CN109828157B - Dielectric substrate dielectric constant measuring mechanism and measuring method thereof - Google Patents
Dielectric substrate dielectric constant measuring mechanism and measuring method thereof Download PDFInfo
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Abstract
The invention discloses a dielectric substrate dielectric constant measuring mechanism and a measuring method thereof, which comprises at least three substrate integrated waveguide resonant cavities arranged on a dielectric substrate, wherein the middle part in the cavity of each substrate integrated waveguide resonant cavity is provided with a metallized blind hole, the sizes of all the metallized blind holes are different, the top layer of each substrate integrated waveguide resonant cavity is provided with a grounding coplanar waveguide and a GSG pads structure, the grounding coplanar waveguide and the GSG pads structure form a feed structure of the substrate integrated waveguide resonant cavity, and the grounding coplanar waveguide is respectively connected with the substrate integrated waveguide resonant cavities and the GSG pads structure. The invention takes the influence of the impedance of the feed structure and the feed structure on the unloaded resonant frequency of the resonant cavity into consideration, and the method of extracting the dielectric constant in the form of simultaneous equations can even remove the influence of external factors such as a probe connected with a vector network analyzer, a transmission line structure and the like, so that the measurement result is more accurate, and the measurement precision is improved.
Description
Technical Field
The invention belongs to the technical field of microwave and millimeter wave, and particularly relates to a dielectric substrate dielectric constant measuring mechanism based on a substrate integrated waveguide resonant cavity and a measuring method thereof.
Background
At present, dielectric constant measuring methods of dielectric substrates mainly include a lumped circuit method, a resonant cavity method, a transmission line method, a free space method and the like, wherein the resonant cavity method is the most common and accurate one. Particularly, after the substrate integrated waveguide is provided, the substrate integrated waveguide resonant cavity overcomes the defects of large volume, difficult integration and the like of the traditional metal waveguide resonant cavity and is widely applied. However, the impedance of the feed structure of the substrate integrated waveguide resonant cavity generates large interference on the extraction of the unloaded frequency of the resonant cavity, and some scholars successively put forward a Foster Circuit equivalent Circuit model and a resonant cavity de-embedding method in order to remove the influence of the feed structure of the resonant cavity. In some scenarios, the methods are effective and reliable, but the methods only consider the influence of the feed structure after the feed structure is cascaded with the resonant cavity, and neglect the influence of the feed structure on the resonant cavity structure. This is not trivial at low frequencies, but in the millimeter, sub-millimeter and even terahertz scenarios, the "damage" of the feed structure to the resonant cavity structure is not negligible, since the feed structure is comparable in size to the resonant cavity. This has led to the difficulty of meeting the high precision requirements of conventional methods for extracting the relative dielectric constant of dielectric substrates.
Therefore, a new technical solution is needed to solve the above problems.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the dielectric substrate dielectric constant measuring mechanism and the measuring method based on the substrate integrated waveguide resonant cavity are provided, and the measuring precision can be improved.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a dielectric substrate dielectric constant measuring mechanism, which includes at least three substrate integrated waveguide resonant cavities arranged on a dielectric substrate, wherein the substrate integrated waveguide resonant cavities have the same cavity size, a metalized blind hole is arranged in the middle of the inside of each cavity of the substrate integrated waveguide resonant cavity, the sizes of all the metalized blind holes are different, a grounded coplanar waveguide and a GSG pads structure are arranged on the top layer of the substrate integrated waveguide resonant cavity, the grounded coplanar waveguide and the GSG pads structure form a feed structure of the substrate integrated waveguide resonant cavity, and the grounded coplanar waveguide is respectively connected with the substrate integrated waveguide resonant cavity and the GSG pads structure.
A dielectric substrate dielectric constant measuring method based on a substrate integrated waveguide resonant cavity comprises the following steps:
1) the GSG pads structure is contacted with the probe and connected to a vector network analyzer, and the vector network analyzer is used for measuring the cascade scattering parameters of each substrate integrated waveguide resonant cavity and the GSG pads structure;
2) extracting the unloaded resonant frequency of the substrate integrated waveguide resonant cavity by using a de-embedding formula and a perturbation principle;
3) and calculating the dielectric constant of the dielectric substrate by using a resonance formula according to the obtained unloaded resonance frequency.
Further, the de-embedding formula in step 2 is as follows:
or
Wherein equation (1) is derived from First Foster's Form, equation (2) is derived from Second Foster's Form, where fLOn-load resonant frequency, f, of a substrate-integrated waveguide resonant cavityuIs the unloaded resonant frequency; qeFor the external quality factor, Q, of the feed networkLThe on-load quality factor of the substrate integrated waveguide resonant cavity can be directly obtained from scattering parameters, QuIntegrating the no-load quality factor of the waveguide resonant cavity for the substrate; x is the number ofeIs a feed network reactance, beIs a feed network susceptance, and k is an external feed network coupling coefficient; b is a coefficient about the influence of the metalized blind holes in the substrate integrated waveguide resonant cavity on the unloaded resonant frequency of the substrate integrated waveguide resonant cavity, and the size of the coefficient is in inverse proportion to the volume V of the substrate integrated waveguide resonant cavity 2; c is a coefficient about the influence of the feed network structure on the unloaded resonant frequency of the substrate integrated waveguide resonant cavity; expanding equations (1) (2) and omitting the min terms, then:
wherein
Thus, the above equation (4) only includes the coefficients related to the feed network;
in addition, according to the perturbation principle, the following results are obtained:
B＝-2V1 (5)
wherein V1The volume of a metallized blind hole in the substrate integrated waveguide resonant cavity;
as a substrateIntegrated waveguide resonant cavity internal resonance f101Mode, no-load resonant frequency fuRelative dielectric constant to dielectric substraterThe relationship of (a) to (b) is as follows:
wherein a iseffAnd deffRespectively equal length and width of the substrate integrated waveguide resonant cavity and equivalent length a of the integrated waveguide resonant cavityeffAnd physical length aSIWThe relationship of (a) to (b) is as follows:
wherein d is the diameter of the metalized through holes of the substrate integrated waveguide resonant cavity, s is the center distance between adjacent metalized through holes, and the unloaded resonant frequency f of the substrate integrated waveguide resonant cavity is extracted in the step 3uThen, the relative dielectric constant of the dielectric substrate is obtained according to the resonance formula (6)r。
In the invention, in order to obtain a higher quality factor without destroying the resonant cavity structure as much as possible, the grounding coplanar waveguide usually works in an under-coupled state.
In the invention, when the influence of the feed structure on the unloaded resonant frequency of the resonant cavity is negligible, the relative dielectric constant of the dielectric substrate can be extracted by only manufacturing two substrate integrated waveguide resonant cavities on the dielectric substrate.
According to the invention, more accurate results can be obtained by increasing the number of the substrate integrated waveguide resonant cavities, and the more the number is within a certain range, the more accurate the results are.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1) the method has accurate measurement result, innovatively takes the influence of the impedance of the feed structure and the feed structure on the unloaded resonant frequency of the resonant cavity into consideration, and even removes the influence of external factors such as a probe connected with a vector network analyzer, a transmission line structure and the like by a method for extracting the dielectric constant in a simultaneous equation set mode, so the measurement result is more accurate, and the measurement precision is improved;
2) the method can acquire all required information by simply measuring the scattering parameters of the sample, can be embedded into the influence of all external connecting devices or conversion structures, and does not need additional measurement and analysis.
Drawings
FIG. 1 is a partial perspective view of a dielectric constant measurement structure of the present invention;
FIG. 2 is a partial top view of a dielectric constant measurement structure of the present invention;
FIG. 3 is a schematic view of sample one of embodiment 1 of the present invention;
FIG. 4 is a schematic view of sample two of example 1 of the present invention;
FIG. 5 is a schematic view of sample three of example 1 of the present invention;
FIG. 6 is a schematic view of sample four of example 2 of the present invention;
FIG. 7 is a schematic view of sample five of example 2 of the present invention;
fig. 8 is a schematic diagram of sample six of embodiment 2 of the present invention.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
Example 1:
as shown in fig. 1 and 2, the thickness is hsubThree substrate integrated waveguide resonant cavities 2 are respectively arranged on a medium substrate 1 with the diameter of 6.52um, the sizes of the three substrate integrated waveguide resonant cavities 2 are 340um × 340um, the middle parts inside the three substrate integrated waveguide resonant cavities 2 are respectively provided with a metallized blind hole 3 which is respectively a first square metallized blind hole 31, a second square metallized blind hole 32 and a first square metallized blind hole 33, so that a sample 1, a sample 2 and a sample 3 are respectively formed on the medium substrate 1, and specific reference is made to fig. 3-5. Three gold in this exampleThe metallized blind holes 3 are all square structures and have the same side length and different heights, and the height of the first square metallized blind hole 31 is h10um, side length l18 um; the second square metallized via hole 32 has a height h22.76um with side length of l18 um; the third square metallized via hole 33 has a height h35.52, side length l1＝8um。
The top layer of the substrate integrated waveguide resonant cavity 2 is provided with a grounding coplanar waveguide 4 and a GSG pads structure 5, the grounding coplanar waveguide 4 and the GSG pads structure 5 form a feed structure of the substrate integrated waveguide resonant cavity 2, the grounding coplanar waveguide 4 is respectively connected with the substrate integrated waveguide resonant cavity 2 and the GSG pads structure 5, and the GSG pads are compatible with a probe with the size of 100 um.
The specific implementation steps are as follows:
1) the GSG pads structure 5 is contacted with the probe and connected to a vector network analyzer, the vector network analyzer is used for measuring the cascade scattering parameters of each substrate integrated waveguide resonant cavity 2 and the GSG pads structure 5, and the on-load resonant frequency f of the sample 1 is obtained through the scattering parametersL1319.17GHz on-load quality factor QL1233.4479; on-load resonant frequency f of sample 2L2318.56GHz on-load quality factor QL2116.5168; on-load resonant frequency f of sample 3L3318.72GHz on-load quality factor QL3＝71.3735；
2) From the embedding equation (3)
From perturbation equation (5):
wherein the volume V of the substrate integrated waveguide resonant cavity 2 is aeff×deff×hsub，aeffAnd deffRespectively equivalent length and equivalent width of the substrate integrated waveguide resonant cavityCalculated from equation (7).
Simultaneous equations (8) and (9) for calculating the unloaded resonant frequency f of the substrate integrated waveguide resonant cavityu＝323.9GHz；
3) According to the obtained unloaded resonant frequency fuThe dielectric constant of the dielectric substrate was calculated from the following resonance equation (6)r：
Example 2:
as shown in fig. 1 and 2, the thickness is hsubThree substrate integrated waveguide resonant cavities 2 are respectively arranged on a medium substrate 1 with the thickness of 6.52um, the sizes of the three substrate integrated waveguide resonant cavities 2 are all 340um multiplied by 340um, and the middle parts inside the three substrate integrated waveguide resonant cavities 2 are all provided with metallized blind holes 3. A fourth square metallized via 34, a fifth square metallized via 35, and a sixth square metallized via 36, respectively, so as to form a sample 4, a sample 5, and a sample 6 on the dielectric substrate 1, respectively, with specific reference to fig. 6 to 8. In this embodiment, the three metallized blind holes 3 are all square structures with the same height and different side lengths, and the fourth square metallized blind hole 34 has a height h45.52um with side length of l 40 um; the fifth square metallized via 35 has a height h45.52um with side length of l 52 um; the height of the sixth metallized blind via 36 is h45.52um with side length of l6＝5um。
The top layer of the substrate integrated waveguide resonant cavity 2 is provided with a grounding coplanar waveguide 4 and a GSG pads structure 5, the grounding coplanar waveguide 4 and the GSG pads structure 5 form a feed structure of the substrate integrated waveguide resonant cavity 2, the grounding coplanar waveguide 4 is respectively connected with the substrate integrated waveguide resonant cavity 2 and the GSG pads structure 5, and the GSG pads are compatible with a probe with the size of 100 um.
The specific implementation steps are as follows:
1) contacting the probe through the GSG pads structure 5 and connecting to a vector network analyzer, each of the substrate integrated waves being measured by the vector network analyzerCascading scattering parameters of the guided resonant cavity and the GSG pads structure, and obtaining the on-load resonant frequency f of the sample 1 through the scattering parametersL4319.17GHz on-load quality factor QL4233.4479; on-load resonant frequency f of sample 2L5318.43GHz on-load quality factor QL5247.5742; on-load resonant frequency f of sample 3L6317.33GHz on-load quality factor QL6＝248.4770；
2) From the embedding equation (3)
According to the above theory, there are:
according to the perturbation formula, the method comprises the following steps:
wherein the volume V of the substrate integrated waveguide resonant cavity 2 is aeff×deff×hsub，aeffAnd deffThe equivalent length and the equivalent width of the substrate integrated waveguide resonant cavity respectively can be calculated by the formula (7).
Simultaneous equations (10) and (11) for calculating the unloaded resonant frequency f of the substrate integrated waveguide resonant cavityu＝323.7GHz；
3) According to the obtained unloaded resonant frequency fuThe dielectric constant of the dielectric substrate was calculated from the following resonance equation (6)r：
Example 3:
in this example, the methods of example 1 and example 2 are compared with conventional dielectric constant measurement methods, and the specific data are shown in the following table:
according to the above table, it can be seen that in the high frequency band, the de-embedding method of the conventional dielectric constant measurement not only does not help to improve the accuracy, but also deteriorates the result. This is because in the millimeter wave submillimeter wave and even terahertz frequency band, the feed structure is comparable with the size of the resonant cavity itself, and the influence of the feed structure on the resonant cavity structure is not negligible. The dielectric constant measurement methods provided by embodiments 1 and 2 of the present invention show the accuracy that other conventional methods of the frequency band do not have, and at the same time, the method is convenient to operate, simple in process, and has a great application value.
Claims (4)
1. A dielectric substrate dielectric constant measuring mechanism is characterized in that: the substrate integrated waveguide resonant cavity comprises at least three substrate integrated waveguide resonant cavities which are arranged on a medium substrate and have the same cavity size, wherein a metalized blind hole is formed in the middle of the inner part of each cavity of each substrate integrated waveguide resonant cavity, the sizes of all the metalized blind holes are different, a grounding coplanar waveguide and a GSG pads structure are arranged on the top layer of each substrate integrated waveguide resonant cavity, the grounding coplanar waveguide and the GSG pads structure form a feed structure of the substrate integrated waveguide resonant cavity, and the grounding coplanar waveguide is connected with the substrate integrated waveguide resonant cavity and the GSG pads structure respectively.
2. A dielectric substrate permittivity measurement mechanism as claimed in claim 1, wherein: the side lengths of all the metallized blind holes on the medium substrate are the same, and the heights of all the metallized blind holes are different.
3. A dielectric substrate permittivity measurement mechanism as claimed in claim 1, wherein: the side lengths of all the metallized blind holes on the medium substrate are different, and the heights of all the metallized blind holes are the same.
4. The method for measuring a dielectric constant measuring mechanism of a dielectric substrate as claimed in claim 1, wherein: the method comprises the following steps:
1) the GSG pads structure is contacted with the probe and connected to a vector network analyzer, and the vector network analyzer is used for measuring the cascade scattering parameters of each substrate integrated waveguide resonant cavity and the GSG pads structure;
2) extracting the unloaded resonant frequency of the substrate integrated waveguide resonant cavity by using a de-embedding formula and a perturbation principle;
3) and calculating the dielectric constant of the dielectric substrate by using a resonance formula according to the obtained unloaded resonance frequency.
The de-embedding formula in the step 2) is as follows:
or
Wherein equation (1) is derived from First Foster's Form, equation (2) is derived from Second Foster's Form, where fLOn-load resonant frequency, f, of a substrate-integrated waveguide resonant cavityuIs the unloaded resonant frequency; qeFor the external quality factor, Q, of the feed networkLThe on-load quality factor of the substrate integrated waveguide resonant cavity can be directly obtained from scattering parameters, QuIntegrating the no-load quality factor of the waveguide resonant cavity for the substrate; x is the number ofeIs a feed network reactance, beIs a feed network susceptance, and k is an external feed network coupling coefficient; b is a coefficient about the influence of the metalized blind holes in the substrate integrated waveguide resonant cavity on the unloaded resonant frequency of the substrate integrated waveguide resonant cavity, and the size of the coefficient is in inverse proportion to the volume V of the substrate integrated waveguide resonant cavity; c is a coefficient about the influence of the feed network structure on the unloaded resonant frequency of the substrate integrated waveguide resonant cavity; expanding equations (1) (2) and omitting the min terms, then:
wherein
Thus, the above equation (4) only includes the coefficients related to the feed network;
in addition, according to the perturbation principle, the following results are obtained:
B＝-2V1 (5)
wherein V1The volume of a metallized blind hole in the substrate integrated waveguide resonant cavity;
the resonance formula in the step 3) is as follows:
formula (6) shows that the substrate integrated waveguide resonant cavity resonates at f101Mode, no-load resonant frequency fuRelative dielectric constant to dielectric substraterIn which a iseffAnd deffRespectively equal length and width of the substrate integrated waveguide resonant cavity and equivalent length a of the integrated waveguide resonant cavityeffAnd physical length aSIWThe relationship of (a) to (b) is as follows:
wherein d is the diameter of the metalized through holes of the substrate integrated waveguide resonant cavity, s is the center distance between adjacent metalized through holes, and the unloaded resonant frequency f of the substrate integrated waveguide resonant cavity is extracted in the step 3uThen, the relative dielectric constant of the dielectric substrate is obtained according to the resonance formula (6)r。
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