Substrate-Integrated Defected Ground Structure for Single- and Dual-Band Bandpass Filters With Wide Stopband and Low Radiation Loss

In this article, two types of substrate-integrated defected ground structure (SIDGS) resonant cells with wide upper stopband and low radiation loss are presented for filter implementation. Such SIDGS resonant cells are composed of two dissimilar DGSs surrounded by the bottom ground and metal-vias, which cannot only introduce wide stopband with low radiation loss but also be flexible for integration. Based on the aforementioned SIDGS resonant cells, single- and dual-band bandpass filters (BPFs) are designed and fabricated. The single-band BPF centered at 2.40 GHz exhibits an ultrawide upper stopband up to 19.7 GHz with a rejection level of 31 dB, whereas the measured stopband total loss (i.e., including radiation, metal, and substrate loss) remains about 30% up to 19.3 GHz. The dual-band BPF operated at 2.10 and 3.78 GHz exhibits an ultrawide upper stopband up to 17.8 GHz with a rejection level of 23 dB, whereas the measured stopband total loss is less than 16% up to 11.4 GHz.

Recently, multiple methods are introduced to implement BPFs with good performance. The single-band [6]- [8] and dual-band [9] substrate-integrated waveguide (SIW) filters are proposed with good in-band performance and low radiation loss. However, the stopband bandwidth of these filters is limited. To extend the stopband bandwidth, the wiggly line [10], compact microstrip resonant cell resonator [11], parallel-coupled line [12], and periodically nonuniform coupled microstrip line [13] are proposed for single-band design, while the CPW-to-microstrip [14] and net-type resonators [15] are proposed for dual-band design. Nevertheless, these structures either suffer from a high insertion loss or a low stopband rejection level. To further extend the stopband bandwidth with enhanced stopband rejection level, single-and dual-band BPFs using stepped-impedance resonators (SIRs) [16]- [22] and defected ground structure (DGS) cells [23]- [25] are proposed. However, the radiation loss at stopband still remains a great challenge. For example, as shown in Fig. 1(a), the EM field of DGS is divergent and affected by adjacent devices, which means that such DGS is not suitable for system integration. Therefore, the flexibly integrated BPFs with wide stopband and low radiation still need to be further investigated.
As shown in Fig. 1(b), the DGS shielded by surrounding metal-vias and bottom ground II could confine most of the EM field between the DGS and bottom ground. Then, to further reduce the radiation loss, the substrate-integrated DGS (SIDGS) is proposed [26], as shown in Fig. 1(c), where the DGS is fully integrated into the substrate. Meanwhile, the metal-vias connected to the upper layer could confine the upward EM field in the substrate. Therefore, the radiation loss is suppressed and the proposed SIDGS resonant cells can be integrated into wireless system without suffering from the performance degeneration caused by the influence from nearby circuits. Then, two types of SIDGS resonant cells are proposed for BPF designs. Each SIDGS resonant cell can introduce an ultrawide stopband with high stopband rejection level. Based on such SIDGS cells, two compact BPFs with single-and dualband operations are designed and fabricated, respectively. The measured results exhibit merits of low radiation loss, wide stopband with high rejection level, and low insertion loss.
In [26], a single-band BPF using SIDGS is designed and fabricated. Following the previous SIDGS BPF design, this article expands the detailed theoretical analysis of SIDGS cells for filter design, including resonance, spurious suppression, and radiation suppression. Meanwhile, a new dual-band BPF using SIDGS is proposed and the related design method is discussed. In Section II, the detailed analysis of the proposed two types of SIDGS resonant cells is presented including resonance, spurious suppression, and radiation suppression. Section III demonstrates the coupled schemes of two types of SIDGS resonant cells. After that, Section IV presents the design examples of single-and dual-band BPFs based on SIDGS resonant cells. Finally, a brief conclusion is given in Section V.

II. SUBSTRATE-INTEGRATED DEFECTED
GROUND STRUCTURE Fig. 1(a) shows the E-field and H -field distributions of a conventional DGS, where the EM field is not constrained, which results in a large radiation loss [27]. Then, to decrease the radiation loss, the surrounding metal-vias and bottom ground II can be utilized and integrated with DGS structures. As shown in Fig. 1(c), the EM field is mostly confined in the substrate, which effectively minimizes the radiation loss. Based on the basic concept of SIDGS mentioned earlier, two types of SIDGS resonant cells (i.e., type-A and type-B) are proposed, as shown in Fig. 2, which are employed for singleand dual-band filter implementations with specific coupling schemes. Both SIDGS resonant cells are composed of two stepped-impedance DGSs, which are surrounded by the bottom ground and metal-vias. To fulfill the coupling scheme for a resonator-coupled filter, the coupling side of the cell could not locate metal-vias. Note that the physical size of these DGSs cannot meet the theoretical definition of slotline [27] (i.e., W <0.25λ g / √ ε r , W /h≤1, and b≤7W , where W is the width of the slot, b is the width of the metallization, and h is the thickness of the substrate). The stepped-impedance microstrip is introduced as the feed line in each cell.
To further investigate the mechanism of proposed SIDGS resonant cells, the dielectric substrate RO4003C (i.e., ε r = 3.55, h 1 = 0.203 mm, and h 2 = 0.303 mm) and EM simulator HFSS are used.

A. Resonance
It is known that the etched defect in a DGS disturbs the current distribution on the ground [28], which implies that the DGSs integrated with the surrounding ground and metal-vias in each cell possess their own resonant frequencies. Fig. 3(a) and (b) shows the configurations and equivalent circuits of two SIDGS resonators (i.e., R1 and R2) in the type-A SIDGS cell. Then, the input admittances of two resonators (i.e., Y A1 and Y A2 ) are derived as follows: where Z A and Z B are the input impedances defined in Fig. 3(b). The detailed derivations are presented in the Appendix. The resonant frequencies (i.e., f 11 and f 12 ) of these two separate resonators are obtained under the cases of Y A1 = 0 and Y A2 = 0, respectively. Here, the microstrip line source and load ports (i.e., ports 1 and 2) are introduced to extract the resonant characteristics of type-A SIDGS cell, and the coupling scheme of the resonators is shown in Fig. 3(c). The resonant frequencies of the cell f p1 , f p2 are derived as follows [29]: where m 1 is the coupling coefficient of these two resonators obtained by simulation [29] and f 11 and f 12 are the resonant frequencies of separated SIDGS resonators. Fig. 4(a) and (b) shows the calculated and simulated resonant frequencies  f p1 and f p2 with the variation of s 11 and l 13 , respectively. The electrical length and characteristic impedance of the SIDGS resonators can be extracted by full-wave simulation. Good agreement between the calculation and the simulation is achieved. Fig. 5(a) and (b) shows the configurations and equivalent circuits of two SIDGS resonators (i.e., R1 and R2 ) of type-B SIDGS cell. Then, the input admittances of two resonators (i.e., Y B1 and Y B2 ) are derived in (4) and (5) [as shown at the bottom of the page] as follows: where Z C and Z D are the input impedances defined in Fig. 4(b). The Appendix presents the detailed derivations. Y B1 = 0 and Y B2 = 0 are the resonant conditions for these two separate resonators. To discuss the resonant characteristics of type-B SIDGS cell, the coupling scheme of the resonators is shown in Fig. 5(c). Note that the peninsula topology cannot only generate dual resonance but also introduce a deep transmission zero between two resonances [30], [31]. The resonant frequencies of the whole SIDGS resonant cell at f d1 and f d2 are defined as [25] where M 1 and M 2 are expressed as Note that f 21 and f 22 are the resonant frequencies of the separate SIDGS resonators. γ 21 and γ 22 are the parameters that define the transformations of two resonators [30]. m 2 is the coupling coefficient between these two resonators.

B. Spurious Suppression
To discuss the harmonic shifting, a simplified capacitively loaded slow-wave transmission line will be discussed first, as shown in Fig. 7(a). By using the ABCD matrix [32], the characteristic equations of the circuit are expressed as follows: 2π where Z a and θ a are the characteristic impedance and the electric length of the unloaded transmission line, respectively, f 0 is the fundamental resonant frequency, f 1 is the first spurious resonant frequency, and β is the propagation constant  Meanwhile, the calculated ratios of the spurious resonant frequency to the fundamental one for different capacitance loading are presented in Fig. 7(e). It implies that the ratio is increased with the loading capacitance increasing, indicating the slow-wave effect [32]. Fig. 7(b) and (c) shows the capacitor distribution (i.e., C 1 , C 2 , C 1 , and C 2 ) [33] of two types of the SIDGS cells. Note that the integrated ground II could further increase the effective capacitance in each capacitor area. Thus, the slow-wave model in Fig. 7(a) is used to explain wide stopband characteristics of the cells. To verify the slowwave effect, the simulated transmission responses in the weakcoupled feeding scheme are presented in Fig. 8 Note that the wider metal pad with smaller DGS width could generate a larger effective capacitance. Therefore, the increasing of l 16 and w 17 means a larger effective capacitance in C 1 and C 2 . Then, the value of f h1 / f p1 is enhanced and a wider stopband performance in the type-A cell is achieved. Meanwhile, the increasing of s 25 and l 24 means a larger effective capacitance in C 1 and C 2 . Therefore, the value of f h2 / f p2 is enhanced and a wider stopband performance in the type-B cell is achieved.
In addition, the stepped-impedance feed line is used in the strong-coupling feeding scheme of two types of the SIDGS cells to enhance the stopband rejection level at higher frequency. The external quality factors of the cells in the strongcoupling feeding scheme are decreased compared with the weak-coupling feeding scheme [29]. Note that too large or too small external quality factor could increase mismatch and reduce the resonant strength of the coupled resonators in filter design [29]. As shown in Fig. 8(a) and (b), the larger external quality factor increases the mismatch at the fundamental resonant frequency in the weak-coupling feeding scheme. Thus, the decreasing of the external quality factor could decrease the mismatch and increase the fundamental resonant strength. Meanwhile, the smaller external quality factor increases the mismatch at the spurious resonant frequency in the weakcoupling feeding scheme. Thus, the decreasing of the external quality factor could further increase the mismatch and decrease the spurious resonant strength. As a result, the spurious suppression at higher frequency is improved by using the strong coupling stepped-impedance feed line.

C. Radiation Suppression
The radiation suppression of the SIDGS cells could be discussed in the following three parts with five cases (i.e., case A-E) shown in Fig. 9(a).

1) Shield Ground II:
Compared with the conventional DGS, ground II is an additional boundary condition in the SIDGS. Such a boundary condition can restrict the E-field and H -field between the two conductors, which decreases the radiation loss of the structure. To verify the function of ground II, radiation loss rates (i.e., R r1 and R r2 ) of the type-A and type-B cells without ground II and metal-vias (i.e., case A) and with ground II and without metal-vias (i.e., case B) are simulated under the case of lossless substrate and metal, as shown as the blue and red dashed curves in Fig. 9(b) and (c). R r is calculated by Note that compared with case A, the radiation in case B is decreased by the shield ground II.
2) Surrounding Metal-Vias: Even though the shield ground II is introduced, the conductor-backed DGS will also radiate at high frequency due to the wave leaking from the edge of the two conductors [34]. Then, the metalvias surrounding the conductor-backed DGS are proposed. Note that the metal-vias guarantee the middle metal layer grounded. Thus, unwanted outward-traveling TEM waves between the middle metal layer and the bottom metal layer in conductor-backed DGS [34] are decreased, which further minimizes the radiation. Meanwhile, two adjacent metal-vias with grounds I and II connected can be regarded as a rectangular waveguide. The cutoff frequency of a rectangular waveguide can be expressed as follows [35]: where a is the distance between two metal-vias. Thus, for f < f c10 , the E-field and H -field will be blocked, which further reduces the radiation loss of the structure. To verify the function of metal-vias, the radiation loss rates of the type-A and type-B cells with ground II and metal-vias (h 1 = 0.203 mm and h 2 = 0.303 mm) (i.e., case C) are shown as the black solid curves in Fig. 9(b) and (c). Compared with cases A and B, the radiation in case C is further reduced by the metal-vias.

3) Substrate Thickness of the SIDGS:
It is known that a surface wave is a propagating mode guided by the airdielectric surface for a dielectric substrate on the conductor ground plane [29, p. 82]. With the increase of the substrate thickness, the surface wave is easier to propagate, which will cause high radiation. Considering the fabrication limitation, two relatively thin substrates are chosen to decrease the radiation in the implementation of the SIDGS cells. To verify the effect of the substrate thickness, radiation loss rates of the type-A and type-B cells with ground II and metal-vias (h 1 = 1 mm and h 2 = 0.303 mm) (i.e., case D) and with ground II and metal-vias (h 1 = 0.203 mm and h 2 = 1 mm) (i.e., case E) are presented as the green and purple dash curves in Fig. 9(b) and (c). Note that for two tiers of substrates, the thickness of the upper substrate has a greater influence on the radiation since the upper substrate has a larger surface contacted with air, which is easier to propagate the surface wave. To investigate the radiation characteristics of SIDGS resonant cells, the EM-simulated E-field of the substrate between grounds I and II in two types of cells under case C at stopband is shown in Fig. 9(d) and (e). Note that the E-field is concentrated near the DGS in the substrate. Most E-field is confined in the substrate by using metal-vias and surrounding ground.

III. SIDGS RESONANT CELLS WITH QUASI-COUPLED SCHEMES
Two identical SIDGS resonant cells can be utilized to design a coupled filter, and each SIDGS resonant cell is constituted of two dissimilar SIDGS resonators. First, to illustrate the coupling characteristics of SIDGS, the field distributions of the DGS line resonator at fundamental resonance are shown in Fig. 10. Note that each of the DGS line resonators has the maximum electric field density and the minimal magnetic field density at the middle of the line. Meanwhile, it has the maximum magnetic field density and the minimal electric field density at the end of the line [27]. The field distribution could be verified by simulation. By properly adjusting the physical dimension and the configuration of the coupled SIDGS resonators, the magnetic coupling and electric coupling can be obtained for filter design. Then, the coupling coefficient k i j of the asynchronous SIDGS resonant cells can be extracted by the following equation: where f 0i and f 0 j are the resonant frequencies of the dissimilar SIDGS resonators and f pi,di and f pj,d j are the resonant frequencies of two resonators under the coupled conditions in type-A and type-B SIDGS resonant cells, respectively. Here, the two resonant frequencies of these SIDGS resonators are set to be equal, and thus, (14) could be simplified as [29] k i j = Fig. 11 shows the configuration of the coupling scheme and the coupling-node diagram of two type-A SIDGS cells. Then, the couplings of these coupled cells could be concluded in six parts: 1) broadside coupling k 23 between R2 and R3; 2) embedded couplings between R1 and R2 (i.e., k 12 ) and R3 and R4 (i.e., k 34 ); 3) cross coupling k 14 between  R1 and R4; 4) coupling k S1 and k 4L between microstrip feed line and R1 or R4, respectively; 5) tiny couplings between microstrip feed line and R2 or R3; and 6) diagonal couplings including k 13 and k 24 . Note that the strong couplings, such as k 12 , k 23 , and k 34 , are mainly generated at the middle of the DGS line resonators, which are dominated by the electric field. The cross coupling of R1 and R4 is mainly produced at the end of the DGS, which is dominated by magnetic field. In this design, the electrical coupling is regarded as positive coupling and the magnetic coupling is regarded as negative coupling. The main couplings k 12 , k 34 , and k 23 are simulated and shown in Fig. 12(a) and (b). The coupling coefficients k 12 , k 34 , and k 23 are increasing with the decreasing widths of the gaps (i.e., w 14 and w 16 ). Meanwhile, Fig. 12(c) and (d) shows that the external quality factor Q is decreasing with the increase of l t 1 or l w1 . Fig. 13 shows the configuration of the coupling scheme and the coupling-node diagram of type-B SIDGS cell. Different from the coupling scheme of type-A SIDGS cells, k 23 is weak coupling, whereas k 14 is strong coupling in the coupling scheme of type-B SIDGS cells. Note that the strong couplings, such as k 12 , k 14 , and k 34 , are mainly generated at the end of the DGS line resonators, which are dominated by the magnetic field. The cross coupling of R2 and R3 is mainly produced at  the middle of the DGS, which is dominated by electric field. In this design, the magnetic coupling is regarded as positive coupling and the electric coupling is regarded as negative coupling. The main couplings k 12 , k 34 , and k 14 are simulated and shown in Fig. 14(a) and (b). The coupling coefficients k 12 , k 34 , and k 14 are increasing with the decreasing widths of the gaps (i.e., w 22 and w 23 ). Meanwhile, Fig. 14(c) and (d) shows that the external quality factor Q is decreasing with the increasing of l t 2 or l w2 .

IV. DESIGN EXAMPLE
To verify the aforementioned principle, a single-band BPF and a dual-band BPF with wide upper stopband and low radiation loss are presented and fabricated. The dielectric substrate RO4003C (i.e., ε r = 3.55, h 1 = 0.203 mm, and h 2 = 0.303 mm) is utilized for the manufacturing.

A. Single-Band BPF Design
Based on the type-A SIDGS cell, a prototype of a four-order single-band BPF is proposed, as shown in Fig. 15. Two type-A SIDGS cells are coupled using a symmetric coupled scheme. Then, the BPF is implemented with specifications as follows: Compared with the traditional design using coupling matrix, the fractional bandwidth of 25% is larger. Since the wideband definition in cases [37]- [40] is larger than 40%, 25% is considered as the edge between wideband and narrowband. Thus, the coupling matrix is used as a reference for filter design. To achieve the filter with high agreement with the design specification, the physical dimensions of the filters could be optimized at the later stage. The center frequency is determined by the physical dimensions of the type-A SIDGS cell. Note that coupling coefficients k i j and Q can be derived as Thus, the corresponding main coupling coefficients and external quality factor can be obtained from the investigation mentioned earlier. With proper dimensions of the type-A SIDGS cells and optimized coupling relationships, the singleband SIDGS BPF is designed. The theoretical S-parameters calculated by coupling matrix and the lossless simulation result are shown in Fig. 16, which exhibits a fairly fine agreement. Then, a single-band BPF is fabricated, as shown in Fig. 17. Besides, radiation/conductor/dielectric loss rates of the BPF are simulated and calculated, as shown in Fig. 18. The radiation loss is simulated under the case of lossless metal and substrate (i.e., S 11r , S 21r ). The radiation loss L r is calculated as The conductor loss L c and dielectric loss L d can be calculated under the cases of lossless dielectric (i.e., S 11c and S 21c ) or  lossless metal (i.e., S 11d and S 21d ), respectively. L c and L d can be derived as The calculated radiation loss under the case of lossless substrate and metal is less than 13% up to 20 GHz. The simulated and measured results of S-parameters are shown in Fig. 19. The Agilent 5230A network analyzer is used to measure. The center frequency of the BPF is 2.4 GHz with the 3-dB FBW of 24%. The minimum in-band insertion loss is 1.62 dB. Meanwhile, the stopband is up to 19.7 GHz with a rejection level higher than 31 dB. The measured stopband total loss is less than 30% up to 19 GHz except a high loss point at 14.1 GHz, as shown in Fig. 18. The simulated loss is solved under the case of the complete filter structure without the connectors. Note that the radiation at 14.1 GHz (i.e., green dashed line) in Fig. 18 is mainly allocated at the feed line surrounded by the metal-vias at the side of the filter. Meanwhile, with the implementation of connectors for test, the feed line is longer, while the EM fields of the ground at the side are affected. Thus, the radiation around 14.1 GHz (i.e., black solid line) in measurement further Measured/simulated total loss rates and calculated radiation/conductor/dielectric loss rates of the single-band BPF.  increases. In addition, the core circuit size of the BPF is 12.3 mm × 12.2 mm (i.e., 0.16 λ g × 0.16 λ g , where λ g is the microstrip guided wavelength at the center frequency of 2.4 GHz). Note that the feed line is shorter compared to the previous work [26], which improves the performance. A comparison of the single-band filter with the state of the arts is shown in Table I, which reveals that the proposed filter has merits of wide upper stopband, low radiation loss, and compact size.

B. Dual-Band BPF Design
A prototype of a two-order dual-band BPF is proposed based on the type-B SIDGS cell, as shown in Fig. 20. Then, the BPF is implemented with specifications as follows: lower center frequency of 2.0 GHz, 3-dB FBW = 26.0%, 15-dB return loss and upper center frequency of 3.55 GHz, 3-dB FBW = 15.4%, and 15-dB return loss. The optimized coupling matrix [M p ] can be exhibited as follows [36]: Here, the center frequencies are determined by the physical dimensions of the type-B SIDGS cell. The theoretical Sparameters calculated by the coupling matrix and the lossless simulation result are shown in Fig. 21. Then, a dual-band BPF is fabricated, as shown in Fig. 22. Besides, radiation/ conductor/dielectric loss rates of the BPF are simulated and calculated, as shown in Fig. 23. The calculated radiation loss  under the case of lossless substrate and metal is less than 12% up to 16.7 GHz.
The simulated and measured results of S-parameters are shown in Fig. 24. The center frequency of lower passband is 2.1 GHz with 3-dB FBW of 25.2% and the minimum in-band insertion loss of 0.95 dB. The center frequency of upper passband is 3.78 GHz with 3-dB FBW of 12.7% and the minimum in-band insertion loss of 1.39 dB. Moreover, the stopband with a rejection level higher than 23 dB is up to 17.8 GHz. Furthermore, Fig. 23 shows that the measured stopband total loss is less than 16% up to 11.5 GHz. The operation of the radiation at 11.8 GHz in Fig. 23 is similar to the effect of 14.1 GHz in Fig. 18. The core circuit size of the BPF is 12.3 mm × 12.2 mm (i.e., 0.13 λ g × 0.13 λ g , where λ g is the microstrip guided wavelength at the lower passband center frequency of 2.1 GHz). The difference between the measured and simulated results is mainly caused by the fabrication errors. A comparison of the dual-band filter with the state of the arts is shown in Table II. It reveals that this filter has merits of wide upper stopband, low radiation loss, compact size, and low insertion loss.

V. CONCLUSION
In this article, two types of SIDGS resonant cells with different transmission responses are proposed. Both cells can not only introduce an ultrawide stopband bandwidth due to the strong slow-wave effect but also suppress their radiation loss in a wide range by their instinct structural superiority. Based on the proposed SIDGS resonant cells, single-and dual-band BPFs are analyzed, designed, and fabricated. The design examples inherit the merits of DGS, such as wide stopband, low insertion loss, and compact size. Meanwhile, a strong suppression of the radiation is also obtained. With such good performance and the instinct structure advantage of the flexible integration, the proposed SIDGS and single-/dual-band BPFs are attractive for practical applications.

APPENDIX
As shown in Figs. 3 and 5, the input impedances Z A , Z B , Z C , and Z D of the equivalent circuits can be calculated using the transmission line impedance equations [35], which can be Z A = Z 12 · Z 13 (Z X + j Z 13 tan θ 13 ) + j Z 12 tan θ 12 (Z 13 + j Z X tan θ 13 ) Z 12 (Z 13 + j Z X tan θ 13 ) + j Z 13 tan θ 12 (Z X + j Z 13 tan θ 13 ) expressed as (22)- (25), shown at the bottom of the previous page, where Z X is expressed as (26).