A Common-Mode Noise Suppression Filter for Gigahertz Differential Signals Based on Substrate Integrated Waveguide Resonators

A common-mode noise suppression filter for microstrip differential lines based on substrate integrated waveguide resonator (SIWR) is proposed in this article. The proposed common-mode filter (CMF) consists of cascaded SIWR units with different size. The equivalent characteristic impedance circuit model of the proposed CMF is given to predict the common-mode suppression characteristics by introducing the spectral domain approach (SDA). Simulated results show that the common-mode noise is decreased more than 35 dB from 4.5 GHz to 11.4 GHz, and −30 dB rejection band is obtained in the frequency band of 4.3-15 GHz. Moreover, the insertion loss and the group delay in the frequency domain show that there is little degradation for differential signals. In the time domain, 86.5% amplitude suppression of common-mode noise is achieved. In addition, the eye diagrams in the time domain are investigated to explain the effectiveness of the proposed CMF and indicate that the CMF can maintain the differential signal integrity. The prototype is fabricated to verify the validity of the proposed structure, and the measurement results show good agreement with the simulation results.


I. INTRODUCTION
Differential signals have played an important role in the signal transmission of modern high-speed circuits. Common applications include serial advanced technology attachment III (SATA III), high definition multimedia interface (HDMI) and universal serial bus (USB) devices [1]. The advantages of using differential signals include lower levels of unintentional radiation, reduced susceptibility to external interference and more accurate system timing sequence compared with traditional single-ended signals. However, it is inevitable that common-mode noise will be generated due to non-ideal asymmetric differential lines, which could be caused by fabrication tolerance, circuit layout or coupled spurious signals. When common-mode noises pass through the interconnection in the system packaging structure of highspeed circuits, it will cause serious electromagnetic radiation, The associate editor coordinating the review of this manuscript and approving it for publication was Bo Pu . and affect the signal integrity (SI) and power integrity (PI) of the circuits. Therefore, how to design CMF with high performances, which can not only suppress common-mode noise, but also ensure effective and lossless transmission of differential signals, has become one of the hotspots that need to be studied urgently in high-speed interconnection.
There have been some methods for designing CMF. The common-mode choke [2]- [4] using ferrite material is employed to suppress the common-mode noise of differential signals. However, it is not suitable for gigahertz differential signals. Low-temperature co-fired ceramic (LTCC) filters [5] also can be used to reduce the common-mode noise, but it may increase the fabrication complexity and costs.
Recently, there are some reported CMFs in the differential signals based on defected ground structure (DGS) [6]- [8]. DGS method can realize good performances of suppressing common-mode noise in a wide frequency band by interfering the common-mode current on the ground. The fractional bandwidth of the stopband over 15 dB can reach 87% and 118% in literatures [6] and [7], respectively. However, DGS method cannot be implemented in multilayer structure because the performance will deteriorate if there is a metal plane under DGS structure [1]. Electromagnetic bandgap (EBG) [9]- [18] is another common CMF structure which can be used in multilayer structure. In [9] and [10], EBG filters are introduced to reduce the common-mode noises of differential striplines. Traditional EBG structure of mushroom and planar EBG are implemented for the suppression of common-mode noise of differential signals in [12] and [13], respectively. Literature [15] has reported a removable CMF based on EBG. Nevertheless, EBG filter is limited in applications because it usually cannot realize a wideband commonmode noise reduction. In addition, there are some literatures with a combination of aforementioned methods. Commonmode noise suppression below −20 dB is obtained in the frequency band of 3.3-7 GHz with EBG and DGS in [19]. In [20], [21], the fractional bandwidth of 34% and 98% in common-mode rejection are achieved using complementary split ring resonators (CSRR) and double slit complementary split ring resonator (S-DBCSRR) based on DGS, respectively. Chen et.al presented a CMF based on varactor-loaded slot-ring resonator on the ground [22]. Artificial transmission lines are used to reject dual-band common-mode noise in [29]. Similarly, they are not appropriate for multilayer structures due to the defected ground.
Besides, open stub grounded resonators are employed for rejecting the common-mode radiation and electromagnetic interference in [23]. In the same way, a simple CMF using quarter-wavelength open stub resonator is investigated comprehensively in literature [1], and the ultra-wideband common-mode noise rejection can be obtained using cascaded quarter-wavelength resonators with different size. Furthermore, [24] and [25] proposed the CMFs with periodically corrugated reference plane (PCRP) and inter-digital fingers for the common-mode noise rejection in high-speed differential signals, respectively. Common-mode noise rejection is realized for balanced bandpass filters in multilayer liquid crystal polymer technology by using folded stepped impedance resonator (SIR) and the proposed 4-cell commonmode rejection structure in [30].
In this article, a common-mode noise suppression filter for high-speed differential signals based on substrate integrated waveguide resonator (SIWR) is presented. To obtain an ultrawideband common-mode noise suppression, SIWR units with different size are cascaded. The fractional bandwidth of rejection band for the common-mode noise below −35 dB can reach over 86% and the common-mode noise suppression less than −30 dB can be obtained in the frequency band of 4.3-15 GHz. For further investigating the characteristic of the proposed CMF, the equivalent characteristic impedance circuit model of the proposed CMF is given to explain the principle by using the SDA, and the group delay in the frequency domain and the eye diagram in the time domain are studied to prove the effectiveness of the proposed structure. The detailed structure and equivalent circuit analysis of the proposed CMF unit are presented in section II. In section III, the characteristic is analyzed for the cascaded CMF units with different size. Then, the designed prototype is fabricated and measured, and the measurement results are discussed and compared with the simulated results in section IV, followed by conclusions in section V.

A. CMF UNIT STRUCTURE DESIGN AND WORKING PRINCIPLE
The schematic model of the proposed CMF unit is presented in Fig. 1. The CMF unit consists of three layers. The differential microstrip lines are on the top layer. The SIWR structure is placed under the differential microstrip lines, and three columns of vias are used to connect the second layer and the third layer (the ground). The dielectric substrate FR4 (ε r = 4.4 and tan δ = 0.02) has a thickness of 1.1 mm and the SIWR structure has a height of 1 mm. As is known, most of differential signals propagate close to the plane that differential microstrip lines are located due to reverse voltages, while most of common-mode noises propagate between the differential microstrip lines and the ground. Based on these propagation characteristics for differential signals and common-mode signals, a substrate integrated waveguide structure is introduced to realize the common-mode noise suppression. SIWR structure has the similar characteristics as rectangle waveguides resonators, and the standing wave pattern will be formed inside when the working frequency is equal to the resonant frequency of resonators. Therefore, the common-mode noises will be rejected around the resonant frequency of SIWR because most of common-mode noises pass through the SIWR structure. On the other hand, there is little impact on the differential signals due to that most of waves propagate close to the plane that the differential microstrip lines are located for differential signals. Fig. 2 (a) and (b) show the electric field distribution of the proposed CMF at the common-mode resonant frequency of 8.9 GHz for even-mode and odd-mode, respectively. It can be seen that TE 110 mode is excited when even-mode signals propagate through the SIWR, while there are almost no interactions between SIW CMF and the coupled microstrip lines when differential signals are propagating.

Fig. 3 (a) and (b)
show the equivalent circuits of the proposed CMF unit for the odd-mode and even-mode, respectively. In the case of odd-mode, it is equal to place a perfect electric wall in the middle of differential microstrip lines so that short-circuit is formed here, which indicates that the second layer has the same potential as the ground. Therefore, for the odd-mode case, the impedance Z 0o and Z 0o l will be equivalent to the odd-mode impedances of coupled microstrip lines with the height of 0.1 mm and 1.1 mm, respectively. Similarly, for the even-mode case, corresponding open-circuit will appear in the middle of differential microstrip lines where a perfect magnetic wall is placed. The odd-mode and even-mode characteristic impedances of coupled microstrip lines are presented in equations (1a) and (1b).
where ε re and Z c are the static effective dielectric constant and the characteristic impedance of single microstrip of width W , respectively. ε e re and ε o re denote effective dielectric constants for even and odd modes, respectively [31]. The values of Q 4 and Q 10 are given in literature [31].

C. CHARACTERISTIC IMPEDANCE OF BROADSIDE-COUPLED LINES
As shown in Fig. 3 (b), in the even-mode case, the interaction between the coupled microstrip lines and CMF can be represented by a broadside-coupled lines with one open-end. For obtaining the characteristic impedance of broadside-coupled lines in the equivalent circuit, spectral domain approach (SDA) is used here. It should be noted that the vias are not taken into account when using the SDA, as seen in Fig. 4, which is because we use the inductor L in the equivalent circuit of Fig. 3(b) to represent the effect of vias. The details of SDA was presented in [33], so we only give the essential steps here. The first step is to impose the boundary conditions at the interfaces along the z-direction in the space domain. We designate three regions, 0 < z < h 1 , h 1 < z < h, and h < z < h + t, corresponding to the index 1, 2 and 3 in Fig. 4, then the interface conditions to be satisfied can be expressed as follows: where ϕ i (y, z), i = 1, 2, 3 denote the potentials in three regions, ρ (y) and ρ s (y) represent the unknown charge distributions on the upper strip and lower strip, respectively. In addition, v (y) and ϕ 0 (y) are unknown potential distributions at the interfaces. Then the expressions (3a)-(3c) and (4a)-(4c) are transformed in the spectral domain by using Fourier transforms. On the other hand, when Fourier transformed, the Laplace equation for ϕ becomes: And the solutions of (5a) in each region arẽ Next, we substitute the expressions (6a)-(6c) into the transformed expressions in the spectral domain of (3a)-(3c) and (4a)-(4c), and express A n , B s n , B c n , and C n in terms ofρ andρ s . The following equations will obtained G 11 k n ρ k n +G 12 k n ρ s k n =φ V 2 +φ 0 (7a) wherẽ We expand unknownρ andρ s in terms of linear combinations of known sets of basis functions as Finally, we can derive the following system of linear equations by applying Galerkin's method along with Parseval's relation.
whereρ i andρ sj are the basis functions, here we select the Chebyshev's polynomials of the first kind [34] as the basis functions taking the edge effect into consideration. V 1 and V 2 represent the known potential on the upper strip and lower strip, respectively. To obtain accurate characteristic impedance, we need to set W and t infinity because our proposed structure is not the shielded structure as the literature [33] mentioned. Then the quasi-static capacitance per unit length for c-mode (the upper and lower strips are excited by equal potential, V 1 = V 2 = 1) and π-mode (the upper and lower strips are excited by opposite potential, VOLUME 8, 2020 V 1 = −V 2 = 1) can be obtained by solving the equation (14).
Finally, the characteristic impedances of equivalent circuit for even-mode case are computed by the following the equations [33]: where c denotes the light velocity in free space, C air is the line capacitance per unit length for the hypothetical problem for which ε r =1 in the same structure. Consider one CMF unit where the geometry parameters w, w 1 , w 2 , s, d, r, l and W are 0.35 mm, 2.5 mm, 6 mm, 0.1 mm, 0.5 mm, 0.8 mm, 1.75 mm and 10 mm, respectively. Corresponding odd-mode and even-mode characteristic impedances Z 0o , Z 0o l , Z 0e l for the equivalent circuit are 28.4 , 44. 3 and 166.8 , respectively, by using equation (1a) and (1b). And c-mode and π-mode characteristic impedances for the broadside-coupled lines are 17.7 and 122.8 by using abovementioned SDA method, while the inductor L is approximately equal to 0.45 nH by using the equation (2) [32]. The proposed CMF unit is simulated with the software of CST Microwave Studio, and Fig. 5 depicts the comparison of the full-wave and equivalent circuit results for the CMF unit, which shows a good agreement.  Fig. 6 presents the insertion loss of common-mode signals when the CMF unit includes one, two or three columns of vias, respectively. It is evident that the common-mode noise suppression becomes better with the increase of column number, here, we select three columns of vias for the CMF unit.  The insertion losses of differential and common-mode signals when the values of (a) w 2 are 6 mm, 7 mm and 8 mm while h 1 is 1mm (b) h 1 are 0.8 mm, 0.9 mm and 1 mm while w 2 is 6mm. Fig. 7 (a) and (b) show the insertion loss of the differential and common-mode signals with the different values of w 2 and h 1 , respectively. It can be observed that the resonant frequency point shifts to lower frequency with the increase of the variables w 2 or h 1 . Moreover, the common-mode noise suppression depth will be smaller when the value of h 1 decreases, therefore, the height of SIWR structure is set to 1 mm. The equations of the CMF unit resonant frequency are summarized for predicting the common-mode noise rejection characteristic in advance:

D. PARAMETERS ANALYSIS
where ε and µ denote the permittivity and permeability of the substrate, respectively, and w e is the equivalent width of the SIW structure [26].

III. WIDEBAND CMF ANALYSIS
For obtaining wideband common-mode noise suppression, the cascaded CMF units with different resonant frequencies of common-mode is an effective solution [27].
A. TWO CASCADED CMF UNITS ANALYSIS Fig. 8 shows the simulated insertion loss of differential signals and common-mode noise with two cascaded CMF units, and it can be clearly seen that the common noise suppression bandwidth is broaden when two CMF units with different SIWR width are cascaded. Besides, the effects of the gap between two CMF units on the common-mode noises rejection are depicted. The gap must be large enough to allow the common-mode signals current to return through SIWR structure so that the larger depth of common-mode rejection can be achieved [1]. As shown in Fig. 8, when the gap exists, the suppression of common-mode noises is better than no gap, but the suppression characteristic is not changed much when the value of g is larger than 0.2 mm. Accordingly, the value of g is set to 0.2 mm. Moreover, the comparison of the equivalent circuit results and the full-wave simulation results for two cascaded CMF units is presented in Fig. 8, which shows a good agreement. On the other hand, the insertion loss of differential signals is less than 1.2 dB up to 10.5 GHz as depicted in Fig. 8. Moreover, to keep good signal integrity for the differentialmode signals, in addition to small insertion loss, the group velocity is also a very important indicator [6]. Fig. 9 depicts the group delay comparisons with and without two cascaded common-mode filter units, and it can be seen that there are almost no effects on the group delay characteristic with the addition of the two-unit CMF. Therefore, signal integrity of differential signals is preserved.

B. ULTRA-WIDEBAND CMF ANALYSIS IN FREQUENCY DOMAIN
As shown in Fig. 10, eleven CMF units with different SIWR widths are cascaded to realize an ultra-wideband commonmode noise suppression. The values of eleven CMF units width are from 4 mm to 14 mm. Fig. 11 presents the insertion loss comparisons of differential and common-mode signals with and without the wideband CMF. We can see that the common-mode noise rejection below −35 dB is achieved from 4.5 GHz to 11.4 GHz, and the fractional bandwidth of rejection band for the common-mode noises below -30 dB can  reach over 110%. For the differential signals, it can be seen that the insertion loss is less than 4.2 dB up to 15 GHz and there is almost no degradation compared with the reference board without CMF structure. The group delay comparisons for differential signals with and without the wideband CMF are depicted in Fig. 12. The group delays of differential signals of the reference board and that of CMF board with eleven SIW units are approximately 0.235 ns and 0.245 ns, respectively, at the central frequency of 7.5 GHz, which indicates that a good signal integrity of the differential signals is maintained because of small insertion loss and group velocity for differential signals when they pass through the ultra-wideband CMF.

C. ULTRA-WIDEBAND CMF ANALYSIS IN TIME DOMAIN
To verify the common-mode suppression characteristic of CMF in the time domain, a signal skew is created by designing a delay line of 4 mm [6], as shown in Fig. 13. Fig. 14 (a) and (b) show the common-mode and differentialmode voltage comparisons received at Port 2 when  differential-mode signals are excited at Port 1 with the reference board and CMF board, respectively. The common-mode noise is defined as half of the sum of voltages received at two output ports of differential traces [6]. Therefore, in the ideal case, the common-mode noise will not be excited due to that voltages received at two output ports have equal amplitude and inverse phase. However, the common-mode noise will be produced due to the change of amplitude and phase of voltages received when the signal skew is introduced. Fig. 14 (a) depicts that the peak-to-peak common-mode voltages of 0.146 V and 0.0197V are obtained, respectively, using the reference board and CMF board. Approximately 86.5% amplitude common-mode noise suppression is realized. For differential signals in the time domain, it can be seen that two curves almost overlap each other, which means that the signal integrity of differential signals is retained. It can be explained that most of waves propagate close to the plane that differential microstrip lines are located for differential signals. Fig. 15 (a) and (b) present the simulated eye diagrams of differential signals at data ratio of 10 Gb/s with the reference board and CMF board, respectively. The maximum eye height, maximum eye width and jitter are three important indicators to evaluate the quality of eye diagrams [6], and they are given in Table 1 for the CMF board and the reference board. It can be seen that the larger eye width and height are obtained with the CMF board, while there is smaller jitter than the reference board, which verifies that the signal integrity of differential signal is preserved when the CMF is introduced.

IV. FABRICATION AND MEASUREMENTS
In order to validate the performance of the proposed common-mode noise suppression filter, the proposed prototype is fabricated as shown in Fig. 16. The prototype was fabricated using printed circuit board technology. The proposed structure comprises of top differential microstrip lines, a substrate with buried SIWR structure, and a metal ground. The substrate used here is FR4 (ε r = 4.4 and tan δ = 0.02) with a thickness of 1.1 mm. The thickness of top metal patches and ground is 0.035 mm. It is worth noting that four right-angle bent patches are introduced to connect with differential microstrip lines for measuring the fabrication using SMAs. In addition, the right-angled triangles are removed at right-angled bends to decrease the losses that the bend discontinuity introduces [28].
Two ports of a vector network analyzer (Agilent N5227A) are connected with fabricated prototype, while another two ports of the fabrication are connected with 50 matching loads to measure the characteristic in frequency domain. Fig. 17 shows the simulated and measured result comparisons of differential-mode and common-mode signals, and it can be seen that the common-mode stopband below −25 dB is achieved from 4.4 GHz to 14.4 GHz, while the measured insertion loss of differential signals is less than 4.7 dB up to 15 GHz. The main reason that insertion loss increases compared with the simulated results without right-angled bends but with CMF may attribute to the attenuation of differential signals at the right-angles bends, which can be FIGURE 17. The simulated and measured results comparisons of (a) common-mode (b) differential-mode signals (RB: right-angled bends).  proved by the good agreement between the simulated and measured results with right-angled bends and CMF. On the other hand, fabrication tolerance also may cause the increase of the insertion loss.
To measure the common-mode noises suppression property in time domain, arbitrary waveform generator (Tektronix 7122C) and digital serial analyzer (Tektronix 71604) are used, as shown in Fig. 18. Two-way identical signals are generated by arbitrary waveform generator to connect with two input ports of CMF board, and we select the sinusoidal waves with the magnitude of 0.5 V and the frequency of 5.5 GHz here. Another two ports of CMF board are connected with two channels of digital serial analyzer. Common-mode signals are defined with the voltage sum of two differential microstrip lines [1]. Fig. 19 shows the measured results of common-mode signals received at output ports with CMF board when two input ports are excited with  ideal sinusoidal waves. The peak-to-peak common-mode signals are 2 V for input ports, while this value is decreased to 0.2 V when the CMF is introduced. 90% amplitude rejection is realized for common-mode noises, which proves the validation of the proposed CMF.
The comparison of this article with previous research is presented in Table 2. Our proposed design has advantages of wide bandwidth and suppression depth for common-mode rejection.

V. CONCLUSION
A common-mode noise suppression filter for high-speed differential signals based on substrate integrated waveguide resonators (SIWR) is presented in this article. The proposed common-mode filter (CMF) is comprised of cascaded SIWR units. The common-mode noise is decreased more than 25 dB from 4.4 GHz to 14.4 GHz and −15 dB rejection band is obtained in the frequency band of 4.2-17.2 GHz after the CMF is introduced. Moreover, the insertion loss and the group delay in the frequency domain and common-mode noises amplitude suppression and eye diagrams in the time domain are investigated to validate the effectiveness of the proposed CMF. The prototype is fabricated to verify the validity of the proposed structure, and the measurement results show good agreement with the simulation results. Based on these characteristics, the proposed CMF can be a potential candidate for common-mode noises suppression in high-speed circuits.