On-Chip mm-Wave Second-/Third-Order BPF and Balun With Wide Stopband and Low Radiation Loss Using SIDGS Resonators in 40-nm CMOS

In this article, two millimeter-wave substrate-integrated defected ground structure (SIDGS) resonators are proposed for filters and balun implementation. Such SIDGS resonators are composed of defected ground structure (DGS) with grounded shield and surrounding vias, which not only exhibit wide stopband with low radiation loss but also are flexible to integrate with active circuits. Using different coupling methods, second-/third-order bandpass filters (BPFs) and filtering balun are designed based on the proposed SIDGS resonators. The filters and balun are fabricated in a standard 40-nm complementary metal-oxide-semiconductor (CMOS) technology. The second-order filter is centered at 28 GHz with an insertion loss of the 2.7 db and 3-dB FBW of 20.4%. Meanwhile, the stopband extends to 140 GHz with a rejection level of 30 dB. The third-order filter operates at 28 GHz with an insertion loss of the 2.9 db and 3-dB FBW of 47%. Meanwhile, the stopband extends to 170 GHz with a rejection level of 27 dB. The filtering balun operating at 25 GHz with the 3-dB FBW of 32% exhibits in-band amplitude/phase imbalances of 0.6 dB and ±1.1°, respectively. The minimum in-band insertion loss is 2 dB excluding the theoretical 3-dB loss. The stopband extends to 175 GHz with a rejection level of 30 dB.

Balun is also an essential passive component in on-chip millimeter-wave circuits, which converts single-ended signals into balanced signals. Balanced signals improve the overall performance of circuits such as differential amplifiers, mixers, and frequency multipliers [23], [24], [25]. Marchand balun is widely used in on-chip balun due to its flexible implementation [26], [27], [28]. Coupled-CPW Marchand balun [29] is designed for large bandwidth, which suffers from the relatively large amplitude/phase imbalances and size. The size could be reduced by broadside-coupled spiral transmission line [30]. To further reduce amplitude and phase imbalances, the self-coupled compensation line is implemented in balun design [31]. To simplify the system design, filtering balun is proposed by integrating the function of filtering and balanceto-imbalance to one component. In [32] and [33], on-chip filtering baluns with good performance are designed for 5-GHz applications. To satisfy the application at mm-wave, a 24-GHz multicoupled line filtering balun is proposed [34]. However, such prototypes suffer from either relatively large phase imbalance or narrow stopband bandwidth. Therefore, the design of on-chip mm-wave filtering balun with good in-band performance, wide stopband, and compact size for flexible integration remains a great challenge.
Recently, substrate-integrated defected ground structure (SIDGS) [35], [36], [37], [38], [39] is proposed for a series of high-performance passive components, which shows merits of wide stopband, low radiation loss, compact size, and low insertion loss. However, all these components are implemented on PCB, which is hard to integrate with active circuits directly.
In this article, two types of on-chip millimeter-wave SIDGS resonators are proposed, which are composed of defected ground structure (DGS) with grounded shield and surrounding vias. Such resonators not only exhibit wide stopband with low radiation loss but also are flexible to integrate with active circuits. Using different coupling methods combining with such SIDGS resonators, second-/third-order BPFs and filtering balun can be designed. Full simplified equivalent circuit models of the filters and balun are provided. By analyzing such models, guidelines for implementation of the filters and balun can be given. To verify the principle, the filters and balun are fabricated in a standard 40-nm complementary metal-oxidesemiconductor (CMOS) technology. The measured results exhibit merits of wide stopband with high rejection level, low radiation loss, low insertion loss, and good in-band amplitude/phase imbalances.
Compared with the SIDGS implemented on PCB technology in previous work [35], [36], [37], [38], [39], the SIDGS on the 40-nm CMOS in this work is a stacked structure with etched defects at different metal layers, while the previous work has only one layer of etched defect. Meanwhile, the complete bottom ground of SIDGS on PCB is replaced by the grounded shield in the design of SIDGS using the CMOS process. The reason for such a change is to satisfy the design rules of the 40-nm CMOS technology and avoid excessive parasitic capacitance. The CMOS-type SIDGS with the stacked structure can achieve a more compact size compared with the PCB-type SIDGS. Moreover, the on-chip SIDGS exhibits wider stopband bandwidth and lower radiation loss compared with other on-chip mm-wave structures and components. The article is organized as follows. In Section II, detailed analysis of the proposed two types of SIDGS resonators is presented. Section III demonstrates the implementation of the second-/third-order filters using the proposed SIDGS resonators and the analysis combining with the full simplified equivalent models. Then, Section VI presents theory and design example of the filtering balun. Finally, a brief conclusion is given in Section V.

II. ON-CHIP MILLIMETER-WAVE SIDGS RESONATORS
The 3-D view of the proposed SIDGS resonators and the metal stack-up used for implementation are shown in Fig. 1. The metal stack-up is from a standard 40-nm CMOS technology. Resonator 1 consists of DGS located in M7 with the grounded shield in M6 and surrounding vias in V6. Resonator 2 consists of DGS located in M8 integrated with the grounded shield in M6 and surrounding vias in V6 and V7 connected by M7. Note that the physical size of these DGSs cannot meet the  theoretical definition of slotline [40]. In SIDGS, the E-field and H -field of DGS can be confined by the grounded shield and surrounding vias, as illustrated in [35]. Thus, the loss of the resonators caused by the Si-substrate and radiation of the DGS can be minimized.
To further illustrate the characteristic of the resonators, the simplified equivalent models based on the transmission lines and inductors are given. Fig. 2 shows the configuration and equivalent circuit of SIDGS resonator 1. The electrical length and characteristic impedance of the transmission line and the inductance could be extracted from the layout by full-wave simulation [41], [42]. Then, the input impedance of the resonator (i.e., Z in1 ) is derived as (1), shown at the bottom of the page. The simulated and calculated input  impedances are shown in Fig. 3(a), which show a good agreement. Meanwhile, the simulated unloaded quality factor Q u is 22.3. The resonant frequency of the resonator can be tuned by characteristic impedance of the transmission line and the inductance of the inductor, as shown in Fig. 3(b). Meanwhile, such resonator exhibits an ultrawide stopband. To illustrate harmonic shifting, a simplified inductor-loaded transmission line will be discussed, as shown in Fig. 4(a). The input impedance is derived as To further investigate the characteristic of the resonator, Z in1 can be rewritten as Assume that Z in1 can be rewritten as Note that the electrical length of the transmission line is affected by α, which is related to L. The equivalent electrical length (i.e., θ d ) and the equivalent phase velocity (i.e., v pd ) of the inductor-loaded transmission line can be derived as [43] ωl where v p0 is the phase velocity of the transmission line without loaded inductor, and l is the length of the transmission line. According to (7), a slow wave effect is achieved by the loaded inductor. With the loading inductance increasing, the slow wave effect is stronger. Fig. 4(b) shows plots of the input impedance of the inductor-loaded transmission line (Z a = 20 and θ a = 90 • at 60 GHz) under different inductance L. The resonance occurs when |Z in1 | = ∞. Note that both fundamental resonant frequency (i.e., f 0 ) and spurious resonant frequency (i.e., f 1 ) decrease with the increase in L due to the slow wave effect. Combining (5) and (6), f 0 is obtained under the case of θ d = π/2 and f 1 is obtained under the case of θ d = 3π/2. Thus, and v pd1 are the equivalent phase velocities of the inductor-loaded line at the fundamental and first spurious resonant frequencies, respectively. The ratio of f 1 to f 0 can be derived as According to (8), the slow wave effect can change the ratio of f 1 to f 0 by affecting the equivalent phase velocity v pd . The calculated ratios of f 1 to f 0 for different loading inductances are presented in Fig. 4(c). It implies that with the loading inductance increasing, f 1 / f 0 increases. Thus, the wide stopband could be achieved. Fig. 5 shows the configuration and equivalent circuit of SIDGS resonator 2. Then, the input impedance of the resonator  (i.e., Z in2 ) is derived as (9), shown at the bottom of the page, where Z A can be calculated as The simulated and calculated input impedances are shown in Fig. 6(a). Meanwhile, the simulated unloaded quality factor Q u is 21.4. The resonant frequency of the resonator can be tuned by different parameters, as shown in Fig. 6(b). The resonator also exhibits a characteristic of wide stopband. To illustrate harmonic shifting, a simplified inductor-connected transmission line will be discussed, as shown in Fig. 7(a). The even-and odd-mode circuits are shown in Fig. 7(b) and (c). The odd-mode circuit is similar to the simplified circuit in Fig. 4, which exhibits a slow wave effect affected by the loaded inductor. The even-mode circuit is a typical half-wavelength resonator. The input impedances are derived as  inductor-connected transmission line (i.e., f 2 ) is determined by the first-harmonic resonant frequency of the odd-mode circuit (i.e., f o1 ). Thus, with the increase in L, f 0 and f 2 decrease while f 1 is fixed according to the characteristics of the evenand odd-mode circuits. Meanwhile, the calculated ratios of f 1 to f 0 for different inductance are presented in Fig. 7(e), which exhibits the ratio increasing with the inductance increasing. Thus, the wide stopband could be achieved.

III. IMPLEMENTATION AND ANALYSIS OF BPF USING SIDGS RESONATORS
To prove that the proposed resonators are useful in practice, two on-chip second-and third-order BPF design examples are given. The full simplified equivalent circuits of the filters are provided for analyzing and assisting the design.

A. Implementation and Analysis of Second-Order BPF
To design a second-order BPF, two identical SIDGS resonator 1 are coupled to form a dual-resonance cell. Meanwhile, two T-stubs are used as the feed-line. The source-load coupling is achieved by interdigital capacitors connected to the feedlines. The configuration and simplified equivalent circuit of the second-order BPF are shown in Figs. 8 and 9. To acquire the frequency response of the equivalent circuit, the evenand odd-mode analyses are used, as shown in Fig. 9(b) and (c). Using the Z -matrix of coupled line and transmission line impedance equation [43], the one-port input odd-mode admittance Z ino can be derived as h, k, and g can be derived as a, b, d, e, and Z x can be derived as Z y can derived as The one-port input even-mode admittance Z ine can be derived as Z m can be calculated as Z i j , Z i j , and Z i j (i , j = 1, 2, 3, 4) are the Z -matrix parameters of coupled line, which are derived in Appendix. Therefore, the S-parameters of the proposed circuit shown in Fig. 9(a) can be expressed as where Z 0 = 50 . The calculated results of various cases are given in Figs. 10 and 11. To clarify the order, the calculated even-and odd-mode impedances under the case of C = 0 fF are shown in Fig. 10(a). Two transmission poles (TPs) are generated by even-and odd-mode circuits, which implies that the BPF is second-order. The center frequency of the second-order BPF is mainly determined by the parameters of resonators, as mentioned in Section II. Note that two resonators are coupled by two additional inductors L 3 , as shown in Fig. 9. Thus, the bandwidth of the second-order BPF can be tuned by changing L 3 . Fig. 10(b) shows the S-parameter under different L 3 . The bandwidth of the filter increases with the increase in L 3 . After the bandwidth is determined, the loading strength of the feed-line can be adjusted by Z 2o of the coupled line. Fig. 10(c) shows the S-parameter under different Z 2o . Suitable loading strength of the feed-line could be found by tuning Z 2o .
To enhance the passband selectivity and stopband rejection level, additional TZs should be generated. According to (27), the TZs could be generated under the condition of Z ine = Z ino . In this design, the TZs could be generated by changing the odd-mode impedance using source-load coupling capacitor C. Fig. 11(a) shows Z ino and Z ine under C = 16 fF. Compared with Fig. 10(a), the curves of the evenand odd-mode impedances intersect at the positions of TZ1 and TZ2. Fig. 11(b) shows the calculated S-parameter under different capacitance C. With the increase in C, the TZs are closer to the passband. The calculated and simulated Sparameters of the proposed second-order BPF are shown in Fig. 12(a), which shows a good agreement. Besides, radiation/conductor/dielectric loss rates of the second-order BPF are simulated and calculated, as shown in Fig. 12(b). 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 , S 21c ) or lossless metal (i.e., S 11d , S 21d ), respectively. L c and L d can be derived as The design procedure of the second-order BPF is summarized as follows. The first step is to obtain the parameters of the resonators according to the center frequency of the filter specifications. Note that the center frequency of the filter mainly depends on the resonant frequency of the resonators. According to Figs. 3(b) and 6(b), the specific parameters of resonators under different resonant frequencies can be obtained. The second step is to obtain the parameters about coupling relationship of the resonators and feed-line according to the specification of bandwidth and TZ. The desired bandwidth can be obtained by adjusting the value of coupling inductor L 3 , as shown in Fig. 10(b). After L 3 is determined, the suitable loading strength of feed-line can be obtained by adjusting the value of Z 2o , according to Fig. 10(c). Then, the desired location of TZ can be obtained by adjusting the value of source-load coupling capacitor C, according to Fig. 11(b). The third step is to implement the layout of the filters according to the parameters of the equivalent circuits.
Based on the design procedure mentioned above, the second-order BPF is fabricated in a standard 40-nm CMOS technology, as displayed in Fig. 13(a). The pitch between the ground pad to the signal pad is 85 μm. The feed-line is 50 CPW. The thru-reflect-line (TRL) calibration is used for measurement. The measurement is calibrated to the tips of probes. Thus, the measured result is including the influence of ground-signal-ground (GSG) pad and feed-lines. The simulated and measured results of the S-parameters are shown in Fig. 13(b). The vector network analyzer is used to measure. The center frequency of the BPF is 28 GHz with the 3-dB FBW of 20.4%. The minimum in-band insertion loss is 2.7 dB. Meanwhile, the stopband is up to 140 GHz with a rejection level higher than 30 dB. The stopband |S 11 | is higher than −4 dB up to 140 GHz, which implies that the BPF exhibits a low radiation loss within a wide frequency range using SIDGS. In addition, the core circuit size of the BPF is 225 × 225 μm 2 .

B. Implementation and Analysis of Third-Order BPF
To design a wideband third-order BPF, three stacked-coupled SIDGS resonators 1 and 2 are used. Such stacked-coupled scheme can reduce the size of the filter. The feed-lines are tapped to two resonator 2. Meanwhile, the cross coupling of two resonator 2 is introduced by the parallel-plate capacitor. The configuration and simplified equivalent circuit of the third-order BPF are shown in Figs. 14 and 15, respectively. To demonstrate the mechanism, the equivalent circuit should be analyzed first using evenand odd-mode circuits, as shown in Fig. 15(b) and (c), respectively. To acquire the frequency response of the circuit, the one-port input even-and odd-mode impedances Y ine and Y ino can be derived as [43] and [44] (30) Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
L 2o , M, and Z n are derived as where A x 1,2 , B x 1,2 , C x 1,2 , and D x 1,2 (x = a, b, c) are derived in (40)- (43), as shown at the bottom of the page.
Then, the S-parameters of proposed circuit shown in Fig. 15(a) can be calculated by (26) and (27). The calculated results of various cases are given in Figs. 16 and 17. To confirm the order of the BPF, C is set as 0 fF and k 2 is set as 0. The calculated even-and odd-mode impedances are shown in Fig. 16(a). Three TPs are generated by even-and odd-mode cos θ 2 j Z 2 cos θ 2 jY 2 sin θ 2 cos θ 2 cos 2θ 1 j Z 1 cos 2θ 1 jY 1 sin 2θ 1 cos 2θ 1 cos θ 2 j Z 2 cos θ 2 jY 2 sin θ 2 cos θ 2 1 j ωL 5 0 1 (41) cos θ 2 j Z 2 cos θ 2 jY 2 sin θ 2 cos θ 2 cos θ 1 j Z 1 cos θ 1 jY 1 sin θ 1 cos θ 1 1 0 4 j ωC 1 × cos θ 1 j Z 1 cos θ 1 jY 1 sin θ 1 cos θ 1 cos θ 2 j Z 2 cos θ 2 jY 2 sin θ 2 cos θ 2 1 j ωL 5 0 1  circuits, which implies that the BPF is third-order. The center frequency of the third-order BPF is mainly determined by the parameters of two types of resonators mentioned in Section II. Note that three resonators are coupled by three inductive parts in series, as shown in Fig. 15(a). Thus, the bandwidth of the third-order BPF can be tuned by changing the coupling coefficient k 1 , as shown in Fig. 16(b). Note that the feed-line is tapped to the filter. Fig. 16(c) depicts the schematic of different tapped positions of the feed-line (i.e., Cases A and B). By changing the tapped position, suitable loading strength of the feed-lines can be obtained for good passband performance, as shown in Fig. 16(d).
To enhance the passband selectivity and stopband rejection level, additional TZs can be generated at the upper and lower stopbands under the condition of Z ine = Z ino , as mentioned in Section III-A. In this design, two cross couplings including the magnetic coupling between the inductor L 2 of two resonator 1  and the electric coupling caused by the parallel-plate capacitors can change Z ino , as shown in Fig. 15. Fig. 17(a) shows Z ino and Z ine under C = 7 fF and k 2 = 0.025, which exhibits two additional intersects compared with Fig. 16(b). Fig. 17(b) demonstrates the S-parameters under different C and k 2 . Note that the magnetic coupling between the inductors of two resonator 1 could generate a TZ at the lower stopband. Meanwhile, the electric coupling caused by the parallel-plate capacitors between two resonator 1 could generate a TZ at the upper stopband. In addition, two TZs can be independently adjusted by C and k 2 , as shown in Fig. 17(c) and (d).
The calculated and simulated S-parameters of the proposed third-order BPF are shown in Fig. 18(a), which shows a good agreement. Besides, radiation/conductor/dielectric loss rates of the third-order BPF are simulated and calculated, as shown in Fig. 18(b).
The design procedure of the third-order BPF is summarized as follows. The first step is to obtain the parameters of the   Fig. 16(b). The suitable loading strength can be obtained by adjusting the tapped position of feed-line, according to Fig. 16(c) and (d). Then, the desired location of TZ can be obtained by adjusting the value of C and k 2 about cross couplings, according to Fig. 17(c) and (d). The third step is to implement the layout of the filter according to the parameters of the equivalent circuits.
Based on the design procedure mentioned above, the third-order BPF is fabricated in a standard 40-nm CMOS technology, as displayed in Fig. 19(a). The simulated and measured results of the S-parameters are shown in Fig. 19(b). The center frequency of the BPF is 28 GHz with the 3-dB FBW of 47%. The minimum in-band insertion loss is 2.9 dB. The return loss is better than 15 dB in the simulated result. However, due to the deviation of the dielectric parameters between simulation and practical fabrication and the parasitic parameters of GSG pad, the measured return loss is worse than 10 dB. Meanwhile, the stopband is up to 170 GHz with a rejection level higher than 27 dB. The stopband |S 11 | is higher than −4 dB up to 155 GHz. In addition, the core circuit size of the BPF is 258×283 μm 2 . A comparison of the on-chip millimeter-wave BPFs with the state-of-the-arts is shown in Table I, which reveals that the proposed filters have merits of low insertion loss, wide stopband with high rejection level, and wideband low radiation.

IV. IMPLEMENTATION AND ANALYSIS OF FILTERING BALUN USING SIDGS RESONATORS
The proposed SIDGS resonators are also useful in filtering balun design. The balun is implemented by three stacked-coupled SIDGS resonators. The feed-lines are tapped to each resonator for the input and two unbalanced outputs. The configuration and simplified equivalent circuit of the balun are shown in Figs. 20 and 21, which are similar to the third-order BPF with an additional port. To demonstrate the principle of the filtering balun, an open-circuited terminal of the equivalent circuit is replaced by a load (i.e., P4) to form a fully symmetrical network, as shown in Fig. 21(a). Thus, the even-and odd-mode analyses can be used for calculation, as shown in Fig. 21(b) and (c), respectively. According to [45], S 21 = −S 31 can be achieved when Γ even and Γ odd are the input reflection coefficients of the evenand odd-mode circuits, respectively, and T even denotes the transmission coefficient of the even-mode circuit. To obtain T even , the input impedance Z ine of the even-mode circuit in Fig. 21(c) can be derived as Γ even can be derived as Note that Z ine is imaginary. Thus, |Γ even | = 1 and |T even | = 0, which satisfy the condition of S 21 = −S 31 in (44).  To calculate the frequency response of the balun, the input impedance Z ino of the odd-mode circuit can be derived as (47), shown at the bottom of the page, from the circuit in Fig. 21(c), where Z y is derived as Z x can be derived as where Y 0 = 1/50 S. Y 11 , Y 22 , Y 12 , and Y 21 are calculated as A i , B i , C i , and D i (i = 1, 2) can be derived as (54), shown at the bottom of the page, and (55).
The filtering balun is fabricated in a standard 40-nm CMOS technology, as displayed in Fig. 23. The simulated and measured results of the S-parameters are shown in Fig. 24. The center frequency of the BPF is 25 GHz with the 3-dB FBW of 32%. The minimum in-band insertion loss is 2 dB excluding the theoretical 3-dB loss. The in-band amplitude and phase imbalances are 0.6 dB and ±1.1 • , respectively. Meanwhile, the stopband is up to 175 GHz with a rejection level higher than 30 dB according to simulation. Limited by the setup of the measurement, the stopband of the balun over 50 GHz cannot be measured. In addition, the core circuit size of the balun is 273 × 355 μm 2 . A comparison of the on-chip millimeter-wave filtering balun with the state-of-the-arts is shown in Table II, which reveals that the proposed balun has merits of low inband amplitude/phase imbalance and wide stopband with high rejection level.

V. CONCLUSION
In this article, two types of millimeter-wave SIDGS resonators are proposed for filter and balun implementation on the 40-nm CMOS. Such SIDGS resonators are composed of DGS with grounded shield and surrounding metal vias, which not only exhibit wide stopband with low radiation loss but also be flexible to integrate with active circuits. Different coupling methods based on the proposed SIDGS resonators are used to design second-/third-order BPFs and filtering balun. To verify the principle, the proposed filters and balun are fabricated in a standard 40-nm CMOS technology. The narrowband second-order filter and wideband third-order filter have merits of low insertion loss, wide upper stopband with high rejection level, wideband low radiation loss, and good passband selectivity. The filtering balun shows merits of low in-band amplitude/phase imbalances and wide stopband with high rejection level.
The relationship between physical dimensions of the coupled line and Z 2e , Z 2o can be established using the method in [46] with EM simulation.