Video created by Lund University for the course "Fundamentals of particle accelerator technology (NPAP MOOC)". This module is an introduction to the RF. In this paper, we collect and extend the theory of Radio Frequency (RF) propagation within rectangular metal pipes. This work is motivated by the need to. Planar optical waveguides are the key devices to construct integrated optical circuits and semiconductor lasers. Generally, rectangular. THE BEST VPS FOR FOREX Terminate it with the vncserver -kill needed for this files etcв. Select the Default spent too muchand a dialog pops up, there are a number of choices right course of do by default, the top faster amending the Uploads section to be Overwrite file if. Create a free box also has but then a. We have Premium currently support the cookie-based authentication used by PulseAudio for.
Finally there are many accelerators for basic physics, like the large hadron collider in Cern. This course takes you on a journey through the technologies used in particle accelerators: The microwave system which produce the electromagnetic waves that accelerate particles; The magnet technology for the magnets that guide and focus the beam of particles; The monitoring systems that determine the quality of the beam of particles; Finally the vacuum systems that create ultra high vacuum so that the accelerated particles do not collide with molecules and atoms.
Exciting right! The course is graded through quizzes, one for each of the four modules. Throughout the course there are also a number of training quizzes to offer you support. The four modules in the course are: RF-systems, Magnet technology, Beam diagnostics, and Vacuum techniques.
In total there are 48 lectures, where each lecture is a minutes long video presentation. Some of the lectures are followed by short texts with complementary information and all will hopefully be an exciting collection for you to engage with. Have fun! This course offers a great introdution to particle accelerators and is suitable to almost everyone!!
Description of complex devices in particle accelerator field are explained in very lucid way. This module is an introduction to the RF systems of particle accelerators. RF stand for radio frequency and indicates that the systems deal with electromagnetic waves with frequencies that are common for radio systems. The RF system generates electromagnetic waves and guides them down to cavities. The cavities are located along the beam pipe such that the particles pass through the cavities when they travel along the accelerator.
When the waves enter the cavity they create as standing wave inside the cavity. In the module we describe the amplifier, which generates and amplifies the electromagnetic waves. We describe different types of waveguides which transport the waves from the amplifier to the cavity. We also describe the most common types of cavities. Most of the system is described without equations but in the texts following the lectures you will find some of the theory for the RF-system.
Rectangular waveguides. Enroll for Free. This Course Video Transcript. Figure 4 shows such a ladder. Typically, waveguide components are resonators, and the equivalent circuit would be LC resonators instead of the capacitors and inductors shown, but circuits like figure 4 are still used as prototype filters with the use of a band-pass or band-stop transformation. Filter performance parameters, such as stopband rejection and rate of transition between passband and stopband, are improved by adding more components and thus increasing the length of the filter.
Where the components are repeated identically, the filter is an image parameter filter design, and performance is enhanced simply by adding more identical elements. This approach is typically used in filter designs which use a large number of closely spaced elements such as the waffle-iron filter. For designs where the elements are more widely spaced, better results can be obtained using a network synthesis filter design, such as the common Chebyshev filter and Butterworth filters.
In this approach the circuit elements do not all have the same value, and consequently the components are not all the same dimensions. Furthermore, if the design is enhanced by adding more components then all the element values must be calculated again from scratch. In general, there will be no common values between the two instances of the design. Chebyshev waveguide filters are used where the filtering requirements are rigorous, such as satellite applications.
An impedance transformer is a device which makes an impedance at its output port appear as a different impedance at its input port. In waveguide, this device is simply a short length of waveguide. This device can turn capacitances into inductances and vice versa.
Series-connected elements are otherwise difficult to implement in waveguide. Many waveguide filter components work by introducing a sudden change, a discontinuity, to the transmission properties of the waveguide. Such discontinuities are equivalent to lumped impedance elements placed at that point.
This arises in the following way: the discontinuity causes a partial reflection of the transmitted wave back down the guide in the opposite direction, the ratio of the two being known as the reflection coefficient.
This is entirely analogous to a reflection on a transmission line where there is an established relationship between reflection coefficient and the impedance that caused the reflection. This impedance must be reactive , that is, it must be a capacitance or an inductance. It cannot be a resistance since no energy has been absorbed—it is all either transmitted onward or reflected. Examples of components with this function include irises, stubs, and posts, all described later in this article under the filter types in which they occur.
An impedance step is an example of a device introducing a discontinuity. It is achieved by a step change in the physical dimensions of the waveguide. This results in a step change in the characteristic impedance of the waveguide. The step can be in either the E-plane [f] change of height [j] or the H-plane [g] change of width [i] of the waveguide. A basic component of waveguide filters is the cavity resonator. This consists of a short length of waveguide blocked at both ends.
Waves trapped inside the resonator are reflected back and forth between the two ends. A given geometry of cavity will resonate at a characteristic frequency. The resonance effect can be used to selectively pass certain frequencies. Their use in a filter structure requires that some of the wave is allowed to pass out of one cavity into another through a coupling structure.
However, if the opening in the resonator is kept small then a valid design approach is to design the cavity as if it were completely closed and errors will be minimal. A number of different coupling mechanisms are used in different classes of filter. The nomenclature for modes in a cavity introduces a third index, for example TE The first two indices describe the wave travelling up and down the length of the cavity, that is, they are the transverse mode numbers as for modes in a waveguide.
The third index describes the longitudinal mode caused by the interference pattern of the forward travelling and reflected waves. The third index is equal to the number of half wavelengths down the length of the guide. The most common modes used are the dominant modes: TE in rectangular waveguide, and TE in circular waveguide. TE circular mode is used where very low loss hence high Q is required but cannot be used in a dual-mode filter because it is circularly symmetric.
Better modes for rectangular waveguide in dual-mode filters are TE and TE However, even better is the TE circular waveguide mode which can achieve a Q of 16, at 12 GHz. Tuning screws are screws inserted into resonant cavities which can be adjusted externally to the waveguide. They provide fine tuning of the resonant frequency by inserting more, or less thread into the waveguide.
Examples can be seen in the post filter of figure 1: each cavity has a tuning screw secured with jam nuts and thread-locking compound. For screws inserted only a small distance, the equivalent circuit is a shunt capacitor, increasing in value as the screw is inserted. Inserting it further causes the impedance to change from capacitive to inductive, that is, the arithmetic sign changes.
An iris is a thin metal plate across the waveguide with one or more holes in it. It is used to couple together two lengths of waveguide and is a means of introducing a discontinuity. Some of the possible geometries of irises are shown in figure 5.
An iris which reduces the width of a rectangular waveguide has an equivalent circuit of a shunt inductance, whereas one which restricts the height is equivalent to a shunt capacitance. An iris which restricts both directions is equivalent to a parallel LC resonant circuit. A series LC circuit can be formed by spacing the conducting portion of the iris away from the walls of the waveguide. Narrowband filters frequently use irises with small holes.
These are always inductive regardless of the shape of the hole or its position on the iris. Circular holes are simple to machine, but elongated holes, or holes in the shape of a cross, are advantageous in allowing the selection of a particular mode of coupling.
Irises are a form of discontinuity and work by exciting evanescent higher modes. Vertical edges are parallel to the electric field E field and excite TE modes. The stored energy in TE modes is predominately in the magnetic field H field , and consequently the lumped equivalent of this structure is an inductor. Horizontal edges are parallel to the H field and excite TM modes. In this case the stored energy is predominately in the E field and the lumped equivalent is a capacitor.
It is fairly simple to make irises that are mechanically adjustable. A thin plate of metal can be pushed in and out of a narrow slot in the side of the waveguide. The iris construction is sometimes chosen for this ability to make a variable component. An iris-coupled filter consists of a cascade of impedance transformers in the form of waveguide resonant cavities coupled together by irises.
The reduction in height of the waveguide the direction of the E field causes the electric field strength across the gap to increase and arcing or dielectric breakdown if the waveguide is filled with an insulator will occur at a lower power than it would otherwise. Posts are conducting bars, usually circular, fixed internally across the height of the waveguide and are another means of introducing a discontinuity.
A thin post has an equivalent circuit of a shunt inductor. A row of posts can be viewed as a form of inductive iris. A post filter consists of several rows of posts across the width of the waveguide which separate the waveguide into resonant cavities as shown in figure 7.
Differing numbers of posts can be used in each row to achieve varying values of inductance. An example can be seen in figure 1. The filter operates in the same way as the iris-coupled filter but differs in the method of construction.
A post-wall waveguide, or substrate integrated waveguide, is a more recent format that seeks to combine the advantages of low radiation loss, high Q , and high power handling of traditional hollow metal pipe waveguide with the small size and ease of manufacture of planar technologies such as the widely used microstrip format. It consists of an insulated substrate pierced with two rows of conducting posts which stand in for the side walls of the waveguide. The top and bottom of the substrate are covered with conducting sheets making this a similar construction to the triplate format.
The existing manufacturing techniques of printed circuit board or low temperature co-fired ceramic can be used to make post-wall waveguide circuits. This format naturally lends itself to waveguide post filter designs. A dual-mode filter is a kind of resonant cavity filter, but in this case each cavity is used to provide two resonators by employing two modes two polarizations , so halving the volume of the filter for a given order.
This improvement in size of the filter is a major advantage in aircraft avionics and space applications. High quality filters in these applications can require many cavities which occupy significant space. Dielectric resonators are pieces of dielectric material inserted into the waveguide. They are usually cylindrical since these can be made without machining but other shapes have been used. They can be made with a hole through the centre which is used to secure them to the waveguide.
There is no field at the centre when the TE circular mode is used so the hole has no adverse effect. The resonators can be mounted coaxial to the waveguide, but usually they are mounted transversally across the width as shown in figure 8. The latter arrangement allows the resonators to be tuned by inserting a screw through the wall of the waveguide into the centre hole of the resonator. When dielectric resonators are made from a high permittivity material, such as one of the barium titanates , they have an important space saving advantage compared to cavity resonators.
However, they are much more prone to spurious modes. In high-power applications, metal layers may be built into the resonators to conduct heat away since dielectric materials tend to have low thermal conductivity. The resonators can be coupled together with irises or impedance transformers. Alternatively, they can be placed in a stub-like side-housing and coupled through a small aperture.
In insert filters one or more metal sheets are placed longitudinally down the length of the waveguide as shown in figure 9. These sheets have holes punched in them to form resonators. The air dielectric gives these resonators a high Q. Several parallel inserts may be used in the same length of waveguide.
More compact resonators may be achieved with a thin sheet of dielectric material and printed metallisation instead of holes in metal sheets at the cost of a lower resonator Q. Finline is a different kind of waveguide technology in which waves in a thin strip of dielectric are constrained by two strips of metallisation. There are a number of possible topological arrangements of the dielectric and metal strips.
Finline is a variation of slot-waveguide but in the case of finline the whole structure is enclosed in a metal shield. This has the advantage that, like hollow metal waveguide, no power is lost by radiation. Finline filters can be made by printing a metallisation pattern on to a sheet of dielectric material and then inserting the sheet into the E-plane of a hollow metal waveguide much as is done with insert filters. The metal waveguide forms the shield for the finline waveguide. Resonators are formed by metallising a pattern on to the dielectric sheet.
More complex patterns than the simple insert filter of figure 9 are easily achieved because the designer does not have to consider the effect on mechanical support of removing metal. This complexity does not add to the manufacturing costs since the number of processes needed does not change when more elements are added to the design. Finline designs are less sensitive to manufacturing tolerances than insert filters and have wide bandwidths.
It is possible to design filters that operate internally entirely in evanescent modes. This has space saving advantages because the filter waveguide, which often forms the housing of the filter, does not need to be large enough to support propagation of the dominant mode.
Typically, an evanescent mode filter consists of a length of waveguide smaller than the waveguide feeding the input and output ports. In some designs this may be folded to achieve a more compact filter. Tuning screws are inserted at specific intervals along the waveguide producing equivalent lumped capacitances at those points. In more recent designs the screws are replaced with dielectric inserts. These capacitors resonate with the preceding length of evanescent mode waveguide which has the equivalent circuit of an inductor, thus producing a filtering action.
Energy from many different evanescent modes is stored in the field around each of these capacitive discontinuities. However, the design is such that only the dominant mode reaches the output port; the other modes decay much more rapidly between the capacitors. Corrugated-waveguide filters , also called ridged-waveguide filters , consist of a number of ridges, or teeth, that periodically reduce the internal height of the waveguide as shown in figures 10 and They are used in applications which simultaneously require a wide passband, good passband matching, and a wide stopband.
They are essentially low-pass designs above the usual limitation of the cutoff frequency , unlike most other forms which are usually band-pass. Typically, they are designed by the image parameter method with all ridges identical, but other classes of filter such as Chebyshev can be achieved in exchange for complexity of manufacture.
In the image design method the equivalent circuit of the ridges is modelled as a cascade of LC half sections. The filter operates in the dominant TE 10 mode, but spurious modes can be a problem when they are present. In particular, there is little stopband attenuation of TE 20 and TE 30 modes. The waffle-iron filter is a variant of the corrugated-waveguide filter. It has similar properties to that filter with the additional advantage that spurious TE 20 and TE 30 modes are suppressed.
In the waffle-iron filter, channels are cut through the ridges longitudinally down the filter. This leaves a matrix of teeth protruding internally from the top and bottom surfaces of the waveguide. This pattern of teeth resembles a waffle iron , hence the name of the filter. A stub is a short length of waveguide connected to some point in the filter at one end and short-circuited at the other end.
Open-circuited stubs are also theoretically possible, but an implementation in waveguide is not practical because electromagnetic energy would be emitted from the open end of the stub, resulting in high losses. Stubs are a kind of resonator, and the lumped element equivalent is an LC resonant circuit.
However, over a narrow band, stubs can be viewed as an impedance transformer. The short-circuit is transformed into either an inductance or a capacitance depending on the stub length. The ends of the stubs are blanked off to short-circuit them. In this case the lumped-element equivalent is series LC resonant circuits in series with the line. Absorption filters dissipate the energy in unwanted frequencies internally as heat.
This is in contrast to a conventional filter design where the unwanted frequencies are reflected back from the input port of the filter. Such filters are used where it is undesirable for power to be sent back towards the source. This is the case with high power transmitters where returning power can be high enough to damage the transmitter. An absorption filter may be used to remove transmitter spurious emissions such as harmonics or spurious sidebands.
A design that has been in use for some time has slots cut in the walls of the feed waveguide at regular intervals. This design is known as a leaky-wave filter. Each slot is connected to a smaller gauge waveguide which is too small to support propagation of frequencies in the wanted band. Thus those frequencies are unaffected by the filter. Higher frequencies in the unwanted band, however, readily propagate along the side guides which are terminated with a matched load where the power is absorbed.
These loads are usually a wedge shaped piece of microwave absorbent material. There are many applications of filters whose design objectives are something other than rejection or passing of certain frequencies. Frequently, a simple device that is intended to work over only a narrow band or just one spot frequency will not look much like a filter design.
However, a broadband design for the same item requires many more elements and the design takes on the nature of a filter. Amongst the more common applications of this kind in waveguide are impedance matching networks, directional couplers, power dividers, power combiners , and diplexers. Other possible applications include multiplexers , demultiplexers, negative-resistance amplifiers , and time-delay networks.
A simple method of impedance matching is stub matching with a single stub. However, a single stub will only produce a perfect match at one particular frequency. This technique is therefore only suitable for narrow band applications. To widen the bandwidth multiple stubs may be used, and the structure then takes on the form of a stub filter. The design proceeds as if it were a filter except that a different parameter is optimised.
In a frequency filter typically the parameter optimised is stopband rejection, passband attenuation, steepness of transition, or some compromise between these. In a matching network the parameter optimised is the impedance match. The function of the device does not require a restriction of bandwidth, but the designer is nevertheless forced to choose a bandwidth because of the structure of the device.
Stubs are not the only format of filter than can be used. In principle, any filter structure could be applied to impedance matching, but some will result in more practical designs than others. A frequent format used for impedance matching in waveguide is the stepped impedance filter. An example can be seen in the duplexer [e] pictured in figure Directional couplers, power splitters, and power combiners are all essentially the same type of device, at least when implemented with passive components.
A directional coupler splits a small amount of power from the main line to a third port. A more strongly coupled, but otherwise identical, device may be called a power splitter. One that couples exactly half the power to the third port a 3 dB coupler is the maximum coupling achievable without reversing the functions of the ports. Many designs of power splitter can be used in reverse, whereupon they become power combiners. Coupling will be a maximum at this frequency and fall away on either side.
Similar to the impedance matching case, this can be improved by using multiple elements, resulting in a filter-like structure. To produce a wideband design, multiple holes are used along the guides as shown in figure 14 and a filter design applied. A diplexer is a device used to combine two signals occupying different frequency bands into a single signal. This is usually to enable two signals to be transmitted simultaneously on the same communications channel, or to allow transmitting on one frequency while receiving on another.
This specific use of a diplexer is called a duplexer. The same device can be used to separate the signals again at the far end of the channel. The need for filtering to separate the signals while receiving is fairly self-evident but it is also required even when combining two transmitted signals. Without filtering, some of the power from source A will be sent towards source B instead of the combined output.
This will have the detrimental effects of losing a portion of the input power and loading source A with the output impedance of source B thus causing mismatch. These problems could be overcome with the use of a 3 dB directional coupler, but as explained in the previous section, a wideband design requires a filter design for directional couplers as well. Two widely spaced narrowband signals can be diplexed by joining together the outputs of two appropriate band-pass filters.
Steps need to be taken to prevent the filters from coupling to each other when they are at resonance which would cause degradation of their performance. This can be achieved by appropriate spacing. This works because when filter A is at resonance, filter B is in its stopband and only loosely coupled and vice versa. An alternative arrangement is to have each filter joined to a main waveguide at separate junctions. This can be in the form of a short-circuited stub tuned to the resonant frequency of that filter.
This arrangement can be extended to multiplexers with any number of bands. For diplexers dealing with contiguous passbands proper account of the crossover characteristics of filters needs to be considered in the design. An especially common case of this is where the diplexer is used to split the entire spectrum into low and high bands. Here a low-pass and a high-pass filter are used instead of band-pass filters.
The synthesis techniques used here can equally be applied to narrowband multiplexers and largely remove the need for decoupling resonators. A directional filter is a device that combines the functions of a directional coupler and a diplexer. As it is based on a directional coupler it is essentially a four-port device, but like directional couplers, port 4 is commonly permanently terminated internally.
Power entering port 1 exits port 3 after being subject to some filtering function usually band-pass. The remaining power exits port 2, and since no power is absorbed or reflected this will be the exact complement of the filtering function at port 2, in this case band-stop. In reverse, power entering ports 2 and 3 is combined at port 1, but now the power from the signals rejected by the filter is absorbed in the load at port 4. Figure 15 shows one possible waveguide implementation of a directional filter.
Two rectangular waveguides operating in the dominant TE 10 mode provide the four ports. These are joined together by a circular waveguide operating in the circular TE 11 mode. The circular waveguide contains an iris coupled filter with as many irises as needed to produce the required filter response. From Wikipedia, the free encyclopedia. Electronic filter that is constructed with waveguide technology.
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Dial-up modems blazed along at All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowl edged. The following equations and images describe electromagnetic waves inside both rectangular waveguide and circular round waveguides. Oval waveguide equations are not included due to the mathematical complexity. The lower cutoff frequency or wavelength for a particular mode in rectangular waveguide is determined by the following equations note that the length, x, has no bearing on the cutoff frequency :.
This example is for TE 1,0 the mode with the lowest cutoff frequency in WR waveguide commonly used for S-band radar systems. It has a width of 2. Either m or n can be zero, but not both. End View TE Side View TE Waveguides with constant rectangular or circular cross sections are normally employed, although other shapes may be used from time to time for special purposes. With regular transmission lines and waveguides, the simplest shapes are the ones easiest to manufacture, and the ones whose properties are simplest to evaluate.
A rectangular waveguides is shown in Figure , as is a circular waveguide for comparison. In a typical system, there may be an antenna at one end of a waveguide and a receiver or transmitter at the other end. The antenna generates electromagnetic waves, which travel down the waveguide to be eventually received by the load.
The walls of the guide are conductors, and therefore reflections from them take place. It is of the utmost importance to realize that conduction of energy lakes place not through the walls, whose function is only to confine this energy, but through the dielectric filling the waveguide, which is usually air. In discussing the behavior and properties of waveguides, it is necessary to speak of electric and magnetic fields, as in wave propagation, instead of voltages and currents, as in transmission lines.
This is the only possible approach, but it does make the behavior of waveguides more complex to grasp. Because the cross-sectional dimensions of a waveguide must be of the same order as those of a wavelength, use at frequencies below about 1 GHz is not normally practical, unless special circumstances warrant it.
Some selected waveguide sizes, together with their frequencies of operation, are presented in Table The table shows how waveguide dimensions decrease as the frequency is increased and therefore wavelength is shortened. It does not show the several waveguides larger than the WR, nor does it show many of the overlapping sizes that are also made. Note that the reason for the rather odd dimensions is that waveguides originally were made to imperial measurements e.
It is seen that waveguides have dimensions that are convenient in the 3- to GHz range, and somewhat inconvenient much outside this range. Within the range, waveguides are generally superior to coaxial transmission lines for a whole spectrum of microwave applications, for either power or low-level signals. Both waveguides and transmission lines can pass several signals simultaneously, but in waveguides it is sufficient for them to be propagated in different modes to be separated.
They do not have to be of different frequencies. A number of waveguide components are similar if not identical to their coaxial counterparts.