Material compositions and waveguide widths of waveguides

Abstract

A substrate integrated waveguide comprises: a base substrate formed from a dielectric material and comprising a relative dielectric permittivity (ε r ) and a waveguide length (l), and a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), and each of the plurality of vias comprises a via diameter (d); wherein: the substrate integrated waveguide is configured to propagate an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ), and the relative dielectric permittivity (ε r ) is between a lower dielectric permittivity bound (ε r, min ) and an upper dielectric permittivity bound (ε r, max ).

Description

MATERIAL COMPOSITIONS AND WAVEGUIDE WIDTHS OF WAVEGUIDESCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority under 35 U.S.C. §119 of U.S. Provisional Application Serial No. 63 / 604425 filed on November 30, 2023, the content of which is relied upon and incorporated herein by reference in its entirety.BACKGROUNDField

[0002] The present disclosure generally relates to material compositions and waveguide widths of waveguides, and more specifically, to dielectric permittivity bounds for materials of a substrate-integrated waveguide, minimization of waveguide width for substrate- integrated waveguides, integrated digital radio-frequency circuit systems having waveguides having dielectric permittivities within dielectric permittivity bounds and minimized waveguide widths, and methods for manufacturing substrate-integrated waveguides having dielectric permittivities within dielectric permittivity bounds and minimized waveguide widths.Technical Background

[0003] Radio-frequency (“RF”) transceivers may desire the incorporation of small antennas to reduce the size of such RF transceivers. In certain contexts of use (for example, as patch antennas), RF transceivers may often desire minimizing size, and RF transceivers often utilize microstrip antenna designs to decrease a size of the RF transceivers. However, substrate-integrated waveguides (“SIWs”) may offer advantages over microstrip antenna designs by lowering loss, lowering fringing radiation, increasing manufacturability by using conventional printed circuit board (“PCB”) and silicon processing techniques, and reducing size and thickness of RF transceivers.

[0004] SIWs often consist of a dielectric material either with an interior air channel or an interior dielectric -filled channel. SIWs may typically incorporate polymer-based substrates as dielectric materials. However, polymer-based substrates may provide limited printed circuit board tolerances and low dimensional stability for structures incorporating polymer-based substrates and printed circuit boards. Low temperature cofired ceramics (“LTCCs”) may be an alternative to polymers as compositions of substrates for substrate-integrated waveguides,however surfaces of LTCCs may be rough and cause dimensional uncertainty due to errors often inherent to manufacturing waveguides from LTCCs.

[0005] SIWs may have a conductive coating on a top and / or bottom of a substrate of the SIW, with one or more arrays of vias (for example, through-holes) through a thickness of the SIW. To reduce a size of the SIW and / or RF transceivers incorporating the same, arrays of vias may be positioned closer together (for example, reducing a waveguide width of the SIW). However, positioning arrays of vias closer together may increase crosstalk between such, introducing greater levels of error in RF signals transmitted or received by the SIW.

[0006] Accordingly, a need exists for determining dielectric permittivity bounds for materials used to fabricate SIWs to achieve desired dielectric permittivities of materials used to fabricate SIWs and for achieving desired waveguide width of SIWs without exceeding maximum acceptable crosstalk bounds.SUMMARY

[0007] According to a first embodiment Al, a substrate integrated waveguide may comprise: abase substrate formed from a dielectric material and comprising a relative dielectric permittivity (εr) and a waveguide length (l); and a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), each of the plurality of vias comprises a via diameter (d), the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ), the relative dielectric permittivity (εr) is between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) is determined by:the upper dielectricpermittivity bound (εr,max) is determined by:and c is thespeed of light.

[0008] A second embodiment A2 includes the substrate integrated waveguide according to the first embodiment Al, wherein: the substrate integrated waveguide may further comprise an upper crosstalk bound (Cmax); the plurality of vias may define a number of vias (N); the electromagnetic wave signal may further comprise a vacuum wavelength (λ); and thewaveguide width (a) may be defined by: , wherein ξ is 0.048and wherein r is 0.6366.

[0009] A third embodiment A3 includes the substrate integrated waveguide according to the second embodiment A2, wherein a total crosstalk in decibels (Cdb) may be less than or equal to 30 decibels; and the total crosstalk in decibels Cdb) may be defined by: Cdb= 10(Log10((l)(Cmax)).

[0010] A fourth embodiment A4 includes the substrate integrated waveguide according to any of the embodiments Al -A3, wherein the base substrate may further comprise a substrate thickness, and wherein the substrate thickness may be less than twenty five times the via diameter (d).

[0011] A fifth embodiment A5 includes the substrate integrated waveguide according to any of the embodiments A1-A4, the dielectric material may comprise an inorganic material.

[0012] A sixth embodiment A6 includes the substrate integrated waveguide according to the fifth embodiment A5, wherein the dielectric material may comprise: an inorganic glass; an ion-exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

[0013] A seventh embodiment A7 includes the substrate integrated waveguide according to any of the embodiments A1-A6, wherein the base substrate may be formed from a plurality of dielectric materials.

[0014] An eighth embodiment A8 includes the substrate integrated waveguide according to the seventh embodiment A7, wherein the plurality of dielectric materials may comprise organic materials and / or inorganic materials.

[0015] A ninth embodiment A9 includes the substrate integrated waveguide according to the seventh embodiment A7 or the eighth embodiment A8, wherein the plurality of dielectric materials may be layered.

[0016] According to a tenth embodiment Bl, a substrate integrated waveguide may comprise: a base substrate formed from a dielectric material and comprising a waveguide length (l); a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a number of vias (N), the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposedalong the waveguide length (l), and each of the plurality of vias comprises a via diameter (d); and an upper crosstalk bound (Cmax), wherein: the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ). the waveguide width (a) is defined by: , and is 0.048 and r is0.6366.

[0017] An eleventh embodiment B2 includes the substrate integrated waveguide according to the tenth embodiment Bl, wherein a total crosstalk in decibels (Cdb) may be less than or equal to 30 decibels; and the total crosstalk in decibels (Cdb) may be defined by: Cdb= 10(Log10((l)(Cma)).

[0018] A twelfth embodiment B3 includes the substrate integrated waveguide according to the tenth embodiment Bl or the eleventh embodiment B2, wherein the base substrate further may comprise a relative dielectric permittivity (εr); the electromagnetic wave signal may further comprise a frequency (f); the relative dielectric permittivity (εr) may be between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max; the lower dielectric permittivity bound (εr,min) is determined by: εr,min= the upper dielectricpermittivity bound (εr,max) may be determined by: εr,max = . . and c may bethe speed of light.

[0019] A thirteenth embodiment B4 includes the substrate integrated waveguide according to any of the embodiments B1-B3, wherein the base substrate may further comprise a substrate thickness, and wherein the substrate thickness may be less than twenty five times the via diameter (d).

[0020] A fourteenth embodiment B5 includes the substrate integrated waveguide according to any of the embodiments B1-B4, wherein the dielectric material may comprise an inorganic material.

[0021] A fifteenth embodiment B6 includes the substrate integrated waveguide according to the fourteenth embodiment B5, wherein the dielectric material may comprise: aninorganic glass; an ion-exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

[0022] A sixteenth embodiment B7 includes the substrate integrated waveguide according to any of the embodiments B1-B6, wherein the base substrate may be formed from a plurality of dielectric materials.

[0023] A seventeenth embodiment B8 includes the substrate integrated waveguide according to the sixteenth embodiment B7, wherein the plurality of dielectric materials may comprise organic materials and / or inorganic materials.

[0024] An eighteenth embodiment B9 includes the substrate integrated waveguide according to the sixteenth embodiment B7 or the seventeenth embodiment B8, wherein the plurality of dielectric materials may be layered.

[0025] According to a nineteenth embodiment C 1 , an integrated digital radio-frequency(“RF”) circuit system may comprise: a spacer layer; an antenna layer; and a substrate integrated waveguide comprising: a base substrate formed from a dielectric material and comprising a waveguide length (l) and a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a number of vias (A), the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), each of the plurality of vias comprises a via diameter (d), and the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ).

[0026] A twentieth embodiment C2 includes the integrated digital RF circuit system according to the nineteenth embodiment Cl, wherein the base substrate may comprise an upper crosstalk bound (Cmax) and wherein the waveguide width (a) may be defined by:, wherein ξ may be 0.048 and rmay be 0.6366.

[0027] A twenty-first embodiment C3 includes the integrated digital RF circuit system according to the twentieth embodiment C2, wherein a total crosstalk in decibels (Cdb) may be less than or equal to 30 decibels; and the total crosstalk in decibels Cdb) may be defined by: Cdb= 10(Log10((l)(Cmax)).

[0028] A twenty-second embodiment C4 includes the integrated digital RF circuit system according to any of the embodiments C1-C3, wherein the dielectric material maycomprise a relative dielectric permittivity (A) and wherein the relative dielectric permittivity (εr) may be between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) may be determined by the u pperdielectric permittivity bound (εr,max) is determined by: εr,max=and c is thespeed of light

[0029] A twenty-third embodiment C5 includes the integrated digital RF circuit system according to any of the embodiments C1-C4, wherein the base substrate may further comprise a substrate thickness, and wherein the substrate thickness may be less than twenty five times the via diameter (d).

[0030] A twenty-fourth embodiment C6 includes the integrated digital RF circuit system according to any of the embodiments C1-C5, wherein the dielectric material may comprise an inorganic material.

[0031] A twenty-fifth embodiment C7 includes the integrated digital RF circuit system according to the twenty-fourth embodiment C5, wherein the dielectric material may comprise: an inorganic glass; an ion-exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

[0032] A twenty-sixth embodiment C8 includes the integrated digital RF circuit system according to any of the embodiments C1-C7, wherein the base substrate may be formed from a plurality of dielectric materials.

[0033] A twenty-seventh embodiment C9 includes the integrated digital RF circuit system according to the twenty-sixth embodiment C8, wherein the plurality of dielectric materials may comprise organic materials and / or inorganic materials.

[0034] A twenty-eighth embodiment CIO includes the integrated digital RF circuit system according to the twenty-sixth embodiment C8 or the twenty-seventh embodiment C9, wherein the plurality of dielectric materials may be layered.

[0035] According to a twenty -ninth embodiment DI, a method for manufacturing an integrated digital radio-frequency (“RF”) circuit system may comprise: forming and / or using a base substrate from a dielectric material, the base substrate comprising a waveguide length (l);forming a substrate integrated waveguide by forming a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a number of vias (N), the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (1), each of the plurality of vias comprises a via diameter (d), and the substrate integrated waveguide is configured to propagate an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ); attaching the substrate integrated waveguide to a first side of a spacer layer; and attaching an antenna layer to a second side of the spacer layer opposite the first side of the spacer layer.

[0036] A thirtieth embodiment D2 includes the method according to the twenty-ninth embodiment DI, wherein the base substrate may comprise an upper crosstalk bound (Cmax) and wherein the waveguide width (a) may be defined by:wherein may be 0.048 and rmay be 0.6366.

[0037] A thirty-first embodiment D3 includes the method according to the thirtieth embodiment D2, wherein a total crosstalk in decibels (Cdb) may be less than or equal to 30 decibels; and the total crosstalk in decibels Cdb) may be defined by: Cdb= 10(Log10((l)(Cmax)).

[0038] A thirty-second embodiment D4 includes the method according to any of the embodiments D1-D3, wherein the dielectric material may comprise a relative dielectric permittivity (εr) and wherein the relative dielectric permittivity (εr) may be between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) may be determined by: εr,min=the upper dielectricpermittivity bound (εr,max) is determined by: εr,max=and c is thespeed of light

[0039] A thirty-third embodiment D5 includes the method according to any of the embodiments D1-D4, wherein the base substrate may further comprise a substrate thickness, and wherein the substrate thickness may be less than twenty five times the via diameter (d).

[0040] A thirty-fourth embodiment D6 includes the method according to any of the embodiments D1-D5, wherein the dielectric material may comprise an inorganic material.

[0041] A thirty-fifth embodiment D7 includes the method according to the thirty-fourth embodiment D5, wherein the dielectric material may comprise: an inorganic glass; an ion- exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

[0042] A thirty-sixth embodiment D8 includes the method according to any of the embodiments D1-D7, wherein the base substrate may be formed from a plurality of dielectric materials.

[0043] A thirty-seventh embodiment D9 includes the method according to the thirtysixth embodiment D8, wherein the plurality of dielectric materials may comprise organic materials and / or inorganic materials.

[0044] A thirty-eighth embodiment D10 includes the method according to the thirtysixth embodiment D8 or the thirty-seventh embodiment D9, wherein the plurality of dielectric materials may be layered.

[0045] Additional features and advantages of the aspects described herein will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the aspects described herein, including the detailed description, which follows, the claims, as well as the appended drawings.

[0046] It is to be understood that both the foregoing general description and the following detailed description describe various aspects and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various aspects, and are incorporated into and constitute a part of this specification. The drawings illustrate the various aspects described herein, and together with the description serve to explain the principles and operations of the claimed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The embodiments set forth in the drawings are illustrative and exemplary in nature and not intended to limit the subject matter defined by the claims. The following detailed description of the illustrative embodiments can be understood when read in conjunction with the following drawings, wherein like structure is indicated with like reference numerals and in which:

[0048] FIG. 1 schematically depicts a perspective view of a substrate-integrated waveguide, according to one or more embodiments shown and described herein;

[0049] FIG. 2 schematically depicts an overhead view of a portion of a top surface of a substrate-integrated waveguide having two rows of vias, according to one or more embodiments shown and described herein;

[0050] FIG. 3 schematically depicts a portion of a top surface of a substrate-integrated waveguide having three rows of vias, according to one or more embodiments shown and described herein;

[0051] FIG. 4 schematically depicts a perspective view of a cross section of a substrate- integrated waveguide, according to one or more embodiments shown and described herein;

[0052] FIG. 5A schematically depicts an exploded view of an antenna layer, a spacer layer, and a substrate-integrated waveguide of an integrated digital RF circuit system, according to one or more embodiments shown and described herein;

[0053] FIG. 5B schematically depicts a cross-sectional view of an integrated digital RF circuit system, according to one or more embodiments shown and described herein;

[0054] FIG. 6 is a flow diagram of a method for manufacturing an integrated digital RF circuit system, according to one or more embodiments shown and described herein; and

[0055] FIG. 7 is a plot of effective permittivity versus Topas® thickness (y-axis: effective permittivity of a Topas® laminate (farads per meter); x-axis: Topas® thickness of the laminate (microns)) of an exemplary laminate of a substrate-integrated waveguide, according to one or more embodiments shown and described herein.DETAILED DESCRIPTION

[0056] The present disclosure, in one form, is related to substrate-integrated waveguides (“SIWs”) and material compositions and waveguide widths thereof, in particular for use in integrated digital radio-frequency (“RF”) circuit systems. Reference will now be made in detail to various embodiments of SIWs, integrated digital RF circuit systems, and methods of manufacturing the same.

[0057] Specifically, in embodiments, SIWs described herein may include a base substrate formed from a dielectric material and comprising a relative dielectric permittivity and a plurality of vias extending through the base substrate and formed from metal. The plurality of vias may define a via spacing. The plurality of vias may define a waveguide length and awaveguide width. The plurality of vias may be disposed along the waveguide length. Each of the plurality of vias may comprise a via diameter. The substrate-integrated waveguide may propagate and / or be configured to propagate an electromagnetic wave signal comprising a frequency and a vacuum wavelength. The relative dielectric permittivity may be between a lower dielectric permittivity bound and an upper dielectric permittivity bound. The lower permittivity bound may be a function of the via spacing, the frequency of the electromagnetic wave signal, and the via diameter.

[0058] In embodiments, SIWs described herein may include a base substrate formed from a dielectric material and a plurality of vias extending through the base substrate and formed from metal. The plurality of vias may define a via spacing. The plurality of vias may define a waveguide length and a waveguide width. The plurality of vias may be disposed along the waveguide length. Each of the plurality of vias may comprise a via diameter. The SIW may further include an upper crosstalk bound. The SIW may further include a number of apertures between each of the plurality of vias. The SIW may propagate and / or be configured to propagate an electromagnetic wave signal comprising a frequency and a vacuum wavelength. The waveguide width may be a function of the upper crosstalk bound, the vacuum wavelength, the number of apertures, the via diameter, the via spacing, and the waveguide width.

[0059] It should be understood that the term “crosstalk” as used herein refers to the coupling of light propagating through or propagated by a first structure with light propagating through or propagated by a second structure, and loss that may occur due to the same. It should be understood that the term “loss” as used herein refers to the attenuation of a light wave as it travels through a structure or as it is propagated by a structure.

[0060] An advantage of the present disclosure is that the various aspects described herein improve upon typical solutions in that SIWs described herein may have a reduced and / or desired waveguide width, a reduced and / or desired size of the SIW, and / or reduced and / or desired crosstalk between waveguides of the SIW. Accordingly, embodiments described herein may enable the creation of waveguides (and, in embodiments, associated antennas of broader integrated digital RF circuit systems incorporating such waveguides) having improved dimensions. Another advantage of the present disclosure is that various aspects described herein improve upon typical solutions in that SIWs described herein may be formed from one or more materials having, individually and / or collectively, reduced and / or desired dielectric constants and / or reduced and / or desired dielectric loss. Further, by reducing and / or adjustingdielectric constants of an SIW, materials may be chosen for forming the SIW which reduce manufacturing costs of the SIW.

[0061] Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0062] Directional terms as used herein - for example up, down, right, left, front, back, top, bottom - are made only with reference to the figures as drawn and are not intended to imply absolute orientation.

[0063] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation, and; the number or type of embodiments described in the specification.

[0064] As used herein, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise.

[0065] Turning now to the drawings, the embodiment of FIG. 1 depicts a substrate- integrated waveguide 100 (also referred to herein as “the SIW 100”). In embodiments, the SIW 100 includes a plurality of vias 102 extending through a portion of a waveguide surfacesurface 100a occupied, in part, by the vias 102 may be defined by a waveguide length (l) and a waveguide surface width (w). In embodiments, the vias 102 may be defined by the base substrate 100b (for example, as gaps, such as gaps 104, as depicted in FIG. 5B and described in further detail below). In embodiments, the vias 102 may be formed from a metal and, in certain such embodiments, the metal may line gaps in the base substrate 100b as a coating of walls of such gaps, thereby defining the vias 102. In embodiments, any, some, or all of the vias 102 may extend entirely through the SIW 100, as defined by a substrate thickness (h) of the SIW 100. In other embodiments, any, some, or all of the vias 102 may extend only partially through the SIW 100. In embodiments, the vias 102 define a number of vias (N). In the embodiment of FIG. 1, the number of vias (N) is 8; however, in other embodiments, the SIW 100 may have any number of vias. Accordingly, in embodiments, the number of vias (N) may instead be 10 or more, 100 or more, 250 or more, 500 or more, or even 1,000 or more.

[0066] In the embodiment of FIG. 1, the vias 102 are organized into a first row of vias 102a and a second row of vias 102b. However, in other embodiments (and as is described in further detail below and depicted in FIG. 3) the vias 102 may be organized into any number of rows, including, in embodiments, 2 rows, 3 rows, 4 rows, or even more than 4 rows. Each row of vias 102 may be linear or substantially linear.

[0067] In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm (microns), greater than or equal to 50 pm, greater than or equal to 100 pm, greater than or equal to 200 pm, or even greater than or equal to 300 pm. In embodiments, the substrate thickness (h) may be less than or equal to 400 pm, less than or equal to 300 pm, less than or equal to 200 pm, or even less than or equal to 50 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm and less than or equal to 400 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm and less than or equal to 300 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm and less than or equal to 200 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm and less than or equal to 100 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 10 pm and less than or equal to 50 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 50 pm and less than or equal to 400 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 50 pm and less than or equal to 300 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 50 pm and less than or equal to 200 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 50 pm and less than or equal to 100 pm. In embodiments,the substrate thickness (h) may be greater than or equal to 100 pm and less than or equal to 400 pm. In embodiments, the substrate thickness (h) may be greater than or equal to 100 pm and less than or equal to 300 qm. In embodiments, the substrate thickness (h) may be greater than or equal to 100 qm and less than or equal to 200 qm. In embodiments, the substrate thickness (h) may be greater than or equal to 200 qm and less than or equal to 400 qm. In embodiments, the substrate thickness (h) may be greater than or equal to 200 qm and less than or equal to 300 qm. In embodiments, the substrate thickness (h) may be greater than or equal to 300 qm and less than or equal to 400 qm.

[0068] In embodiments, the SIW 100 may propagate and / or be configured to propagate an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ). In embodiments, the SIW 100 may propagate and / or be configured to propagate the electromagnetic wave signal along waveguide length (l) (for example, parallel to the z-axis) between each of the rows of vias 102a, 102b, wherein the waveguide length (l) extends along a propagation direction of the electromagnetic wave signal through the SIW 100. In embodiments having more than two rows of the vias 102 (for example, as depicted in the embodiment of FIG. 3 and described in further detail below), each additional parallel row of the vias 102 may further define an additional waveguide along which an additional electromagnetic wave signal may be propagated.

[0069] In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz (gigahertz), greater than or equal to 30 GHz, greater than or equal to 50 GHz, greater than or equal to 100 GHz, greater than or equal to 200 GHz, or even greater than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be less than or equal to 400 GHz, less than or equal to 300 GHz, less than or equal to 200 GHz, less than or equal to 100 GHz, less than or equal to 50 GHz, or even less than or equal to 30 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz and less than or equal to 400 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz and less than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz and less than or equal to 200 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz and less than or equal to 100 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 3 GHz and less than or equal to 50 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greaterthan or equal to 3 GHz and less than or equal to 30 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 30 GHz and less than or equal to 400 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 30 GHz and less than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 30 GHz and less than or equal to 200 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 30 GHz and less than or equal to 100 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 30 GHz and less than or equal to 50 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 50 GHz and less than or equal to 400 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 50 GHz and less than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 50 GHz and less than or equal to 200 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 50 GHz and less than or equal to 100 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 100 GHz and less than or equal to 400 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 100 GHz and less than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 100 GHz and less than or equal to 200 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 200 GHz and less than or equal to 400 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 200 GHz and less than or equal to 300 GHz. In embodiments, the frequency (f) of the electromagnetic wave signal may be greater than or equal to 300 GHz and less than or equal to 400 GHz.

[0070] In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 qm. greater than or equal to 1 mm (millimeter), greater than or equal to 10 mm, greater than or equal to 50 mm, or even greater than or equal to 1 cm (centimeter). In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be less than or equal to 10 cm, less than or equal to 1 cm, less than or equal to 50 mm, less than or equal to 10 mm, or even less than or equal to 1 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 qm and less than or equal to 10 cm. In embodiments, the vacuum wavelength (λ) of the electromagneticwave signal may be greater than or equal to I μ m and less than or equal to 1 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 μm and less than or equal to 50 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 pm and less than or equal to 10 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 qm and less than or equal to 1 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 mm and less than or equal to 10 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 mm and less than or equal to 1 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 mm and less than or equal to 50 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 mm and less than or equal to 10 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 10 mm and less than or equal to 10 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 10 mm and less than or equal to 1 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 10 mm and less than or equal to 50 mm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 50 mm and less than or equal to 10 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 50 mm and less than or equal to 1 cm. In embodiments, the vacuum wavelength (λ) of the electromagnetic wave signal may be greater than or equal to 1 cm and less than or equal to 10 cm.

[0071] Referring now to FIG. 2, in embodiments, the vias 102 may define a via spacing (p) (for example, a pitch of the SIW 100), which is the distance between each via of the vias 102 and each via of the same row (for example, the row of vias 102a or the row of vias 102b), that neighbors the via of the vias 102. For example, the via spacing (p) can be the distance between the center of a via and the center of an adjacent via of the same row (e.g., a center-to- center distance). In embodiments, the via spacing (p) may be substantially constant between distinct rows of vias. For example, in the embodiment of FIG. 2, the via spacing (p) defined by the first row of vias 102a may be substantially equal to the via spacing (p) defined by the second row of vias 102b. However, in other embodiments, the via spacing (p) may not be substantially constant across distinct rows of vias. For example, in embodiments, the row ofvias 102a may define a via spacing (p) of differing length than a via spacing (p) defined by the row of vias 102b.

[0072] In embodiments, the via spacing (p) may be greater than or equal to 50 pm, greater than or equal to 100 pm, greater than or equal 250 pm, greater than or equal to 500 pm, or even greater than or equal to 750 pm. In embodiments, the via spacing (p) may be less than or equal to 1 mm, less than or equal to 750 pm, less than or equal to 500 pm, less than or equal to 250 pm, or even less than or equal to 100 pm. In embodiments, the via spacing (p) may be greater than or equal to 50 pm and less than or equal to 1 mm. In embodiments, the via spacing (p) may be greater than or equal to 50 pm and less than or equal to 750 pm. In embodiments, the via spacing (p) may be greater than or equal to 50 pm and less than or equal to 500 pm. In embodiments, the via spacing (p) may be greater than or equal to 50 pm and less than or equal to 250 pm. In embodiments, the via spacing (p) may be greater than or equal to 50 pm and less than or equal to 100 pm. In embodiments, the via spacing (p) may be greater than or equal to 100 pm and less than or equal to 1 mm. In embodiments, the via spacing (p) may be greater than or equal to 100 pm and less than or equal to 750 pm. In embodiments, the via spacing (p) may be greater than or equal to 100 pm and less than or equal to 500 pm. In embodiments, the via spacing (p) may be greater than or equal to 100 pm and less than or equal to 250 pm. In embodiments, the via spacing (p) may be greater than or equal to 250 pm and less than or equal to 1 mm. In embodiments, the via spacing (p) may be greater than or equal to 250 pm and less than or equal to 750 pm. In embodiments, the via spacing (p) may be greater than or equal to 250 pm and less than or equal to 500 pm. In embodiments, the via spacing (p) may be greater than or equal to 500 pm and less than or equal to 1 mm. In embodiments, the via spacing (p) may be greater than or equal to 500 pm and less than or equal to 750 pm. In embodiments, the via spacing (p) may be greater than or equal to 750 pm and less than or equal to 1 mm.

[0073] In embodiments, the vias 102 define a waveguide width (a), wherein the waveguide width (a) is a distance between the centers of vias of adjacent rows (for example, a distance between a center of a via of the row of vias 102a and a center of an adjacent via of the row of vias 102b). For example, the waveguide width (a) can be the distance between an axis of one row of vias (e.g., a line passing through the center of each via in the row of vias) and an axis of an adjacent row of vias. In embodiments, the waveguide width (a) may be substantially equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100. In embodiments, the waveguide width (a) may be greater than or equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100 minus0.05 mm and less than or equal to half the vacuum wavelength (λ) plus 0.05 mm. In embodiments, the waveguide width (a) may be greater than or equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100 minus 0.1 mm and less than or equal to half the vacuum wavelength (λ) plus 0.1 mm. In embodiments, the waveguide width (a) may be greater than or equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100 minus 0.15 mm and less than or equal to half the vacuum wavelength (λ) plus 0.15 mm. In embodiments, the waveguide width (a) may be greater than or equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100 minus 0.2 mm and less than or equal to half the vacuum wavelength (λ) plus 0.2 mm. In embodiments, the waveguide width (a) may be greater than or equal to half of a vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100 minus 0.25 mm and less than or equal to half the vacuum wavelength (λ) plus 0.25 mm.

[0074] In embodiments, the waveguide width (a) may be greater than or equal to 0. 1 mm, greater than or equal to 0.5 mm, greater than or equal to 1 mm, greater than or equal to 2.5 mm, or even greater than or equal to 5 mm. In embodiments, the waveguide width (a) may be less than or equal to 10 mm, less than or equal to 5 mm, less than or equal to 2.5 mm, less than or equal to 1 mm, or even less than or equal to 0.5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.1 mm and less than or equal to 10 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.1 mm and less than or equal to 5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0. 1 mm and less than or equal to 2.5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0. 1 mm and less than or equal to 1 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.1 mm and less than or equal to 0.5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.5 mm and less than or equal to 10 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.5 mm and less than or equal to 5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.5 mm and less than or equal to 2.5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 0.5 mm and less than or equal to 1 mm. In embodiments, the waveguide width (a) may be greater than or equal to 1 mm and less than or equal to 10 mm. In embodiments, the waveguide width (a) may be greater than or equal to 1 mm and less than or equal to 5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 1 mm and less than or equal to 2.5 mm. In embodiments, the waveguide width(a) may be greater than or equal to 2.5 mm and less than or equal to 10 mm. In embodiments, the waveguide width (a) may be greater than or equal to 2.5 mm and less than or equal to 5 mm. In embodiments, the waveguide width (a) may be greater than or equal to 2.5 mm and less than or equal to 5 mm.

[0075] In embodiments, each of the vias 102 comprise a via diameter (d). In embodiments, the via diameter (d) may be substantially constant for each of the vias 102. In embodiments, the via diameter (d) may differ between any, some, or all of the vias 102. In embodiments, the via diameter (d) may be substantially equal for vias of distinct rows of vias. For example, in the embodiment of FIG. 2, a via diameter (d) of the vias 102 of the first row of vias 102a may be substantially equal to a via diameter (d) of the vias 102 of the second row of vias 102b. However, in other embodiments, the via diameter (d) may not be substantially equal for vias of distinct rows of vias. For example, in the embodiment of FIG. 2, avia diameter (d) of the vias 102 of the first row of vias 102a may differ from a via diameter (d) of the vias 102 of the second row of vias 102b.

[0076] In embodiments, the via diameter (d) may be greater than or equal to 1 pm, greater than or equal to 10 pm, greater than or equal to 25 pm, greater than or equal to 50 pm, greater than or equal to 75 pm, greater than or equal to 100 pm, or even greater than or equal to 250 pm. In embodiments, the via diameter (d) may be less than or equal to 500 pm, less than or equal to 250 pm, less than or equal to 100 pm, less than or equal to 75 pm, less than or equal to 50 pm, less than or equal to 25 pm, or even less than or equal to 10 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 500 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 250 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 100 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 75 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 50 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 25 pm. In embodiments, the via diameter (d) may be greater than or equal to 1 pm and less than or equal to 10 pm. In embodiments, the via diameter (d) may be greater than or equal to 10 pm and less than or equal to 500 pm. In embodiments, the via diameter (d) may be greater than or equal to 10 pm and less than or equal to 250 pm. In embodiments, the via diameter (d) may be greater than or equal to 10 pm and less than or equal to 100 pm. In embodiments, the via diameter (d) may be greater than or equal to 10 pm and less than or equal to 75 pm. Inembodiments, the via diameter (d) may be greater than or equal to 10 qm and less than or equal to 50 qm. In embodiments, the via diameter (d) may be greater than or equal to 10 qm and less than or equal to 25 qm. In embodiments, the via diameter (d) may be greater than or equal to 25 qm and less than or equal to 500 qm. In embodiments, the via diameter (d) may be greater than or equal to 25 qm and less than or equal to 250 qm. In embodiments, the via diameter (d) may be greater than or equal to 25 qm and less than or equal to 100 qm. In embodiments, the via diameter (d) may be greater than or equal to 25 qm and less than or equal to 75 qm. In embodiments, the via diameter (d) may be greater than or equal to 25 qm and less than or equal to 50 qm. In embodiments, the via diameter (d) may be greater than or equal to 50 qm and less than or equal to 500 qm. In embodiments, the via diameter (d) may be greater than or equal to 50 qm and less than or equal to 250 qm. In embodiments, the via diameter (d) may be greater than or equal to 50 qm and less than or equal to 100 qm. In embodiments, the via diameter (d) may be greater than or equal to 50 qm and less than or equal to 75 qm. In embodiments, the via diameter (d) may be greater than or equal to 75 qm and less than or equal to 500 qm. In embodiments, the via diameter (d) may be greater than or equal to 75 qm and less than or equal to 250 qm. In embodiments, the via diameter (d) may be greater than or equal to 75 qm and less than or equal to 100 qm. In embodiments, the via diameter (d) may be greater than or equal to 100 qm and less than or equal to 500 qm. In embodiments, the via diameter (d) may be greater than or equal to 100 qm and less than or equal to 250 qm. In embodiments, the via diameter (d) may be greater than or equal to 250 qm and less than or equal to 500 qm.

[0077] In embodiments, the substrate thickness (h) may be less or equal to than 25 times the via diameter (d), less than or equal to 15 times the via diameter (d), less than or equal to 10 times the via diameter (d), less than or equal to 5 times the via diameter (d), or even less than or equal to 3 times the via diameter (d). In embodiments, the substrate thickness (h) may be greater than or equal to 1.5 times the via diameter (d), greater than or equal to 3 times the via diameter (d), greater than or equal to 5 times the via diameter (d), greater than or equal to 10 times the via diameter (d), or even greater than or equal to 15 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 25 times the via diameter (d) and greater than or equal to 1.5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 25 times the via diameter (d) and greater than or equal to 3 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 25 times the via diameter (d) and greater than or equal to 5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 25 times the via diameter (d)and greater than or equal to 10 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 25 times the via diameter (d) and greater than or equal to 15 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 15 times the via diameter (d) and greater than or equal to 1.5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 15 times the via diameter (d) and greater than or equal to 3 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 15 times the via diameter (d) and greater than or equal to 5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 15 times the via diameter (d) and greater than or equal to 10 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 10 times the via diameter (d) and greater than or equal to 1.5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 10 times the via diameter (d) and greater than or equal to 3 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 10 times the via diameter (d) and greater than or equal to 5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 5 times the via diameter (d) and greater than or equal to 1.5 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 5 times the via diameter (d) and greater than or equal to 3 times the via diameter (d). In embodiments, the substrate thickness (h) may be less or equal to 3 times the via diameter (d) and greater than or equal to 1.5 times the via diameter (d).

[0078] Referring to FIG. 3, in an embodiment, the SIW 100 may, rather than including only 2 rows of vias 102a, 102b (as in the embodiment of FIG. 2), include three rows of vias 102a, 102b, 102c. In embodiments, the via spacing (p) may be substantially constant between any, some, or all of the rows of vias 102a, 102b, 102c. In embodiments, the via spacing (p) may differ between any, some, or all of the rows of vias 102a, 102b, 102c. In embodiments, a waveguide width (a) between the first row of vias 102a and the second row of vias 102b may be substantially equal to a waveguide width (a) between the second row of vias 102b and the third row of vias 102c. In embodiments, a waveguide width (a) between the first row of vias 102a and the second row of vias 102b may differ from a waveguide width (a) between the second row of vias 102b and the third row of vias 102c. In embodiments, a via diameter (d) of the vias 102 of the first row of vias 102a may differ from a via diameter (d) of the vias 102 of the second row of vias 102b. In embodiments, a via diameter (d) of the vias 102 of the first row of vias 102a may differ from a via diameter (d) of the vias 102 of the third row of vias 102c. In embodiments, a via diameter (d) of the vias 102 of the third row of vias 102c maydiffer from a via diameter (d) of the vias 102 of the second row of vias 102b. In embodiments, a via diameter (d) of the vias 102 of the first row of vias 102a may be substantially equal to a via diameter (d) of the vias 102 of the second row of vias 102b . In embodiments, a via diameter (d) of the vias 102 of the first row of vias 102a may be substantially equal to a via diameter (d) of the vias 102 of the third row of vias 102c. In embodiments, a via diameter (d) of the vias 102 of the third row of vias 102c may be substantially equal to a via diameter (d) of the vias 102 of the second row of vias 102b.

[0079] Referring to FIG. 4, the SIW 100 may include a first layer 105a, a second layer 105b, and a third layer 105c. In embodiments, any, some, or all of the layers 105a, 105b, 105c may be formed from a dielectric material. In embodiments, the dielectric material of the first layer 105a may be the same dielectric material as the dielectric material of the second layer 105b. In embodiments, the dielectric material of the first layer 105a may be the same dielectric material as the dielectric material of the third layer 105c. In embodiments, the dielectric material of the third layer 105c may be the same dielectric material as the dielectric material of the second layer 105b. In embodiments, the dielectric material of the first layer 105a may be the same dielectric material as the dielectric material of the second layer 105b and the dielectric material of the third layer 105c. In embodiments, the dielectric material of the first layer 105a may be a different dielectric material than the dielectric material of the second layer 105b. In embodiments, the dielectric material of the first layer 105a may be a different dielectric material than the dielectric material of the third layer 105c. In embodiments, the dielectric material of the third layer 105c may be a different dielectric material than the dielectric material of the second layer 105b. In embodiments, the dielectric material of the first layer 105a may be a different dielectric material than the dielectric material of the second layer 105b and the dielectric material of the third layer 105c. In embodiments, any, some, or all of the layers 105a, 105b, 105c may be the same layer. In embodiments, any, some, or all of the layers 105a, 105b, 105c may include sub-layers. In certain such embodiments, sub-layers of any, some, or all of the layers 105a, 105b, 105c may be formed from distinct dielectric materials. In other such embodiments, sub-layers of any, some, or all of the layers 105a, 105b, 105c may be formed from the same dielectric material(s). In embodiments, any, some, or all of the layers 105a, 105b, 105c may be formed from a plurality of dielectric materials.

[0080] In embodiments, a dielectric material forming any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may include a glass (including, in embodiments, any, some, or all of lithium potassium borosilicate glass, silica glass, and / or an inorganic glass), aceramic (including, in embodiments, any, some, or all of a polycrystalline ceramic, a polycrystalline inorganic material, a polycrystalline aluminum oxide, alumina, and / or silica), a glass-ceramic (including, in embodiments, Coming 9606® cordierite glass-ceramic), a polymer, (including, in embodiments, polycarbonate and / or Topas®), a polycrystalline ceramic, a single crystal ceramic (including, in embodiments, sapphire), and / or any combination thereof. In embodiments, a dielectric material forming any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be an inorganic material. In embodiments, a dielectric material forming any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be an organic material. In embodiments, any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be formed from a plurality of dielectric materials. In embodiments, any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be formed from a plurality of dielectric materials including one or more organic materials and / or one or more inorganic materials. In embodiments, any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be formed from a plurality of dielectric materials which are layered (as, for example, the layers 105a, 105b, 105c). In embodiments, the first layer 105a and / or the SIW 100 may be formed (in embodiments, in whole or in part) from Topas®. In embodiments, the second layer 105b and / or the SIW 100 may be formed (in embodiments, in whole or in part) from alumina and / or silica. In embodiments, the third layer 105c and / or the SIW 100 may be formed (in embodiments, in whole or in part) from Topas®. In embodiments, the dielectric material forming any, some, or all of the layers 105a, 105b, 105c and / or the SIW 100 may be a mixture of two or more dielectric materials. In embodiments, either or both of the layers 105a, 105c may be laminates applied to the second layer 105b, and, in certain such embodiments, the layers 105a, 105c may be formed from dielectric materials having lower dielectric permittivities than a dielectric permittivity of the second layer 105b to, for example, decrease a dielectric permittivity of the SIW 100.

[0081] In embodiments, the dielectric materials of any, some, or all of the dielectric materials of the layers 105a, 105b, 105c may define a relative dielectric permittivity (εr) of the SIW 100 (for example, a dielectric constant of the SIW 100). In embodiments, reducing the relative dielectric permittivity (εr) may reduce loss of an electromagnetic wave signal at air interfaces (for example, at the waveguide surface 100a of the SIW 100) at vias 102 of the SIW 100; however, reducing the relative dielectric permittivity (εr) may increase dielectric loss of an electromagnetic wave signal propagated by the SIW 100. In embodiments, dielectric loss may be caused by, for example and with reference to FIG. 3, crosstalk between a firstwaveguide defined by the first row of vias 102a and the second row of vias 102b and a second waveguide defined by the second row of vias 102b and the third row of vias 102c). In embodiments, dielectric loss may be caused, for example, by additional factors, such as surface roughness of the SIW 100, inhomogeneities in the relative dielectric permittivity (εr) of the SIW 100 as defined by the dielectric materials of any, some, or all of the dielectric materials of the layers 105a, 105b, 105c, changes in the relative dielectric permittivity (εr) of the SIW 100 as defined by the dielectric materials of any, some, or all of the dielectric materials of the layers 105a, 105b, 105c (as caused by, for example, variance in temperature and humidity of an environment of the SIW 100), and other factors.

[0082] Accordingly, it may be advantageous to determine a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max) for the SIW 100, such that a dielectric permittivity (εr) of the SIW 100 (as determined by, for example, the dielectric materials of the layers 105a, 105b, 105c) may reduce and / or minimize loss at air interfaces of the vias 102 while also reducing and / or minimizing dielectric loss of the SIW 100. As is described in further detail below, once the waveguide width (a) of the SIW 100 and the frequency (f) of an electromagnetic wave signal to be propagated by the SIW 100 have been selected, a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max) may be calculated to determine one or more dielectric permittivities (εr) (and, accordingly, dielectric materials of any, some, or all of the layers 105a, 105b, 105c and / or of the SIW 100) which may reduce and / or minimize both air loss at interfaces of the vias 102 and dielectric loss of the SIW 100 of the electromagnetic wave signal propagated by the SIW 100. In embodiments, reducing dielectric permittivities of surface layers (for example, the layers 105a, 105c) of the SIW 100 may be desirable to, for example, minimize coupling capacitance between the SIW 100 and devices coupled to the SIW 100 (for example, in embodiments, an antenna layer 210 and / or a spacer layer 220, as are described in further detail below and depicted in FIG. 5).

[0083] In embodiments, a range of allowable dielectric permittivities (for example, the lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max)) for the SIW 100 (as determined by, for example, the waveguide width (a) of the SIW 100 and the frequency (f) of an electromagnetic wave signal to be propagated by the SIW 100) may be determined by a cutoff frequencies of the two lowest order transverse electric (“TE”) modes of the SIW 100. In embodiments, the lowest order mode of the SIW 100 may be the TEio mode (for example, a mode having a lowest cutoff frequency). In embodiments, the second lowest23order mode of the SIW 100 may be the TE20 mode of the SIW 100 (for example, a mode wherein an electric field of an electromagnetic wave signal propagated by the SIW 100 may be perpendicular to a direction of propagation of the electromagnetic wave signal (for example, in the z-direction, as indicated in FIG. 4). As described in “Design Procedure to Determine the Taper Transition for Impedance Matching Between Microstrip Line and SIW Component” (Ricardo Caranicola Caleffo, Design Procedure to Determine the Taper Transition for Impedance Matching Between Microstrip Line and SIW Component, Journal of Microwaves, Optoelectronics and Electromagnetic Applications (On-line Version), ISSN 2179-1074, July / Sept. 2016), which is incorporated by reference herein, a first cutoff frequency of a TE10mode (fc 10) of an electromagnetic wave signal propagated by the SIW 100 may be provided by the following equation:(1)

[0084] Further, a second cutoff frequency of a TE20mode (fc 20) of an electromagnetic wave signal propagated by the SIW 100 may be provided by the following equation: (2)

[0085] In each of equations (1) and (2), and in the subsequent equations described below, c is the speed of light in vacuum, d is the via diameter (d) of the SIW 100 (as depicted in, for example, FIGS. 1-3), p is the via spacing (p) of the SIW 100 (as depicted in, for example, FIGS. 1-3), a is the waveguide width (a) of the SIW 100 (as depicted in, for example, FIGS. 1-3), and εris the dielectric permittivity (εr) of the SIW 100. In embodiments, the SIW 100 may be designed to operate between the first cutoff frequency (fc10) and the second cutoff frequency (fc 20) (for example, by, in embodiments, propagating an electromagnetic wave signal having a frequency (f) between the first cutoff frequency (fc10) and the second cutoff frequency (fc10)), such that, in embodiments, the SIW 100 supports only one mode. In embodiments, the via diameter (d) and the waveguide width (p) of the SIW 100 may, as is described in further detail below, be chosen to minimize and / or reduce crosstalk between the vias 102.

[0086] In embodiments, and as described in “Design Procedure to Determine the Taper Transition for Impedance Matching Between Microstrip Line and SIW Component,” as incorporated by reference hereinabove, it may be desirable to operate the SIW 100 at a frequency (l) within a frequency range defined by the following equation: (3)

[0087] Accordingly, in embodiments, the lower dielectric permittivity bound of the SIW 100 may be calculated using 1 (or, in other embodiments, or another lower frequency bound) in the following equation: (4)

[0088] Further, in embodiments, the upper dielectric permittivity bound (εr,max) of the SIW 100 may be calculated using 0.95fc20(or, in other embodiments, fc20or another upper frequency bound). By solving equations (1) and (2) for the two limiting conditions of equation (3), the upper dielectric permittivity bound can be derived and provided in the following equation: (5)

[0089] Accordingly, equations (4) and (5) can be used, for a given frequency (f) of an electromagnetic wave signal propagated by the SIW 100 and for a given waveguide width (a) of the SIW 100 (as a function of, for example, the via diameter (d) and the via spacing of the SIW 100), a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound of the SIW 100 may be calculated.

[0090] For example, in an embodiment of the SIW 100 having a via diameter of 0.25 mm and a via spacing of 0.4 mm and propagating an electromagnetic wave signal having a frequency (f) of 77 GHz, equations (4) and (5) may be used to calculate a lower dielectric permittivity bound of 1.866 and an upper dielectric permittivity bound of 4.194. Accordingly, in such embodiments, dielectric materials of the SIW 100 and / or of any, some, or all of the layers 105a, 105b, 105c may be chosen to provide the SIW 100 with a dielectric permittivity (sr) of any value greater than or equal to 1.866 and less than or equal to 4.194. Referring again to FIG. 4, in such embodiments, the layers 105a, 105c may be formed from Topas® and have athickness of 50 pm, while the second layer 105b may be formed from alumina and have a thickness of 40 pm may have a dielectric permittivity of (εr) of 3.85, despite alumina having a dielectric constant of 9.5 (for example, greater than the upper dielectric permittivity bound of 4.194). Accordingly, in embodiments, the lower dielectric permittivity bound and the upper dielectric permittivity bound may be referenced to form the SIW 100 and / or layers of the SIW 100 from dielectric materials having high dielectric permittivities by further forming the SIW 100 and / or layers of the SIW 100 withmaterials (for example, Topas®, silica, and / or lithium potassium borosilicate glass applied as, in embodiments, laminates to the second layer 105b of the SIW 100).

[0091] By calculating upper and lower dielectric permittivity bounds, SIWs (such as, in embodiments, the SIW 100) may have base substrates (such as, in embodiments, the base substrate 100b) formed from dielectric materials which provide a relative dielectric permittivity between calculated upper and lower dielectric permittivity bounds, enabling, in embodiments, the manufacturing of base substrates having desired and / or reduced relative dielectric permittivities and, in embodiments, enabling such manufacturing to be done at a reduced cost (for example, by choosing materials for forming the base substrate which reduce costs while resulting in a relative dielectric permittivity between the calculated upper and lower dielectric permittivity bounds).

[0092] Referring now to FIG. 5 A with reference to FIG. 1, in embodiments, the SIW 100 may be a component of an integrated digital RF circuit system 200 further comprising an antenna layer 210 and a spacer layer 220.

[0093] In embodiments, the integrated digital RF circuit system 200 may be used for, for example, telecommunication applications for third generation (3G), fourth generation (4G), fifth generation (5G), and / or sixth generation (6G) cellular network technology and long term evolution (LTE) technology, Bluetooth communication, near field communication (NFC), radio frequency identification (RFID) signals, global positioning system (GPS) signals, satellite to satellite communications, radar, and other radio frequency applications. Accordingly, in embodiments, the antenna layer 210 may include antenna elements 212 (depicted in FIG. 5B and described below) which may send and / or receive and / or be configured to send and / or receive an RF signal (for example, as an electromagnetic wave signal). In embodiments, the antenna layer 210 may thereby send and / or receive and / or be configured to send and / or receive an electromagnetic signal through the spacer layer 220 and via the SIW 100 to a printed circuit board (“PCB”) 230 electrically coupled to the SIW 100. In embodiments, the antenna layer 210 may be formed from a dielectric material, such as, in embodiments, a glass (including, in embodiments, any, some, or all of lithium potassium borosilicate glass, silica glass, and / or an inorganic glass), a ceramic (including, in embodiments, any, some, or all of a polycrystalline ceramic, a polycrystalline inorganic material, a polycrystalline aluminum oxide, alumina, and / or silica), a glass-ceramic (including, in embodiments, Coming 9606® cordierite glass-ceramic), a polymer, (including, in embodiments, polycarbonate and / or Topas®), a polycrystalline ceramic, a single crystalceramic (including, in embodiments, sapphire), and / or any combination thereof. In embodiments, the antenna layer 210 may be formed from the same dielectric material(s) as the SIW 100, which may, in embodiments, reduce bending of the integrated digital RF circuit system 200.

[0094] In embodiments, the spacer layer 220 may be positioned between the antenna layer 210 and the SIW 100, by attaching the SIW 100 to a first side of the spacer layer 220 and attaching the antenna layer 210 to a second side of the spacer layer 220 opposite the first side of the spacer layer 220. By positioning the spacer layer 220 between the antenna layer 210 and the SIW 100, the spacer layer 220 may create a resonant structure, enabling the SIW 100 to propagate an electromagnetic wave signal from the PCB 230 and to the antenna layer 210 and / or from the antenna layer 210 and to the PCB 230. In embodiments, the spacer layer 220 may be formed from a dielectric material, such as, in embodiments, a glass (including, in embodiments, any, some, or all of lithium potassium borosilicate glass, silica glass, and / or an inorganic glass), a ceramic (including, in embodiments, any, some, or all of a polycrystalline ceramic, a polycrystalline inorganic material, a polycrystalline aluminum oxide, alumina, and / or silica), a glass-ceramic (including, in embodiments, Coming 9606® cordierite glassceramic), a polymer, (including, in embodiments, polycarbonate and / or Topas®), a polycrystalline ceramic, a single crystal ceramic (including, in embodiments, sapphire), and / or any combination thereof. In embodiments, the spacer layer 220 may be formed from the same dielectric material(s) as the SIW 100 and / or the antenna layer 210, which may, in embodiments, reduce bending of the integrated digital RF circuit system 200.

[0095] Referring now to FIG. 5B, a cross-sectional view of the integrated digital RF circuit system 200 displays the vias 102, in addition to conductive material 103 (for example, the layers 105a, 105b as depicted in FIG. 4) forming a surface on the dielectric material 101 of the SIW 100. The antenna layer 210 includes antenna elements 212, positioned opposite gaps 104 in the conductive material 103. In embodiments, the antenna elements 212 may be patch antennas or slot antennas (for example, occupancy detectors or close range proximity detectors). In embodiments, the antenna elements 212 may be spaced by half of the vacuum wavelength (λ) of an electromagnetic wave signal propagated by the SIW 100. In embodiments, the SIW 100, spacer layer 220, and antenna layer 210 may be attached by an adhesive (for example, an organic adhesive), soldering, ambient temperature laser welding, laser sintering, optical contacting (for example, wringing), thermal diffusion bonding between metal layers, and / or any other attachment mechanisms, as are known in the art. In embodimentswhrein any, some, or all of the SIW 100, the spacer layer 220, and / or the antenna layer 210 are attached by an adhesive, the adhesive may be applied, in embodiments, by roller, inkjet, spraying, pre-cut adhesive films, or any combination thereof.

[0096] In embodiments, certain applications of integrated digital RF circuit systems (such as, in embodiments, the integrated digital RF circuit system 200) may desire minimization of a size (for example, volume and / or two-dimensional area, as defined by, for example, the waveguide surface 100a as depicted in FIG. 1) of the integrated digital RF circuit systems and / or components thereof, such as, in embodiments, the SIW 100. Accordingly, in embodiments, it may be desirable to decrease a size of the SIW 100, and therefore, in embodiments, decreasing a size of the SIW 100 may require decreasing the waveguide width (a) (as depicted in, for example, FIGS. 1-3). However, in embodiments, decreasing the waveguide width (a) of the SIW 100 may increase crosstalk loss of electromagnetic wave signals propagated by the SIW 100. In embodiments, applications of the SIW 100 and / or devices including the SIW 100 (for example, in embodiments, the integrated digital RF circuit system 200) may have upper crosstalk bounds (as determined by, for example, a maximum acceptable loss parameter of the application and / or of the device(s) including the SIW 100). Accordingly, for a given upper crosstalk bound, it may be, in embodiments, desirable to be able to configure the SIW 100 to have a waveguide width (a) which minimizes a size of the waveguide surface 100a without increasing crosstalk beyond an upper crosstalk bound.

[0097] In embodiments, crosstalk can be measured and / or modeled in multiple ways. For example, in embodiments, crosstalk can be measured by using an actual sample and / or by modeling structures (for example, the SIW 100) using a full wave finite element model. One method of measuring crosstalk is described in “Crosstalk in Substrate Integrated Waveguides” (Marco Pasian, M.B., Crosstalk in Substrate Integrated Waveguides, IEEE Transactions on Electromagnetic Compatibility, 57(1), 2015, pgs. 80-86), which is incorporated by reference herein, which describes that crosstalk (C) can be determined by the following equation: (6)

[0098] In equation (6), N is the number of vias (A) (as described hereinabove), a is the waveguide width (a) (as described hereinabove and depicted in FIGS. 1-3), d is the via diameter (d) (as described hereinabove and depicted in FIGS. 1-3), p is the via spacing (p) (as described hereinabove and depicted in FIGS. 1-3), λ is the vacuum wavelength (λ) (as describedhereinabove) of an electromagnetic wave signal (propagated by, for example, the SIW 100), and and τ are constants equal to 0.048 and 0.6366, respectively (as described in Pasian, which is incorporated by reference hereinabove. To calculate a total crosstalk (Ctotal) of a waveguide (for example, any of the rows of vias 102a, 102b, 102c), the crosstalk (C) found in equation (6) must be multiplied by the waveguide length (l), which may be defined by the following equation: (7a)

[0099] Accordingly, the total crosstalk (Ctoto / ) may thereby be provided by: (7b)

[0100] In embodiments, an upper crosstalk bound may be measured in decibels. Accordingly, a total crosstalk of a waveguide in decibels (Cdb) may be provided by: (8)

[0101] Accordingly, in embodiments, a waveguide may have an upper crosstalk bound (Cmax). In embodiments, by using the upper acceptable crosstalk bound (Cmax) (as measured in, for example, decibels) in the equations (6) and (8), with pre-determined values for the via diameter (d), the waveguide length (l), the via spacing (p), and the vacuum wavelength (λ) (for example, of electromagnetic wave signals propagated by the waveguide), a waveguide width (a) may be calculated which may, in embodiments, be a minimum waveguide width of, for example, the SIW 100 which may be modeled to have a total crosstalk (Ctotal) of the waveguide at or below the upper crosstalk bound (Cmax).

[0102] In embodiments, a total crosstalk in decibels (Cdb) of a waveguide may be greater than or equal to 10 decibels, greater than or equal to 20 decibels, or even greater than or equal to 30 decibels. In embodiments, a total crosstalk in decibels (Cdb) of a waveguide may be less than or equal to 40 decibels, less than or equal to 30 decibels, or even less than or equal to 20 decibels. In embodiments, a total crosstalk in decibels Cdbof a waveguide may be greater than or equal to 10 decibels and less than or equal to 40 decibels. In embodiments, a total crosstalk in decibels (Cdb) of a waveguide may be greater than or equal to 10 decibels and less than or equal to 30 decibels. In embodiments, a total crosstalk in decibels (Cdb) of a waveguide may be greater than or equal to 10 decibels and less than or equal to 20 decibels. In embodiments, a total crosstalk in decibels (Cdb) of a waveguide may be greater than or equal to 20 decibels and less than or equal to 40 decibels. In embodiments, a total crosstalk indecibels (Cdbof a waveguide may be greater than or equal to 20 decibels and less than or equal to 30 decibels. In embodiments, a total crosstalk in decibels Cdbof a waveguide may be greater than or equal to 30 decibels and less than or equal to 40 decibels.

[0103] Accordingly, in embodiments, calculating an upper crosstalk bound (Cmax) may enable the manufacturing of an SIW (for example, the SIW 100) and / or an integrated digital RF circuit system (for example, the integrated digital RF circuit system 200) which may, in embodiments, keep crosstalk between waveguides below the upper crosstalk bound while also, in embodiments, enabling the waveguide and associated antenna elements (for example, the antenna elements 212) to have optimized and / or reduced dimensions.

[0104] FIG. 6 depicts a flow diagram of an illustrative method 600 of manufacturing the SIW 100 of FIGS. 1-4 and / or various components of the integrated digital RF circuit system 200 of FIGS. 5A-5B, as described herein. While the method 600 generally relates to the manufacture of the SIWs and integrated digital RF circuit systems described herein, it should be understood that a similar process may be used for manufacturing solely an SIW (for example, by omitting the blocks 630-640) and / or other waveguides and / or circuit systems incorporating waveguides.

[0105] Referring to FIG. 6 and with reference to FIGS. 1-4, the method 600 includes manufacturing the base substrate 100b, as described herein at block 610. That is, the method 600 may include, in embodiments, forming the base substrate 100b from the dielectric material 101, the base substrate 100b comprising a relative dielectric permittivity (εr) and a waveguide length (l). In embodiments, the base substrate 100b may be formed from a plurality of dielectric materials. In certain such embodiments, the plurality of dielectric materials may be layered, such as, in embodiments, by comprising the layers 105a, 105b, 105c.

[0106] Referring again to FIG. 6 and with reference to FIGS. 1-4, the method 600 includes forming the SIW 100 by forming the plurality of vias 102 extending through the base substrate 100b, as described herein at block 620. In embodiments, the plurality of vias 102 may be formed from metal. In certain such embodiments, the metal forming the plurality of vias 102 may be, for example, a solid metal (for example, a fully fdled via), a continuous metal coating on a surface of each via of the plurality of vias 102, or a continuous transparent conductive oxide coating on a surface of each via of the plurality of vias 102. In embodiments, the plurality of vias 102 may define a number of vias (N). In embodiments, the plurality of vias 102 may define a via spacing (p). In embodiments, the plurality of vias 102 may define awaveguide width (a). In embodiments, the plurality of vias 102 may be disposed along the waveguide length (l). In embodiments, each via of the plurality of vias 102 may comprise a via diameter (d). In embodiments, the SIW 100 may comprise an upper crosstalk bound (Cmax). In embodiments, the SIW 100 may propagate and / or be configured to propagate an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ).

[0107] Referring again to FIG. 6 and with reference to FIGS. 5A-5B, in embodiments, the method 600 includes attaching the SIW 100 to a first side of the spacer layer 220. The method 600 further includes attaching the antenna layer 210 to a second side of the spacer layer 220 opposite the first side of the spacer layer 220.

[0108] It should now be understood that the present disclosure relates to various SIWs and material compositions and waveguide widths thereof, in particular for use in integrated digital RF circuit systems. The SIWs and RF circuit systems described herein may provide reduced and / or desired waveguide width, a reduced and / or desired size of the SIW, and / or reduced and / or desired crosstalk between waveguides of the SIW and may be formed from one or more materials having, individually and / or collectively, reduced and / or desired dielectric constants and / or reduced and / or desired dielectric loss.EXAMPLES

[0001] In order that various embodiments be more readily understood, reference is made to the following examples, which are intended to illustrate various embodiments of the laser bonding methods described herein.

[0109] Referring now to FIG. 7, a plot 700 demonstrates effective permittivity of electromagnetic waves propagating through a Topas® laminate of a layer (for example, a laminate applied to the second layer 105b so as to comprise the layers 105a, 105c, as described above) relative to a thickness of the Topas laminate®. As exemplified, at, for example, a 100 micron thickness of the Topas® laminate (corresponding to, for example, a 50 micron thickness Topas® laminate applied to each side of the layer, resulting in 100 total microns of thickness of the Topas® laminate), the effective permittivity is roughly 3. In embodiments, an SIW (for example, the SIW 100) may have an allowable single mode permittivity range, when propagating an electromagnetic wave having a frequency of 77 GHz, between 1.866 and 4. 194. Accordingly, in embodiments, a 100 micron total thickness of a Topas® laminate may provide an effective permittivity within an allowable range of an SIW propagating an electromagnetic wave having a frequency of 77 GHz.

[0110] While particular embodiments have been illustrated and described herein, it should be understood that various other changes and modifications may be made without departing from the spirit and scope of the claimed subject matter. Moreover, although various aspects of the claimed subject matter have been described herein, such aspects need not be utilized in combination. It is therefore intended that the appended claims cover all such changes and modifications that are within the scope of the claimed subject matter.

Claims

CLAIMSWhat is claimed is:1 . A substrate integrated waveguide comprising: a base substrate formed from a dielectric material and comprising a relative dielectric permittivity (εr) and a waveguide length (l); and a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), each of the plurality of vias comprises a via diameter (d), the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f), = the relative dielectric permittivity (εr) is between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) is determined by:the upper dielectric permittivity bound (εr,max) is determined by: andc is the speed of light in vacuum.

2. The substrate integrated waveguide of claim 1, wherein: the substrate integrated waveguide further comprises an upper crosstalk bound (Cmax); the plurality of vias define a number of vias (N); the electromagnetic wave signal further comprises a vacuum wavelength (λ); and the waveguide width (a) is defined by: , wherein ξis 0.048 and wherein τ is 0.6366.

3. The substrate integrated waveguide of claim 2, wherein:a total crosstalk in decibels Cdbis less than or equal to 30 decibels; and the total crosstalk in decibels (Cdb) is defined by: Cdb= 10(Log10((l)(Cmax)).

4. The substrate integrated waveguide of claim 1, wherein the base substrate further comprises a substrate thickness, and wherein the substrate thickness is less than twenty five times the via diameter (d).

5. The substrate integrated waveguide of claim 1, wherein the dielectric material comprises an inorganic material.

6. The substrate integrated waveguide of claim 5, wherein the dielectric material comprises: an inorganic glass; an ion-exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

7. The substrate integrated waveguide of claim 1, wherein the base substrate is formed from a plurality of dielectric materials.

8. The substrate integrated waveguide of claim 7, wherein the plurality of dielectric materials comprise organic materials and inorganic materials.

9. The substrate integrated waveguide of claim 7, wherein the plurality of dielectric materials are layered.

10. A substrate integrated waveguide comprising: a base substrate formed from a dielectric material and comprising a waveguide length (l) ;a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a number of vias (N), the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), and each of the plurality of vias comprises a via diameter (d); and an upper crosstalk bound (Cmax), wherein: the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ), the waveguide width (a) is defined byξ is 0.048 and r is 0.6366.

11. The substrate integrated waveguide of claim 10, wherein: a total crosstalk in decibels (Cdb) is less than or equal to 30 decibels; and the total crosstalk in decibels (Cdb) is defined by: Cdb= 10(Log10((l)(Cmax)).

12. The substrate integrated waveguide of claim 10, wherein: the base substrate further comprises a relative dielectric permittivity (εr); the electromagnetic wave signal further comprises a frequency (f); the relative dielectric permittivity (εr) is between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max),' the lower dielectric permittivity bound (εr,min) is determined by:the upper dielectric permittivity bound (εr,max) is determined by:c is the speed of light in vacuum.

13. The substrate integrated waveguide of claim 10, wherein the base substrate further comprises a substrate thickness, and wherein the substrate thickness is less than twenty five times the via diameter (d).

14. The substrate integrated waveguide of claim 10, wherein the dielectric material comprises an inorganic material.

15. The substrate integrated waveguide of claim 14, wherein the dielectric material comprises: an inorganic glass; an ion-exchanged glass; a ceramic; a glass-ceramic; a polymer; a polycrystalline ceramic; a single crystal ceramic; or any combination thereof.

16. The substrate integrated waveguide of claim 10, wherein the base substrate is formed from a plurality of dielectric materials.

17. The substrate integrated waveguide of claim 16, wherein the plurality of dielectric materials comprise organic materials and inorganic materials.

18. The substrate integrated waveguide of claim 16, wherein the plurality of dielectric materials are layered.

19. An integrated digital RF circuit system comprising: a spacer layer; an antenna layer; and a substrate integrated waveguide comprising: a base substrate formed from a dielectric material and comprising a relative dielectric permittivity (εr) and a waveguide length ( / ), an upper crosstalk bound (Cmax), and a plurality of vias extending through the base substrate and formed from metal, wherein: the plurality of vias define a number of vias (A),the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), each of the plurality of vias comprises a via diameter (d), the substrate integrated waveguide propagates an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength ( ). the waveguide width (a) is defined by: Cmax=is 0.048 and r is 0.6366, the relative dielectric permittivity (εr) is between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) is determined by:the upper dielectric permittivity bound (εr,max) is determined by: andc is the speed of light in vacuum.

20. A method for manufacturing an integrated digital RF circuit system, the method comprising: forming a substrate integrated waveguide by forming a plurality of vias extending through a base substrate and formed from metal, the base substrate formed from a dielectric material and comprising a relative dielectric permittivity (εr) and a waveguide length (l), wherein: the plurality of vias define a number of vias (N), the plurality of vias define a via spacing (p), the plurality of vias define a waveguide width (a), the plurality of vias are disposed along the waveguide length (l), each of the plurality of vias comprises a via diameter (d),the substrate integrated waveguide comprises an upper crosstalk bound (Cmax), and the substrate integrated waveguide is configured to propagate an electromagnetic wave signal comprising a frequency (f) and a vacuum wavelength (λ); attaching the substrate integrated waveguide to a first side of a spacer layer; and attaching an antenna layer to a second side of the spacer layer opposite the first side of the spacer layer, wherein: the waveguide width (a) is defined by:is 0.048 and r is 0.6366, the relative dielectric permittivity (εr) is between a lower dielectric permittivity bound (εr,min) and an upper dielectric permittivity bound (εr,max), the lower dielectric permittivity bound (εr,min) is determined by:the upper dielectric permittivity bound (εr,max) is determined by: andc is the speed of light in vacuum.

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