Technical Field

The invention relates to a cavity resonator. Furthermore, the invention also relates to a filter device comprising such a cavity resonator and to a method for manufacturing such a cavity resonator.

Background

Micromachined cavity resonators and filters based on coupled resonators are typically composed of multiple layers of substrate processed by etching such as silicon wafers, etc. Micromachined cavity resonators and filters based on coupled resonators suffer from high sensitivity to non-verticality of side walls caused by so called underetching. This is in particular the case for large cavity sizes. The responses of such filters get severely detuned due to increased resonant frequencies and to the fact that the coupling coefficient changes.

In a conventional solution, silicon micromachined waveguide cavity filters with a substantially high underetching value are designed and fabricated taking into account the side wall angle. The underetching, or the sidewall angle, is determined experimentally using a test fabrication run, which however requires extra costs. Another drawback is the state of the etching tool which changes with time and produces different side wall angles, which requires test runs all the time and is unsuitable for mass production.

In another conventional solution, a releasable filling structure technique is used. The production technique allows to fabricate cavities with very low underetching but requires designing a more complex photomask with the filling structures and auxiliary elements, which demands substantial effort. The fabrication hence needs longer time and higher cost.

Summary

An objective of embodiments of the invention is to provide a solution which mitigates or solves the drawbacks and problems of conventional solutions.

A further objective of embodiments of the invention is to provide a solution which minimizes or reduces detuning of cavity resonators and filters comprising such cavity resonators.

The above and further objectives are solved by the subject matter of the independent claims. Further advantageous embodiments of the invention can be found in the dependent claims. According to a first aspect of the invention, the above mentioned and other objectives are achieved with a cavity resonator comprising: an input configured to receive an electrical input signal; an output configured to provide an electrical output signal in response to the electrical input signal; a body comprising a first part, a second part and a third part, wherein the second part is located above the first part and the third part is located between the first part and the second part; and a resonator cavity that is bounded laterally by two opposite inner surfaces of the body, wherein the two opposite inner surfaces of the body are parallel to each other in the third part.

An advantage of the cavity resonator according to the first aspect is that the problem of detuning due to underetching is reduced or eliminated compared to conventional solutions.

In an implementation form of a cavity resonator according to the first aspect, the two opposite inner surfaces of the body are inclined relative to each other in the first part and in the second part.

This means that the first part and the second part comprise underetching structures while the third part does not.

In an implementation form of a cavity resonator according to the first aspect, the first part, the second part and the third part are bonded to each other.

In an implementation form of a cavity resonator according to the first aspect, the third part is bonded directly to the first part and directly to the second part, respectively.

In an implementation form of a cavity resonator according to the first aspect, the input is located above the resonator cavity, and the output is located below the resonator cavity.

In an implementation form of a cavity resonator according to the first aspect, the first part comprises a first handle layer and a first device layer, the first device layer forming a bottom of the cavity resonator, and the second part comprises a second handle layer and a second device layer, the second device layer forming a top of the cavity resonator. In an implementation form of a cavity resonator according to the first aspect, the two opposite inner surfaces of the body are inclined relative to each other in the first handle layer and in the second handle layer.

In an implementation form of a cavity resonator according to the first aspect, the cavity resonator further comprises an additional resonator cavity that is bounded laterally by two opposite additional inner surfaces of the body, wherein the two opposite additional inner surfaces of the body are parallel to each other in the third part, and wherein the additional resonator cavity is coupled to the resonator cavity by means of a coupling iris extending between the resonator cavity and the additional resonator cavity.

An advantage with this implementation form is the third part can be fabricated on a cheaper substrate, e.g. in a silicon wafer without multiple layers such as a handle layer and a device layer.

In an implementation form of a cavity resonator according to the first aspect, the third part comprises a third handle layer and a third device layer, and wherein the coupling iris is arranged inside the third handle layer and the third device layer and extends in a longitudinal extension of the cavity resonator between the resonator cavity and the additional resonator cavity.

An advantage with this implementation form is the third part can be fabricated in the same batch with the first part and the second part. Thereby, reducing cost and fabrication time.

In an implementation form of a cavity resonator according to the first aspect, the third device layer has an opening directed towards the first handle layer or the second handle layer.

In an implementation form of a cavity resonator according to the first aspect, the opening is aligned with the coupling iris and forms a part of the coupling iris.

In an implementation form of a cavity resonator according to the first aspect, the coupling iris is formed as a slit in the third handle layer.

In an implementation form of a cavity resonator according to the first aspect, the cavity resonator further comprises an additional third part in which the two opposite inner surfaces of the body are parallel to each other. An advantage with this implementation form is that the coupling between the resonators is independent of the underetching in the first part and the second part, and is implemented in the third part, i.e. , a very accurate coupling is achieved.

In an implementation form of a cavity resonator according to the first aspect, the additional third part comprises an additional third handle layer and an additional third device layer, and wherein a minimum longitudinal extension of the resonator cavity or the additional resonator cavity in the first handle layer is less than a longitudinal extension of the resonator cavity or the additional resonator cavity in the additional third handle layer; and a minimum longitudinal extension of the resonator cavity or the additional resonator cavity in the first handle layer is less than the longitudinal extension of the resonator cavity or the additional resonator cavity in the additional third handle layer.

An advantage with this implementation form is that the resonant frequency of the cavity resonator is mainly determined by the size of the cavity in the third part. Hence, the sizes of the cavities fabricated in the first part and the second part, provided that they have smaller longitudinal extension, have minor influence on the resonant frequency.

In an implementation form of a cavity resonator according to the first aspect, the third part has been produced by etching with fall-out structures.

Thereby, the third part may be produced without underetching.

According to a second aspect of the invention, the above mentioned and other objectives are achieved with a filter device for signal processing of an electrical input signal, the filter device comprising a cavity resonator according to any implementation form of a cavity resonator according to the first aspect.

According to a third aspect of the invention, the above mentioned and other objectives are achieved with a method for manufacturing a cavity resonator, the method comprising: arranging a second part above a first part and arranging a third part between the first part and the second part; and bonding the third part directly to the first part and bonding the third part directly to the second part to form a body comprising a resonator cavity that is bounded laterally by two opposite inner surfaces of the body, wherein the two opposite inner surfaces of the body are parallel to each other in the third part.

The method according to the third aspect of the invention means that cavity resonators and hence also filters can be produced without the detuning problematics of cavity resonators produced with conventional methods.

In an implementation form of a method according to the third aspect, the method further comprises: producing the third part by etching with fall-out structures.

Thereby, the third part can be produced without underetching.

In an implementation form of a method according to the third aspect, the method further comprises: arranging an input of the cavity resonator above the resonator cavity and arranging an output of the cavity resonator below the resonator cavity.

Further applications and advantages of the embodiments of the invention will be apparent from the following detailed description.

Brief Description of the Drawings

The appended drawings are intended to clarify and explain different embodiments of the invention, in which:

- Fig. 1 and 2 shows a cavity resonator according to a conventional solution;

- Fig. 3 illustrates so called underetching in a handle layer;

- Fig. 4 shows a cavity resonator according to an embodiment of the invention having one intermediate part;

- Fig. 5 shows a cavity resonator according to an embodiment of the invention having two intermediate parts;

- Fig. 6a and 6b shows a cavity resonator according to an embodiment of the invention in which one intermediate part comprises a handle layer and a device layer;

- Fig. 7a and 7b shows a cavity resonator according to an embodiment of the invention in which two intermediate parts each comprises a handle layer and a device layer;

- Fig. 8a and 8b shows coupled cavity resonators according to an embodiment of the invention having one intermediate part and two resonator cavities connected by a coupling iris; - Fig. 9 shows the coupled cavity resonators of Fig. 8a and 8b in an exterior perspective view from above;

- Fig. 10a and 10b shows coupled cavity resonators according to an embodiment of the invention having two intermediate parts and two resonator cavities connected by a coupling iris;

- Fig. 11 shows the coupled cavity resonators of Fig. 10a and 10b in an exterior perspective view from above;

- Fig. 12a and 12b shows a flow chart for manufacturing a cavity resonator according to an embodiment of the invention;

- Fig. 13 illustrates a method for manufacturing a cavity resonator;

- Fig. 14 and 15 shows exemplary architectures for cavity resonators; and

- Figs. 16 to 18 shows some general performance results.

Detailed Description

Fig. 1 and 2 show a cavity resonator according to a conventional solution in which Fig. 1 shows the cavity resonator in a longitudinal cross-section view and Fig. 2 shows the cavity resonator of Fig. 1 in a transversal cross-section view along line Z - Z'. The shown conventional cavity resonator has two resonators connected to each other by a coupling iris. The conventional designs use two layers or chips, i.e. chip 1 and chip 2, fabricated on silicon-on-insulator (SOI) wafers. Each chip comprises a device layer and a handle layer. The device layer may be understood as a thinner silicon layer of a SOI wafer and are in cavity resonators and filters usually used as a top wall or a bottom wall. Slots in the device layer can be utilized for excitation of cavities and filters. The handle layer may be understood as a thicker silicon layer of the SOI wafer. For making a cavity using SOI wafers, the handle layer is usually etched according to a desired pattern and the non-etched parts of the handle layer comprise side walls of the cavities. Chip 1 and 2 are bonded handle layer to handle layer as shown in Fig. 1 and 2. The underetching in chip 1 and 2 is clearly visible in Fig. 1 and 2.

Fig. 3 further illustrates the non-verticality of the micromachined waveguide’s side walls due to underetching which is due to the production method, e.g. by fabrication tolerances, etc. The non-verticality is usually located in the handle layer and the amount of underetching denoted D may be defined as the horizontal component of a non-verticality vector which deviates from verticality. In a strict mathematical sense, the amount of underetching is the length of the vertical projection of the inside wall on the bottom wall cross-sectioned by a plane orthogonal to both inside walls. The value D is related to the thickness of the handle and device layers which e.g. in common applications may have a thickness of for the handle layer Hhan = 275 pm and for the device layer Hdev = 30 m. Underetching in cavity resonators leads to increased sizes of cavities and coupling irises. Further, the resonant frequencies and the coupling coefficients are changed due to underetching which means that cavity resonators and its applications, such as filter applications, get severely detuned with reduced performance as the result.

Therefore, it is herein disclosed a cavity resonator design reducing or eliminating the influence of fabrication tolerances on the responses of multilayer micromachined filters and increasing the product uniformity, which is in particular important for high volume production. The novel cavity resonator design herein disclosed allows fabricating cavity resonator and filters with reduced design effort and cost. This may be achieved by e.g. using micromachined chip layers with low or substantially no underetching in the middle of the assembled chip stack, while using layers with underetching, e.g. fabricated on the same wafer, on top and bottom of the chip stack forming the cavity resonator.

Fig. 4 shows a cross-section of a cavity resonator 100 according to an embodiment of the invention having one intermediate part also denoted third part or third layer in this disclosure. The cavity resonator 100 comprises an input 102 configured to receive an electrical input signal S _In , and also an output 104 configured to provide an electrical output signal S _Out in response to the electrical input signal S _In . The cavity resonator 100 further comprises a body 106 having a first part 110, a second part 120 and a third part 130. The second part 120 is located above the first part 110 and the third part 130 is located between the first part 110 and the second part 120. The cavity resonator 100 further comprises a resonator cavity 140 that is bounded laterally by two opposite inner surfaces 152, 154 of the body 106. The two opposite inner surfaces 152, 154 of the body 106 are parallel to each other in the third part 130.

The resonator cavity 140 is defined or limited by the two opposite inner surfaces 152, 154. That the two opposite inner surfaces 152, 154 are parallel or substantially parallel may be understood such that the inner surfaces 152, 154 do not have any underetching. The body 106 of the cavity resonator 100 may be understood to comprise plurality of parts or layers stacked onto each other to form a common body enclosing one or more inside cavities defined by its inner surfaces. The shape of the inner cavities is not limited to any specific shapes and may depend on the specific application.

Generally, the different parts of the cavity resonator 100 are bonded together to form what may be called a stack. Hence, the first part 110, the second part 120 and the third part 130 are bonded to each other using any suitable bonding techniques. For example, thermo- compression bonding techniques may be employed for producing the cavity resonator 100. In embodiments of the invention for avoiding intermediate layers, sheets or films between the different parts of the body, the third part 130 is bonded directly to the first part 110 and directly to the second part 120, respectively, for tight bonding of the parts.

In yet further embodiments of the invention, which is also disclosed in Fig. 4, the two opposite inner surfaces 152, 154 of the body 106 are arranged in an inclined angle relative to each other in the first part 110 and in the second part 120. Hence, that the two opposite inner surfaces are inclined relative to each other means that the first and second parts both have or comprises underetching sections. Inclined may herein mean that the inner surfaces 152, 154 are not parallel, e.g. that respective inner surface is not vertical, i.e. non-vertical if the body is oriented in such a manner.

Fig. 5 shows a cavity resonator 100 according to an embodiment of the invention instead having two intermediate parts also denoted third part 130 and an additional third part 130' herein. In the design of Fig. 5, the two opposite inner surfaces 152, 154 of the body 106 are also parallel to each other in the additional third part 130' for eliminating the negative effects of underetching as previously discussed.

From Fig. 4 and 5 it may further be noted that the first part 110 comprises a first handle layer 112 and a first device layer 114. The first device layer 114 forms a bottom section of the cavity resonator 100. Correspondingly, the second part 120 comprises a second handle layer 122 and a second device layer 124, and the second device layer 124 forms a top section of the cavity resonator 100. The adjectives “top” and “bottom” are defined in a spatial reference frame (or coordinate system) that is fixed relative to the cavity resonator. If the cavity resonator 100 is rotated relative to e.g. the Earth, the top section and the bottom section are still referred to as the top section and the bottom section, respectively, regardless of the orientation of the cavity resonator 100 relative to the Earth. In other words, “top” and “bottom” are defined relative to the cavity resonator 100 itself, not relative to the Earth. When the first part 110 comprises a first handle layer 112 and the second part 120 comprises a second handle layer 122 it may be noted that the two opposite inner surfaces 152, 154 of the body 106 are inclined relative to each other in the first handle layer 112 and in the second handle layer 122.

Moreover, the input 102 of the cavity resonator 100 is located above the resonator cavity 140 and the output 104 is located below the resonator cavity 140 in embodiments of the invention. However, the input 102 and the output 104 may in other examples be arranged at the side walls of the cavity resonator 100 through coupling irises for certain applications. The input 102 and the output 104 may be realized in a different number of ways. In one non-limiting example, the input 102 and output 104 are formed as slots, slits or any other suitable opening in the device layers through which the electrical input signal S _In and the electrical output signal S _Out propagates via the resonator cavity 140.

Fig. 6a and 6b shows a cavity resonator 100 according to an embodiment of the invention in which the third part 130 also comprises a handle layer 132 and a device layer 134. Fig. 6a shows the cavity resonator 100 in a longitudinal (L) cross-section view and Fig. 6b shows the cavity resonator 100 of Fig. 6a in a transversal (T) cross-section view along line A - A'.

A waveguide flange 162 is arranged around the input slot 102 and another waveguide flange 164 is arranged around the output slot 104. The device layers of the first part 110 and the second part 120 act as top and bottom walls of the waveguide and the inner surfaces of the resonating cavities are metallized and thus enable the current to flow at the inner surface. Waveguide flanges are connectors used to join sections of waveguides and corresponding waveguide devices, such as filters. The waveguide may e.g. be a closed metal pipe with various cross-sections and fillings utilized to transmit electromagnetic waves. Generally, rectangular waveguides with rectangular cross-section are mostly used at micro- and millimeter waves. For example, the EIA (Electronic Industries Alliance) standard describes sizes of the rectangular cross-sections used at various frequencies. Hence, for 75-110 GHz band (used in the example design), the EIA waveguide standard is WR10 with sizes of 2.54 mm by 1.27 mm.

Fig. 7a and 7b shows a cavity resonator 100 according to an embodiment of the invention in which the third part 130 and the additional third part 130' each comprises a handle layer 132, 132' and a device layer 134, 134', respectively. Fig. 7a shows the cavity resonator 100 in a longitudinal cross-section view and Fig. 7b shows the cavity resonator 100 of Fig. 7a in a transversal cross-section view along line B - B'. By having four layers or parts instead of three layers or parts, the quality factor of the resonators increases and thus the losses decrease, but the risk of cracking, breaking or misalignment during bonding increases because by introducing more layers more operations are needed at manufacturing.

Fig. 8a and 8b shows coupled cavity resonators 100 comprising one third part and two resonator cavities coupled to each other with a coupling iris 144. Fig. 8a shows a longitudinal cross-section view of the coupled cavities and Fig. 8b shows a transversal cross-section view of the coupling iris 144 along line C - C'. Fig. 9 shows the coupled cavity resonators 100 of Fig. 8a and 8b in a perspective view from above which also shows an input 102 and an output 104. Hence, in the disclosed example of Fig. 8a and 8b, the cavity resonator 100 comprises an additional resonator cavity 142 that is bounded laterally by two opposite additional inner surfaces 152', 154' of the body 106. The previous explained principles apply which means that the two opposite additional inner surfaces 152', 154' of the body 106 are parallel to each other in the third part 130. There is therefore no underetching in the third part 130. The additional resonator cavity 142 is coupled to the resonator cavity 140 by means of the coupling iris 144 which extends between the resonator cavity 140 and the additional resonator cavity 142. The function of the coupling iris 144 is to connect the resonator cavities so that the electromagnetic energy confined in one resonator cavity can interact with the electromagnetic energy in the other resonator cavity with a designed coefficient of interaction, i.e. the coupling coefficient. The coupling iris 144 is arranged inside the third handle layer 132 and extends in a longitudinal extension of the cavity resonator 100 between the resonator cavity 140 and the additional resonator cavity 142. The coupling iris 144 may be formed as a slit, slot or any suitable opening in the third handle layer 132 and the third device layer 134.

Further, the third device layer 134 may have an opening 136 that is directed towards the first handle layer 112 as shown in Fig. 8b. However, the opening 136 may also be directed towards the second handle layer 122, which is not shown in the Figs. It is also be noted that the opening 136 is aligned with the coupling iris 144 and hence form a part of the coupling iris 144 according to further embodiments of the invention. The opening 136 may be etched away when the third part 130 is fabricated using fall-out structures. In the previous disclosed designs, the coupling iris 144 is arranged in a single intermediate part, i.e. in the third part 130, and fabricated using fall-out structures. Therefore, underetching is zero or negligible in the coupling iris 144. By arranging the coupling iris only in the third part(s) and by using fall-out structures at fabrication high accuracy of the coupling between the resonator cavities is achieved.

Fig. 10a and 10b shows coupled cavity resonators comprising two intermediate parts and two resonator cavities coupled to each other with a coupling iris 144. Fig. 10a shows a longitudinal cross-section view of the coupled cavities and Fig. 10b shows a transversal cross-section of the coupling iris 144 along line D - D'. Fig. 11 shows the coupled cavity resonators 100 of Fig. 10a and 10b in a perspective view from above.

Generally, the distance d2, which is the maximum longitudinal extension of the cavity or in other words the size of the cavity in the third part or in the additional third part, will define the cavity size of the cavity resonator and hence the resonance frequency. However, if the following relation holds d1 + 2*D > d2, where d1 denotes the minimum longitudinal extension of the resonator cavity 140 and D denotes the underetching in the device layers of the first part 110 or the second part 120, d1 will instead define the resonance frequency which is not desired. Therefore, in embodiments of the invention shown in Fig. 10a and 10b, a minimum longitudinal extension d1 of the resonator cavity 140 or the additional resonator cavity 142 in the first handle layer 112 is less than a longitudinal extension of the resonator cavity 140 or the additional resonator cavity 142 in the additional third handle layer 132. Moreover, a minimum longitudinal extension d of the resonator cavity 140 or the additional resonator cavity 142 in the first handle layer 112 is less than the longitudinal extension of the resonator cavity 140 or the additional resonator cavity 142 in the additional third handle layer 132'.

Fig. 12a and 12b shows two flow charts for manufacturing a cavity resonator 100 according to embodiments of the invention. With reference to Fig. 12a, the method 300 comprises arranging 302 a second part 120 above a first part 110 and arranging a third part 130 between the first part 110 and the second part 120. The method 300 further comprises bonding 304 the third part 130 directly to the first part 110 and bonding the third part 130 directly to the second part 120 to form a body 106 comprising a resonator cavity 140 that is bounded laterally by two opposite inner surfaces 152, 154 of the body 106. The two opposite inner surfaces 152, 154 of the body 106 being parallel to each other in the third part 130.

In further embodiments of the invention, the method 300 may comprise one or more additional steps. Therefore, with reference to Fig. 12b, the method 300 may further comprise the step of producing 306 the third part 130 by etching with fall-out structures. Non-limiting exemplary values for Silicon-On-lnsulator wafer parameters may be for handle layer Hhandie = 275 pm and device layer Hdevice = 30 pm. By using this production method underetching can be avoided in the handle layer and the device layer of the third part 130. This also implies that the third part 130 may in embodiments been produced by etching with fall-out structures.

With further reference to Fig. 12b, the method 300 may further comprise the step of arranging 308 an input 102 of the cavity resonator 100 above the resonator cavity 140 and arranging an output 104 of the cavity resonator 100 below the resonator cavity 140. Steps 302 and 304 in Fig. 12b are however the same as in Fig. 12a.

Fig. 13 illustrates a method for manufacturing a cavity resonator according to an embodiment of the invention (right side in Fig. 13) compared to a conventional manufacturing method (left side in Fig. 13). In the conventional method, a bottom part (i.e. first part 110) is produced in step 1 and a top part (i.e. second part 120) is produced in step 2, where both the bottom part and the top part has underetching. In step 3 the bottom part and the top part are bonded together to form a body having a cavity with underetching. According to embodiments of the invention, an intermediate part (i.e. third part 130) is also produced in step 4, e.g. etched using fall-out structures, where the underetching is negligible or non-existent compared to the bottom part and the top part. The intermediate part is bonded to the bottom part and top part, respectively, in step 5 instead to form a body 106 having a cavity inside where the inner side walls or surfaces are parallel to each other and vertical, i.e. have no underetching.

Embodiments of the invention also relates to a filter device 200 for signal processing of an electrical input signal. Such a filter device 200 may comprise any number of cavity resonators 100 according to embodiments of the invention. The shape, dimensions, coupling structures, etc. of the cavity resonators may vary depending on the application. Fig. 14 and 15 therefore shows two non-limiting exemplary architectures or designs of filter devices comprising the cavity resonator disclosed herein. They may e.g. be produced as silicon micromachined cavity filters. Both filter devices 200 in Fig. 14 and 15 are 5 ^th -order direct-coupled filters, each with five resonators coupled through coupling irises 144. The filter device 200 in Fig. 14 comprises of five hollow rectangular resonators while the filter device 200 in Fig. 15 instead comprises five hollow circular resonators with circular ridges. Both filters are designed with an arrangement of chip layers or parts corresponding to the herein disclosed designs. As aforementioned, the coupling irises 144 are arranged in the intermediate layer, i.e. the third part 130, which has lower or no underetching while the top part, i.e. second part 120, and the bottom part, i.e. first part 110, each has a high level of underetching. The input 102 and output 104 are arranged through rectangular slots in the 1 ^st and 5 ^th resonators in these particular examples. The filter 200 may also comprise pins for aligning the input and output of the filter with the waveguide opening located on a flange used for connecting the filter to any signal processing system.

Simulated frequency responses of filters designed for operation at 76-77 GHz are shown in Fig. 16 and 17. Figs. 16 shows the influence of the underetching D on the resonant frequencies fo and Fig. 17 shows the coupling coefficients k _i2 between the resonators for three considered designs where: design A denotes a conventional solution, design B denotes the design shown in Fig. 9 and design C denotes the design shown in Fig. 11. The x-axis shows the underetching in pm and the y-axis the resonant frequency in GHz in Fig. 16 while the y-axis in Fig. 17 shows the coupling coefficient as a function of the underetching. For all mentioned designs, sensitivity of the resonant frequencies fo and the coupling coefficients ki2 between the resonators is studied. The cavity resonators are designed for the same resonant frequency of o = 75.5 GHz under the condition that D = 0 pm. The coupling irises are designed to achieve the same coupling coefficient value /C12 = 0.04 under the same condition. The amount of underetching D is varied between typically observed values D = 0... 100 pm. It is evident from Fig. 16 and 17 that the resonant frequencies linearly depend on the underetching for all the designs. At the same time, the resonant frequency decreases 100% faster for the conventional design A than for the design C and 50% faster that for design B. The coupling coefficients for design B and C however remain almost unchanged linearly decreasing by only 5.2% and 4.5%, respectively. The coupling coefficient for the conventional design A on the other hand increases by 150% for the same variation of the underetching. Fig. 16 and 17 therefore indicates that the proposed designs B and C demonstrate much better sensitivity to underetching than the conventional solution and hence achieve more robust designs.

Fig. 18 shows the frequency responses of the filter shown in Fig. 14 with all identical dimensions except of the underetching, which is increased by 15 pm comparing to the initial value of D = 25 pm. As a result of the increased underetching, the observed frequency shift of the response is only 0.3%, while the detuning of the response in the passband is very minor, the minimum return loss in the passband has increased just by 1.5 dB.

Finally, it should be understood that the invention is not limited to the embodiments described above, but also relates to and incorporates all embodiments within the scope of the appended independent claims.