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CN113036332B - Dual-mode dual-passband dielectric filter capable of generating out-of-band zero - Google Patents

Dual-mode dual-passband dielectric filter capable of generating out-of-band zero Download PDF

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CN113036332B
CN113036332B CN202110329038.3A CN202110329038A CN113036332B CN 113036332 B CN113036332 B CN 113036332B CN 202110329038 A CN202110329038 A CN 202110329038A CN 113036332 B CN113036332 B CN 113036332B
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dual
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feeder
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dielectric resonator
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CN113036332A (en
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于玮
陈建新
唐为浩
徐林
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Prologis Communication Technology Suzhou Co Ltd
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Nantong University
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    • H01—ELECTRIC ELEMENTS
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    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P1/00—Auxiliary devices
    • H01P1/20—Frequency-selective devices, e.g. filters
    • H01P1/207—Hollow waveguide filters
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
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Abstract

本发明涉及一种可产生带外零点的双模双通带介质滤波器，包含金属腔体、位于金属腔体内的级联的第一双模介质谐振器和第二双模介质谐振器、以及固定在金属腔体底壁上分别与所述第一、第二双模介质谐振器一一对应的第一激励结构和第二激励结构，第一激励结构为直线型馈线，第二激励结构为折线形馈线，该折线形馈线包含自下而上依次相连的位于介质谐振器斜45°平面内的竖直的第一馈线、水平的第二馈线和竖直的第三馈线，第三馈线靠近第二双模介质谐振器设置。本发明通过特殊的折线形馈电结构，使双模双通带介质滤波器在带外产生零点，提高了通带的选择性。

Figure 202110329038

The invention relates to a dual-mode dual-pass-band dielectric filter capable of generating out-of-band zeros, comprising a metal cavity, a cascaded first dual-mode dielectric resonator and a second dual-mode dielectric resonator located in the metal cavity, and The first excitation structure and the second excitation structure are fixed on the bottom wall of the metal cavity, respectively corresponding to the first and second dual-mode dielectric resonators. The first excitation structure is a linear feeder, and the second excitation structure is A zigzag feeder, the zigzag feeder includes a vertical first feeder, a horizontal second feeder and a vertical third feeder that are located in the 45° inclined plane of the dielectric resonator and are connected in sequence from bottom to top, and the third feeder is close to the A second dual-mode dielectric resonator setup. The invention makes the dual-mode dual-pass-band dielectric filter generate a zero point outside the band through a special fold-line feeding structure, thereby improving the selectivity of the pass-band.

Figure 202110329038

Description

Dual-mode dual-passband dielectric filter capable of generating out-of-band zero
Technical Field
The invention belongs to the technical field of wireless communication, relates to a dual-mode dual-passband dielectric filter capable of generating an out-of-band zero point, and particularly relates to a feed structure capable of generating the out-of-band zero point.
Background
A communication system needs to obtain a useful signal while shielding noise, and thus a filter circuit is used in a large amount. The out-of-band transmission zero of the filter passband is beneficial to improving the selectivity of the passband, so how to conveniently and rapidly generate the out-of-band zero is an important index for research in academia and industry.
For the cavity filter circuit, in order to generate a zero point in the amplitude-frequency response, an additional resonant cavity or an additional coupling probe is often required, which finally results in a significant increase in design and processing costs and even in the circuit volume. This is contrary to the trend of low cost and miniaturization of future communication systems.
The dual-passband filter is a research direction for realizing low cost and miniaturization of the filter, is commonly used for processing two paths of parallel signals in an antenna system, and can reduce the number of required filters by half while improving the transmission efficiency.
The applicant filed patent application CN201710736587.6 to the national institute at 24/8/2017, and relates to a dual-passband differential filter based on a miniaturized dual-mode dielectric resonator, wherein a rectangular dielectric resonator with a square cross section is directly placed at the bottom of a metal cavity after being chamfered. Because the symmetrical plane of each group of differential excitation structures is parallel to the symmetrical plane of the other group of differential excitation structures, the structure enables one transmission zero point to be generated between two differential mode pass bands, and improves the isolation between the two pass bands, however, the structure cannot generate more transmission zero points outside the band.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a dual-mode dual-passband dielectric filter capable of generating out-of-band zero, which is beneficial to improving the selectivity of a passband.
In order to achieve the object of the present invention, the dual-mode dual-passband dielectric filter capable of generating an out-of-band zero point provided by the present invention comprises a metal cavity, a first dual-mode dielectric resonator and a second dual-mode dielectric resonator which are cascaded and located in the metal cavity, and a first excitation structure and a second excitation structure which are fixed on the bottom wall of the metal cavity and respectively correspond to the first dual-mode dielectric resonator and the second dual-mode dielectric resonator one to one, wherein the first excitation structure is a linear type feeder line, and the dual-mode dual-passband dielectric filter is characterized in that: the second excitation structure is a zigzag feeder line, the zigzag feeder line comprises a vertical first feeder line, a horizontal second feeder line and a vertical third feeder line which are sequentially connected from bottom to top and are positioned in a plane inclined by 45 degrees of the dielectric resonator, and the third feeder line is arranged close to the second double-mode dielectric resonator.
In addition, the invention also provides a design method of the dual-mode dual-passband dielectric filter capable of generating the out-of-band zero, which comprises the following steps:
step 1, calculating respective corresponding low-pass prototype lumped parameters according to performance indexes required by two pass bands of the filter, and respectively calculating external quality factors of ports required for constructing a first pass band (generated by a mode A) and a second pass band (generated by a mode B) on the basis of the respective low-pass prototype lumped parametersQ eAAndQ eB) And a coupling coefficient; due to the structural symmetry of the low-pass prototype, the input-side external quality factor is always equal to the output-side external quality factor, whether mode a or mode B is excited.
And 2, establishing a dielectric cavity model of the dual-mode dual-passband dielectric filter, and adjusting a gap in the middle of the metal cavity to enable the coupling quantity between the two dual-mode dielectric resonators to meet the coupling coefficient obtained by calculation in the step 1.
And 3, loading a first excitation structure in the first double-mode dielectric resonator, and determining design parameters of the first excitation structure according to the port external quality factors required by the first passband and the second passband which are calculated in the step 1, wherein the design parameters comprise the feeder line length and the feed position.
And 4, loading a second excitation structure, and adjusting the cross coupling amount between the first excitation structure and the second excitation structure by adjusting the length of the first feeder in the second excitation structure and the distance between the first feeder and the second double-mode dielectric resonator, so as to determine the position of the out-of-band transmission zero point.
Step 5, adjusting the main coupling quantity between the second excitation structure and the second double-mode dielectric resonator by adjusting the length of a third feeder in the second excitation structure and the distance between the third feeder and the second double-mode dielectric resonator to enable the main coupling quantity to meet the external quality factor required by the output end, namely the external quality factor calculated in step 1Q eAAndQ eB。
further, the second excitation structure is arranged in a vertical plane where a diagonal line of the second double-mode dielectric resonator is located, the lengths of the first feeder line and the third feeder line and the vertical distances from the first feeder line and the third feeder line to the second double-mode dielectric resonator are adjusted, if the external quality factor meets the design requirement, the design of the double-mode double-passband dielectric filter is completed, otherwise, the vertical distance from the feeder line to the non-corner-cut side of the dielectric resonator is adjusted, and the external quality factor meets the design requirement.
The second excitation structure of the dual-mode dual-passband dielectric filter is a zigzag feeder, and the cross coupling between the two excitation structures is realized through the first feeder of the second excitation structure to generate an out-of-band zero point, so that the selectivity of a passband is improved.
Drawings
The invention will be further described with reference to the accompanying drawings;
FIG. 1 is a three-dimensional view of a dual-mode dual-passband dielectric filter of the present invention that produces an out-of-band zero.
Fig. 2 is a top view of a dual-mode dual-passband dielectric filter of the present invention that may generate an out-of-band zero.
Fig. 3(a) is a graph of port external quality factor versus feeder position extracted by simulation for a feeder length of 26 mm.
Fig. 3(b) is a graph of port external quality factor versus feeder position extracted by simulation for a feeder length of 28 mm.
FIG. 4 is a graph of the amplitude-frequency response of a dual-mode dual-passband dielectric filter that may generate an out-of-band zero in accordance with the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
The dual-mode dual-passband dielectric filter capable of generating the out-of-band zero point comprises a broken line probe for feeding the dual-mode dielectric resonator, is convenient for obtaining the required main coupling amount and cross coupling amount at the same time, and has a simple structure and easy realization. As shown in fig. 1 and fig. 2, the dual-mode dual-passband dielectric filter of this embodiment includes a metal cavity 1, and a first dual-mode dielectric resonator 2 and a second dual-mode dielectric resonator 3 which are located in the metal cavity and are cascaded. The first double-mode dielectric resonator 2 and the second double-mode dielectric resonator 3 are coupled through a gap in the middle of the metal cavity 1. And a first excitation structure 4 and a second excitation structure 5 which are respectively in one-to-one correspondence with the first double-mode dielectric resonator 2 and the second double-mode dielectric resonator 3 are further fixed on the bottom wall of the metal cavity 1.
The double-mode dielectric resonator is obtained by arranging a pair of cut corners for separating orthogonal degenerate modes at diagonal positions of a rectangular dielectric resonator with a square cross section, the bottom of the double-mode dielectric resonator is in direct contact with the bottom surface of the metal cavity, and the top of the double-mode dielectric resonator is spaced from the top of the metal cavity by a certain distance.
The first excitation structure 4 is a linear feeder (length ofl 1) The second excitation structure 5 is a zigzag feeder including vertical first feeders (having a length of 45 ° to the top) sequentially connected from bottom to top in a plane inclined by 45 ° to the dielectric resonatorl 21) A horizontal second feeder (length ofl 22) And a vertical third feeder (of lengthl 23) The third feeder is arranged close to the second double-mode dielectric resonator 3, and the first feeder is arranged at a corner and far away from the second double-mode dielectric resonator 3.
The third feedline of the second excitation structure 5 is used to achieve a main coupling between the port and the second dual mode dielectric resonator 3. The first feed line of the second excitation structure 5 is closer to the first-stage resonator (the first dual-mode dielectric resonator 2), so that the cross coupling between the first excitation structure 4 and the second excitation structure 5 is facilitated. The second feeder is used for connecting the first feeder and the third feeder. The main coupling quantity and the cross coupling quantity can be independently controlled by respectively adjusting the lengths of the third feeder line and the first feeder line and the distance between the feeder line and the intracavity dielectric resonator.
The design method of the dual-mode dual-passband dielectric filter of the embodiment comprises the following steps:
step 1, calculating respective corresponding low-pass prototype lumped parameters according to performance indexes required by two pass bands of a filter, and respectively calculating and constructing a first pass band (mode A generation) and a second pass band (mode A generation) on the basisB generating) the required external quality factor of the port (B)Q eAAndQ eB) And a coupling coefficient; due to the structural symmetry of the low-pass prototype, the input-side external quality factor is always equal to the output-side external quality factor, whether mode a or mode B is excited.
And 2, establishing a dielectric cavity model of the dual-mode dual-passband dielectric filter, and adjusting a gap in the middle of the metal cavity to enable the coupling quantity between the two dual-mode dielectric resonators to meet the coupling coefficient obtained by calculation in the step 1.
And 3, loading a first excitation structure in the first double-mode dielectric resonator, and determining design parameters of the first excitation structure according to the port external quality factors required by the first passband and the second passband which are calculated in the step 1, wherein the design parameters comprise the feeder line length and the feed position.
And 4, loading a second excitation structure, and adjusting the cross coupling amount between the first excitation structure and the second excitation structure by adjusting the length of the first feeder in the second excitation structure and the distance between the first feeder and the second double-mode dielectric resonator, so as to determine the position of the out-of-band transmission zero point.
Step 5, adjusting the main coupling quantity between the second excitation structure and the second double-mode dielectric resonator by adjusting the length of a third feeder in the second excitation structure and the distance between the third feeder and the second double-mode dielectric resonator to enable the main coupling quantity to meet the external quality factor required by the output end, namely the external quality factor calculated in step 1Q eAAndQ eB。
at the beginning of the design, the second excitation structure 5 is first arranged in the vertical plane of the diagonal of the second dual-mode dielectric resonator 3, i.e. the parameters are not adjustedd，dIs 12.5mm ifgAndlafter the determination, the desired one still cannot be obtained at the same timeQ eAAndQ eBthen by adjusting the parameters at this timedTo perform fine tuning. Because when the feed line is at 0<d<When the horizontal movement is carried out within the range of 12.5mm, the horizontal movement can be independently regulated and controlledQ eBAnd does not affectQ eAA value of (d); when the feed line is at 12.5mm<d<When the horizontal movement is carried out within the range of 25mm, the horizontal movement can be independently regulated and controlledQ eAAnd does not affectQ eBThe value of (c). The above characteristics are advantageous for rapidly obtaining the amount of main coupling between the second excitation structure 5 and the second dual-mode dielectric resonator 3, which is required to construct two pass bands.
As shown in fig. 3(a) and 3(B), when the feeder length is equal to 26mm and 28mm, respectively, the external quality factor of the port corresponding to the two modes (mode a and mode B) extracted by simulation is plotted against the feeder position. The polarization directions of mode a and mode B are shown by the arrows in the inset of fig. 3 (a). After the two dielectric resonators are cascaded, the mode A constructs a first passband, and the mode B constructs a second passband. In the figure, the position of the upper end of the main shaft,lrepresents: feeder length (adapted for selectionl 1Andl 23the value of (d),drepresents: the perpendicular distance from the feed line to the non-chamfered side of the dielectric resonator,grepresents: the perpendicular distance of the feed line to the dielectric resonator. Port external figures of merit for mode A and mode BQ eAAndQ eB) May be considered independently controllable. Specifically, when 0<d<When the thickness of the steel wire is 12.5mm,Q eAthe value of (a) is kept substantially constant,Q eBis as followsdIs increased and decreased (monotonically decreasing). When the diameter is 12.5mm<d<When the thickness is 25mm, the thickness of the film is small,Q eAis as followsdIs increased (monotonically increasing),Q eBthe value of (c) remains substantially unchanged.
Therefore, the conclusion is drawn from the graph of fig. 3: with followinggThe increase of the value of the additive is increased,Q eAandQ eBare all increased; and with the length of the feeder linelThe increase of the value of the additive is increased,Q eAandQ eBare all reduced. At the same time, when the feed line is at 0<d<When the horizontal movement is carried out within the range of 12.5mm, the horizontal movement can be independently regulated and controlledQ eBAnd does not affectQ eAA value of (d); when the feed line is at 12.5mm<d<When the horizontal movement is carried out within the range of 25mm, the horizontal movement can be independently regulated and controlledQ eAAnd does not affectQ eBThe value of (c). The above characteristics are favorable for rapidly obtaining the main required by each of the two pass bandsThe amount of coupling.
The device parameters of the dual-mode dual-passband dielectric filter capable of generating the out-of-band zero in the embodiment are as follows:
the metal cavity is 83mm long, 40mm wide and 32mm high, and the gap width in the middle of the cavity is 13 mm; the length of a side of the dual-mode dielectric resonator D =25mm, the height of the dual-mode dielectric resonator is 20mm, and the length of a side of a corner cut s =8 mm; the length of a feeder line of the first excitation structure 4 is 23mm, and the vertical distance from the feeder line of the first excitation structure 4 to the first double-mode dielectric resonator 2 is 2.9 mm; the lengths of the first feeder line, the second feeder line and the third feeder line of the second excitation structure 5 are respectively 8mm, 10.5mm and 18mm, and the vertical distances from the third feeder line of the second excitation structure 5 to the second double-mode dielectric resonator 3 are respectively 2.3 mm. Based on the values of the parameters, the method is characterized in thatdWhen the thickness is not less than 12.5mm, the thickness can just meet the requirement simultaneouslyQ eAAndQ eBso that the second excitation structure 5 in this embodiment just does not need to pass the parametersdTo perform fine tuning.
As shown in fig. 4, which is a graph of the amplitude-frequency response of the dual-mode dual-passband dielectric filter of the present embodiment, it can be known from the graph that: a total of 3 transmission zeros are generated in the dual-passband filter response, two transmission zeros appearing at the low frequency end (1.44 GHz) and the high frequency end (1.74 GHz) are generated by the zigzag feeder structure provided by the invention, and the transmission zero (1.58 GHz) between the two passbands is generated by equal amplitude and opposite phase of induced currents at the output ends corresponding to the mode A and the mode B.
In addition to the above embodiments, the present invention may have other embodiments. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.

Claims (6)

1.一种可产生带外零点的双模双通带介质滤波器，包含金属腔体（1）、位于金属腔体内的级联的第一双模介质谐振器（2）和第二双模介质谐振器（3）、以及固定在金属腔体底壁上分别与所述第一、第二双模介质谐振器一一对应的第一激励结构（4）和第二激励结构（5），所述第一激励结构（4）为直线型馈线，其特征在于：所述第二激励结构（5）位于第二双模介质谐振器（3）所在金属腔体的一角且靠近所述第一双模介质谐振器（2），并且所述第二激励结构（5）位于第二双模介质谐振器（3）所在金属腔体的对角线所在的竖直平面内，第二激励结构（5）为折线形馈线，该折线形馈线包含自下而上依次相连的竖直的第一馈线、水平的第二馈线和竖直的第三馈线，所述第一馈线位于角落处且远离第二双模介质谐振器（3），所述第三馈线靠近第二双模介质谐振器（3）设置。1. A dual-mode dual-passband dielectric filter capable of generating out-of-band zeros, comprising a metal cavity (1), a cascaded first dual-mode dielectric resonator (2) and a second dual-mode dielectric resonator located in the metal cavity a dielectric resonator (3), and a first excitation structure (4) and a second excitation structure (5) fixed on the bottom wall of the metal cavity and corresponding to the first and second dual-mode dielectric resonators, respectively, The first excitation structure (4) is a linear feeder, characterized in that the second excitation structure (5) is located at a corner of the metal cavity where the second dual-mode dielectric resonator (3) is located and is close to the first The dual-mode dielectric resonator (2), and the second excitation structure (5) is located in the vertical plane where the diagonal of the metal cavity where the second dual-mode dielectric resonator (3) is located, and the second excitation structure ( 5) It is a zigzag feeder, which includes a vertical first feeder, a horizontal second feeder, and a vertical third feeder connected in sequence from bottom to top, the first feeder is located at the corner and away from the first feeder. Two dual-mode dielectric resonators (3), and the third feeder is arranged close to the second dual-mode dielectric resonator (3). 2.根据权利要求1所述的可产生带外零点的双模双通带介质滤波器，其特征在于：所述第一双模介质谐振器（2）与第二双模介质谐振器（3）通过金属腔体（1）中部的缝隙进行耦合。2. The dual-mode dual-passband dielectric filter capable of generating out-of-band zeros according to claim 1, characterized in that: the first dual-mode dielectric resonator (2) and the second dual-mode dielectric resonator (3) ) are coupled through the gap in the middle of the metal cavity (1). 3.根据权利要求1所述的可产生带外零点的双模双通带介质滤波器，其特征在于：双模介质谐振器是通过横截面呈正方形的矩形介质谐振器在对角线位置设置用于分离正交简并模式的一对切角而得到，其底部与金属腔体的底面直接接触，该双模介质谐振器的顶部与金属腔体顶部之间存在间隔。3. The dual-mode dual-pass-band dielectric filter capable of generating out-of-band zeros according to claim 1, wherein the dual-mode dielectric resonator is set at a diagonal position through a rectangular dielectric resonator with a square cross-section A pair of cut corners for separating orthogonal degenerate modes are obtained, the bottom of which is in direct contact with the bottom surface of the metal cavity, and there is a space between the top of the dual-mode dielectric resonator and the top of the metal cavity. 4.根据权利要求1所述的可产生带外零点的双模双通带介质滤波器，其特征在于：第二激励结构（5）的第三馈线用于实现端口与第二双模介质谐振器（3）之间的主耦合，第二激励结构（5）的第一馈线用于实现第一激励结构（4）与第二激励结构（5）之间的交叉耦合。4. The dual-mode dual-passband dielectric filter capable of generating out-of-band zeros according to claim 1, wherein the third feeder of the second excitation structure (5) is used to realize the port and the second dual-mode dielectric resonance The first feeder of the second excitation structure (5) is used to realize the cross-coupling between the first excitation structure (4) and the second excitation structure (5). 5.权利要求1-4任一项可产生带外零点的双模双通带介质滤波器的设计方法，包含如下步骤：5. any one of claim 1-4 can produce the design method of the dual-mode dual-passband dielectric filter of out-of-band zero, comprising the steps: 步骤1、根据滤波器两个通带所需的性能指标计算各自对应的低通原型集总参数，在此基础上分别计算构建由模式A产生的第一通带和由模式B产生的第二通带所需的端口外部品质因数以及耦合系数;Step 1. Calculate the corresponding low-pass prototype lumped parameters according to the performance indicators required by the two passbands of the filter. On this basis, calculate and construct the first passband generated by mode A and the second generated by mode B. The external quality factor of the port and the coupling coefficient required for the passband; 步骤2、建立权利要求1所述双模双通带介质滤波器的介质腔体模型，调节金属腔体中部的缝隙，使两个双模介质谐振器之间的耦合量满足步骤1中计算得到的耦合系数；Step 2. Establish the dielectric cavity model of the dual-mode dual-pass-band dielectric filter described in claim 1, and adjust the gap in the middle of the metal cavity so that the coupling amount between the two dual-mode dielectric resonators satisfies the calculation in step 1. The coupling coefficient of ; 步骤3、在第一双模介质谐振器（2）内加载第一激励结构（4），根据步骤1中计算得到的第一通带和第二通带所需的端口外部品质因数，确定第一激励结构的设计参数，包括馈线长度和馈电位置；Step 3. Load the first excitation structure (4) in the first dual-mode dielectric resonator (2), and determine the first passband according to the external quality factors of the ports required for the first passband and the second passband calculated in step 1. 1. The design parameters of the excitation structure, including the length of the feeder and the position of the feeder; 步骤4、在第二双模介质谐振器（3）内加载第二激励结构（5），通过调整第二激励结构（5）中第一馈线的长度以及第一馈线到第二双模介质谐振器（3）之间的距离，以调节第一激励结构（4）与第二激励结构（5）之间的交叉耦合量，从而确定带外传输零点的位置；Step 4. Load the second excitation structure (5) in the second dual-mode dielectric resonator (3), by adjusting the length of the first feeder in the second excitation structure (5) and the resonance between the first feeder and the second dual-mode dielectric to adjust the cross-coupling amount between the first excitation structure (4) and the second excitation structure (5), so as to determine the position of the out-of-band transmission zero; 步骤5、通过调整第二激励结构（5）中第三馈线的长度和第三馈线到第二双模介质谐振器（3）之间的距离，以调节第二激励结构（5）与第二双模介质谐振器（3）之间的主耦合量，使其满足输出端所需的外部品质因数，即步骤1中计算得到的第一通带和第二通带所需的端口外部品质因数。Step 5. By adjusting the length of the third feed line in the second excitation structure (5) and the distance between the third feed line and the second dual-mode dielectric resonator (3), the second excitation structure (5) and the second excitation structure (5) are adjusted. The main coupling amount between the dual-mode dielectric resonators (3) makes it meet the external quality factor required at the output end, that is, the external quality factor of the port required for the first passband and the second passband calculated in step 1 . 6.权利要求5所述可产生带外零点的双模双通带介质滤波器的设计方法，其特征在于：首先将第二激励结构（5）设置于第二双模介质谐振器（3）的对角线所在竖直平面内，调节第一馈线和第三馈线的长度和它们分别到第二双模介质谐振器的垂直距离，若外部品质因数达到设计要求，则完成本双模双通带介质滤波器的设计，否则调节馈线到介质谐振器未切角一侧的垂直距离，使外部品质因数达到设计要求。6. The method for designing a dual-mode dual-passband dielectric filter capable of generating out-of-band zeros according to claim 5, characterized in that: firstly, the second excitation structure (5) is set on the second dual-mode dielectric resonator (3) Adjust the lengths of the first feeder and the third feeder and their vertical distances to the second dual-mode dielectric resonator in the vertical plane where the diagonal of Design with a dielectric filter, otherwise adjust the vertical distance from the feeder to the uncut side of the dielectric resonator to make the external quality factor meet the design requirements.
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