Design of a Novel Ultra-Wideband Common-Mode Filter Using a Magnified Coupled Defected Ground Structure

Abstract

An ultra-wideband common-mode (CM) filter for a gigahertz (GHz) data rate signal is proposed in this paper. The proposed filter was designed only on the printed circuit board (PCB) ground plane; no additional components wererequired. We took advantage of producing second-order transmission zero by an asymmetrical magnified coupled DGS to extend the suppression bandwidth. Full-wave simulations and equivalent circuit models of the DGS resonator were established to predict the suppression performance. The measured differential-mode insertion loss (S_dd21) from direct current (DC) to 12.35 GHz was obtained within the −3 dB definitionin the frequency domain. The CM noise was suppressed by more than10 dB in the frequency range from 2.9 GHz to 16.2 GHz. The fractional bandwidth (FBW) reached 139.3%. The proposed filter blocked 62.3% of the CM noise magnitude in the time domain measurement. In addition, the eye diagram measurement proved that good transmission quality was maintained. The proposed filter can be widely implemented to reduce electromagnetic interference (EMI) in radio frequency (RF) andWi-Fi (wireless fidelitystandard) 5 and 6E wireless communication applications.

1. Introduction

At present, electronic products tend to operate at high data rates and complexities. Transmission at a GHz data rate is widely used in modern digital circuits, such as serial advanced technology attachment (SATA) III/6 Gbit/s, universal serial bus (USB) 3.2/10 Gbit/s, and peripheral component interconnect express (PCIe or PCI-e) 4.0/16 GT/s. Differential transmission is the most suited for high-speed data raterequirements. Differential pairs should be symmetrical to maintain good signal integrity (SI) and avoid electromagnetic interference (EMI). However, asymmetric routing is unavoidablein practical situations, even when using smooth bend structures [1], as it results in common-mode (CM) noise because of an imbalanced amplitude or a timing skew on the differential signal paths. CM noise may generate unwanted radiation and cause severe EMI problems, which results in a decreased performance of high-speed circuits [2]. Therefore, we expect the common-mode filter to maintain a good SI and EMI to avoid interfering with the sensor signals in the system.

The conventional method is to use CM choke coils with high-permeability ferrite cores [3] or compact CM filters that were built on multilayer, low-temperature, co-fired ceramics [4]. They suppress the CM noise in the megahertz frequency domain. However, CM chokes do not work well in the frequency domain above 2 GHz. Furthermore, they are not practical for compact circuit designs.

The differential-mode bandpass filter (BPF) and CM noise bandstop filter are better suited for GHz digital circuit systems; several methods are discussed in [5,6,7,8,9,10,11,12,13,14,15,16,17,18]. First, the stopband-extended balanced BPF [5] and balanced dual-band BPF [6] were proposed as design concepts of the resonator for differential signaling. They achieved narrow passbands using adequately designed resonators. Next, wideband or ultra-wideband differential-mode BPFs were proposed in [7,8,9]. The results showed that differential-mode BPFs were limited in high-speed digital circuit applications because the BPFs did not pass low-frequency terms.

In addition, the authors of [10,11,12,13,14,15,16,17,18] proposed many CM suppression filter designs using defected ground structures (DGSs). The primary design concept differed from the differential-mode BPF introduced earlier; CM filter designs can pass both passband and low-frequency differential signals. Theoretically, the differential signals were propagated on two coupled microstrip lines in the odd mode. The signal current traveled through one trace and returned through the other trace. In other words, the DGS on the ground plane was negligible in the odd propagation mode because the return current passed through the opposite line of the coupled microstrip line. On the other hand, the CM noises were propagated in the even mode; the return current of the CM noises flowed through the ground plane. Therefore, we designed an inductance (L) and capacitance (C) resonant circuit using the DGS on the ground plane. It acted as an ideal open circuit and reduced the magnitude of CM noise because the DGS blocked the return current.

First, a dumbbell-shaped DGS in [10] obtained a bandstop frequency range from 3.3 GHz to 5.7 GHz using a −20 dB definition. In [11], quarter-wavelength open-circuit stub resonators with 8.5 mm and 6.5 mm lengths achieved a broadband-frequency-range performance from 4.27 GHz to 8.2 GHz using a −20 dB definition.

Next, DGSs in [12,13,14,15,16,17] obtained a bandstop range using a −15 dB definition. The DGS in [12] used one H- and two C-shaped units to achieve a bandstop frequency range of 3.68 GHz to 8.43 GHz. Similarly, the DGS in [13] obtained a bandstop frequency range of 5.4 GHz to 11.4 GHz. In [14], a CM suppression filter design using two quarter-wavelength resonators in multiple sets of differential pairs achieved a bandstop frequency range of 3.75 GHz to 6.95 GHz. The authors of [15] proposed a reconfigurable filter based on three varactor-loaded compactDGSs, in which the bandstop frequency range was adjustable from 1.8 GHz to 2.9 GHz and from 2.9 GHz to 8.1 GHz. In the design described in [16], the authors symmetrically etched the DGS filter using a UH-shaped patterned ground plane to form three mutually coupled resonators for wideband CM noise suppression. It effectively reduced the CM noise in the frequency range from 3.6 GHz to 9.1 GHz. In [12,13,14,15,16], these designs took advantage of a simple structure and a low fabrication cost, but none could achieve an ultra-wide bandstop frequency range, even with three DGS units. Furthermore, the authors of [17] designed a three-pole DGS filter to reduce the CM noise in the frequency range from 3.2 GHz to 12.4 GHz. However, the physical size of the filter was 10 mm × 10 mm, which is not practical for a compact circuit design. Details of the CM suppression filters are listed in

Table 1. Details of the bandstop filters.

Ref.	fL (GHz)	fH (GHz)	fC (GHz)	FBW (%)
[12]	3.68	8.43	6.1	78.4
[13]	5.4	11.4	8.4	71.4
[14]	3.75	6.95	5.35	59.8
[15]	1.8	2.9	2.35	46.8
	2.9	8.1	5.5	94.5
[16]	3.6	9.1	6.35	86.6
[17]	3.2	12.4	7.8	117.9

, including the lower frequency (f_L), upper frequency (f_H), central frequency (f_C), and fractional bandwidth (FBW), where the FBW is defined as the absolute bandwidth divided by the central frequency and is expressed as a percentage of the central frequency. It is given by [19]

$$\mathrm{F}\mathrm{B}\mathrm{W}=2\times \frac{f_1-f_2}{f_1+f_2}$$

(1)

where f₁ and f₂ are the upper frequency (f_H) and lower frequency (f_L) of the stopband, respectively.

After that, CM suppression filters in [18,19,20] obtained a bandstop range using a −10 dB definition. In CM rejection filters based on a complementary split-ring resonator design [18], the authors proposed three glide symmetry implementations to achievea maximum FBW of 26.8%. A reconfigurable common-mode (CM) filter with a wide tunable bandwidth and frequency range was proposed in [19]. It obtained three tunable CM suppressions of frequency range from 1.9 to 3 GHz, 2.5 to 5.9 GHz, and 3.3 to 7 GHz, achieving a maximum FBW of 75.5%. In the enhanced coupled DGS design [20], the filter used only two C-shaped DGSs to achieve wideband CM noise suppression. Two C-shaped DGSs were the same size and in opposite directions on the ground plane and were symmetrical to the centerline of the differential microstrip. The simulation results for each half-structure indicated two resonant frequenciesclose to 8 GHz. The enhanced coupling mechanism of the two C-shaped DGSs shifted the first-order resonant frequency to 4.5 GHz and the second-order resonant frequency to 7 GHz. They suppressed the CM noise in the frequency range from 3.7 GHz to 10.8 GHz using the definition of −10 dB, as shown in the simulated result; the stopband FBW reached 97.9%. The physical sizes were 7 mm × 7 mm. However, the simulated results showed that the second-order transmission zero did not bring an extended stopband to suppress the CM noise in the higher-frequency domain due to an insufficient coupling magnitude between the two DGS units. As an extension design of [20], we propose an ultra-wideband CM suppression filter with an asymmetrical magnified coupled DGS in this paper. We take advantage of the second-order transmission zero produced by the asymmetrical magnified coupled DGS, which provides a more pronounced coupling effect than [20].

Next, the proposed CM suppression filter’s design details are presented in Section 2, including full-wave simulations using high-performance electronic design automation (EDA) software ANSYS HFSS 2022 R1 and equivalent circuit modelsusing the circuit simulation tool Agilent ADS. Section 3 presents measurements to validate the simulated results, including frequency and time domain measurements. Section 4 presents discussions. Finally, the conclusion is providedin Section 5.

2. Methods

2.1. Full-Wave Simulation

The ultra-wideband CM suppression filter was simulated on a standard FR4 (Ɛr = 4.4) substrate; the loss tangent was 0.02. The printed circuit board (PCB) thickness was 1.035 mm. We used 1 oz copper on the top layer and layer 2, where layer 2 was ground plane. The computer configurations include Intel i7 CPU, 8 GB RAM, and 500 GB solid-state drive (SSD).

Figure 1 shows the PCB stack-up. Two microstrip lines were on the top layer; their width (W) and spacing (S) were 0.18 mm and 0.36 mm, respectively. We designed W and S to meet a 100 Ω differential pair to maintain good SI in the differential mode. Figure 2 shows the PCB top view. Two DGS units were placed close to each other on the ground plane to form long and narrow bridges on that plane. The detailed geometry parameters of the DGS resonators are also summarized in

Table 2. Detailed list of geometry parameters.

Parameters	Value	Parameters	Value	Parameters	Value	Parameters	Value	Parameters	Value
W	0.18	S	0.36	t	0.035	h1	0.1	h2	0.865
Wt	5.2	Ws	2.5	Wb	0.2	Lt	5.04	Wg1	0.2
Wb1	2.4	Wb2	4.6	Lb1	0.56	Lb2	0.4	Wg2	0.3

Unit: mm.

.

We first simulated the two half-structure DGS units of the proposed suppression filter using ANSYS HFSS; they are referred to as “Left DGS” and “Right DGS” to simplify the following analysis. Next, we simulated the proposed ultra-wideband CM suppression filter.

Figure 3 demonstrates the full-wave simulations of the differential-mode insertion loss (S_dd21) by the blue curve and the common-mode insertion loss (S_cc21) by the red curve in the Left DGS. From the S_cc21 simulated result, we obtained a −3 dB cut-off frequency (f_CL) at 2.72 GHz and a resonant frequency (f_0L) at 7.3 GHz.

Similarly, Figure 4 shows the full-wave-simulated S_dd21 and S_cc21 in the Right DGS. The simulation results of the −3 dB cut-off frequencies f_CR1 and f_CR2 of S_cc21 were 2.6 GHz and 9 GHz, respectively; the resonant frequencies of the first-order frequency (f_0R1) and second-order frequency (f_0R2) of 6.6 GHz and 13.7 GHz, respectively, were also obtained.

Finally, Figure 5 shows the S_dd21 and S_cc21 of the proposed suppression filter using the magnified coupled DGS. Three resonant frequencies, f₀₁, f₀₂, and f₀₃, were identified, which were 3.2 GHz, 10.3 GHz, and 14.2 GHz, respectively. Since the two DGS units, the Left DGS and the Right DGS, were placed close to each other to produce a mutual coupling effects, it was easy to determinethe frequency separation and the ultra-wide stopband. All the frequencies of the Left DGS, the Right DGS, and the proposed suppression filter are listed in

Table 3. Cut-off and resonant frequencies of Left DGS, Right DGS, and the proposed suppression filter.

Left DGS	fCL	2.72	f0L	7.3
Right DGS	fCR1	2.60	fCR2	9.0	f0R1	6.6	f0R2	13.7
The proposedfilter	f01	3.20	f02	10.3	f03	14.2

Unit: GHz.

.

2.2. Circuit Simulation

In this section, we report the results of characteristic frequencies to derive the circuit parameters. We built the equivalent circuit model for the Left DGS, the Right DGS, and the proposed CM filter in Agilent ADS, represented to be consistent with the full-wave simulation results.

We considered characteristic impedance (Z_even) in an even-mode cascading parallel LC circuit to the ground plane when the CM noise passed through to the DGS. Then, we could extract the equivalent circuit parameters from the simulation results in Section 2.1. First, we modeled a parallel LC-equivalent circuit from a transmission zero in the Left DGS. The parameters of the parallel LC resonator were derived by the resonant frequency (f_0L) of 7.3 GHz and the −3 dB cut-off frequency (f_CL) of 2.72 GHz. We calculated the parameters of the parallel capacitance (C) and inductance (L) using Formulas (2) and (3), as given by [21],

$$C=\frac{1}{4\pi \times Z_{even}}\left(\frac{f_C}{f_0{}^2-f_C{}^2}\right)$$

(2)

$$L=\frac{1}{4{\pi }^2{f}_0{}^{2}C}$$

(3)

since

$$f_0=\frac{1}{2\pi \sqrt{L\times C}}$$

(4)

The equivalent circuit model of the Left DGS is shown in Figure 6. The even-mode impedance Z_even equaled 49.46 Ω. The equivalent circuit model of the Left DGS resulted in the following parallel capacitance and inductance parameters: C_L1 and L_L1 were 0.095 pF and 4.98 nH, respectively. Figure 7 shows the comparison of the full-wave simulation parameter S_cc21 for the red curve and the equivalent circuit model for the black curve.

Similarly, the equivalent circuit model of the Right DGS is shown in Figure 8. It consists of two LC elements in parallel, since two transmission zeros were obtained from the Right DGS simulation. We obtained the circuit parameters C_R1, C_R2, L_R1, and L_R2, which were 0.114 pF, 0.136 pF, 5.12 nH, and 0.99 nH, respectively. Figure 9 shows the comparison of the insertion loss of the full-wave simulation and the equivalent circuit model.

Following this, we used the general formulation (5) for extracting the coupling coefficient k, regardless of whether the coupling was electric, magnetic, or mixed; k_x is the mixed coupling coefficient and is given as Formula (6), where k_m and k_e are the magnetic and electric coupling coefficients, respectively. The coupling coefficient k is given by [22].

$$k=\pm \frac{1}{2}\left(\frac{f_{02}}{f_{01}}+\frac{f_{01}}{f_{02}}\right)\sqrt{{\left(\frac{f_{p2}{}^2-f_{p1}{}^2}{f_{p2}{}^2+f_{p1}{}^2}\right)}^2-{\left(\frac{f_{02}{}^2-f_{01}{}^2}{f_{02}{}^2+f_{01}{}^2}\right)}^2}$$

(5)

$$k_x=k_e-k_m$$

(6)

We analyzed the coupling characteristics of the DGS resonator using a single-ended microstrip line model [21], as shown in Figure 10. The peak frequencies corresponding to the resonant characteristics are obtained by S21 simulation in Figure 11; three peak frequencies, f_p1, f_p2, and f_p3, were at 4.9 GHz, 7.7 GHz, and 13.1 GHz, respectively. In addition, we obtained the resonant frequencies of the Left DGS and the Right DGS—6.6 GHz, 7.3 GHz, and 13.7 GHz for f_0R1, f_0L, and f_0R2, respectively—as reported in Section 2.1.

The coupling coefficients k_x1 and k_x2 of the asynchronously tuned coupled resonators were obtained as 0.413534 and 0.612251, respectively, for which k_x is a crucial design parameter. Using k_x and Z_even, we built the equivalent circuit model of the proposed suppression filter. Figure 12 shows the equivalent circuit model of the proposed suppression filter. Figure 13 compares the insertion loss of the equivalent circuit model and the full-wave simulation. Finally, we summarize the detailed parameters of the equivalent circuit model in

Table 4. Parameters of the equivalent circuit model.

Zeven	49.46 Ω	CL1	0.095 pF	LL1	4.98 nH
CR1	0.114 pF	LR1	5.12 nH	CR2	0.136 pF	LR2	0.99 nH
fp1	4.9 GHz	fp2	7.7 GHz	fp3	13.1 GHz
f0R1	6.6 GHz	f0L	7.3 GHz	f0R2	13.7 GHz
kx1	0.413534	ke1	0.202218	km1	0.211316
kx2	0.612251	ke2	0.261125	km2	0.351126

. From the results, this equivalent circuit model still effectively predicted the ultra-wide stopband produced by the proposed suppression filter.

3. Results

We fabricated four PCB test samples using a chemical etching process to verify our proposed design. The PCB size was 60 mm × 40 mm. First, two PCBs are shown in Figure 14a,b: a reference board with a solid ground plane and a proposed filter board. As shown in Figure 14b, the proposed filter was located in the center of the PCB. Later, we used the Keysight E5071C ENA Vector Network Analyzer to measure the S-parameters in the frequency domain. We also measured and observed the differences in the eye diagrams in the time domain. Additionally, we measured and observed the noise magnitude for time-domain performance verification using another two PCBs with a 5 mm delay line, as shown in Figure 15a,b.

3.1. Frequency-Domain Performance

As shown in Figure 16, we obtained the S_dd21 measurement from DC to 12.35 GHz within the −3 dB definition. In addition, the CM noise stopband is shown as the S_cc21 measurement. The frequency range was from 2.9 GHz to 16.2 GHz using a −10 dB definition.

3.2. Time-Domain Performance

In the following, we also used an eye diagram and a CM noise magnitude (V_common) measurement to verify the capability of the proposed filter in the time domain. We measured the eye diagram to verify the proposed suppression filter that maintained good SI for differential signal transmission. First, we excited an 8 Gbps signal to ports 1 and 2 with a 2⁷−1 pseudo-random binary sequence (PRBS), where the amplitude was ±0.5 V and the rise time was 50 ps. The eye diagram measurement is shown in Figure 17 from ports 3 and 4.

Table 5. Detailed parameters of the eye diagram.

	Eye Height	Eye Width	Timing Jitter
Reference Board	807.8 mV	117.4 ps	3.125 ps
Filter Board	762.3 mV	116.8 ps	2.344 ps

summarizes the detailed parameters of the eye diagram, including the eye height, width, and timing jitter. As shown by the results, this system still maintained a good transmission quality, although there was a small amount of degradation on the filter board measurement.

Furthermore, we excited CM noise to one of the differential lines with an implemented 5 mm delay line using a two-step function to measure the CM noise magnitude. Figure 18 shows the CM noise magnitude measurements for the reference and the proposed suppression filter boards with a 5 mm delay line. The results showed that the peak voltage was 138 mV and 52 mV, respectively. The measurement results of the CM noise showed that the proposed filter suppressed 62.3% of the magnitude.

4. Discussion

A parallel resonant circuit stores circuit energy in the inductor’s magnetic field and the capacitor’s electric field. Currents through inductors and capacitors are always equal and opposite. We can adjust the geometry parameters of the capacitor (W_g1) and inductor (W_b, W_b1, and W_b2) in Figure 2 to obtain the resonant frequency. The smaller W_g1 has larger capacitance. Thinner W_b or longer W_b1 and W_b2 produce larger inductance. In addition, larger capacitance or inductance leads to lower frequency from Formula (3) in Section 2.2. As seen in Figure 7, Figure 9, and Figure 13, the S_cc21 of the equivalent circuit model agrees very well with the full-wave simulation result. It shows differences in the high-frequency domain since the full-wave simulation is realistic and different from the equivalent circuit model; it should be considered in additional parasitic capacitances and inductances, such as PCB vias. In addition, the equivalent circuit model does not include some distribution effects, such as complex boundary conditions.

In Section 2.2, we quickly predict the first- and second-order transmission zero using the circuit simulation tool Agilent ADS. The Left and Right DGS are considered asynchronously tuned coupled resonator circuits [22] because two DGSs obtain three different resonant frequencies. The coupling coefficient changes and affects the frequency characteristics because of the stored electromagnetic field distributions. In other words, the bandwidth is extended due to the asynchronously tuned coupling.

According to the S_cc21 measurement in Section 3.1, from 2.9 GHz to 16.2 GHz, the fractional bandwidth (FBW) of the proposed design reaches 139.3%, where the stopband’s central frequency is 9.55 GHz. The filter’s physical size is 5.04 mm × 5.2 mm. The filter’s electrical size is only 0.292 λ_g × 0.302 λ_g, where λ_g is the guided wavelength of the stopband central frequency. The guided wavelength is given by

$${\lambda }_g=\frac{{\lambda }_0}{\sqrt{{\epsilon }_{re}}},$$

(7)

where λ₀ is the free space wavelength at operation frequency. The effective dielectric constant (${\epsilon }_{re}$) is obtained by the dielectric constant (${\epsilon }_r$), PCB thickness (h), and trace width (W). This work fallsunder the case of W/h ≧ 1; the ${\epsilon }_{re}$ is given by [23],

$${\epsilon }_{re}=\frac{{\epsilon }_r+1}{2}+\frac{{\epsilon }_r-1}{2}\frac{1}{\sqrt{1+12\frac{h}{W}}}.$$

(8)

The measured value has ripples and attenuations in Figure 16, possibly due to impedance mismatch between the PCB and connector; additionally, there are tolerances in PCB manufacturing, and the FR4 substrates have limited performance at high frequencies above 10 GHz. However, S_cc21 still shows a good agreement between the measurements and simulations. This demonstrates that the CM noise is suppressed in an ultra-wide stopband.

We asymmetrically etched the DGS filter in the proposed filter to form three mutually coupled resonators, resulting in a pronounced ultra-wideband suppression effect.

Table 6. Detailed comparison with related DGSs.

	[17]	[18]	[19]	[20]	This Work
Physical size (mm × mm)	10 × 10	—	9.2 × 19	7 × 7	5.04 × 5.2
Electrical size (λg × λg)	—	—	0.22 × 0.46	0.305 × 0.305	0.292 × 0.301
Area	100 mm2/ —	—/ —	174.8 mm2/ 0.1012 λg2	49 mm2/ 0.0929 λg2	26.21 mm2/ 0.0881 λg2
Scc21 < −10 dB (GHz)	3–13	2.4–3.15	1.9–7.3	3.7–10.8	2.9–16.2
FBW	125%	Max. 26.8%	Max. 75.5%	98%	139.3%

lists the detailed comparison with [17,18,19,20]. The proposed work reveals the smallest physical size; compared with [19], the physical size is reduced by 85%. The area at the stopband central frequency is the most compact. In addition, the CM noise suppression band is the most extensive range, and a high frequency reaches 16.2 GHz. Compared with previous research [20], the FBW is increased by 41.3%.

Table 7. Comparison of the noise magnitude.

	[20]	This Work
Reference Board	170 mV	138 mV
Filter Board	98.6 mV	52 mV
Suppression Ratio	42%	62.3%

compares the noise magnitude with previous research. Compared with [20], the suppression ratio increases by 20.3%. This demonstrates that the proposed suppression filter possesses a more excellent CM noise-reduction capability.

5. Conclusions

This paper proposes an ultra-wideband CM noise suppression filter using a magnified coupled DGS. We appropriately designed the resonant frequency using an asynchronously tuned coupled resonant circuit. In the frequency domain, the measurements demonstrated that the S_dd21 from DC to 12.35 GHz was measured within the −3 dB definition and that the CM noise could be reduced by more than −10 dB from 2.9 to 16.2 GHz. In addition, the FBW of the stopband reached 139.3%. In the time domain, the measurement of the CM noise magnitude was reduced by 62.3%.

Although most high-speed interfaces use stripline routing, we could still place the proposed filter near the connector. The proposed filter is characterized by having two simple geometry structures, no additional components, the most compact size on the PCB, and a considerable FBW. As far as we know, this is the first filter to achieve CM noise suppression exceeding 130% FBW in ultra-wideband. Finally, the proposed filter can be widely implemented to reduce the electromagnetic interference in RF and wireless communication applications with Wi-Fi 5 and 6E. In addition, it can be used in satellite and microwave telecommunication applications with the C and X bands, as part of the Ku band.