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Cross‐Coupled Dielectric Waveguide Filter

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Cross‐Coupled Dielectric Waveguide Filter Received: 25 January 2021 Accepted: 28 January 2021 DOI: 10.1002/mmce.22585 RESEARCH ARTICLE Cross-coupled dielectric waveguide filter Zhengwei Huang | Yong Cheng College of Electronic and Optical Engineering and College of Abstract Microelectronics, Nanjing University of A cross-coupled dielectric waveguide filter based on blind holes and via holes Posts and Telecommunications, Nanjing, is proposed in this study. Using a unique all-hole design, a fourth-order cross- China coupled dielectric waveguide bandpass filter is realized by drilling via holes or Correspondence blind holes in a square dielectric waveguide, followed by coating the surface Yong Cheng, College of Electronic and with thin metal. Magnetic coupling is realized using two blind holes located Optical Engineering and College of Microelectronics, Nanjing University of symmetrically above and below each other. Further, electrical coupling is real- Posts and Telecommunications, Nanjing, ized using a combination of two blind holes located symmetrically above and Jiangsu, China. below each other and an interconnecting via hole. Both types of coupling are Email: [email protected] analyzed and designed. Moreover, a circular via hole is provided in the middle of the square cavity to suppress the parasitic response of the filter. Coupling debugging holes, resonant debugging holes, and feed holes are realized using shallow blind holes, thereby alleviating the process of manufacturing and debugging. The structure of the designed filter is discussed, simulated, man- ufactured, and measured. The results show that the proposed filter has a center frequency of 3.5 GHz, an insertion loss of less than 0.5 dB, a return loss of less than 15 dB, and a relative bandwidth of 5%, exhibiting excellent performance that includes two out-of-band transmission zeros. KEYWORDS blind hole, cross-coupled, dielectric waveguide, filter, negative coupling, positive coupling 1 | INTRODUCTION These negative-coupled filters6-8 have been extensively studied based on a substrate integrated waveguide struc- The cross-coupled filter possesses certain out-of-band ture. It is well known that such planar microwave cir- transmission zero points that improve the signal selectiv- cuits possess certain advantages in terms of circuit ity of the filter, leading to its use in a wide range of appli- integration. However, these filters also possess certain cations in modern wireless mobile communication performance defects associated with insertion loss and systems. Generally, this type of cross-coupled filter power capacity. requires both positive coupling and negative coupling to Coupled filters based on metal waveguides possess enable it to be realized. Conventionally, positive coupling excellent performance with high-Q value and high- can be achieved through magnetic coupling, such as in power-capacity. However, their large physical size is not an inductive iris.1,2 Interest in research directed toward conducive to integration into other microwave cir- negative coupling has increased among experts and cuits.9-12 Therefore, to balance the advantages of conve- scholars in the recent years. Negative coupling can be nient integration and high performance, a cross-coupled realized in the following forms: grounded coplanar lines filter based on a dielectric waveguide is considered.13-15 etched into the top of cavities,3 upside-down-folded iris- These filters can be made physically smaller because of coupled resonators,4 and open-ended coplanar probes.5 their high-dielectric constant and flexible I/O Int J RF Microw Comput Aided Eng. 2021;31:e22585. wileyonlinelibrary.com/journal/mmce © 2021 Wiley Periodicals LLC 1of8 https://doi.org/10.1002/mmce.22585 2of8 HUANG AND CHENG configuration, which is convenient for integrated applica- rffiffiffiffiffiffiffiffiffi c 5 tions. Moreover, owing to their high-Q value and high- f = , ð1Þ TM110 2a u ε power-capacity, they have a wide range of applications. r r In Reference 13, a TM01-mode monolithic dielectric filter was designed that incorporated negative coupling where a is the side length of waveguide, c is the speed of achieved using a U-shaped metal probe with a low dielec- light, ur is the relative permeability and εr is the relative tric constant support. In Reference 14, deep capacitive permittivity. The optimal parasitic suppression can be blind holes were used to achieve negative coupling based obtained by controlling the height h of square dielectric on a dielectric waveguide structure. The waveguide filter waveguide. capacitive negative coupling theory was analyzed and dis- cussed in Reference 15. However, these types of coupling require high machining accuracy and necessitate one- 2.2 | Positive coupling design time molding, which is not conducive to mass produc- tion. This study involves the proposal of a type of positive As shown in Figure 2A,B, the proposed positive coupling coupling structure along with a negative coupling struc- configuration is composed of two symmetrically located ture based on a dielectric waveguide cavity. The structure blind holes with a via hole connecting the two blind involves an integrated design, which can be realized by holes, where the diameter D of the blind holes is larger simply setting through holes or blind holes in the dielec- than the diameter d of the via hole. The stepped holes are tric waveguide. After the dielectric waveguide of the filter theoretically equivalent to a parallel inductor post. As is fired and molded, through holes or blind holes are shown in Figure 2C, the parallel inductor and the trans- drilled at the expected locations, and the surface of the mission line with the characteristic impedance of Z0 and dielectric waveguide is completely metalized and coated the electrical length of θ placed symmetrically at both simultaneously, which is very convenient for ends can be equivalent to a K impedance converter. manufacturing and debugging. According to Hunter's theory,17 the following equations Taking a fourth-order bandpass filter as an example, can be known: this study involves the design of a type of dielectric wave- guide cross-coupled filter. Positive coupling is realized 1 − 2 θ = − tan 1 − : ð2Þ using two shallow blind holes located symmetrically 2 B above and below each other with a middle through hole connecting the two blind holes. Negative coupling is real- K = cot θ: ð3Þ ized using two shallow blind holes located symmetrically above and below each other. The positive and negative 1 B = K − : ð4Þ coupling design theories are analyzed, and the forward K design process for the filter is clarified. The manufactured filter has an overall size of 27 × 27 × 5 mm and a mea- sured center frequency of 3.5 GHz. The bandwidth is 5%, the insertion loss is less than 0.5 dB, the in-band return loss is greater than 15 dB, and two out-of-band transmis- sion zeros are generated at 3.25 and 3.65 GHz. 2 | DESIGN AND ANALYSIS 2.1 | Resonator design The resonator used in this design is a square dielectric waveguide with equal broad side and narrow side. As shown in Figure 1, the main mode of the resonator is TM110, and a shallow blind hole for resonant frequency adjustment is located at the center of the waveguide with the strongest electric field. The value of the initial reso- FIGURE 1 The electric field distribution of the square nance frequency16 can be given by dielectric waveguide resonator HUANG AND CHENG 3of8 FIGURE 3 The coupling coefficient vs the depth of the blind hole at different positions of the blind hole and the through hole FIGURE 2 The proposed positive coupling structure: A, Top view. B, Side view. C, The equivalent circuit Since the value of susceptance B is positive, K > 1. There- fore, when the diameters of the blind hole and via hole are kept constant, the positive coupling can be adjusted by changing the depth hm of the blind hole and the dis- tance lm from the center of the hole to the broad side of the waveguide. Here ax is the length between the two res- onators. To facilitate hardware processing and debugging, the blind hole diameter is set to be twice that of the through hole, and the through hole diameter is set to 2 mm. Figure 3 shows the coupling coefficient vs the depth of the blind hole at different positions of the blind hole and the through hole. The greater the depth of the blind holes, the smaller the positive coupling. In addition, the greater the distance between the hole and the center of the broad side of the waveguide, the smaller the posi- FIGURE 4 The proposed negative coupling structure: A, Top tive coupling. view. B, Side view. C, The equivalent circuit 2.3 | Negative coupling design advantage of this structure is that it avoids processing dif- ficulties caused by the excessive depth of single coupling The proposed negative coupling configuration is shown blind holes. In addition, it facilitates coupling debugging. in Figure 4A,B. It is composed of two blind holes placed The negative coupling of the design is equivalent to a symmetrically above and below each other. The series combination of two parallel capacitors, and finally 4of8 HUANG AND CHENG equivalent to parallel capacitive coupling. The equivalent d = 2 mm remains constant, the size of the negative cou- circuit is shown in Figure 4C. Similar to the positive cou- pling decreases as the depth of the blind hole increases. pling theory, the shunt capacitor, and the transmission Similarly, the greater the distance between the blind hole line with characteristic impedance of Z0 and electrical and the center of the broad side of the waveguide, the length of θ placed symmetrically at both ends can also be smaller the negative coupling value. equivalent to a K impedance converter. According to the theory of equivalent matrix,14 the following formula can be obtained: 2.4 | I/O Coupling design 1 − 2 The external Q value of I/O ports can be calculated using θ = tan 1 − : ð5Þ 2 B the following formula18: The relationship between impedance converter K and the f Q = 0 , ð6Þ θ e 2 × electrical length , and the relationship between the ms1 Bw impedance converter K and the admittance B are shown in Equations (3) and (4), respectively.
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