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, manufactured, 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 discussed 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 waveguide 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 measured 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 transmission 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 distance lm from the center of the hole to the broad side of the waveguide. Here ax is the length between the two resonators. 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 coupling 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. Here, K < 0. As where f0 is the center frequency of the filter and Bw is the shown in Figures 4 and 5, the diameter of the blind hole bandwidth of filter. is d, the depth is he, and the distance from the boundary External coupling is achieved using the SMA coaxial of the waveguide wall is le. When the blind hole diameter probe feed, as shown in Figure 6A,B. The blind feed hole is arranged opposite to the blind resonant hole of the resonator. In the case of a fixed blind hole diameter, the I/O coupling is determined by the depth of the blind hole and its location relative to the broad side of the waveguide.17 Figure 7 shows the external coupling Q value vs the depth of the blind hole at different positions of the blind hole. It can be seen from the figure that increasing the depth of the blind hole and increasing the proximity of the blind hole to the center of the resonator decreases the external coupling value. That is, the I/O coupling is strengthened.

3 | CROSS-COUPLED FILTER DESIGN

FIGURE 5 The coupling coefficient vs the depth of the blind The forward design process for the proposed dielectric hole at different positions of the blind hole waveguide filter is as follows:

FIGURE 6 The proposed I/O coupling structure: A, Top view. B, Side view HUANG AND CHENG 5of8

Step 1: The side length of the square dielectric waveguide is roughly calculated using the center frequency of the required filter. Because the influence of the resonant blind hole should be considered, the selection of the side length should generally be slightly larger than the calculated value. Under ideal conditions, the smaller the thickness of the dielectric waveguide, the smaller the influence of the higher-order mode of the filter. However, due to consideration of the actual manufacturing process requirements, the thickness of the dielectric waveguide cannot be made too small. Step 2: According to the theory discussed in Section 2, the dimensions of the proposed positive coupling structure and negative coupling structure can be obtained based on the coupling coefficient. In addition, this design

FIGURE 7 The external coupling Q value vs the depth of the incorporates a through hole with a diameter of d in the blind hole at different positions of the blind hole center of the filter to effectively suppress the out-of-band parasitic response of the filter.

FIGURE 8 The configuration of proposed filter: A, Perspective view. B, Top view. C, Bottom view. D, the electric field distribution at 3.5 GHz 6of8 HUANG AND CHENG

FIGURE 10 The photograph of the manufactured filter: A, Top view. B, Bottom view

Positive coupling is realized using a magnetic coupling hole formed by two blind holes located symmetrically above and below each other. Negative coupling is realized using an electrical coupling hole formed by two blind holes located symmetrically above and below each other with a through hole connecting the two blind holes. The I/O cou- FIGURE 9 The proposed filter: A, The equivalent circuit. B, The coupling topology. C, The S parameter results of the pling is realized by setting shallow feed blind holes under normalized coupling matrix the I/O resonators. The equivalent circuit and coupling matrix of the proposed cross-coupled filter are shown in Figure 9A,B. The Step 3: According to the theory discussed in Sec- filter has four resonators with negative main-coupling tion 2.4, the size of the input and output feed blind holes and positive cross-coupling between resonators 1 and can be obtained using the external coupling. 4. By adjusting the positive cross-coupling, the position of According to the aforementioned steps, a model of the the transmission zeros distance from the passband can be physical structure of the dielectric waveguide filter is adjusted to achieve superior out-of-band suppression. designed in this study, as demonstrated in Figure 8. For input and output couplings,19 Figure 8A shows a perspective view, Figure 8B shows a top pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi view, and Figure 8C shows a bottom view of the design. KS1 = mS1 × Fbw KL4 = mL4 × Fbw, ð7Þ The filter is equivalent to being formed by splicing resonators together composed of four square waveguide cavities and for the couplings between resonators, with a shallow resonant blind hole set at the center of each resonator to adjust the resonant frequency. The boundary Kij = mij × Fbw, ð8Þ between adjacent resonator cavities is replaced by positive coupling or negative coupling. From the electric field mag- where mij are the coupling coefficients of the prototype nitude distributions at 3.5 GHz, the TM110-mode resonance coupling matrix, Kij are the values of impedance con- in the four cavities can be observed clearly in Figure 8D. verter, and Fbw is the relative bandwidth of the filter, HUANG AND CHENG 7of8 which is used to design the working bandwidth of the filter, the size of which is 27 × 27 × 5 mm, excluding the filter. I/O ports. The surface of the dielectric waveguide is fully Based on the characteristics of the filter, the center metallized and gold-plated, and the probe of the SMA frequency is 3.5 GHz, and the bandwidth is 200 MHz. connector is welded into the blind hole below the input The coupling coefficient values of the filter are and output resonators for filter testing. Figure 11 shows synthesized as follows: ms1=mL4=1.05，m12=m34= the electromagnetic simulation results and the measured − 0.86，m23= − 0.80，m14= + 0.23. The S parameter results for the filter proposed in this study. It can be seen results of the normalized coupling matrix are presented from the figure that the measured results of the filter in Figure 9C. indicate an insertion loss of less than 0.5 dB at a frequency of 3.4 to 3.6 GHz and a return loss of greater than 15 dB. The filter has two transmission zeros, one at 4 | SIMULATION AND 3.25 GHz and another at 3.65 GHz, and the out-of-band MEASUREMENT RESULTS suppression is greater than 20 dB. In addition, the group delay variation in the passband is within 3 ns. Through The entire filter structure is simulated using the 3D elec- comparison, the measured filter in-band return loss is tromagnetic simulation software package, Ansys HFSS, found to be 5 dB worse than the simulated loss. Further- and the optimized dimensions are as follows: more, the measured out-of-band parasitism response a=27 mm，D=4mm，d =2mm，d1 = 1.5 mm，h= moved roughly 200 MHz to the pass band vs the simula- 5mm，h1 =1.1mm，h12 = 2.25 mm，h23 = tion result. This may be caused by manufacturing-related 2.25 mm，h34 =2.25mm，h14 = 1.8 mm，hp = 1.8 mm errors on the dielectric waveguide surface. The dielectric (unit: mm). waveguide filter designed in this paper is suitable for The ceramic medium of the filter has a dielectric con- wireless communication base station because of its stant of 21 and dielectric loss tangent value of 0.0006. medium capacity. Figure 10A,B show photographs of the manufactured A performance comparison between the proposed dielectric waveguide filter and similar dielectric waveguide filters reported in recent years is presented in Table 1. It can be seen from the table that when the num- ber of transmission zeros is identical, the proposed filter exhibits superior performance in terms of insertion loss and physical size.

5 | CONCLUSION

This article reports on a cross-coupled bandpass filter based on a dielectric waveguide. Analysis and discussion of the proposed positive coupling structure and negative coupling structure based on blind holes and via holes is presented. A fourth-order cross-coupled dielectric waveguide filter is designed and manufactured based on the FIGURE 11 The S-parameters results of the simulated and the coupling structure. The measurement results show that measured the proposed dielectric waveguide filter possesses several

TABLE 1 Comparison of the proposed cross-coupling dielectric waveguide filter with those of previous works

λ2 Reference Technology Order CF (GHz) FBW (%) TZs IL (dB) Size ( g) Stopband rejection (>20 dB) 4 Folded SIW 4 10 8 3 1 1.1 × 1.4 (0.50f0, 0.92 f0), (1.08f0, 2.26 f0) 5 Combline SIW 4 5.75 1.8 1 1 0.86 × 0.86 (0.34f0, 0.98 f0), (1.01f0, 1.82 f0) 13 Monoblock DW 4 2.6 1.9 2 0.6 1.4 × 1.4 (0.84f0, 0.98 f0), (1.02f0, 1.44 f0) 14 DW 6 1.73 3.5 2 1.2 1.9 × 1.9 (0.91f0, 0.97 f0), (1.02f0, 1.12 f0)

This work DW 4 3.5 5.7 2 0.5 1.0 × 1.0 (0.86f0, 0.93 f0), (1.04f0, 1.37 f0)

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