Adapter structure with waveguide channels

10658761 · 2020-05-19

Assignee

Inventors

Cpc classification

International classification

Abstract

An adapter structure for transferring an electromagnetic signal between an electronic component and an antenna, the adapter structure includes an adapter body having a base surface. The adapter structure further includes at least one ridged adapter waveguide channel, wherein the at least one adapter waveguide channel extends from the base surface into the adapter body. The adapter structure further includes an electromagnetic band gap structure with a plurality of band gap elements, wherein the band gap elements are spaced apart relative to each other, project from the base surface and have a front face spaced apart from the base surface. At least one band gap element is arranged as extension of a ridge of an associated adapter waveguide channel.

Claims

1. An adapter structure for transferring an electromagnetic signal between an electronic component (2) and an antenna (3), the adapter structure comprising: an adapter body (3c) having a base surface (130b); at least one ridged adapter waveguide channel (170), wherein the at least one adapter waveguide channel (170) extends from the base surface (130b) into the adapter body (3c); an electromagnetic band gap structure with a plurality of band gap elements, wherein the band gap elements (160, 161) are spaced apart relative to each other, project from the base surface (130b) and have a front face spaced apart from the base surface (130b); wherein at least one band gap element (161) is arranged as an extension of a ridge of the at least one adapter waveguide channel (170).

2. The adapter structure according to claim 1, wherein the at least one adapter waveguide channel (170) is double-ridged.

3. The adapter structure according to claim 2, wherein two band gap elements (161) are arranged as extensions of the two ridges of the at least one adapter waveguide channel (170).

4. The adapter structure according to claim 1, comprising a plurality of adapter waveguide channels (170), wherein for each of the adapter waveguide channels (170) at least one band gap element (161) is arranged as extension of a ridge of the associated waveguide channel (170).

5. The adapter structure according to claim 4, wherein the adapter waveguide channels (170) are of substantially identical electrical length.

6. The adapter structure according to claim 4, wherein the plurality of adapter waveguide channels (170) forms a distribution structure.

7. The adapter structure according to claim 1, wherein the at least one adapter waveguide channel is curved.

8. The adapter structure according to claim 1, wherein the adapter structure is made from injected-moulded plastics.

9. The adapter structure according to claim 1, wherein the adapter structure includes a printed circuit board alignment structure for mutually aligning the adapter structure with a printed circuit board (2) and/or an antenna alignment structure for mutually aligning the adapter structure with the antenna (3).

10. The adapter structure according to claim 1, wherein the base surface (130b) is, in an area of the electromagnetic band gap structure, planar with exception of the band gap elements (160, 161).

11. The adapter structure according to claim 1, wherein the adapter structure is an adapter device (1) for transferring a microwave signal between a component waveguide coupling structure of an electronic component, in particular a microwave semiconductor component (21) mounted on a printed circuit board (2), and an antenna waveguide coupling structure of the antenna (3), the adapter structure further including: an antenna-facing adapter surface (10a); an antenna-opposing adapter surface (10b), the antenna-opposing adapter surface (10b) being spaced apart from the antenna-facing adapter surface (10a); wherein the antenna-opposing adapter surface (10b) has a component-receiving recess (13), the component-receiving recess (13) being dimensioned to receive at least part of the microwave semiconductor component (21) and the component-receiving recess (13) having a recess ground (13b) that defines the base surface; wherein the at least one adapter waveguide channel (17) extends in the adapter body between the recess ground (13b) and the antenna-facing adapter surface (10a).

12. The adapter structure according to claim 11, including a printed circuit board mounting structure, the printed circuit board mounting structure being arranged on the antenna-opposing adapter surface (10b).

13. An antenna (3) comprising an adapter structure according to claim 1, the antenna (3) having a top surface with at least one waveguide opening (34) for transmitting and/or receiving electromagnetic signals, wherein the at least one waveguide opening (34) is operatively connected with the at least one adapter waveguide channel (170).

14. A microwave assembly, including an antenna (3) according to claim 13 and a printed circuit board (2), the printed circuit board having an antenna-facing PCB surface (20a) with at least one waveguide coupling aperture (203), wherein the front faces of the band gap elements (160, 161) face the antenna-facing PCB surface (20a) and the at least one waveguide coupling aperture (203) is aligned and operatively connected with the at least one adapter waveguide channel (170).

15. A method for transmitting at least one electromagnetic signal, in particular a microwave signal, the method including transmitting the at least one electromagnetic signal via an adapter structure according to claim 1.

Description

BRIEF DESCRIPTION OF FIGURES

(1) FIG. 1 shows a microwave assembly in a top view;

(2) FIG. 2 shows the microwave assembly in a side view;

(3) FIG. 3 shows the microwave assembly in a bottom;

(4) FIG. 4 shows the microwave assembly in a partly exploded perspective view;

(5) FIG. 5 shows an embodiment of an adapter device in a perspective top view;

(6) FIG. 6 shows a further embodiment of the adapter device in a perspective top view;

(7) FIG. 7 shows an embodiment of an adapter device in a perspective bottom view;

(8) FIG. 8 shows a further embodiment of a microwave assembly with an antenna and a printed circuit board;

(9) FIG. 9 shows part of the antenna of the embodiment of FIG. 8 in a perspective view;

(10) FIG. 10 shows the recess with electromagnetic band gap structure of the embodiment of FIG. 8;

(11) FIG. 10A, 10B show cross sectional views from FIG. 10;

(12) FIG. 11 shows the antenna-opposing side of the printed circuit board of the embodiment of FIG. 8.

(13) FIG. 12 shows a cross sectional view of the printed circuit board of the embodiment of FIG. 8;

(14) FIG. 13 shows detail of the antenna-facing side of the printed circuit board of the embodiment of FIG. 8.

EXEMPLARY EMBODIMENTS

(15) In the following description of exemplary embodiments, directional terms such as top, bottom, left, right, are referred to with respect to the viewing directions according to the drawings and are only given to improve the reader's understanding. They do not refer to any particular directions or orientations in use. In particular, top and bottom refer to the z-axis as indicated in the figures. Further, the coordinate system that is shown in some figures is provided only for purposes of explanation and clarity only and does not imply any limitations to the generality.

(16) The antenna, the adapter plate and the printed circuit board are stacked in z-direction with footprints being defined traverse to the z-direction where not stated differently. The directions traverse to the z-direction are also referred to as lateral directions. The antenna is the bottom most and the printed circuit board the top-most component.

(17) In the following, reference is first made to FIG. 1 to FIG. 3. FIG. 1 shows an exemplary microwave assembly in accordance with the present disclosure in top view; FIG. 2 shows the microwave assembly in a side view; FIG. 3 shows the microwave assembly in bottom view.

(18) The microwave assembly includes an adapter device 1, a printed circuit board 2 with at least one microwave semiconductor component (the latter being hidden in FIG. 1 to FIG. 3), and an array antenna 3 in a mounted state. The shown microwave assembly is a multiple-input and multiple-output (MIMO) radio device.

(19) The antenna 3 and the adapter device 1, form, in combination, an antenna assembly which is realized by a stack of coplanar layers of exemplarily identical rectangular footprint, while the printed circuit board 2 has exemplarily smaller rectangular footprint. By way of example, the antenna 3 is itself realized by a stack of four coplanar layers. Layer 3d is the adapter facing outer antenna layer to which the adapter device 1 attached e. g. via adhesive bonding or is screwed together with a set of screws. Layer 3a is an adjacent outer antenna layer and comprises e. g. horn-shaped waveguide openings 34 for transmitting and/or receiving electromagnetic waves, in particular microwaves on an outer surface 30a of the antenna 3. Layers 3b and 3c are intermediate layers and comprise a waveguide transmission and/or distribution structure (not visible).

(20) In the following, reference is additionally made to FIG. 4, showing the microwave assembly in a perspective and partially exploded view.

(21) On the antenna-opposing adapter surface 10b, the adapter device 1 comprises a circumferential alignment ridge 11 that enclosed area of which receives the printed circuit board 2 with tight tolerance. A planar circumferential printed circuit board coupling surface 12 provides a supporting surface for a corresponding counter-surface of the adapter-facing printed circuit board surface 20a.

(22) The printed circuit board coupling surface 12 surrounds the component-receiving recess 13 in which a band-gap structure is arranged (not referenced in FIG. 4). The ground of the component receiving recess 13 (in z-direction) is the recess ground 13b.

(23) Exemplarily two microwave semiconductor components 21 are mounted on the adapter-facing printed circuit board surface 20a such that they are, in an assembled state, received by the component-receiving recess 13. A total number of exemplarily eight component waveguide coupling elements (not visible in detail) are arranged on the adapter-facing surface 21a of the two microwave semiconductor components 21. The printed circuit board is mounted to the adapter device 1 via exemplarily four screws 4.

(24) The distance by which the microwave semiconductor components 21 raise above the adapter-facing printed circuited board surface 20a, the distance by which the band gap elements project into the component-receiving recess, and the printed circuit board coupling surface 12 are dimensioned such that a defined gap is present between the adapter-facing component surfaces 21a of the two microwave semiconductor components 21 and the component-facing ends of the band gap elements, which is bridged by an optional sheet-like coupling member 15.

(25) On the adapter-facing antenna surface 30b, a number of exemplarily double-ridged antenna waveguide coupling openings 31 is arranged in a row, with each antenna waveguide coupling opening being in a one-to-one correspondence with a waveguide coupling element of one of the microwave semiconductor components 21. The single antenna waveguide coupling openings 31 are exemplarily equally spaced apart.

(26) Alignment recesses 32 are present in the circumferential edge of each of the antenna layers 3a, 3b, 3c, 3d. Exemplarily, the alignment recesses have the contour of a concave cylinder jacket section. Corresponding alignment recesses 14 are also present in the circumferential edge of the adapter device 1. The alignment recesses 32, 14 form, in combination, a concave cylinder jacket for alignment with external alignment members, such as alignment posts or alignment pins (not shown) during manufacture of the antenna assembly.

(27) In the following, reference is additionally made to FIG. 5, showing an exemplary embodiment of the adapter device 1 in a perspective top view, together with a detailed view of a section of the component receiving recess.

(28) The band gap structure is realised by a regular pattern of band gap elements 16 in form of square-sectioned posts that project from the recess ground 13b perpendicularly into the component-receiving recess 13. In a typical exemplary embodiments, the band gap elements 16 have a square footprint of (0.60.6) mm.sup.2, project into the component receiving recess 13 by a height of one mm (z-direction) and are laterally spaced apart (x- and y-direction) by 0.6 mm.

(29) The U-shaped component-facing channel openings 17b of the single-ridged adapter waveguide channels 17 are arranged between the band gap elements 16. Each of the component-facing channel openings 17b is, in the assembled state, aligned (in z-direction) with a corresponding component waveguide coupling element. As best seen in the detailed view, a band gap element 16 continues as ridge into the adapter waveguide channel 17.

(30) In the following, reference is additionally made to FIG. 7, showing the adapter device in a perspective bottom view. Exemplarily eight U-shaped antenna-facing channel openings 17a are provided on the antenna facing adapter surface 10a. The antenna-facing channel openings 17a are aligned in a row such that each antenna-facing channel opening is, in an assembled state, aligned with a corresponding antenna waveguide coupling opening 31. Each pair of an antenna-facing channel opening 17a and a component-facing channel opening 17b form the ends of a corresponding single-ridged adapter waveguide channel 17.

(31) As further visible from FIG. 7, the single-ridged adapter waveguide channels 17 have a section that runs parallel to the antenna-facing adapter surface 10a and is further open to the antenna-facing adapter surface 10a, with the antenna-facing channel opening 17a forming an end section of the single-ridged adapter waveguide channel 17. In an assembled state, the open section of the adapter waveguide channel is, with exception of the antenna-facing channel opening 17a, covered by the adapter-facing antenna-surface 30b.

(32) As best visible from FIG. 5 and FIG. 7 in combination, the geometric pattern of the component-facing channel openings 17b (identical to the geometric pattern of the component waveguide coupling elements) is different from the geometric pattern of the antenna-facing channel openings 17a (identical to the geometric pattern of the antenna waveguide coupling openings 31). The curved adapter waveguide channels accordingly form a distribution structure. The single-ridged adapter waveguide channels 17 are further individually optimized for identical wave guiding characteristics respectively microwave transmission characteristics and in particular an identical electrical length. Since the electrical length of the adapter waveguide channels 17 depends on both on their physical/geometrical length and cross section, the physical length and/or the cross sections, e. g. the cross section over a section of the physical length, may be tuned or modified for this purpose.

(33) As best visible in FIG. 7, the single-ridged adapter waveguide channels 17 form a three-dimensional (spatial) curve that is different for different adapter waveguide channels in dependence of the position of the corresponding antenna-facing channel opening 17a and component-facing channel opening 17b.

(34) In the following, reference is additionally made to FIG. 6, showing a further exemplary embodiment of the adapter device 1 in view corresponding to FIG. 5, with the bottom view being substantially the same as shown in FIG. 7. Since this embodiment is similar to the before-described embodiments in a number of aspects, only differences are discussed in the following.

(35) The component-facing channel openings 17b of this embodiment are arranged in channel posts 18 of exemplarily square cross section that project, like the band gap elements 16, in z-direction from the recess ground 13b by the same height as the band gap elements 16. The component-facing channel openings 17b accordingly lay in a common plane with the component-facing end surfaces of the band gap elements 16. A component-sided straight end section of each single-ridged adapter waveguide channel 17 is arranged inside the channel posts and in parallel alignment with the channel post 18.

(36) In the following, reference is made to FIG. 8 to FIG. 13, showing a further microwave assembly. FIG. 8 shows a PCB 2 together with an antenna 3 in a partly exploded perspective bottom view. The antenna 3 is made from a stack of a number of coplanar layers as generally explained before. For the sake of conciseness and clarity, only the bottom layer 3c that contacts the PCB 2 and the next following layer 3b are individually referenced. All further layers are, in combination, referenced as 3a.

(37) The bottom layer 3c that is arranged between the PCB 2 and the other layers 3b, 3a is realized as adapter structure. Surface 120 of the bottom layer 3c is a peripheral surface that serves as printed circuit board coupling surface. The bottom layer 3c further forms the adapter body.

(38) The PCB 2 has an integrated microwave structure for coupling the microwave semiconductor component to the antenna 3. In FIG. 8, a metallization 22 is visible from which microstrip lines 23 extend to the microwave semiconductor component 21a for signal coupling. The design of the PCB 2 is discussed in more detail further below.

(39) A microwave semiconductor 21 is mounted on the PCB 2. In contrast to the before-described embodiments, the microwave semiconductor 21 is arranged in the antenna-opposing PCB surface 20b, facing away from the antenna 3.

(40) FIG. 9 shows the two bottom-most layers 3b, 3c in a perspective bottom view. FIG. 10 shows a detailed top view of recess 130 in bottom layer respectively adapter body 3c. Band gap elements 160, 161 project from the recess ground 130b. H-shaped component-facing channel openings 170b are arranged in the recess ground 130b along a straight line. The band gap elements 160, 161 are arranged in a pattern of rows and columns, respectively as matrix, with the center line of the component-facing waveguide openings being symmetric with respect to two neighboring rows of band gap elements 160, 161. In this way, electromagnetic sealing is achieved.

(41) It can be seen that between each pair of neighboring component-facing channel openings 170, there is a further column of band gap elements 160, 161. Further, these band gap elements are flush with edges of the component-facing channel openings, i. e. the distance between the edges of two neighboring component-facing channel openings 170b along the direction of the rows corresponds to the width of the band gap elements 161 in between them.

(42) FIG. 10A, 10B are cross-sectional views through adapter waveguide channels 170 as indicated in FIG. 10. It can be seen that band gap elements 161 are arranged as continuous extensions of the ridges with a smooth transition. As further visible in FIG. 10, there is a further continuous and uninterrupted row of band gap elements 160 on both sides of the two rows of band gap elements 161. In FIG. 10A, 10B it can be further seen that that the band gap elements 160, 161 stand slightly back behind the printed circuit board coupling surface 120.

(43) FIG. 11 and FIG. 13 show a view onto the antenna-opposing PCB surface 20b and the antenna-facing PCB surface 20a, respectively. FIG. 12 is a cross-sectional view along line Q-Q as indicated in FIG. 11.

(44) The PCB 2 is a sandwich from three dielectric layers D1, D2, D3 that are separated by prepreg (preimpregnated fibres) layers P1, P2. The outer surface of the first dielectric layer D1 forms the antenna-opposing PCB surface 20b and the outer surface of the third dielectric layer D3 forms the antenna-facing PCB surface 20a. The outer surfaces of the first dielectric layer D1 and the third dielectric layer D3 are generally metalized. On the antenna-opposing PCB-surface 20b, however, the metallization is partly removed to form metallization 22 with microstrip lines 23 as visible in FIGS. 8, 11. Exemplarily eight microstrip lines 23 (exemplarily aligned with the y-direction) are present, corresponding to eight inputs/outputs of the microwave semiconductor component 21. The inner surfaces of the dielectric layer D1, D2, D3 are generally non-metallized within the SIW waveguide channels with the exception of connection strips 206 as explained further below. Outside the SIW channels the inner layers can be metalized in order to act as low frequency signals or power distribution layers for the microwave semiconductor component 21. The outer metallization of the antenna-facing PCB-surface 20a is referenced as M in FIG. 12. It is noted that the use of microstrips is not essential, but that other type of wave-guiding structures, such as coplanar waveguides or striplines could be used as well.

(45) Adjacent to the microstrip lines 23, substrate integrated waveguides (SIWs) are arranged. There are microstrip to SIW transitions 22a which couple microstrip lines 23 to the corresponding SIW waveguides 204. Such transitions are known in the art (see, e.g. D. Deslandes, Design equations for tapered microstrip-to-Substrate Integrated Waveguide transitions, 2010 IEEE MTT-S International Microwave Symposium, Anaheim, Calif., 2010, pp. 704-707.). Traverse to the direction of wave propagation W (exemplarily corresponding to the y-direction), the single SIWs are delimited and separated from each other by an arrangement of through-going vias 201 that extend in parallel lines, parallel to the direction of wave propagation inside the SIWs. The arrangement of through-going vias 201 separates each SIW in two sections that are adjacent to each other in the direction of wave propagation W. In a first SIW section 204, each SIW is delimited traverse to direction of the SIWs by a separate line (exemplarily aligned with the y-direction) of through-going vias 201, resulting in pairs of through-going vias 201 in a side-by-side arrangement between neighboring first SIW sections 204.

(46) Adjacent to the first SIW section 204, there is, for each SIW, a second SIW section 205. The second SIW sections 205 are separated from each other by single lines of through-going vias 201 that are arranged in line with the center lines of the pairs of through-going vias 201 for the first SIW sections 204. Neighbouring second SIW sections 205 accordingly share a common line of through-going vias 201 that is arranged between them (exemplarily aligned with y-direction FIG. 11). Thereby, the second SIW sections 205 have a width w2 that is wider than w1. The second SIW sections 205 are delimited traverse to the direction of wave propagation by a continuous line of through-going vias 201 (exemplarily aligned with x-direction FIG. 11). At least in the area of the first SIW sections 204 and second SIW sections 205, all inner metalizations of the dielectric layers D1, D2, D3 are removed in the relevant area with the exception of connection strips 206 as explained further below.

(47) As best visible in FIG. 12, the through-going vias 201 bridge all layers D1, P1, D2, P2, D3 and connect the metallization 22 on the antenna-opposing PCB surface 20b with the metallization M of antenna-facing PCB surface 20a. Thereby, the whole thickness of the PCB 21 serves as SIW It further noted that the through-going vias 201 (like the blind vias 202 as discussed further below) are shown as solid cylinders in FIG. 12 in the interest of a clear drawing).

(48) As best visible in FIG. 13, H-shaped PCB waveguide coupling apertures 203 are arranged on the third dielectric layer D3 that are realized by a corresponding partial H-shaped removal of the metallization M. In an assembled configuration of the PCB 2 and the antenna 3, each of the PCB waveguide coupling apertures 203 is aligned with a corresponding component-facing channel opening 17b.

(49) As best visible from FIG. 11, FIG. 12, and FIG. 13, a blind via 202 is further present for each of the second SIW sections 205. The blind vias 202 extend from the antenna-opposing PCB surface 20b like the through-going vias 201. In contrast to the through-going vias 201, however, they do not bridge all layers of the PCB. Instead, they extend only through the first dielectric layer D1, the first prepreg layer P1 and the second dielectric layer D2. While the metallization of the inner layers is generally removed as explained before, the blind ends of the blind vias 202 are galvanically connected by way of a connection strip 206 of remaining metallization on the antenna-facing side of the dielectric layer D2, with a through-going via 201. The connection strip 206 is arranged on the surface of the second dielectric layer D2 that points towards the antenna-facing PCB surface 20a and runs parallel to the extension direction of the second SIW section 205 (direction W of wave propagation). Thereby, it connects the ground or blind end of the blind via 202 with an associated through-going via 201 of the line of through-going vias 201 that delimit the second SIW sections 205 traverse to the direction of wave propagation W.

(50) As best visible in FIG. 13, each blind via 202 is laterally positioned such that its center is aligned with the second SIW section 205 and the PCB waveguide coupling aperture 203 in the direction of the width of the waveguide apertures 205 (traverse to the direction of wave propagation W). In direction of the wave propagation W, half of the blind via 202 lies within the area of the PCB waveguide coupling aperture 203, while the other half lies under the metallization M, towards the line of through-going vias 201 that delimit the second SIW sections 205 traverse to the direction of wave propagation W.

(51) The arrangement of second SIW sections 205 (both delimited by through-going vias 201), blind vias 202 and waveguide-coupling apertures 203 forms a waveguide coupling structure that deflect the electromagnetic waves from the wave propagation direction W (tangential to the PCB 2) by 90 degrees such that they enter and/or exit the waveguide coupling openings 203 traverse to the PCB 2. Further, the arrangement serves for impedance matching between the SIW sections 204 and 205 and the adapter waveguide channels 170.

(52) The purpose of blind via 202 is to deflect the electric field direction from perpendicular to the propagation direction W to a direction more tangential to the PCB waveguide coupling aperture 203. In this way, the coupling between second SIW section 205 and adapter waveguide channel 170 is improved.

(53) The distance between the centre of a PCB waveguide coupling aperture 203 and the end of the associated second SIW section 205 as defined by the line of through-going vias 201 perpendicular to the direction of wave propagation W is favourably selected to be about a quarter of a guided wavelength (inside the second SIW section) at the central frequency of operation, thereby transforms a short at the end of the second SIW section into open load at the plane of the PCB waveguide coupling aperture and maximizing the electric field at this plane which increases the coupling between PCB 2 and the antenna layer 3c.

(54) The width w1 of the first SIW section 204 is favourably selected, for a main frequency of operation of the system, such that it lies above the cut-off frequency of the first mode and below the cut-off frequency of the second mode.

(55) The width 22 of the second SIW section 205 is favourably selected slightly larger than the width w1 SIW in order to accommodate the PCB waveguide coupling aperture 203.

(56) The length of the second SIW section 205 (along the direction of wave propagation W) is favourably selected sufficiently long to accommodate the PCB waveguide coupling aperture 203 and a quarter guided wavelength distance between the end of the second SIW section 205 and the centre of the PCB waveguide coupling aperture 203. Favourable the total length of the second SIW section 205 should be least half of guided wavelength or more. It is noted that tuning of this dimension is critical since it is constrained by the fact that the number of vias is necessarily an integral number.

(57) The footprint of the PCB waveguide coupling aperture 203 is generally similar to the footprint of the associated component facing channel opening 17b. It may be favourably tuned by way of numerical optimization. The width of the via connecting strip is also tuned by way of numerical optimization.

REFERENCE SIGNS

(58) 1 adapter device 2, 2 printed circuit board (PCB) 3, 3 antenna 3a, 3b, 3c, 3d antenna layer 3a, 3b, 3c antenna layers 4 screw 10a antenna-facing adapter surface 10b antenna-opposing adapter surface 11 alignment ridge 12, 120 printed circuit board coupling surface 13 component-receiving recess 13b recess ground 14 alignment recess 15 coupling member 16, 160, 161 band gap element 17 single-ridged adapter waveguide channel 17a antenna-facing channel opening 17b component-facing channel opening 18 channel post 20a adapter-facing PCB surface 20b antenna-opposing PCB surface 20a antenna-facing PCB surface 21, 21 microwave semiconductor component 21a adapter-facing component surface 22 metallization 23 microstrip line 30a outer surface/top surface of antenna 30b adapter-facing antenna surface 31 antenna waveguide coupling opening 32 alignment recess 34 waveguide opening 130 recess 130b recess ground/base surface 170 double-ridged adapter waveguide channel 201 through-going via 202 blind via 203 PCB waveguide coupling aperture 204 first SIW section 205 second SIW section 206 connection strip D1, D2, D3 dielectric layers M metallization P1, P2 prepreg layers W direction of wave propagation in SIWs w1 First SIW section width w2 second SIW section width