Grounding coplanar waveguide-to-quasi-coaxial interconnection structure radiation field analytical model construction method

Abstract

The invention provides a grounding coplanar waveguide to coaxial interconnection structure radiation field analytical model construction method, and belongs to the technical field of system packaging, and the method comprises the steps: according to the structure of the upper half plane of a grounding coplanar waveguide and the characteristics that the current of the upper half plane and the current of the lower half plane are equal in amplitude and reverse in direction; obtaining an electric field model, a magnetic field model and a directional diagram model of the grounding coplanar waveguide far region radiation field; regarding the similar axes as a plurality of antenna arrays, and obtaining an electric field model, a magnetic field model and a directional diagram of a similar axis far-region radiation field; and superposing the electric field model, the magnetic field model and the directional diagram of the variable grounding coplanar waveguide and the quasi-coaxial far region radiation field to obtain a grounding coplanar waveguide-to-quasi-coaxial radiation analysis model. The invention aims to solve the problem that a radiation model of a grounding coplanar waveguide-to-similar coaxial interconnection structure does not exist when the electromagnetic radiation characteristic between interconnection lines of a high-density packaging body is researched at present.

Description

Technical Field

[0001] The present invention belongs to the technical field of system packaging, and in particular relates to a method for constructing an analytical model of a radiation field of a grounded coplanar waveguide-to-quasi-coaxial interconnection structure. Background Art

[0002] As electronic devices and systems continue to advance in speed, density, and power consumption, and as system architectures become increasingly complex, power integrity, signal integrity, and electromagnetic interference (EMI) issues within system packaging are becoming increasingly prominent. Electromagnetic radiation from high-speed signal interconnects within system packaging components, particularly horizontal-to-vertical grounded coplanar waveguide-to-quasi-coaxial (GCPW) structures, is a major contributor to SI, PI, and EMI issues.

[0003] However, current analytical modeling research on the radiation field of system-in-package high-speed interconnect structures mainly focuses on single regular transmission structures such as microstrip lines, but has not studied the radiation characteristics of horizontal-to-vertical structures such as grounded coplanar waveguide to coaxial-like structures. Summary of the Invention

[0004] In order to solve the problem that the characteristics of a complex structure such as a grounded coplanar waveguide to quasi-coaxial structure have not been studied at present, the present invention provides a method for constructing an analytical model of the radiation field of a grounded coplanar waveguide to quasi-coaxial interconnection structure.

[0005] In order to achieve the above object, the present invention provides the following technical solutions: The upper half plane of the grounded coplanar waveguide is equivalent to a slot antenna array, and the slot antenna array is equivalent to an electric conductor antenna array. The radiation field of the electric conductor antenna array is solved to obtain the electric field model and directional function of the equivalent far-field radiation field of the upper half plane of the grounded coplanar waveguide; based on the current distribution of the equivalent slot antenna array, the far-field radiation field and directional function of the lower half plane of the grounded coplanar waveguide are obtained. The electric field model and directional function of the far-zone radiation field of the upper half plane of the grounded coplanar waveguide, as well as the far-zone radiation field and directional function of the lower half plane of the grounded coplanar waveguide are superimposed to obtain the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the grounded coplanar waveguide; Multiple antenna arrays are divided within the quasi-coaxial structure; the electric field model, magnetic field model, and directional function of the far-zone radiation field of all antenna arrays within the quasi-coaxial structure are superimposed respectively to obtain the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body; the multiples of the length of the quasi-coaxial structure in the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body are adjusted to obtain the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body; The coordinate system of the far-field radiation field of the grounded coplanar waveguide is transformed, and the electric field model, magnetic field model and current phase in the quasi-coaxial far-field radiation field are corrected; The electric field model, magnetic field model, and pattern model of the far-field radiation field of the grounded coplanar waveguide after coordinate system transformation are superimposed with the electric field model, magnetic field model, and pattern model of the quasi-coaxial far-field radiation field after current phase correction to obtain the analytical model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial.

[0006] Furthermore, the specific steps of obtaining the electric field model and directional function of the equivalent far-zone radiation field in the upper half plane of the grounded coplanar waveguide are as follows: Divide the upper half plane of the grounded coplanar waveguide into two slot antennas and The plane is viewed as an antenna array consisting of two slot antennas; The amplitude of the traveling wave current in the grounded coplanar waveguide is obtained by using transmission line theory; The slot antenna array in the upper half plane of the grounded coplanar waveguide is equivalent to an electric conductor antenna array through the Babinet principle and the duality principle. The electric field model and directional function of the far-zone radiation field in the upper half plane of the equivalent grounded coplanar waveguide are obtained.

[0007] Furthermore, the specific steps of obtaining the electric field model, magnetic field model and pattern model of the far-field radiation field of the grounded coplanar waveguide are as follows: According to the characteristics of equal amplitude and opposite direction of current in the upper and lower half planes of the grounded coplanar waveguide, the upper and lower half planes of the grounded coplanar waveguide are approximated as an antenna array; According to the electric field model and directional function of the far-zone radiation field of the equivalent grounded coplanar waveguide upper half plane, the electric field model and directional pattern model of the far-zone radiation field of the equivalent grounded coplanar waveguide are obtained; The equivalent pattern model of the far-zone radiation field of the grounded coplanar waveguide is recorded as the initial pattern model of the far-zone radiation field of the grounded coplanar waveguide; The electric field model of the equivalent far-field radiation field of the grounded coplanar waveguide is transformed by the Babinet principle to obtain the initial electric field model and initial magnetic field model of the far-field radiation field of the grounded coplanar waveguide; According to the comparison between the directional pattern model of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model and the initial directional pattern model of the far-zone radiation field of the grounded coplanar waveguide, the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the grounded coplanar waveguide are obtained through the initial electric field model, initial magnetic field model and initial directional pattern model of the far-zone radiation field of the grounded coplanar waveguide.

[0008] Furthermore, the specific steps of obtaining the electric field model, magnetic field model and pattern model of the far-field radiation field of the grounded coplanar waveguide are as follows: Obtain the phase error between the main lobe of the directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model and the initial directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide; Since the phase error of the main lobes of the two pattern models is less than 5%, the initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide are recorded as the electric field model and magnetic field model of the far-zone radiation field of the grounded coplanar waveguide; The initial pattern model of the far-zone radiation field of the grounded coplanar waveguide is recorded as the pattern model of the far-zone radiation field of the grounded coplanar waveguide.

[0009] Furthermore, the specific steps of obtaining the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: Multiply the electric field model, magnetic field model and the length of the quasi-coaxial in the pattern model of the far-zone radiation field of the quasi-coaxial body by 3 to obtain the initial electric field model, initial magnetic field model and initial pattern model of the entire quasi-coaxial far-zone radiation field; Obtain the entire quasi-coaxial far-zone radiation pattern model in the HFSS analytical model; According to the phase error of the main lobe of the initial pattern model of the entire quasi-coaxial far-zone radiation field and the pattern model of the entire quasi-coaxial far-zone radiation field in the HFSS analytical model, the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are obtained through the initial electric field model, initial magnetic field model and initial pattern model of the entire quasi-coaxial far-zone radiation field.

[0010] Furthermore, the specific steps of obtaining the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: Comparing the initial directivity pattern of the entire quasi-coaxial far-zone radiation field with the directivity pattern model of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model, it is found that the initial directivity pattern of the entire quasi-coaxial far-zone radiation field splits into multiple cone lobes faster than the directivity pattern of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model; Adjusting the multiple of the quasi-coaxial length in the initial directional pattern of the entire quasi-coaxial far-zone radiation field to obtain the initial directional pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment; The initial directivity pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment is compared with the directivity pattern of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model, and the degree of consistency between the initial directivity pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment and the directivity pattern of the quasi-coaxial far-zone radiation field obtained by the HFSS finite element model is obtained, and the multiple change is obtained as follows: When , the agreement is the highest; Change the multiples of the length of the quasi-coaxial in the initial electric field model, initial magnetic field model, and initial directional pattern of the entire quasi-coaxial far-zone radiation field to , and obtain the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field.

[0011] Furthermore, the specific steps of transforming the coordinate system of the far-field radiation field of the grounded coplanar waveguide are as follows: The plane where the far-zone radiation field of the grounded coplanar waveguide is located is transformed from the xoz plane to the xoy plane, and the electric field model, magnetic field model and the directional pattern model of the far-zone radiation field of the grounded coplanar waveguide are transformed into the xoz plane. , The relevant sine and cosine terms are mathematically transformed according to the change of the coordinate system, and the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide after the coordinate transformation are obtained.

[0012] Furthermore, the specific calculation steps for correcting the current phase in the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: In the electric field model, magnetic field model and pattern model of the quasi-coaxial far-field radiation field, the current of the central signal conductor is multiplied by a phase factor , the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field after phase change are obtained; where j is the imaginary unit, k is the electromagnetic wave propagation constant, and l is the length of the grounded coplanar waveguide.

[0013] Furthermore, the specific steps of obtaining the analytical model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial are as follows: The directional pattern model of the far-field radiation field of the grounded coplanar waveguide after coordinate transformation is superimposed with the directional pattern model of the quasi-coaxial far-field radiation field after phase change to obtain the initial directional pattern model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial; The initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide after coordinate transformation are superimposed on the initial electric field model and initial magnetic field model of the quasi-coaxial far-zone radiation field after phase change, respectively, to obtain the initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial; The initial pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial transmission was compared with the pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial transmission obtained by the HFSS finite element model. The phase error between the two patterns was found to be less than 5%. The initial electric field model, initial magnetic field model and initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial are recorded as the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial, and the analytical model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial is obtained; The analytical model of the grounded coplanar waveguide-to-quasi-coaxial far-field radiation field includes an electric field model, a magnetic field model and a directivity pattern model of the grounded coplanar waveguide-to-quasi-coaxial far-field radiation field.

[0014] The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure provided by the present invention has the following beneficial effects: when obtaining the radiation model of a grounded coplanar waveguide to quasi-coaxial interconnect structure, the present invention first obtains the radiation model of the upper half plane of the grounded coplanar waveguide based on the radiation model of the slot antenna, based on the feature that the upper half plane of the grounded coplanar waveguide is relatively similar to the slot antenna array composed of two slot antennas, thereby solving the current gap of no radiation model of the upper half plane of the grounded coplanar waveguide; based on the feature that the currents in the upper half plane and the lower half plane of the grounded coplanar waveguide are of equal amplitude and opposite direction, the upper and lower half planes of the grounded coplanar waveguide are first regarded as an antenna respectively, and the grounded coplanar waveguide is regarded as an antenna array composed of the upper and lower half planes, and the radiation model of the grounded coplanar waveguide is obtained through the radiation model of the upper half plane of the grounded coplanar waveguide, thereby solving the problem of no radiation model of the grounded coplanar waveguide; when obtaining the quasi-coaxial radiation model, the present invention creatively regards the quasi-coaxial as several antenna arrays, thereby obtaining the quasi-coaxial according to the radiation model of the existing antenna. The present invention solves the problem of the lack of a quasi-coaxial radiation model. Based on the mirror principle, the upper and lower ground planes connected to the quasi-coaxial are respectively equivalent to the radiation model of the quasi-coaxial body. Through the radiation model of the quasi-coaxial body, a quasi-coaxial radiation model is obtained that takes into account the radiation characteristics of the ground planes connected to the upper and lower layers of the quasi-coaxial, so that the quasi-coaxial radiation model in this method is more in line with the actual situation. When obtaining the radiation model of the grounded coplanar waveguide to quasi-coaxial based on the radiation model of the grounded coplanar waveguide and the quasi-coaxial, the current first flows through the grounded coplanar waveguide and then flows into the quasi-coaxial, causing the initial phase of the current in the quasi-coaxial radiation model to change. According to the influence of the grounded coplanar waveguide on the phase of the current, the phase in the quasi-coaxial radiation model is modified, and the quasi-coaxial radiation model after phase modification is superimposed with the radiation model of the grounded coplanar waveguide after coordinate transformation to obtain the radiation model of the grounded coplanar waveguide to quasi-coaxial, which solves the problem of the lack of a radiation model of the grounded coplanar waveguide to quasi-coaxial in the current research field. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] To more clearly illustrate the embodiments of the present invention and its design, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0016] Figure 1 This is a flow chart of a method for constructing an analytical model of the radiation field of a grounded coplanar waveguide-to-quasi-coaxial interconnect structure according to embodiment 1 of the present invention; Figure 2 Schematic diagram of a grounded coplanar waveguide and its complementary structure, (a) represents a top view, (b) represents a side view, (c) represents a complementary structure-ideal magnetic conductor, and (d) represents a complementary structure-ideal electric conductor; Figure 3 A structural diagram of a grounded coplanar waveguide; Figure 4 This is the grounded coplanar waveguide model in Ansys HFSS, (a) represents the overall model, and (b) represents the top view; Figure 5 The effect of signal conductor length on radiation pattern, (a) represents signal conductor length of 5mm, (b) represents signal conductor length of 10mm, (c) represents signal conductor length of 15mm, and (d) represents signal conductor length of 20mm; Figure 6 It is a schematic diagram of a quasi-coaxial structure, (a) represents the side view, and (b) represents the top view; Figure 7 It is a quasi-coaxial model in HFSS; Figure 8 These are the side and top views of the quasi-coaxial model in HFSS, (a) represents the side view, and (b) represents the top view; Figure 9 The effect of quasi-coaxial height on the radiation pattern, (a) represents the quasi-coaxial height of 3mm, (b) represents the quasi-coaxial height of 5mm, (c) represents the quasi-coaxial height of 10mm, and (d) represents the quasi-coaxial height of 15mm; Figure 10 Schematic diagram of the grounded coplanar waveguide to quasi-coaxial structure, (a) represents the side view, (b) represents the top view; Figure 11 is a schematic diagram of the coordinate transformation of the grounded coplanar waveguide, (e) represents the coordinate transformation of (d); Figure 12 This is a schematic diagram of the ground plane waveguide-to-quasi-coaxial model in HFSS, where (a) represents the overall model and (b) represents the local amplification. Figure 13This is the effect of the grounded coplanar waveguide signal conductor length on the radiation pattern. (a) represents the signal conductor length of 1mm, (b) represents the signal conductor length of 7mm, (c) represents the signal conductor length of 10mm, and (d) represents the signal conductor length of 15mm. DETAILED DESCRIPTION

[0017] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0018] Example 1 The present invention provides a method for constructing an analytical model of the radiation field of a grounded coplanar waveguide to coaxial interconnect structure, specifically as follows Figure 1 Shown, including: Step S001: Equivalent the upper half plane of the grounded coplanar waveguide to a slot antenna array, and equivalent the slot antenna array to a conductor antenna array, solving the radiation field of the conductor antenna array to obtain the electric field model and directional function of the equivalent far-field radiation field of the upper half plane of the grounded coplanar waveguide; according to the current distribution of the equivalent slot antenna array, obtain the far-field radiation field and directional function of the lower half plane of the grounded coplanar waveguide; superimpose the electric field model and directional function of the far-field radiation field of the upper half plane of the grounded coplanar waveguide and the far-field radiation field and directional function of the lower half plane of the grounded coplanar waveguide to obtain the electric field model, magnetic field model and directional pattern model of the far-field radiation field of the grounded coplanar waveguide.

[0019] It should be noted that when analyzing the radiation characteristics of a horizontal-to-vertical structure such as a grounded coplanar waveguide to quasi-coaxial structure, it is necessary to first obtain the analytical models of the radiation field of the grounded coplanar waveguide and the analytical models of the radiation field of the quasi-coaxial structure.

[0020] It should be further explained that In electromagnetic field theory, radiation fields are divided into far-field radiation and near-field radiation, based on the distance between the observation point and the radiation source. In practical applications, far-field radiation dominates. Specifically, in system packaging structures, electromagnetic radiation interference is often caused by far-field radiation. Therefore, this paper only analyzes the far-field radiation of grounded coplanar waveguides and quasi-coaxial systems.

[0021] It should be further explained that when obtaining the far-field radiation field of a grounded coplanar waveguide, it is necessary to first obtain the current distribution on the grounded coplanar waveguide. Then, based on this current distribution, an analytical model of the far-field radiation field of the grounded coplanar waveguide is derived. When designing the transmission structure, it is necessary to ensure that the impedances at both ends of the grounded coplanar waveguide are matched as much as possible. When the impedances at both ends of the grounded coplanar waveguide are matched, the current distribution on the grounded coplanar waveguide exhibits a traveling wave distribution. The current distribution on the grounded coplanar waveguide is obtained using transmission line theory.

[0022] It should be further explained that in obtaining the grounded coplanar waveguide When radiating a field, the grounded coplanar waveguide is obtained by manufacturing a central signal conductor strip on one surface of a dielectric substrate and manufacturing conductor planes on both sides adjacent to the central signal conductor strip. The slot antenna is an antenna formed by a slot on the conductor surface, so that the upper half plane of the grounded coplanar waveguide can be regarded as consisting of two slot antennas. Assume the graphs are Figure 2 in and . Figure 3 is a side view of the grounded coplanar waveguide, where Figure 3 The conductor (blue area) below the dielectric (green area) in the figure is the lower half plane of the grounded coplanar waveguide. Figure 3 The center strip, ground strip, and the area between the center strip and the ground strip are all the upper half plane of the grounded coplanar waveguide.

[0023] It should be further explained that since the upper half plane of the grounded coplanar waveguide can be regarded as a slot antenna array composed of two slot antennas, when obtaining the far-field radiation field of the upper half plane of the grounded coplanar waveguide, the far-field radiation field of a slot antenna and the directional function of the far-field radiation field are first obtained, and then The directional functions of the far-zone radiation field and the far-zone radiation field of a slot antenna are multiplied by the array factor to obtain the directional functions of the far-zone radiation field and the far-zone radiation field of the slot antenna array, and then the directional functions of the far-zone radiation field and the far-zone radiation field of the upper half plane of the grounded coplanar waveguide are obtained.

[0024] It should be further explained that, since the grounded coplanar waveguide is divided into two half-planes, the lower half-plane of the grounded coplanar waveguide is used as the return current plane, so that the current in the upper half-plane of the grounded coplanar waveguide and the current in the lower half-plane are equal in amplitude and opposite in direction, that is, the upper half-plane of the grounded coplanar waveguide can be regarded as an antenna array, the lower half-plane can also be regarded as an antenna array, and the upper and lower planes of the grounded coplanar waveguide are approximately an antenna array. Therefore, the directional function of the far-field radiation field of the grounded coplanar waveguide is obtained by the directional function of the far-field radiation field of the upper half-plane of the grounded coplanar waveguide and the directional function of the far-field radiation field.

[0025] It should be further explained that because it is difficult to directly solve the far-field radiation field of a slot antenna, the slot antenna array is equivalent to an electric conductor antenna array using the Babinet principle and the duality principle to obtain the equivalent electric field model of the grounded coplanar waveguide. Using the Babinet principle and the duality principle, the equivalent electric field model of the grounded coplanar waveguide is converted into its own electric and magnetic field models.

[0026] It should be further explained that, currently, after obtaining an object's radiation model, its radiation pattern needs to be compared with the radiation pattern of the object in common commercial finite element simulation software such as the HFSS finite element model to verify the validity of the analytical model. Therefore, the obtained electric and magnetic field models of the grounded coplanar waveguide were verified using the HFSS finite element model.

[0027] Furthermore, when comparing the far-field radiation pattern obtained from the analytical model with the far-field radiation pattern from the finite element model, the analytical model was validated based on the phase error of the main lobe, as the radiation pattern is divided into main and side lobes. The main lobe radiates the most energy, and the industry focuses on the changes in the main lobe.

[0028] Specifically, the upper half plane of the grounded coplanar waveguide is divided into two slot antennas, and the traveling wave current in the grounded coplanar waveguide is obtained using transmission line theory. Determining the traveling wave current in the grounded coplanar waveguide using transmission line theory is a well-known technique and will not be described in detail in this embodiment.

[0029] Furthermore, the grounded coplanar waveguide is placed in the spherical coordinates, and the radiation field observation point of the grounded coplanar waveguide in the spherical coordinates is obtained. Angle, the distance from the radiation field observation point of the grounded coplanar waveguide to the origin in spherical coordinates, the radiation field observation point of the grounded coplanar waveguide in spherical coordinates horn.

[0030] Furthermore, the slot antenna array in the upper half plane of the grounded coplanar waveguide is equivalent to an electric conductor antenna array through the Babinet principle and the duality principle, and the electric field model and directional function of the far-zone radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide are obtained.

[0031] Furthermore, the specific calculation formulas for the electric field model and directional function of the far-zone radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide are as follows: Where, The electric field model of the far-zone radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide is shown. represents the distance between the radiation field observation point of the grounded coplanar waveguide and the origin in spherical coordinates, represents the imaginary unit, represents the amplitude of the traveling current on the grounded coplanar waveguide, The directional function of the far-field radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide is represented by: The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the propagation constant of electromagnetic waves, represents the signal conductor length of the grounded coplanar waveguide, represents the sine function in trigonometric function, Represents the cosine function in trigonometric functions.

[0032] Furthermore, the directional function of the far-zone radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide is multiplied by the array factor to obtain the directional function of the far-zone radiation field of the upper half plane of the equivalent grounded coplanar waveguide. The specific calculation formula of the directional function of the far-zone radiation field of the upper half plane of the equivalent grounded coplanar waveguide is as follows: Where, It represents the directional function of the far-zone radiation field in the upper half plane of the equivalent grounded coplanar waveguide, The directional function of the far-field radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide is represented by: represents the propagation constant of electromagnetic waves, represents the distance between the two slots in the upper half plane of the grounded coplanar waveguide, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the sine function in trigonometric function, represents the cosine function in trigonometric function, Represents the array factor.

[0033] Wherein, obtaining the directional function of the far-field radiation field of the antenna array in which the antenna is located based on the directional function of the far-field radiation field of an antenna is a prior art known in the art and will not be described in detail in this embodiment.

[0034] Furthermore, based on the electric field model of the far-zone radiation field of a slot antenna in the upper half plane of the equivalent grounded coplanar waveguide, the calculation formula of the electric field model of the far-zone radiation field in the upper half plane of the equivalent grounded coplanar waveguide is obtained as follows: Where, The electric field model representing the far-zone radiation field in the upper half plane of the equivalent grounded coplanar waveguide is: represents the amplitude of the traveling current on the grounded coplanar waveguide, represents the distance between the radiation field observation point of the grounded coplanar waveguide and the origin in spherical coordinates, represents the imaginary unit, represents the propagation constant of electromagnetic waves, represents the signal conductor length of the grounded coplanar waveguide, represents a natural constant, also known as Napier's constant, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the sine function in trigonometric function, Represents the cosine function in trigonometric functions.

[0035] Among them, obtaining the electric field model of the conductor antenna array including two conductors based on the electric field model of one conductor is a prior art technology and will not be described in detail in this embodiment.

[0036] It should be noted that because the lower half plane of the GCPW serves as the return current plane, the upper and lower half planes of the GCPW can be approximated as an antenna array. That is, the upper and lower half planes of the GCPW can be considered an antenna, and the upper and lower planes of the GCPW can also be considered an antenna, with the upper and lower planes of the GCPW approximating an antenna array. Therefore, based on the equivalent electric field model of the upper half plane of the GCPW and the directional function of the far-field radiation field, the far-field radiation field and the directional pattern of the far-field radiation field of the GCPW are obtained. The directional pattern of the equivalent far-field radiation field of the GCPW is denoted as the directional pattern of the initial far-field radiation field of the GCPW.

[0037] Furthermore, the calculation formula for obtaining the initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide is as follows: Where, represents the initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the propagation constant of electromagnetic waves, represents the signal conductor length of the grounded coplanar waveguide, represents the sine function in trigonometric function, represents the cosine function in trigonometric function, represents the distance between the two slots in the upper half plane of the grounded coplanar waveguide, Indicates the thickness of the medium, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn.

[0038] Furthermore, the specific calculation formula for obtaining the electric field model of the equivalent grounded coplanar waveguide far-zone radiation field is as follows: Where, The electric field model representing the equivalent far-zone radiation field of the grounded coplanar waveguide is: represents the amplitude of the traveling current on the grounded coplanar waveguide, represents the imaginary unit, represents the distance between the radiation field observation point of the grounded coplanar waveguide and the origin in spherical coordinates, represents the propagation constant of electromagnetic waves, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the signal conductor length of the grounded coplanar waveguide, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the sine function in trigonometric function, Represents the cosine function in trigonometric functions.

[0039] Furthermore, the calculation formula of the electric field model of the equivalent grounded coplanar waveguide far-zone radiation field is transformed by the duality principle and the Babinet principle, and the specific calculation formulas of the initial electric field model and the initial magnetic field model of the grounded coplanar waveguide far-zone radiation field are obtained: Where, The initial electric field model representing the far-zone radiation field of the grounded coplanar waveguide is: It means that through Babinet's principle The magnetic current converted into represents the amplitude of the traveling current on the grounded coplanar waveguide, represents the imaginary unit, represents the distance between the radiation field observation point of the grounded coplanar waveguide and the origin in spherical coordinates, represents the propagation constant of electromagnetic waves, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the signal conductor length of the grounded coplanar waveguide, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the dielectric thickness of the grounded coplanar waveguide, Represents 180 degrees in radians.

[0040] Where, The initial magnetic field model representing the far-field radiation field of the grounded coplanar waveguide, It means that through Babinet's principle The magnetic current converted into represents the amplitude of the traveling current on the grounded coplanar waveguide, represents the imaginary unit, represents the distance between the radiation field observation point of the grounded coplanar waveguide and the origin in spherical coordinates, represents the propagation constant of electromagnetic waves, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the signal conductor length of the grounded coplanar waveguide, The radiation field observation point of the grounded coplanar waveguide in spherical coordinates is represented by horn, represents the dielectric thickness of the grounded coplanar waveguide, Represents 180 degrees in radians.

[0041] Furthermore, the initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide is compared with the directivity pattern of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model, and the phase error of the main lobe of the initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide and the directivity pattern of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model is obtained. If the phase error is less than 5%, the initial electric field model, initial magnetic field model and initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide are recorded as the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide. Figure 5 This image compares the far-field radiation pattern of the GCPW in the HFSS finite element model with the initial far-field radiation pattern of the GCPW. Because the phase difference between the main lobe of the GCPW's far-field radiation pattern and the GCPW's radiation pattern in the HFSS finite element model is less than 5%, the initial electric field model, initial magnetic field model, and initial pattern model of the GCPW's far-field radiation field are denoted as the electric field model, magnetic field model, and pattern model of the GCPW's far-field radiation field.

[0042] At this point, the electric field model, magnetic field model and pattern model of the far-zone radiation field of the grounded coplanar waveguide are obtained.

[0043] Step S002: Divide multiple antenna arrays in the quasi-coaxial area; superimpose the electric field model, magnetic field model and directional function of the far-zone radiation field of all antenna arrays in the quasi-coaxial area respectively to obtain the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the quasi-coaxial body; adjust the multiples of the length of the quasi-coaxial in the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the quasi-coaxial body to obtain the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the quasi-coaxial body.

[0044] It should be noted that in the field of electronic engineering technology, a coaxial structure has a signal through hole in the center, and multiple peripheral shielding through holes are distributed near the signal through hole. Figure 6 in The figure shows the side view of the coaxial The figure shows a top view of a quasi-coaxial cable. In practical applications, the top and bottom sides of the quasi-coaxial cable are each connected to a ground plane, allowing the ground planes connected to the top and bottom of the quasi-coaxial cable to be considered as a current loop. Therefore, when deriving an analytical model for the far-field radiation field of the quasi-coaxial cable, it is necessary to consider not only the radiation characteristics of the quasi-coaxial cable itself but also the radiation characteristics of the two ground planes connected to the quasi-coaxial cable.

[0045] It's also important to note that when considering the radiation effect of the two ground planes connected to the quasi-coaxial cable, the current distribution of the ground plane cannot be directly derived. Instead, the radiation effect of the ground plane is equated using the mirror principle. Therefore, the two ground planes are treated as mirror images of the quasi-coaxial cable itself, and the radiation effect of the two ground planes connected to the quasi-coaxial cable is considered an extension of the current distribution of the quasi-coaxial cable itself. In other words, the quasi-coaxial cable's far-field radiation field can be calculated by multiplying the length of the quasi-coaxial cable within the far-field radiation field of the quasi-coaxial cable itself by three.

[0046] It should be further explained that when obtaining the far-field radiation field of the quasi-coaxial body, because the impedance matching at both ends of the quasi-coaxial body is maintained as much as possible during the design process, when obtaining the quasi-coaxial radiation analytical model, the current on the quasi-coaxial body can be considered to be distributed as a traveling wave. Therefore, based on the transmission line theory, the traveling wave current of the central signal conductor in the quasi-coaxial body is obtained. Then, based on the characteristics that the current in the peripheral shielding vias in the quasi-coaxial body is opposite to the current in the central signal conductor, the current amplitude of all peripheral shielding vias in the quasi-coaxial structure is the same, and the sum of the current amplitudes of all peripheral shielding vias in the quasi-coaxial structure is the same as the current amplitude of the central signal conductor, the traveling wave current in the central signal conductor and the peripheral shielding vias in the quasi-coaxial structure is obtained.

[0047] It should be further explained that, within a quasi-coaxial structure, the purpose of arranging peripheral shielding vias near the center signal conductor is to form an electromagnetic isolation barrier around the center signal conductor and a current loop with the center signal conductor. An electric conductor antenna array refers to an antenna system composed of radiating elements made of conductive materials arranged in a specific geometric pattern, which achieves beam steering by controlling the current distribution of each element. That is, because the shielding vias around the center signal conductor prevent external electromagnetic interference with the center signal conductor, the center signal conductor can be divided into the same number of small center signal conductors as the number of peripheral shielding vias. A small center signal conductor and a peripheral shielding via are then considered an electric conductor antenna array, resulting in the number of antenna arrays within a quasi-coaxial structure being the same as the number of peripheral shielding vias. Therefore, based on the electric field model, magnetic field model, and far-field radiation field directional function of each electric conductor antenna array, the electric field model, magnetic field model, and far-field radiation field directional pattern of the quasi-coaxial structure itself are obtained.

[0048] It should be further explained that when the electric field model, magnetic field model, and far-field radiation pattern of the electric conductor antenna array are derived based on the electric field model, magnetic field model, and far-field radiation pattern of a single antenna within the electric conductor antenna array, the phase of the array factor of each electric conductor antenna array differs due to the different positions of the peripheral shielding vias within the quasi-coaxial array on the central signal conductor. Therefore, the array factor of each electric conductor antenna array is derived based on the positional relationship between each peripheral shielding via and the central signal conductor, and furthermore, the electric field model, magnetic field model, and far-field radiation pattern of the quasi-coaxial array are derived. The electric field model, magnetic field model, and far-field radiation pattern of the entire quasi-coaxial array are multiplied by three within the magnetic field model, electric field model, and far-field radiation pattern of the quasi-coaxial array to obtain the electric field model, magnetic field model, and far-field radiation pattern of the entire quasi-coaxial array.

[0049] It should be further explained that when obtaining the radiation analytical model for each object, the far-field radiation pattern of the object must be compared with the radiation pattern of the object within the HFSS finite element model to verify the validity of the quasi-coaxial analytical model. The parameter that most significantly influences the radiation pattern in the quasi-coaxial radiation analytical model is the length of the center signal conductor within the quasi-coaxial structure. Therefore, if the quasi-coaxial analytical model is insufficiently valid, the length of the center signal conductor within the quasi-coaxial structure is adjusted to ensure that the inferred quasi-coaxial analytical model is valid.

[0050] Specifically, transmission line theory is used to calculate the traveling wave current on the central signal conductor within the quasi-coaxial system. The amplitude of the traveling wave current on the central signal conductor within the quasi-coaxial system is divided by the number of shielding vias within the quasi-coaxial system. This value is recorded as the amplitude of the traveling wave current within the quasi-coaxial system's peripheral shielding vias. The direction of the current within the quasi-coaxial system is opposite to that within the peripheral shielding vias.

[0051] Furthermore, the quasi-coaxial is placed in the spherical coordinates, and the observation point of the quasi-coaxial radiation field in the spherical coordinates is obtained. The distance between the observation point of the quasi-coaxial radiation field and the origin in spherical coordinates, the distance between the observation point of the quasi-coaxial radiation field and the origin in spherical coordinates, horn.

[0052] Further, the The antenna array where the peripheral shielding through hole is located is recorded as Antenna array, the The calculation formula for the array factor of the antenna array where the peripheral shielding through hole is located is as follows: Where, Indicates the The array factor of the antenna array where the peripheral shielding vias are located, represents the electromagnetic wave propagation constant, Indicates the distance between the center signal via and the peripheral shielding via. Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn, Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn, Indicates the The order value of shielding vias, represents the sine function, represents the cosine function, Represents 180 degrees in radians.

[0053] What needs to be explained is that It is related to the number and position of the peripheral shielding vias. In this paper, the eight shielding vias are located along the spherical coordinates. The corner goes around the center signal through hole, so the difference between every two adjacent shielding through holes is Angle That is, the shielding vias from the 1st to the 8th are located The angle is 0, , , , , , , .

[0054] Furthermore, the directional function of the far-zone radiation field of the antenna array where each peripheral shielding through-hole is located is obtained as follows: Where, Indicates the The directional function of the far-zone radiation field of the antenna array where the peripheral shielding through-hole is located, Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn, represents the propagation constant of electromagnetic waves, Indicates the length of the quasi-coaxial axis, represents the sine function in trigonometric function, represents the cosine function in trigonometric function, Indicates the The array factor of the antenna array where the peripheral shielding via is located.

[0055] Furthermore, the specific calculation formulas for the electric field model and magnetic field model of the far-zone radiation field of the antenna array where each peripheral shielding through-hole is located are as follows: Where, Indicates the The electric field model of the far-zone radiation field of the antenna array where the peripheral shielding through-holes are located, Indicates the amplitude of the traveling current on the center signal conductor, represents the imaginary unit, represents the propagation constant of electromagnetic waves, Indicates the length of the quasi-coaxial axis, represents a natural constant, also known as Napier's constant, represents the distance between the observation point of the quasi-coaxial radiation field and the origin in spherical coordinates, Indicates the The array factor of the antenna array where the peripheral shielding vias are located, represents the sine function in trigonometric function, Represents the cosine function in trigonometric functions.

[0056] Where, Indicates the The magnetic field model of the far-field radiation field of the antenna array where the peripheral shielding through-holes are located, Indicates the amplitude of the traveling current on the center signal conductor, represents the imaginary unit, represents the propagation constant of electromagnetic waves, Indicates the length of the quasi-coaxial axis, represents a natural constant, also known as Napier's constant, represents the distance between the observation point of the quasi-coaxial radiation field and the origin in spherical coordinates, Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn, Indicates the The array factor of the antenna array where the peripheral shielding vias are located, represents the sine function in trigonometric function, Represents the cosine function in trigonometric functions.

[0057] Furthermore, the electric field model and magnetic field model of the far-field radiation field of the antenna array where all peripheral shielding through-holes on the quasi-coaxial are located are superimposed with the directional function model to obtain the electric field model, magnetic field model, and pattern model of the far-field radiation field of the quasi-coaxial body; the length of the quasi-coaxial within the electric field model, magnetic field model, and pattern model of the far-field radiation field of the quasi-coaxial body is multiplied by 3 to obtain the initial electric field model, initial magnetic field model, and initial pattern model of the entire quasi-coaxial far-field radiation field. The specific calculation formulas for the initial electric field model and initial magnetic field model of the entire quasi-coaxial far-field radiation field are as follows:

[0058] Where, Represents the initial electric field model of the entire quasi-coaxial far-zone radiation field, Represents the initial magnetic field model of the entire quasi-coaxial far-zone radiation field, Indicates the amplitude of the traveling current on the center signal conductor, represents the imaginary unit, represents the propagation constant of electromagnetic waves, Indicates the length of the quasi-coaxial axis, represents a natural constant, also known as Napier's constant, represents the distance between the observation point of the quasi-coaxial radiation field and the origin in spherical coordinates, Indicates the distance between the center signal via and the peripheral shielding via. represents the sine function in trigonometric function, represents the cosine function in trigonometric function, Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn, Represents the observation point of the quasi-coaxial radiation field in spherical coordinates horn.

[0059] Furthermore, the initial radiation pattern of the entire quasi-coaxial far-zone radiation field was compared with the radiation pattern of the quasi-coaxial far-zone radiation field obtained by the HFSS finite element model. It was found that the initial radiation pattern of the entire quasi-coaxial far-zone radiation field split into multiple cone lobes faster than the radiation pattern of the quasi-coaxial far-zone radiation field obtained by the HFSS finite element model.

[0060] Furthermore, in order to make the initial far-zone radiation pattern consistent with the far-zone radiation pattern of the finite element model, it is necessary to correct the variable representing the quasi-coaxial length in the initial quasi-coaxial analytical model. Due to the mirror principle, the quasi-coaxial length variable l1 in the initial analytical model is multiplied by a multiple of 3. To correct the analytical model, it is necessary to change the multiple of l1 so that the initial pattern of the far-zone radiation field is consistent with the pattern in the finite element model. After the analytical model changes the multiple and compares it with the pattern in the finite element model, it is finally determined that when the multiple is 3 / 2, the pattern of the far-zone radiation field is most consistent with the pattern of the far-zone radiation field in the finite element model. Therefore, the analytical model with a multiple of 3 / 2 is called the optimal analytical model. When the quasi-coaxial length l1 changes, the overall comparison error between the optimal far-zone radiation pattern obtained by the optimal analytical model and the finite element far-zone radiation pattern is less than 5%, indicating that the pattern obtained by the optimal analytical model is highly consistent with the far-zone radiation pattern of the finite element model.

[0061] Furthermore, the initial electric field model, initial magnetic field model and pattern model of the entire quasi-coaxial far-zone radiation field are incorporated into the formula Multiplying by 3 is changed to and By multiplying them together, we can obtain the electric field model, magnetic field model and direction pattern model of the quasi-coaxial far-zone radiation field.

[0062] Step S003: transforming the coordinate system of the grounded coplanar waveguide far-field radiation field, and correcting the current phase in the electric field model, magnetic field model, and directional pattern model of the quasi-coaxial far-field radiation field; superimposing the electric field model, magnetic field model, and directional pattern model of the grounded coplanar waveguide far-field radiation field after the coordinate system transformation and the electric field model, magnetic field model, and directional pattern model of the quasi-coaxial far-field radiation field after the current phase correction, respectively, to obtain an analytical model of the grounded coplanar waveguide-to-quasi-coaxial far-field radiation field.

[0063] It should be noted that when connecting a grounded coplanar waveguide to a quasi-coaxial structure, the coordinate systems of the two structures must be consistent. Since the analytical model of the far-field radiation field of the grounded coplanar waveguide in step 1 is in the xoz plane, and the analytical model of the far-field radiation field of the quasi-coaxial structure in step 2 is in the xoy plane, the coordinate system of the grounded coplanar waveguide needs to be changed.

[0064] It should be further noted that after connecting the GCPW and the quasi-coaxial structure, the current first flows through the GCPW and then through the quasi-coaxial structure, causing the initial phase of the quasi-coaxial current to be non-zero. Therefore, the phase of the current after passing through the GCPW structure is recorded as the initial phase of the quasi-coaxial structure. Therefore, the phase in the quasi-coaxial far-field radiation field model is modified.

[0065] It should be further explained that 50 ohms is the industry-recognized system impedance value for chip system packaging transmission structure design. Therefore, when designing transmission structures such as grounded coplanar waveguides and quasi-coaxial transmission structures, it is necessary to maintain their characteristic impedance at 50 ohms to achieve impedance matching with other structures. Therefore, the radiated electric field of the grounded coplanar waveguide is superimposed with the radiated electric field of the quasi-coaxial transmission structure, and the radiated magnetic field of the grounded coplanar waveguide is superimposed with the radiated magnetic field of the quasi-coaxial transmission structure to obtain an analytical model for the grounded coplanar waveguide to quasi-coaxial transmission structure.

[0066] Specifically, let the impedance value of the grounded coplanar waveguide and the quasi-coaxial be 50 ohms, transform the plane where the grounded coplanar waveguide is located from the xoz plane to the xoy plane, and transform the electric field model, magnetic field model and pattern model of the far-zone radiation field of the grounded coplanar waveguide into the xoy plane. , The relevant sine and cosine terms are mathematically transformed according to the change of the coordinate system, and the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide after the coordinate transformation are obtained.

[0067] Furthermore, in the electric field model, magnetic field model and pattern model of the quasi-coaxial far-field radiation field, the current of the central signal conductor is multiplied by a phase factor , we obtain the electric field model, magnetic field model, and pattern model of the quasi-coaxial far-zone radiation field after phase change. Where j is the imaginary unit, k is the electromagnetic wave propagation constant, and l is the length of the grounded coplanar waveguide.

[0068] Furthermore, the directivity pattern of the far-zone radiation field of the grounded coplanar waveguide after the coordinate transformation is superimposed with the directivity pattern of the quasi-coaxial far-zone radiation field after the phase change to obtain the initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial. The initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide after the coordinate transformation are superimposed with the initial electric field model and initial magnetic field model of the quasi-coaxial far-zone radiation field after the phase change to obtain the initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial.

[0069] Furthermore, the initial radiation pattern of the GCPW-to-quasi-coaxial far-zone radiation field was compared with the radiation pattern of the GCPW-to-quasi-coaxial far-zone radiation field obtained using the HFSS finite element model. The phase error between the two patterns was found to be around 5%. The initial electric field model, initial magnetic field model, and initial radiation pattern model of the GCPW-to-quasi-coaxial far-zone radiation field are denoted as the electric field model, magnetic field model, and radiation pattern model of the GCPW-to-quasi-coaxial far-zone radiation field.

[0070] Example 2: When the present invention is implemented, according to Figure 1The process shown is divided into three major steps: S1: Derive and verify the analytical model of the far-zone radiation field of a grounded coplanar waveguide.

[0071] S2: Propose an analytical modeling method for the radiation characteristics of a quasi-coaxial structure based on equivalent antenna array analysis and derive a high-precision analytical model.

[0072] S3: Conduct qualitative analysis of the radiation characteristics of the grounded coplanar waveguide-to-quasi-coaxial structure in high-speed interconnection of ceramic packaged TR components, and construct an analytical model of the far-field radiation field of the grounded coplanar waveguide-to-quasi-coaxial structure using theoretical derivation and cascade modeling methods.

[0073] First, the analytical modeling process of S1 is introduced in detail: Establishing an analytical model, that is, deriving the mathematical expression of the far-field radiation field, requires two steps: the first step is to determine the current distribution on the grounded coplanar waveguide; the second step is to obtain the final mathematical expression of the radiation field by superposing and integrating the radiation fields of basic current elements based on the current distribution.

[0074] Step 1: Determine the current distribution. Figure 2 (a) (b) are the top view and side view of the grounded coplanar waveguide, and Figure 2 (c) (d) show the complementary structure of the coplanar waveguide, which is complementary to the gap in the upper layer of the grounded coplanar waveguide. Figure 2 middle, represents the length of the GCPW signal conductor, g represents half the length of the ground plane on the grounded coplanar waveguide, w represents the gap width, d Represents the signal conductor width, and They represent the current distribution on the conductor array in (d) respectively.

[0075] The medium around the grounded coplanar waveguide is set to air. The steps for deriving the far-zone radiation field distribution of the grounded coplanar waveguide are as follows: (1) First, consider the upper half plane of the grounded coplanar waveguide as a slot antenna, that is, Figure 2 (a) can be regarded as a slot antenna array composed of two slot antennas. Then, according to the Babinet principle, this slot antenna array is equivalent to a magnetic conductor antenna array, that is, Figure 2 (c). Finally, according to the duality principle, solving the radiation field of the magnetic conductor antenna array is equivalent to solving the radiation field of the electric conductor antenna array, that is, Figure 2 (d) The radiation field.

[0076] (2) Determined based on the transmission line principle Figure 2 (d) The current distribution of the conductor antenna array can be used to obtain the far-field radiation field of the upper half plane of the grounded coplanar waveguide, that is, Figure 2 (b) The upper half plane. Figure 2 The lower half ground plane in (b) is used as the return current plane, and is equivalent to an electric conductor antenna array using the mirror principle. This electric conductor antenna array is Figure 2 (d) The currents in the electric conductor antenna array are of equal amplitude and opposite phase.

[0077] (3) Add the radiation fields of the electric conductor antenna arrays of (1) and (2), that is, add the radiation fields of the upper and lower planes of the grounded coplanar waveguide, and then convert them through the duality principle and Babinet's principle to obtain the far-field radiation field of the grounded coplanar waveguide. At this time, the radiation fields of the upper and lower planes of the grounded coplanar waveguide can also be regarded as the radiation fields of a new antenna array composed of two electric conductor antenna arrays.

[0078] When the impedances at both ends of the grounded coplanar waveguide structure are matched, the current distribution on the structure is a traveling wave distribution. At the same time, due to the Babinet principle and the duality principle, we first calculate Figure 2 (d) The far-field radiation field. At this time, Figure 2 (d) It can be regarded as a two-element linear wavelength wire antenna array, and its current distribution can be expressed by transmission line theory as follows:

[0079] Formula (1) represents Figure 2 (d) Traveling wave current in the conductor array. The current distribution in the underlying stratum can be equivalent using the mirror principle.

[0080] Where, and Respectively represent the amplitude of the current distribution on the conductor array in (d), which is different from that in Example 1. are the same value.

[0081] Step 2: Calculate the radiation field. Figure 2 (d) The radiation field is the radiation field of the long wire traveling wave antenna, which can be expressed as:

[0082] From the above formula, we know that the directional function of the radiation field is: On this basis, the radiation field direction function of the binary traveling wave antenna array only needs to be multiplied by the array factor in formula (3.2) ,Right now: At this time, the radiation field of the binary traveling wave antenna array is: Formula (5) can be obtained by the duality principle and Babinet principle Figure 2In (b), the radiation field of the upper ground plane and signal conductor of the grounded coplanar waveguide needs to be calculated by the mirror principle. After applying the mirror principle, the radiation field of the lower ground plane can also be equivalent to a two-element linear wavelength conductor antenna array, which is the same as Figure 2 The current distribution in (d) is equal in amplitude and opposite in phase, which can be considered as Figure 2 (d) together form a new antenna array. Therefore, it is only necessary to multiply the array factor based on formula (5) Then, the radiation field pattern is:

[0083] Correspondingly, the radiated electric field is: After transforming formula (7) through the duality principle and Babinet principle, we get: So far, formula (6), formula (8), and formula (9) represent the directivity pattern, radiation electric field, and radiation magnetic field of the far-field radiation field of the grounded coplanar waveguide, respectively. The analytical model of the far-field radiation field of the GCPW includes the directivity pattern, radiation electric field, and radiation magnetic field of the far-field radiation field of the GCPW.

[0084] Table 1 is the HFSS finite element model parameter settings of the grounded coplanar waveguide. Figure 4 This is a view of the GCPW model in HFSS. Electromagnetic compatibility design and structural optimization in system packaging are more challenging at high frequencies. In the following example, the initial frequency is set to 25 GHz, and the surrounding medium of the GCPW is set to air.

[0085] Table 1 Grounded coplanar waveguide model parameter settings Figure 5 In order to keep the parameter settings in Table 1, the radiation electric field pattern of the analytical model and the HFSS finite element model changes with the length of the signal conductor. l The results of changes.

[0086] Depend on Figure 5 It can be seen that the radiation patterns obtained by the analytical model and the HFSS finite element model are highly consistent, proving the effectiveness of this analytical model in analyzing the radiation characteristics of the grounded coplanar waveguide.

[0087] Then the analytical modeling process of S2 is introduced in detail: Step 1: Determine the current distribution.

[0088] Transmission line theory is used to determine the current distribution within the quasi-coaxial structure, including the current distribution within the central signal via and the surrounding shielding vias. The radiation effect of the two ground planes connected to the quasi-coaxial structure must also be considered, using the mirror image principle for equivalent calculations. The signal conductor at the center of the quasi-coaxial structure, along with the surrounding shielding vias, can form an antenna array. The number of antenna arrays depends on the number of surrounding shielding vias. Finally, taking impedance matching into account, the quasi-coaxial structure's radiation effect is equated to a traveling wavelength conductor antenna array.

[0089] The following are the specific calculation steps: (1) Calculate the current distribution of the quasi-coaxial structure: According to the transmission line theory, the current distribution of the central signal conductor of the quasi-coaxial structure is obtained. The current distribution of the peripheral shielding vias is related to the number of shielding vias. The number of shielding vias is n , then its current amplitude is 1 / the current amplitude of the center signal through hole n , the current phase is opposite to the central metal via current phase.

[0090] (2) Consider the quasi-coaxial structure as an antenna array: the central signal conductor and the peripheral n shielding vias can be formed n The current amplitude of the peripheral shielding via is 1 / 2 of that of the central signal via. n , the current phase is opposite to it.

[0091] (3) Calculate the radiation field of the antenna array: calculate n The far-field radiation field of the antenna array is n On this basis, the formation radiation field is superimposed to obtain the analytical model of the far-field radiation field of the quasi-coaxial structure.

[0092] In the present invention, the number of peripheral shielding through holes of the quasi-coaxial structure is 8.

[0093] Figure 6 The side view and top view of the coaxial structure are shown. The current of the signal conductor in the side view (a) is expressed as , the current in one of the surrounding shield vias is expressed as In the side view (a), ① represents the quasi-coaxial structure body, ③ and ② represent the quasi-coaxial structures equivalent to the upper ground plane and the lower ground plane through the mirror principle, respectively, with the same current direction as in ①.

[0094] Under the impedance matching condition, the current of the coaxial structure is distributed in a traveling wave. At the same time, the number of peripheral shielding holes in this paper is set to 8. Figure 6 The through holes in (b) are numbered 1-9, representing: at this time, Figure 6 The current in (b) can be expressed as: Step 2: Calculate the radiation field.

[0095] For the convenience of calculation, Divided into 8 parts, each part can form an antenna array with a shielding through hole, namely: In formula (11), Indicates that After being divided into 8 parts, The combination forms this part of the antenna array, i.e. , at this time, formula (11) expresses Figure 6 In (b), the signal via No. 1 and the shielding via No. 2 form a traveling wavelength conductor antenna array. Other shielding vias can also form an antenna array with the signal via No. 1, in the same form as formula (11).

[0096] Therefore, the radiation field of the quasi-coaxial structure is equivalent to the superposition of eight antenna arrays represented by formula (11). Next, the far-field radiation field of these eight antenna arrays will be derived.

[0097] First, the radiation field of formula (11) is equal to The radiation field is multiplied by the array factor, which is mentioned in S1 . Please note that Figure 6 (b) It can be seen that the eight antenna arrays are placed in different directions, which is expressed in the array factor as Therefore, the array factors of the 8 antenna arrays are different. Taking formula (11) as an example, the array factors corresponding to the 8 antenna arrays are: , , , , , , , Therefore, the radiation direction function corresponding to the 8 antenna arrays is:

[0098] The radiation direction function corresponding to the 8 antenna arrays is: Finally, the far-zone radiation field of the 8-antenna array can be calculated, namely: At this point, the far-zone radiation fields of the eight antenna arrays have been calculated. After that, they only need to be added together to obtain the far-zone radiation field of the coaxial structure itself.

[0099] Next, we need to consider the radiation effect of the two ground planes connected to the quasi-coaxial. Figure 6 (a) shows the current distribution after the two ground planes are equivalent using the mirror principle. The radiation effect of the two ground planes is equivalent to the extension of the current distribution of the quasi-coaxial body. It is only necessary to replace the variable representing the quasi-coaxial length in the formula becomes Therefore, after considering the ground plane radiation effect, taking formula (14) as an example, it will become:

[0100] The radiation pattern of the quasi-coaxial analytical model represented by formula (16) splits into multiple conical lobes more quickly than the radiation pattern of the HFSS finite element model. Therefore, this analytical model needs to be corrected. After repeated verification with HFSS finite element simulation, taking formula (16) as an example, the corrected formula is:

[0101] Formula (16) takes into account the radiation effect of the stratum connected to the quasi-coaxial, so the variable representing the quasi-coaxial length is becomes Formula (17) will becomes , which slows down the splitting speed of the analytical model radiation pattern, which is consistent with the HFSS finite element simulation results. The other seven antenna array analytical models are also modified in the same way as formula (17).

[0102] The derived analytical model is then compared with the HFSS finite element model to verify the validity of this analytical model.

[0103] The parameters of the quasi-coaxial model in HFSS are set as follows, and the surrounding medium is air: Table 2 Quasi-coaxial structure parameter settings Figure 7 It is a quasi-coaxial model in HFSS. Figure 8 (a) and (b) are the side view and top view of the model respectively: Figure 9 Shows the same coaxial height l 0 Comparison of radiation patterns between the analytical model and the HFSS model when changes: The quasi-coaxial analytical model agrees well with the HFSS finite element model, which proves the effectiveness of this analytical model in analyzing quasi-coaxial radiation characteristics.

[0104] Finally, the analytical modeling process of S3 is introduced in detail: Figure 10 A schematic diagram of the grounded coplanar waveguide to quasi-coaxial structure is shown, in which the grounded coplanar waveguide structure is directly connected to the quasi-coaxial structure.

[0105] The specific steps to establish the analytical model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial are as follows: (1) Transform the coordinates of the GCPW far-field radiation field analytical model: In order to connect the GCPW with the coaxial structure, the coordinates of the GCPW need to be transformed, such as Figure 11 shown.

[0106] (2) Change the current distribution of the quasi-coaxial far-zone radiation field analytical model: Since the grounded coplanar waveguide is connected to the quasi-coaxial structure, the initial phase of the current in the quasi-coaxial structure is not 0, and the phase of the current after passing through the grounded coplanar waveguide structure needs to be added.

[0107] (3) Connecting the two structures while maintaining a characteristic impedance of 50 ohms: When designing a grounded coplanar waveguide to a quasi-coaxial structure, in order to design a structure with good transmission performance, it is necessary to maintain a characteristic impedance of 50 ohms for each structure before modeling.

[0108] (4) Cascading and superimposing the two structures' far-field radiation field analytical models: Through the above derivation, the far-field radiation field analytical models of the grounded coplanar waveguide and the quasi-coaxial structure have been obtained and cascaded with a characteristic impedance of 50 ohms. Therefore, the far-field radiation field analytical models of the two structures can be directly superimposed.

[0109] go through Figure 11 The analytical formula for the far-zone radiation field of the grounded coplanar waveguide after coordinate transformation is: The far-field radiation field of one of the antenna arrays after changing the quasi-coaxial initial current phase is: The radiation fields of the remaining seven antenna arrays are similar to formula (20). By superimposing the radiation fields of these eight antenna arrays, we can obtain the analytical formula of the quasi-coaxial far-zone radiation field.

[0110] After the coordinate transformation of the GCPW far-field radiation field analytical model and the modification of the initial current phase of the quasi-coaxial far-field radiation field analytical model, the final GCPW-to-quasi-coaxial far-field radiation field analytical model can be obtained by simply adding the two analytical models together. However, it should be noted that the characteristic impedance of 50 ohms must be maintained when the two structures are connected to maintain a traveling wave current distribution in the link. Because the GCPW structure is cascaded with the quasi-coaxial structure, the current distribution in both structures is continuous and the current amplitude is the same.

[0111] represents the far-zone radiation electric field of the grounded coplanar waveguide after coordinate transformation, It represents the quasi-coaxial far-zone radiation electric field after the initial phase of the current is changed. The radiation magnetic field is the same as the radiation electric field, and the analytical models of the two can be cascaded and added.

[0112] The derived analytical model is compared with the HFSS finite element model to verify the validity of this analytical model. Figure 12 This is a grounded coplanar waveguide-to-quasi-coaxial finite element model in HFSS. The parameter settings of this model in HFSS refer to Table 3. The surrounding medium is air:

[0113] Figure 13 In order to keep the parameter settings in Table 3, the radiation pattern of the analytical model and the HFSS finite element model changes with the length of the signal conductor. l The results of changes.

[0114] Depend on Figure 13 It can be seen that the radiation patterns obtained by the analytical model and the HFSS finite element model are highly consistent, proving the effectiveness of this analytical model in analyzing the radiation characteristics of the grounded coplanar waveguide to quasi-coaxial transmission.

[0115] Table 3 Parameter settings for grounded coplanar waveguide to quasi-coaxial structure It should be noted that the specific embodiments described above can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although this specification and examples have described the present invention in detail, those skilled in the art should understand that the present invention can still be modified or replaced with equivalents; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are included in the scope of protection of the patent for the present invention. Any reference signs in the claims should not be construed as limiting the claims involved.

Claims

1. A method for constructing an analytical model of the radiation field of a grounded coplanar waveguide-to-quasi-coaxial interconnect structure, characterized in that: include: The upper half plane of the grounded coplanar waveguide is equivalent to a slot antenna array, and the slot antenna array is equivalent to an electric conductor antenna array. The radiation field of the electric conductor antenna array is solved to obtain the electric field model and directional function of the equivalent far-field radiation field of the upper half plane of the grounded coplanar waveguide; based on the current distribution of the equivalent slot antenna array, the far-field radiation field and directional function of the lower half plane of the grounded coplanar waveguide are obtained. The electric field model and directional function of the far-zone radiation field of the upper half plane of the grounded coplanar waveguide, as well as the far-zone radiation field and directional function of the lower half plane of the grounded coplanar waveguide are superimposed to obtain the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the grounded coplanar waveguide; Multiple antenna arrays are divided within the quasi-coaxial structure; the electric field model, magnetic field model, and directional function of the far-zone radiation field of all antenna arrays within the quasi-coaxial structure are superimposed respectively to obtain the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body; the multiples of the length of the quasi-coaxial structure in the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body are adjusted to obtain the electric field model, magnetic field model, and directional pattern model of the far-zone radiation field of the quasi-coaxial body; The coordinate system of the far-field radiation field of the grounded coplanar waveguide is transformed, and the electric field model, magnetic field model and current phase in the quasi-coaxial far-field radiation field are corrected; The electric field model, magnetic field model, and pattern model of the far-field radiation field of the grounded coplanar waveguide after coordinate system transformation are superimposed with the electric field model, magnetic field model, and pattern model of the quasi-coaxial far-field radiation field after current phase correction to obtain the analytical model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial.

2. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific steps of obtaining the electric field model and directional function of the equivalent far-zone radiation field in the upper half plane of the grounded coplanar waveguide are as follows: Divide the upper half plane of the grounded coplanar waveguide into two slot antennas and The plane is viewed as an antenna array consisting of two slot antennas; The amplitude of the traveling wave current in the grounded coplanar waveguide is obtained by using transmission line theory; The slot antenna array on the upper half plane of the grounded coplanar waveguide is equivalent to an electric conductor antenna array through the Babinet principle and the duality principle. The electric field model and directional function of the far-zone radiation field in the upper half plane of the equivalent grounded coplanar waveguide are obtained.

3. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific steps of obtaining the electric field model, magnetic field model and pattern model of the far-field radiation field of the grounded coplanar waveguide are as follows: According to the characteristics of equal amplitude and opposite direction of current in the upper and lower half planes of the grounded coplanar waveguide, the upper and lower half planes of the grounded coplanar waveguide are approximated as an antenna array; According to the electric field model and directional function of the far-zone radiation field of the equivalent grounded coplanar waveguide upper half plane, the electric field model and directional pattern model of the far-zone radiation field of the equivalent grounded coplanar waveguide are obtained; The equivalent pattern model of the far-zone radiation field of the grounded coplanar waveguide is recorded as the initial pattern model of the far-zone radiation field of the grounded coplanar waveguide; The electric field model of the equivalent far-field radiation field of the grounded coplanar waveguide is transformed by the Babinet principle to obtain the initial electric field model and initial magnetic field model of the far-field radiation field of the grounded coplanar waveguide; According to the comparison between the directional pattern model of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model and the initial directional pattern model of the far-zone radiation field of the grounded coplanar waveguide, the electric field model, magnetic field model and directional pattern model of the far-zone radiation field of the grounded coplanar waveguide are obtained through the initial electric field model, initial magnetic field model and initial directional pattern model of the far-zone radiation field of the grounded coplanar waveguide.

4. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 3, characterized in that: The specific steps of obtaining the electric field model, magnetic field model and pattern model of the far-field radiation field of the grounded coplanar waveguide are as follows: Obtain the phase error between the main lobe of the directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide in the HFSS finite element model and the initial directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide; Since the phase error of the main lobes of the two pattern models is less than 5%, the initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide are recorded as the electric field model and magnetic field model of the far-zone radiation field of the grounded coplanar waveguide; The initial pattern model of the far-zone radiation field of the grounded coplanar waveguide is recorded as the pattern model of the far-zone radiation field of the grounded coplanar waveguide.

5. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific steps of obtaining the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: Multiply the electric field model, magnetic field model and the length of the quasi-coaxial in the pattern model of the far-zone radiation field of the quasi-coaxial body by 3 to obtain the initial electric field model, initial magnetic field model and initial pattern model of the entire quasi-coaxial far-zone radiation field; Obtain the entire quasi-coaxial far-zone radiation pattern model in the HFSS analytical model; According to the phase error of the main lobe of the initial pattern model of the entire quasi-coaxial far-zone radiation field and the pattern model of the entire quasi-coaxial far-zone radiation field in the HFSS analytical model, the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are obtained through the initial electric field model, initial magnetic field model and initial pattern model of the entire quasi-coaxial far-zone radiation field.

6. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 5, characterized in that: The specific steps of obtaining the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: Comparing the initial directivity pattern of the entire quasi-coaxial far-zone radiation field with the directivity pattern model of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model, it is found that the initial directivity pattern of the entire quasi-coaxial far-zone radiation field splits into multiple cone lobes faster than the directivity pattern of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model; Adjusting the multiple of the quasi-coaxial length in the initial directional pattern of the entire quasi-coaxial far-zone radiation field to obtain the initial directional pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment; The initial directivity pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment is compared with the directivity pattern of the entire quasi-coaxial far-zone radiation field obtained by the HFSS finite element model, and the degree of consistency between the initial directivity pattern of the entire quasi-coaxial far-zone radiation field after each multiple adjustment and the directivity pattern of the quasi-coaxial far-zone radiation field obtained by the HFSS finite element model is obtained, and the multiple change is obtained as follows: When , the agreement is the highest; Change the multiples of the length of the quasi-coaxial in the initial electric field model, initial magnetic field model, and initial directional pattern of the entire quasi-coaxial far-zone radiation field to , and obtain the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field.

7. The method for constructing a radiation field analytical model of a grounded coplanar waveguide-to-quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific steps of transforming the coordinate system of the far-zone radiation field of the grounded coplanar waveguide are as follows: The plane where the far-zone radiation field of the grounded coplanar waveguide is located is transformed from the xoz plane to the xoy plane, and the electric field model, magnetic field model and the directional pattern model of the far-zone radiation field of the grounded coplanar waveguide are transformed into the xoz plane. , The relevant sine and cosine terms are mathematically transformed according to the change of the coordinate system, and the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide after the coordinate transformation are obtained.

8. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific calculation steps for correcting the current phase in the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field are as follows: In the electric field model, magnetic field model and pattern model of the quasi-coaxial far-field radiation field, the current of the central signal conductor is multiplied by a phase factor , the electric field model, magnetic field model and pattern model of the quasi-coaxial far-zone radiation field after phase change are obtained; where j is the imaginary unit, k is the electromagnetic wave propagation constant, and l is the length of the grounded coplanar waveguide.

9. The method for constructing a radiation field analytical model of a grounded coplanar waveguide to quasi-coaxial interconnect structure according to claim 1, characterized in that: The specific steps of obtaining the analytical model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial are as follows: The directional pattern model of the far-field radiation field of the grounded coplanar waveguide after coordinate transformation is superimposed with the directional pattern model of the quasi-coaxial far-field radiation field after phase change to obtain the initial directional pattern model of the far-field radiation field of the grounded coplanar waveguide to quasi-coaxial; The initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide after coordinate transformation are superimposed on the initial electric field model and initial magnetic field model of the quasi-coaxial far-zone radiation field after phase change, respectively, to obtain the initial electric field model and initial magnetic field model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial; The initial pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial transmission was compared with the pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial transmission obtained by the HFSS finite element model. The phase error between the two patterns was found to be less than 5%. The initial electric field model, initial magnetic field model and initial directivity pattern of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial are recorded as the electric field model, magnetic field model and directivity pattern model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial, and the analytical model of the far-zone radiation field of the grounded coplanar waveguide to quasi-coaxial is obtained; The analytical model of the grounded coplanar waveguide-to-quasi-coaxial far-field radiation field includes an electric field model, a magnetic field model and a directivity pattern model of the grounded coplanar waveguide-to-quasi-coaxial far-field radiation field.

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