rejection. However, beyond the resonance frequency of the highest frequency resonator, stopband rejection starts to deteriorate as the resonator moves toward the open circuit. For this reason, filters made for this design often have an additional steped-impedance capacitor as the last element of the filter. It also ensures good rejection at high frequencies.
Another common low-pass design technique is to implement a shunt capacitor as a stub with a resonant frequency set above the operating frequency so that the stub impedance is capacitive in the passband. This implementation has a common-liked counterpart of common shape similar to filter number 6. Where space allows, the stub can be set on the alternate side of the main line as shown in figure 7 (a). The goal is to prevent coupling between adjacent stubs that reduce filter performance by changing the frequency response. However, the structure with all the stubs on the same side is still a valid design. If a stub is required to be a very low impedance line, the stub may not be large. In this case, the possible solution is to connect two narrow bars in parallel. That is, each stub position has a stub on the both sides of the line. The disadvantage of this topology is that additional transverse resonance modes are possible along the way?/2 line length formed by two stubs together. For choke design, the only requirement is to make the maximum possible capacitance, the maximum stub width?/4 can be used with stub in parallel on both sides of the main line. The resulting filter looks somewhat similar to the impedance gauge in Figure 5, but has been designed with completely different principles. The difficulty with using these wide stubs is that the point where they connect to the main line is unclear. A narrow stub compared to? can be considered connected to the center line and calculations based on that assumption will accurately predict the filter response. However, for a wide stub, a calculation that assumes a side branch connected at a fixed point on the main path causes inaccuracies since this is no longer a good model of the transmission pattern. One solution to this difficulty is to use a radial stub instead of a linear stub. A pair of radial bulges in parallel (one on either side of the main line) is called a stub butterfly (see figure 7 (b)). A group of three radial rods in parallel, which can be reached at the end of the line, is called a clover leaf stub.
Filter band-pass
The band-pass filter can be constructed using whatever elements can resonate. Filters using stubs can be clearly made band-pass; many other structures are possible and some are presented below.
Parameter penting ketika membahas filter band-pass adalah bandwidth fraksional. Ini didefinisikan sebagai rasio bandwidth terhadap frekuensi pusat geometrik. Kebalikan dari kuantitas ini disebut Q-factor, Q . Jika? 1 dan? 2 adalah frekuensi tepi passband, maka:
- bandwidth ,
- frekuensi tengah geometrik dan
Filter celah kapasit
The capacitive gap structure consists of a line segment around?/2 length that acts as a resonator and is combined "end-on" by a gap in the transmission line. It is perfect for planar formats, easy to implement with printed circuit technology and has the advantage of taking up no more space than ordinary transmission lines. The limitation of this topology is that performance (especially insertion loss) worsens with increasing fractional bandwidth, and acceptable results are not obtained with Q less than about 5. Further difficulties with producing low- Q design is that the required slit width is smaller for wider fractional bandwidth. Minimum slit width, such as minimum track width, is limited by the resolution of printing technology.
Parallel Connection line filter
The parallel merging line is another popular topology for printed boards, where open circuit lines are the simplest to apply because manufacturing is nothing more than a print path. The design consists of parallel rows?/2 resonator, but just paired?/4 for each adjacent resonator, thus forming a staggered line as shown in Fig. 9. The wider fractional bandwidth is possible with this filter compared to the slit filter capacitance, but the same problem appears on the printed board as a dielectric loss reducing Q . The bottom line- Q requires a tighter coupling and smaller gap between them that is limited by the accuracy of the printing process. One solution to this problem is to print tracks on multiple layers with adjacent lines overlapping but not touching because they are on different layers. In this way, the lines can be combined at their width, resulting in a coupling that is much more powerful than when they are edge-to-edge, and larger gaps become possible for the same performance. For other (non-print) technology, short-circuit lines may be preferred because short circuit provides mechanical attachment point for channel and Q -Reduced dielectric insulator is not required for mechanical support. In addition to mechanical reasons and assembly, there is little preference for open circuits in short circuit circuits. Both structures can realize the same range of filter implementations with the same electrical performance. Both types of parallel-coupled filters, in theory, do not have false passbands twice the center frequency as seen in many other filter topologies (eg, stubs). However, this false passband emphasis requires perfect adjustment of unified merged lines in practice, so there must be some false spurious passband at this frequency.
Hairpin filters are other structures that use parallel-coupled lines. In this case, each pair of parallel lines-connected to the next pair with short links. The "U" shape formed forms the name hairpin filter . In some designs, links may be longer, giving a wide hairpin with a transformer//4 puncture action between the parts. The oblique slope shown in FIG. 10 is common for stripline design and represents a compromise between sharp angles, resulting in large discontinuities, and fine bends, which take up more board areas that can be very limited in some products. Such indentations are often seen in long pieces where they can not be attached to the available space. The equivalent element-equivalent circuit of this type of discontinuity is similar to the jump-impedance discontinuity. Examples of such stubs can be seen in the biased input to some of the components in the photo at the top of the article.
Interdigital filter
An interdigital filter is another form of a dual-lane filter. Any part of the line around?/4 in length and end with a short circuit on one end only, the other end is left open. The ends are short-circuited alternately on each section of the line. This topology is very easy to apply in planar technology, but also specifically allows assembling of mechanical lines mounted inside a metal box. Lines can be either circular bars or rectangular bars, and interface to coaxial format lines is easy. As with parallel-coupled line filters, the advantage of a mechanical arrangement that does not require an isolator for support is the eliminated dielectric loss. Need for spacing between lines is not as tight as the parallel line structure; thus, higher fractional bandwidth can be achieved, and Q values ​​as low as 1.4 are possible.
The comb-line filter is similar to an interdigital filter in which it is suitable for mechanical assembly in metal cases without dielectric support. In the case of the comb-line, all lines are short-circuited at the same end rather than the alternate end. The other end is terminated in the capacitor to the ground, and this design is consequently classified as semi-paralyzed. The main advantage of this design is that the top stopband can be made very wide, ie, free of fake passbands at all interesting frequencies.
Stub band-pass filter
As mentioned above, the stub lends a band-pass design. This common form is similar to a low-pass stub filter except that the main line is no longer a narrow, high-impedance line. Designers have many different stub filter topologies to choose from, some of which produce identical responses. An example of a stub filter is shown in Figure 12; it consists of a row?/4 short-circuits coupled together by?/4 impedance transformer. The stub in the body of the filter is a double parallel stubop while the stub at the end is only single, a setting that has the advantage of impedance matching. Impedance transformers have the effect of changing the line of anti resonator devices into resonator ladder series and anti resonator devices. A filter with similar properties can be constructed with?/4 open-circuit stubs are placed in series with the line and combined together with the/4 impedance transformers, although this structure is not possible in planar technology.
But other available structures are?/2 open-circuit stubs across the line coupled with?/4 impedance transformer. This topology has low-pass and band-pass characteristics. Because it will pass through DC, it is possible to transmit biasing voltage to the active component without the need to block the capacitor. Also, since short-circuit relationships are not required, assembly operations other than board printing are required when implemented as stripline. The disadvantage is that (i) the filter will take up more real estate of the board than the corresponding seal 4 filter, since the stub is twice as long; (ii) the first false passband is on 2? 0 , compared to 3? 0 for filter 4/stub.
Konishi describes a broadband band-band filter of 12 GHz, which uses 60 Â ° butterfly cuts and also has a low-pass response (short-circuit stubs needed to prevent such a response). As is often the case with distributed element filters, the bandform to which the filter is classified depends largely on the desired band and which is considered to be false.
High-pass filter
Source of the article : Wikipedia
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