WAVEGUIDE FILTERS
20220263210 · 2022-08-18
Inventors
- Elena Pucci (Stockholm, SE)
- Oscar QUEVEDO-TERUEL (STOCKHOLM, SE)
- Alberto Monje Real (Danderyd, SE)
- Nelson Fonseca (Noordwijk, NL)
Cpc classification
International classification
H01P11/00
ELECTRICITY
Abstract
A filter for filtering an electromagnetic wave and a filter design method are provided. The filter comprises a cavity with a first plate and a second plate, the first and second plates are opposite to each other. The first plate comprises a number of elements distributed on the side of the first plate facing the cavity, wherein a location of each element on the first plate is defined in a coordinate system. The second plate comprises a number of elements distributed on the side of the second plate facing the cavity according to the locations of the elements on the first plate, wherein each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate.
Claims
1. A filter designed to filter an electromagnetic wave comprising: a cavity with a first plate and a second plate, the first and second plates are opposite to each other, wherein the first plate comprises a number of elements distributed on the side of the first plate facing the cavity, wherein a location of each element on the first plate is defined in a coordinate system; and the second plate comprises a number of elements distributed on the side of the second plate facing the cavity according to the locations of the elements on the first plate, wherein each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate.
2. The filter according to claim 1 is a waveguide filter, wherein the cavity is a rectangular parallelepiped.
3. The filter according to claim 1 further comprising two side plates to prevent leakage of wave energy at the sides of the filter and constrain the electromagnetic wave to propagate along a direction of the cavity from one end to the other, and as the electromagnetic wave is traversing about the elements in the cavity, specific wavelengths are filtered.
4. The filter according to claim 1 further comprising electromagnetic band gap, EBG, surfaces on sides of the first and second plates to constrain the electromagnetic wave to propagate along a direction of the cavity from one end to the other, and as the electromagnetic wave is traversing about the elements in the cavity, specific wavelengths are filtered.
5. The filter according to claim 1, wherein the coordinate system is a three-dimensional orthonormal coordinate system defined by x-y-z- axes with an origin and a center plane between and in parallel with the first and second plates, wherein the x-axis corresponds to a distance from the origin along a transversal direction of the first and second plates, the z-axis corresponds to a distance from the origin along a longitudinal direction of the first and second plates and the y-axis corresponds to a distance from an element to the center plane perpendicular to the first and second plates.
6. The filter according to claim 5, wherein the number of the elements on the first plate are distributed according to a rectangular lattice in x and z directions, and wherein the location of each element on the second plate is defined according to a combination of coordinate transformations in the x and z directions and a mirroring transformation in y direction such that each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate in two directions.
7. The filter according to claim 6, wherein the location of each element on the second plate is defined according to coordinate transformations defined by
8. The filter according to claim 6 wherein the location of each element on the second plate is defined according to a coordinate transformation defined by
9. The filter according to claim 1, wherein the coordinate system is a cylindrical coordinate system for circular waveguides or coaxial waveguides with twist symmetry.
10. The filter according to claim 1, wherein each element is a 3-D structure with any shape.
11. The filter according to claim 1, wherein the elements are any of pins, holes, protrusions, recesses.
12. The filter according to claim 1, wherein size and/or shape of the elements are varied along a given direction.
13. The filter according to claim 1, wherein periodicities of the elements along transversal and longitudinal directions are different.
14. The filter according to claim 1, wherein periodicities of the elements along transversal and longitudinal directions are varied along a given direction.
15. The filter according to claim 1, wherein heights of the elements are adjusted along longitudinal direction to match input and output impedance of the filter.
16. The filter according to claim 1, wherein numbers of elements along transversal and longitudinal directions are different.
17. The filter according to claim 1, wherein numbers of elements along transversal and longitudinal directions are adjusted independently to fit in the cavity of the filter.
18. The filter according to claim 1, wherein the filter is made by any one of metal material, dielectric filled printed circuit board material.
19. (canceled)
20. (canceled)
21. A method for designing a filter for filtering an electromagnetic wave, the method comprising: choosing an element with regarding to geometry; choosing size of a cavity with a first plate and a second plate, the first and second plates are in parallel and opposite to each other; choosing a number of elements distributed on the side of the first plate facing the cavity; defining locations of each element on the first plate by a coordinate system; choosing a number of elements distributed on the side of the second plate facing the cavity; defining locations of the elements on the second plate according to the locations of the elements on the first plate such that each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate; analyzing a unit cell comprising a subset of the chosen elements; assessing performance of the unit cell; modifying elements until improve matching; assessing performance of the filter; and adjusting the size of a cavity, the number of unit cells until the performance of designed filter fulfils specifications of the filter.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Examples of embodiments herein are described in more detail with reference to attached drawings in which:
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DETAILED DESCRIPTION
[0045] Lenses and gap waveguide designs made in glide symmetry have been investigated in prior arts, however, the design of filters made in glide symmetry and their capabilities have never been studied and published so far.
[0046] A glide-symmetric unit cell is therefore studied here and developed to design waveguide filters with large stop-bands and multiple selective pass-bands or stop-bands.
[0047] The term unit cell refers to the smallest periodic unit in the structure. The choice of the unit cell is of great importance, given that its shape and geometry will determine the behaviour of the structure. A unit cell may comprise a subset of elements. Both terms “unit cell” and “element” are used hereafter.
[0048] Filters may be designed by applying the glide symmetric concept along two dimensions (2D), i.e. combining a transformation along the longitudinal direction and a transformation along one of the two transversal directions with a common mirroring direction.
[0049] According to embodiments herein, a filter configured to filter an electromagnetic wave may be designed by a combination of coordinates transformations in two directions. The filter comprises a cavity with a first plate and a second plate, the first and second plates are in parallel and opposite to each other. The first plate comprises a number of elements distributed on the side of the first plate facing the cavity, wherein a location of each element on the first plate is defined in a coordinate system. The second plate comprises a number of elements distributed on the side of the second plate facing the cavity according to the locations of the elements on the first plate, wherein each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate.
[0050] According to some embodiments herein, the coordinate system may be a three- dimensional orthonormal coordinate system defined by x-y-z-axes with an origin and a centre plane, i.e. an x-z plane, between and in parallel with the first and second plates, wherein the x-axis corresponds to a distance from the origin along a transversal direction of the first and second plates, the z-axis corresponds to a distance from the origin along a longitudinal direction of the first and second plates and the y-axis corresponds to a distance from an element to the centre plane and perpendicular to the first and second plates.
[0051] According to some embodiments herein, the number of elements on the first plate may be distributed according to a rectangular lattice in x and z directions, and wherein the location of each element on the second plate is defined according to a combination of coordinate transformations in the x and z directions and a mirroring transformation in y- direction such that each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate in two directions.
[0052] Two implementations may be possible which are described in detail below.
[0053] The first implementation is based on two consecutive 1D transformations, which may be described mathematically as follows:
[0054] The layout of the resulting filter does not depend on the order of the transformations.
[0055] An illustration of the two steps in this transformation is provided in
[0056] For illustration purposes, a two-dimensional lattice of square pins is used here with the same periodicity, dx, dz, along the two axes. The initial lattice of pins, on the top broad wall of the rectangular waveguide, is schematically represented by squares without filling. The lattice of pins obtained through the first transformation G.sub.1, which is located on the bottom broad wall of the rectangular waveguide, is schematically represented by dots filled squares. The transformation G.sub.1 is a glide symmetry along x-axis. The intermediate filter structure is schematically represented in
[0057] The proposed filter design may be generalized introducing so-called “broken” glide symmetry, where the translation along the transformation axis, x-axis and z-axis, is no longer equal to half-a-period of the original lattice, i.e. a “glide factor” αis added. The transformation may be also further generalized introducing a scaling factor βin the mirroring transformation, y-axis, resulting in an asymmetric design, where the mirrored geometry may have a different height. The corresponding transformations introduced above, G.sub.1, G.sub.2 may be re-written as follows:
[0058] where all a parameters, α.sub.x , α.sub.z, referred to as “glide factors”, are within interval [0; 1], corresponding to the ‘broken’ glide symmetry, i.e. corresponding to the offsets in x and z directions respectively, parameters d.sub.x, d.sub.z, are periodicity of each element in x and z directions respectively, while parameters β.sub.x, β.sub.z are positive real numbers, corresponding to a scaling factor in the mirroring transformation.
[0059] An example of glide-symmetric waveguide filter 600 based on this first implementation, i.e. the combination of two 1D glide symmetry transformations is shown in
[0060] Another filter example 700 is shown in
[0061] According to some embodiments herein, a second proposed implementation or design of a 2D glide-symmetric filter which is based on a single 2D transformation, may be described mathematically as follows:
[0062] A schematic representation, following the same nomenclature as in the previous case, squares without filling at the top plate, dots filled squares at the bottom plate, is shown in
[0063] This implementation may also be generalized, when the translation along the axis is no longer equal to half-a-period, by adding a “glide factor” a. The same may be generalized for the mirroring transformation, by adding a scaling factor β. The correspondent transformation may be then re-written as:
[0064] where all parameters a, referred to as “glide factors”, are within interval [0; 1], corresponding to the offsets in x and z directions respectively, parameters d.sub.x, d.sub.z, are periodicity of each element in x and z directions respectively, while parameter βis a positive real number, corresponding to the scaling factor in the mirroring transformation.
[0065] An example of a glide symmetric filter using a single 2D transformation is provided for satellite communication (satcom) applications combining Ku and Ka frequency bands. The corresponding filter design 900 is shown in
[0066] Methods according to embodiments herein for designing a waveguide filter will be described in detail in the following with reference to
[0067] The full design process for a filter starts from the design of a unit cell for the filter. A parametric study is conducted with the aim of helping designs and developments for various filter specifications. Then, a filter is designed using the unit cell as a building block.
[0068] Step 1001. Choosing an element
[0069] The first step is the choice of the elements or embodiments that shall be distributed over the plates. This choice shall be motivated to fulfill design goals. For example, holes may be used to reduce manufacturing cost, while pins could be used for achieving high power handling.
[0070] Step 1002. Choosing the size of the cavity with a first plate and a second plate
[0071] The size of the cavity has to be determined according to the desired performance and size constraints imposed to the design. The width of the cavity may be used to control cutoff frequency to create bandpass filters, or it may be left wide to increase attenuation over total length of the filter. The height of the cavity may be increased to reduce insertion losses or decreased to maximize attenuation per unit length. Finally, the length of the cavity along with the other two dimensions, will constrain the maximum attenuation achievable.
[0072] Step 1003. Choosing a number of elements distributed on the side of the first plate.
[0073] Note that once the size of the cavity and the number of elements are fixed, the periodicity and maximum size of the elements are determined. This will strongly influence the behavior of the filter.
[0074] Step 1004. Defining locations of each element in the first plate.
[0075] In this step, the lattice of elements in the first plate is defined according to the decisions made in steps 1001-1003.
[0076] Step 1005. Choosing a number of elements distributed on the side of the second plate facing the cavity. As discussed above, the number of elements distributed on the second plate may be different from the number of the elements on the first plate.
[0077] Step 1006. Defining locations of the elements on the second plate according to the locations of the elements on the first plate such that each element is distributed on the second plate with an offset with respect to a corresponding element on the first plate. The locations of the elements on the second plate may be defined by a combining of transformations along the longitudinal direction and along one of the two transversal directions as discussed before, i.e. applying glide-symmetric transformations e.g. 2D, two 1D or 1D transformations. When using a combination of two 1D transformations, the first step of the transformation may produce elements on the bottom plate which may be 5 mirrored into the top plate with the second transformation. This has to be taken into account when defining the initial element lattice on the top plate.
[0078] Step 1007. Analysing of a unit cell. The unit cell may comprise a subset of the chosen elements. Particularly it is the subset of those elements that represents the smallest period of the structure.
[0079] The analysis of the unit cell structure starts by analysing the behaviour of an infinite repetition of the smallest periodic unit in the structure. A unit cell obtained as a combination of two 1D glide symmetry transformations with just one central hole along the transversal direction, and with two holes on the opposite plate, is shown in
[0080] In order to understand the behaviour of the structure, it is of great use to carry out a parametric study for each unit cell that is intended to be used for the design. This parametric study helps understanding the variations of the structure with respect to each parameter, simplifying greatly the iterative design process afterwards.
[0081] Table 1 is elaborated as a summary for quick design of a holey unit cell showing the effect of parametric increments on Periodicity, Radius and Gap in the pass-band, first stop-band and second stop-band over the investigated spectrum bandwidth. Arrows pointing upwards indicate increments, while those pointing downwards indicate decrements. The equality sign is used when little or no change has been observed. NA stands for Not Applicable. Note that all variations are given considering that there is an increment in the corresponding parameter. Despite the fact that in the table only bandwidths are provided and not cut-off frequencies, the cut-off frequency is adjusted by varying the width of the waveguide in which the filter is built, since increments in the cavity width cause downshifts in frequency of the response and decrements produce the opposite effect, while keeping the bandwidths mostly unmodified.
TABLE-US-00001 TABLE 1 Unit cell design guidelines, for parameter increments. Stopband Stopband Parameter Passband 1 BW 2 BW Glide factor = ↓ ↑ Glide factor = 0.0 Periodicity ↓ ↓ ↑ (Opposed holes) Radius ↓ ↑ ↑ Gap = ↓ ↓ Glide factor = 0.6 Periodicity ↓ ↓ ↓ (Broken glide) Radius ↓ ↑ ↑ Gap ↑ ↓ ↓ Glide factor = 1.0 Periodicity ↓ NA = (Glide Radius ↓ NA = symmetry) Gap ↑ NA ↓
[0082] Once the analysis of the unit cell is carried out, the unit cell may or may not fulfil the desired behaviour. In case it does not, an iteration process is started, returning to step 1002 and modifying the parameters with a guidance e.g. Table 1 or a similar one elaborated for this purpose. In case the unit cell has the frequency behaviour desired, the filter may be built as the result of a concatenation of unit cells, and the next step is to be followed.
[0083] Step 1008. Modifying of elements until improving matching.
[0084] Parameters such as, but not limited to the height, or the radii, in holey cases, of the elements may be varied along different dimensions of the filter in order to correctly adapt the impedance of the filter to feeding unit.
[0085] After this, full wave analyses are carried out to assess the performance of the filter over frequency. Three scenarios may occur at this point. The first one is that the pass and stop bands are not placed in the correct frequency bands. In this case, further design iterations are required, going back to step 1002. The second scenario addresses the situation in which the pass and stopbands are correctly placed in frequency, but the attenuation is not correct. In this case, step 1009 (below) is applied and then the filter is analysed again. The third possible scenario is that the filter works correctly, i.e. the performance of designed filter fulfils specifications of the filter, in which case the design is completed.
[0086] Step 1009. Adjusting attenuation/roll-off with the number of unit cells
[0087] Given the periodic nature of the unit cells in the filter, the attenuation or roll-off may be adjusted with the number of unit cells in the filter. Of course, the maximum number of unit cells is limited by the maximum size of the cavity that was fixed in step 1002.
[0088] Beside the example filters 500, 600, 700, 800, 900 described above which are designed by the method according to embodiments herein, one more example filter 1200 designed by the method according to embodiments herein is shown in
[0089] Note that glide symmetry in all its variants or implementations presented here may be applied to unit cells or elements of any geometries, such as pins, and it is not limited to holes as in these examples. Also, direct integration of these filters with antennas or antenna arrays is possible.
[0090] Therefore according to some embodiments herein, each element may be a 3-D structure with any shape. The elements may be any of or a combination of pins, holes, protrusions, recesses, etc.
[0091] For mm-waves, metal waveguides are preferred for their low loss, but the concept works as well with dielectric filled waveguides in printed circuit board (PCB). So the filter may be made by any one of metal material, dielectric filled PCB material.
[0092] The number of elements, or unit cells, along the two directions of interest and corresponding periods may be adjusted independently to fit in the waveguide structure while providing the required filtering properties.
[0093] Additional degrees of freedom in the design of the filter may include:
[0094] The periodicity along the transversal and the longitudinal directions, which may be different;
[0095] The number of elements along the two directions of interest, which may be different;
[0096] The shape of the elements, which may be additive metallic e.g. pins or negative or vacuum, e.g. holes.
[0097] A change of periodicity and/or element size and shape along a given direction may also be implemented to enhance further the response of the filter, while maintaining its distinctive two-dimensional structure characteristic of the embodiments herein. So according to some embodiments herein, size and/or shape of the elements may be varied along a given direction. Periodicities of the elements along transversal and longitudinal directions may be varied.
[0098] Further generalizations may be considered, such as extending the property to cylindrical coordinates for circular waveguides with twist symmetry, or polar coordinates for structures with rotational symmetry e.g. parallel plate waveguide lenses. So according to some embodiments herein, the coordinate system may be a cylindrical coordinate system for circular waveguides or coaxial waveguides with twist symmetry.
[0099] The height of the elements, i.e. the elementary geometry e.g., holes, pins, etc. may be adjusted along the longitudinal direction of the structure to match input and output port impedances of the filter to a conventional waveguide, as commonly done in other waveguide filter solutions, such as stub filters.
[0100] The two side plates of the filter function to prevent leakage of wave energy at the sides of the filter and constrain the electromagnetic wave to propagate along a direction of the cavity from one end to the other, and as the electromagnetic wave is traversing about the elements in the cavity specific wavelengths are filtered.
[0101] According to some embodiments herein, the two sides plates may be replaced by EBG surfaces on sides of the first and second plates to prevent wave energy leakage from the sides of the filter and constrain the electromagnetic wave to propagate along a direction of the cavity from one end to the other, and as the electromagnetic wave is traversing about the elements in the cavity specific wavelengths are filtered.
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[0103] The implementation of the embodiments herein is straight forward as it relies on well-known modelling technics as well as conventional manufacturing processes, e.g. milling. Alternative manufacturing techniques may also be considered for cost reduction e.g., Additive Manufacturing.
[0104] The embodiments herein that are based on holey surfaces, rather than pins, are easy and cheap to manufacture for millimetre wave range applications, and may therefore be preferred over embodiments with pins or other types of protrusions for applications at these wavelengths.
[0105] To summarize, the filter and design method herein is to use a 2D glide symmetry unit cell design to make waveguide filters with large stop-band and which can attenuate out-of-band emissions and harmonics. The solution also shows great degrees of freedom to have multiple pass-bands and stop-bands and is cheap to manufacture for mm-wave applications when holes are used. The 2D glide-symmetric filter design may be obtained by having elements along longitudinal and transversal directions, with two possible implementations which have been explained in detail above.
[0106] The filters according to embodiments herein provide: [0107] Large stop-bands to attenuate out-of-band emissions and harmonics; [0108] Easy and cheap manufacturing for mm-waves applications when holes in metal plates are considered; [0109] Multiple selective and flexible pass-bands and stop-bands; [0110] Low losses; [0111] Easy integration or connection with existing components in mm-waves, e.g. may be directly integrated in an antenna structure.
[0112] The filters according to embodiments herein may be employed in various electronic circuits or devices, communication devices or apparatus.