The Beauty of Symmetry: Common-mode rejection filters for high-speed interconnects and balanced microwave circuits

 The Beauty of Symmetry Common-mode rejection filters for high-speed interconnects and balanced microwave circuits 1Ferran Martín, 1Jordi Naqui, 2Armando Fernández-Prieto, 1Paris Vélez, 1Jordi Bonache, 2Jesús Martel, and 2Francisco Medina 1CIMITEC, Departament d’Enginyeria Electrònica Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain Corresponding author: [email protected] 2Grupo de Microondas, Universidad de Sevilla. Avenida Reina Mercedes s/n, 41012 Sevilla, Spain. E-mail: Med[email protected] Common-mode rejection filters operating at microwave frequencies have been the subject of intensive research activity in the last decade. These filters are of interest for the suppression of common-mode noise in high-speed digital circuits, where differential signals are widely employed due to the high immunity to noise, electromagnetic interference (EMI) and crosstalk of differential-mode interconnects. These filters can also be used to improve common-mode rejection in microwave filters and circuits dealing with differential signals. Ideally, common-mode stopband filters should be transparent for the differential mode from DC up to very high frequencies (all-pass), should preserve the signal integrity for such mode, and should exhibit the widest and deepest possible rejection band for the common mode in the region of interest. Moreover, these characteristics should be achieved by means of structures with the smallest possible size. In this article, several techniques for the implementation of common-mode suppression filters in planar technology are reviewed. In all the cases, the strategy to simultaneously achieve common-mode suppression and all-pass behavior for the differential mode is based on selective mode-suppression. This selective mode suppression (either the common or the differential mode) in balanced lines is typically (although not exclusively) achieved by symmetrically loading the lines with symmetric resonant elements, opaque for the common-mode and transparent for the differential mode (common-mode suppression), or vice versa (differential-mode suppression). SELECTIVE MODE SUPPRESSION IN BALANCED LINES Let us review the general principle to achieve selective mode suppression (common mode or differential mode) in balanced lines through symmetric resonators (which is the © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Accepted version. The final version is available at: DOI 10.1109/MMM.2016.2616180 main approach considered in this article). It is well known that a transmission line (either single-ended or balanced) loaded with a resonator coupled to it exhibits a stop band (transmission zero, or notch) at the fundamental resonance frequency (and eventually at higher-order harmonics). Signal propagation is inhibited at these frequencies because the injected power is reflected back to the source. However, depending on the topology of the symmetric resonator and the relative orientation between the resonator and the line, it is possible to prevent the appearance of resonance (and hence the notch in the transmission coefficient) [1], [2]. Let us consider a symmetric line loaded with a symmetric resonator (coupled to it) with its symmetry plane perfectly aligned with the symmetry plane of the transmission line, so that the structure is perfectly symmetric with respect to the bi-section midplane. If the symmetry planes of the line (for the considered mode, i.e., common mode or differential mode) and resonator (for the considered resonance frequency, i.e., fundamental or higher-order harmonic) are of the same electromagnetic nature (either electric or magnetic walls), the resonator is excited, the structure is resonant, and signal propagation is inhibited in the vicinity of the considered resonance frequency. Conversely, if the symmetry plane of the line is an electric wall and the one of the resonator is a magnetic wall, or vice versa, the resonator cannot be excited. The reason is that, due to perfect symmetry, the net electric and magnetic field components “illuminating” the resonator exactly cancel (i.e., the electric and magnetic fluxes over the resonator area are zero) if the symmetry planes of line and resonator are of different nature. Under these conditions, the structure is all-pass, at least in the vicinity of the resonance frequency under consideration. If the symmetry planes of the line and resonator are misaligned, and both elements are close enough, line-to-resonator coupling activates, and the resulting notch depth in the transmission coefficient is determined by the level of misalignment (this idea has been exploited for the implementation of various types of sensors and detectors based on symmetry properties [3]-[8]). For microstrip differential lines, either the common mode or the differential mode can be selectively suppressed while preserving the other mode unaltered (or almost unaltered) by aligning with the line a resonator exhibiting either a magnetic wall or an electric wall, respectively. This filtering functionality, referred to as selective mode suppression [9]-[11], is illustrated in Fig. 1(a) by considering a complementary split ring resonator (CSRR) [12] as a loading (coupled) element. Such a resonant element exhibits a magnetic wall at the fundamental resonance, and hence it inhibits signal propagation at that frequency for the common mode, whereas the line is transparent for the differential mode. Thus, CSRRs are useful for the implementation of common-mode suppression filters. Mode suppression can be reversed by loading the differential line, e.g., with split ring resonators (SRRs) [13] symmetrically placed at the upper metal level, between the pair of lines (Fig. 1b). The reason is that SRRs exhibit an electric wall at their symmetry plane at the fundamental resonance frequency [14],[15] (this resonator is the dual, or complementary, counterpart of the CSRR). The suppression of the differential mode may be of interest in certain applications, but this differential mode suppression phenomenon is beyond the scope of this article, which is primarily focused on common-mode suppression filters. Many other resonant elements can be used for selectively suppressing the common mode in differential lines, including magnetic and electric LC resonators [11], dumbbell-shaped resonators [16], C-shaped resonators [17], and folded slotted stepped impedance resonators. The application of some of these resonant elements to the implementation of common-mode rejection filters is reviewed in the article, where, typically, several resonators are cascaded in order to enhance the common-mode rejection bandwidth. Selective (common) mode suppression can be achieved by any type of structure (not necessarily resonant elements) acting as an efficient rejection filter for the common mode and preserving signal integrity from DC up to very high frequencies for the differential mode. COMMON-MODE REJECTION FILTERS Common-mode rejection filters may be implemented by loading the differential lines with lumped, semi-lumped or distributed elements insensitive to differential signals, but able to prevent the propagation of the common mode. Solutions that use common-mode chokes with high permeability ferrite cores have been proposed [18-20], but chokes represent a penalty in terms of size and frequency operating range, not being useful for high-speed and high-density systems. The main focus of this article is on bi-layer structures based on symmetric patterned ground structures (PGS) [11],[16],[17],[21]- [26]. Approaches based on multilayer or LTCC technology [27]-[35] provide compact solutions, but at the expense of higher fabrication costs and complexity (especially if vias are used [28]-[30]). Common-mode filters based on periodic structures (or electromagnetic bandgaps – EBGs [36], [37]) have been also proposed [38]-[42]. Among these filters, implementations where the transverse dimensions of the differential line are periodically modulated, leaving the ground plane unaltered, have been reported [41]-[42], but at the expense of a limited common-mode rejection bandwidth. COMMON-MODE FILTERS BASED ON PGS Four examples of common-mode suppression filters for differential microstrip lines, based on patterned ground structures (or defected ground planes), are discussed. The ground planes of the different implementations exhibit specific patterns that efficiently suppress the common-mode, leaving the differential-mode unaltered (or almost unaltered). Dumbbell-shaped PGS Slotted dumbbell resonators symmetrically etched in the ground plane of a microstrip line can be modeled, to a first order approximation, as series-connected parallel resonators [43]. These resonators are thus able to inhibit signal propagation in the vicinity of resonance. The symmetry plane of the line and resonator are magnetic walls, and this gives another interpretation to the stop band functionality of these lines, according to the symmetry considerations discussed before. By symmetrically etching slotted dumbbell-shaped resonators in a differential microstrip line, it is expected that the common-mode will be efficiently suppressed, while signal propagation for the differential-mode is preserved. Besides the previous explanation for selective mode suppression, based on symmetry considerations, it can also be argued that the resonant elements open the return current path through the ground plane for the common-mode, whereas the presence of resonators has negligible effect on the differential signals since a relatively small current density returns through the ground plane for such signals [16]. Regardless of the specific interpretation for selective common-mode suppression in differential lines loaded with slotted dumbbell resonators, such structures behave as efficient common-mode filters. Figure 2 depicts a specific common-mode filter topology and the frequency response [16]. The structure is able to efficiently suppress the common-mode with broad stopband in the GHz range (Fig. 2b), yet keeping good differential signal integrity. In addition, mode conversion from differential-mode to common-mode, also shown in the figure, is very small. In [16], the common-mode noise suppression capability of these dumbbell-shaped PGS structures was demonstrated in the time-domain by adding a delay line in one of the differential lines (see inset of Fig. 3). This delay line generates a signal skew which in turn excites the common mode in the differential line. By fabricating an identical structure with solid ground plane (reference board), the time domain responses to a differential signal can be compared. Two pulse trains of 800 mV peak-to-peak voltage and 8 Gb/s were differentially launched into port 1 and port 2 by the authors of [16], and the output waveforms were measured at port 3 and port 4 using a digital oscilloscope. The common-mode noise, Vcommon, defined as half of the sum of the measured voltage at these two output ports, revealed that the peak-to-peak output common-mode voltage for the reference board was 412 mV, whereas it was reduced to 64 mV by employing the dumbbell-shaped resonators (i.e., over 80% improvement was achieved), see Fig. 3. Thus, the common-mode filter based on these PGS structures is revealed to be efficient in rejecting the common mode while preserving the integrity of the differential signals. Measured differential eye diagrams not shown here, but depicted in [16], indicate that the eye diagram parameters are roughly the same in the structure of Fig. 2 and in the same structure with solid ground plane (indicating that the differential signal quality is not degraded when the common-mode filter is present). Complementary split ring resonator (CSRR) CSRRs, originally proposed for the implementation of epsilon-negative [12] or lefthanded [44] one-dimensional metamaterials [15,45], are useful resonators for the selective suppression of the common-mode in differential microstrip lines, as anticipated before. The first common-mode filters based on CSRRs were reported in [22],[23], where it was argued that for the differential-mode there is not a net axial electric field in the inner metallic region of the CSRR able to excite the resonators, whereas for the common-mode the electric field below the transmission lines is codirectional, and the CSRRs are excited (Fig. 4). In order to obtain a significant common-mode rejection bandwidth, several tightly coupled resonant elements are necessary. Moreover, it is necessary to enhance the coupling capacitance between the pair of lines and the CSRRs and to reduce the inductance and capacitance of the CSRR as much as possible. This enhances the stopband bandwidth of an individual resonator, providing a wide stop band for the common mode when several tightly coupled CSRRs are considered. As reported in [22],[23], the requirements to achieve small CSRR inductance and capacitance are wide slot-ring widths and separation. To enhance the coupling capacitance between the pair of lines and the CSRR, the lines must be as wide as possible, and hence as uncoupled as possible. Note that for a given differential-mode characteristic impedance, the width of the pair of lines increases with their separation. Finally, by closely spacing the CSRRs, and by using square-shaped or rectangular CSRR geometries, inter-resonator coupling is favored. The description of CSRR-loaded differential microstrip lines by means of a lumped element equivalent circuit model is very convenient for design purposes. However, CSRRs with wide slot-ring widths and separation cannot be considered to be electrically small. Nevertheless, by considering CSRRs with double slits (i.e., the so-called doubleslit complementary split ring resonator – DS-CSRR, see the topology in Fig. 5), it is possible to obtain small inductance and capacitance with small values of ring width and separation [46]. In [23], a design procedure for such DS-CSRR based common-mode filters is reported. The design procedure is based on the lumped element equivalent circuit of the unit cell, depicted in Fig. 6 (a), where L and C are the inductance and capacitance of the lines, respectively, the resonant element (CSRR or DS-CSRR) is described by the resonant tank Lc-Cc, the coupling capacitance between resonant elements is given by CR, and Lm and Cm account for the magnetic and electric coupling, respectively, between the pair of lines. The lumped element equivalent circuit model for the common and differential modes are depicted in Fig. 6 (b) and (c), respectively. For the differential-mode, the resulting circuit model is simply the circuit model of an ordinary line with modified parameters. The circuit model for the common mode is formally identical to that of CSRR-loaded single-ended microstrip lines with interresonator coupling [47], providing a stopband functionality. Using this model and the dispersion relation derived from it (inferred by means of Bloch-Floquet analysis of the multiport structure), the common-mode stopband bandwidth can be estimated [23]. Interestingly, it was demonstrated in [23] that bandwidth enhancement by interresonator coupling is related to the presence of complex modes [48]-[51]. Fig. 7(a) depicts a fabricated differential line loaded with symmetrically etched, rectangular-shaped and tightly coupled DS-CSRRs. The differential-mode and common-mode responses, depicted in Figs. 7(b) and (c), respectively, reveal that DSCSRRs are efficient elements to suppress the common-mode over a wide band whilst the differential-mode is transmitted in that band (other common-mode filters based on CSRRs are reported in [22]). Figure 8 shows the measured differential eye diagrams with the excitation of 0.2 V amplitude in 2.5 Gb/s for the differential line of Fig. 7(a) with and without DS-CSRRs. The eye diagram quality in terms of eye height, eye width, jitter and eye opening factor is very similar [23]. Therefore, the presence of the DS-CSRRs does not significantly degrade the differential signals. Defected ground plane artificial line Common-mode filters conceptually similar to those presented before, but implemented by means of a completely different ground plane pattern, are discussed in this section. These filters, first presented in [52] and studied in depth in [24], exhibit the topology depicted in Fig. 9. The pair of coupled microstrip lines is loaded with a periodic distribution of centered conductor patches connected to the ground plane by means of narrow (high impedance) strip lines. These lines behave as inductors in the frequency range of interest. Under common-mode operation, the pattern printed in the ground plane, in conjunction with the coupled lines of the top side, behaves as a low-pass filter. The common-mode signal is then expected to be strongly rejected over a wide frequency band above a certain adjustable frequency. To gain insight on this, let us consider the equivalent circuit of the structure (unit cell), depicted in Fig. 10(a). In this circuit, Ls is the inductance of the lines, Cp is the capacitance between each individual line and the central patches, Lp is the inductance of the narrow strips, and Cs is the capacitance between adjacent patches. The equivalent circuits for the common and differential modes are depicted in Figs. 10(b) and (c), respectively. For the differential mode, the lumped element equivalent circuit is the one of an all-pass structure (similar to the circuit model of the CSRR, or DS-CSRR, loaded differential lines for the differential mode). Conversely, for the common-mode, the equivalent circuit indicates that signal is inhibited in certain frequency bands. If the distance between adjacent patches is significant, the coupling capacitance Cs can be neglected, and transmission zeros at the frequencies of the resulting shunt-connected series resonators (Cp-Lp) can be expected (note that if Cs is neglected, the resulting two-port of the unit cell is the building block of elliptic low-pass filters). The analysis is not so simple if such capacitances cannot be neglected. However, the resulting multiport network (common mode) can be studied by using a Bloch-Floquet analysis similar to the one applied to CSRR-based differential lines [23]. Note that the equivalent circuit of Fig. 10(b) resembles the circuit of Fig. 6(b) that describes the CSRR, or DS-CSRR, loaded differential lines for the common mode. However, the inductance Lp in the circuit of Fig. 10(b) replaces the resonant tank Lc-Cc in the circuit of Fig. 6(b). This fact is useful for achieving broader rejection bandwidths for the common mode. A prototype device is depicted in Fig. 11(a), whereas the differential and common mode mode responses are shown in Fig. 11(b) and (c), respectively. The common-mode insertion loss is above 20 dB in the frequency range 2-4 GHz. In terms of fractional bandwidth, this result is better than those corresponding to the common-mode filters of the previous subsections. However the maximum common-mode rejection ratio (CMRR), defined as the maximum ratio (in dB) between the transmission coefficients for the differential and common modes in the common-mode stopband region, is worse in the filter with rectangular patches and inductive strips. The presence of patches and meandered lines in the ground plane does not significantly affect the signal integrity for the differential mode, as revealed by the eye diagram compared to the one of the structure with solid ground plane (reported in [24]). C-shaped PGS The common-mode filters presented in this subsection (reported in [17]) are also based on patterned ground planes, but they are described by a combination of distributed and lumped components. The configuration, shown in Fig. 12, consists of a C-shaped patterned ground structure and two meandered signal lines. The C-shaped slot comprises two main components, i.e., the patch and the bridge (see Fig. 12a). The patch can be considered to be a floating ground connected to the ground plane by means of the bridge. The differential pair is composed of two meandered microstrip lines located on top of the patch, and their coupling is very weak, provided they are distant enough. Note that the C-shaped slot is a folded slotted step impedance resonator. Such a resonant element, similar to dumbbell-shaped PGS or CSRRs, exhibits a magnetic wall at its symmetry plane at the fundamental resonance. Thus, these resonant elements can be used for the suppression of the common mode following a methodology analogous to the one for CSRRs or dumbbell-shaped PGS based common-mode filters. However, in the configuration of Fig. 12, the C-shaped slot cannot be considered to be electrically small at the frequencies of interest, and therefore, a mixed distributed-lumped analysis is required. The circuit schematic of the structure of Fig. 12 is depicted in Fig. 13(a). The patch and the meandered lines on top of it are modeled as a coupled transmission line with singleended characteristic impedance Z1 and corresponding electrical length  1. The C-shaped slot can be considered as four slot-lines: two of them with impedance and electrical length Z2 and  2, respectively, and the other two with impedance and electrical length Z3 and  3, respectively. Note that the two different slot-lines are connected in series and shunt between the patch and ground plane, as shown in Fig. 13(a). The bridge is described by a partial inductance Lb. Similarly, the signal line sections on top of the bridge are also modeled as partial inductances Ls due to the lack of ground metallization below them. The mutual inductances between the signal lines and between the signal line and bridge are also considered in [17]. Such mutual inductances are denoted as Lss and Lsb. The circuit models under differential and common mode excitation are depicted in Figs. 13(b) and (c), respectively, with the indicated equivalence between inductive elements. For the differential mode, the structure is all-pass, according to the circuit model. Conversely, the common-mode is rejected in a certain frequency band due to the interaction of the signal lines, slot lines, and the bridge. Note that this rejection mechanism is different than those of the previous common-mode stopband filters, where the common mode is rejected by a resonance-associated phenomenon. The analysis of the circuit of Fig. 13(c), detailed in [17], gives an expression providing the position of the transmission zero frequencies. Based on this formula, a systematic synthesis method for common-mode stop band filters based on these C-shaped slot structures, with transmission zeros for that mode at desired frequencies, is detailed in [17]. An example of a common-mode stopband filter, with transmission zeros located at 2.6 GHz and 6.6 GHz is depicted in Fig. 14(a), and the corresponding frequency response (common-mode and differential-mode insertion loss) is depicted in Fig. 14(b). It is remarkable that the filter is transparent for the differential mode, with differential mode insertion loss lower than 3 dB from DC up to 9 GHz. However, for the common mode, a 10 dB fractional bandwidth of 130% is obtained, thanks to the two transmission zeros for that mode. The dimensions are as small as 5.65.65 mm2 (i.e., 0.04  2, where  is the wavelength of the stopband central frequency). COMMON-MODE FILTERS BASED ON PERIODIC STRUCTURES Periodic structures are able to inhibit signal propagation at certain frequencies due to the well-known Bragg effect, derived from periodicity [36],[37]. In microwave engineering, periodic transmission lines are usually referred to as electromagnetic bandgap (EBG) based lines, analogous to photonic bandgaps, that is, periodic structures operating at optical frequencies (also known as photonic crystals). Periodicity can be achieved by etching patterns in the ground plane [53],[54], by modulating the transverse dimensions of the line (non-uniform transmission lines) [55],[56] or by periodically loading the line with reactive elements [57],[58]. Microstrip reflectors implemented by periodic nonuniform transmission lines with line width modulation have been reported [56]. According to the Bragg condition, the first forbidden band appears in the vicinity of the frequency satisfying that the period is half the guided wavelength (further band gaps may appear at harmonic frequencies, depending on the harmonic content of the periodic function describing the periodicity) [1],[36],[37]. The bandwidth and rejection level are determined by the number of stages and by the magnitude of the modulation, according to formulas inferred from the coupled mode theory [1],[59],[60]. The reflection properties of EBGs can be used for the selective mode suppression of the common mode in differential microstrip lines. The principle is as simple as determining the transverse dimensions of the line (as a function of the position along it) that are necessary to leave the differential-mode impedance unaltered and, at the same time, periodically modulate the common-mode impedance with a half wavelength period. Under these conditions, the differential line “emulates” a uniform line for the differential mode and a Bragg reflector for the common-mode. One key advantage of this approach is that the ground plane is kept unaltered. However, bandwidth is limited since, given a minimum rejection level at the Bragg frequency (where maximum attenuation occurs), bandwidth is dictated by the magnitude of the modulation [1],[60] and it is limited in practice by the critical (minimum) dimensions (slot and line width) of the technology in use. Common-mode rejection bandwidth can be expanded by cascading several periodic EBG structures with different periods [41], or by means of chirping techniques [42]. Figure 15(a) depicts a common-mode suppressed differential line designed by considering two cascaded periodic structures with periods l1= 2.85 cm and l2= 2.04 cm, corresponding to Bragg frequencies of fB1 = 2 GHz and fB2 = 2.8 GHz, respectively, in the considered substrate. The specific dependence of the common-mode impedance with the position along the line for each EBG was calculated in [41], in order to obtain maximum attenuation of 13 dB with a bandwidth of 66% (fB1) and 93.6% (fB2), considering 3 cells. The previous attenuations and bandwidths correspond to the individual structures. By cascading them, a broader common-mode rejection bandwidth in the vicinity of 2.4 GHz results. Figs. 15(b) and (c) illustrate the insertion and return losses for the common and differential modes. The common-mode insertion loss of a single-tuned EBG-based line with 6 periods and comparable rejection level (30 dB) at 2.4 GHz is also included for comparison purposes. The bandwidth can be notably improved by using two cascaded EBGs, without a penalty in device size (both are comparable). Common-mode suppression filters based on chirped EBGs can be found in [42]. Another approach for the implementation of common-mode suppressed differential lines based on EBGs utilizes the so-called uniplanar compact photonic-bandgap (UCPBG) ground plane concept [61]. These common-mode filters, first presented in [40], exhibit wide stopband bandwidths for the common mode, but at the expense of etching the ground plane. The UC-PBG is a two dimensional array of complementary Jerusalem crosses that behave as parallel LC tanks, thus presenting a high impedance path for the currents traveling through the structure. The capacitance and inductance are provided by the thin gap between the adjacent metallic patches and the narrow branches connecting each unit-cell, respectively. This structure exhibits a significant slow-wave effect [61] that substantially increases the phase constant in the propagation bands. The result is that compact EBG stop band structures can be achieved with this approach. The structure reported in [40], where 10 unit cells are etched in the ground plane, is depicted in Fig. 16(a), whereas the frequency response is shown in 16(b). The design procedure was based on the dispersion analysis, using eigenmode solvers. The differential mode signals are insensitive to the presence of the UC-PBG structure up to roughly 8.5 GHz, whereas the common mode is rejected with a suppression level below 20 dB between 3.3 GHz and 7 GHz, representing a fractional bandwidth of 70%. Other EBG-based common mode stop band filters that use three metal levels have been presented in [38],[39], but these filters are able to suppress specific frequencies, as compared to the realizations presented so far. Figures       Figure 1. Illustration of selective mode suppression in microstrip differential lines by using CSRRs etched in the ground plane (a), and SRRs etched in the upper metal layer, between the pair of lines (b). ( a ) ( b )           Figure 2. Common-mode stop band filter implemented by slotted dumbbell-shaped resonators (a), and frequency response for the differential (Sdd) and common modes (Scc) (b). The simulated transmission of mode-conversion from differential mode to common mode, Scd, is also shown in (b). Reprinted with permission from Ref. [16]; copyright 2008 IEEE.   (b) (a)               Figure 3. Measured time-domain waveforms for common-mode output of the reference differential structure (without patterned ground plane) and the proposed structure of ref. [16] (with slotted dumbbell resonators). Reprinted with permission from Ref. [16]; copyright 2008 IEEE.      Figure 4. Cross sectional view of a differential microstrip line and electric field lines for the differential (a) and common (b) modes. Figure 5. Topology of the square-shaped DS-CSRR                         Figure 6. Lumped element equivalent circuit model (unit cell) of a differential microstrip line loaded with CSRRs or DS-CSRRs (a), equivalent circuit model for the common mode (b), and equivalent circuit model for the differential mode (c). /2L CC m C m L / 2 L / 2 L / 2 L c L c C m L 2 R C 2 R C 2m C = o CC m L / 2= / 2 o LL m L / 2= / 2 o LL ( a ) ( b ) ( c ) 2 R C2 R C /2 c C 2 c L /2= /2 e LL /2= /2 e LL m L m L = e CC                 Figure 7. Photograph (a), differential-mode return loss Sdd11 and insertion loss Sdd21 (b), and commonmode return loss Scc11 and insertion loss Scc21 (c) of the differential line with common-mode suppression based on DS-CSRRs. Reprinted with permission from [23]; copyright 2012 IEEE.      (a) (b) TOPBOTTOM (c)                    Figure 8. Measured differential eye diagrams for the differential line of Fig. 7 with (a) and without (b) DS-CSRRs. Reprinted with permission from [23]; copyright 2012 IEEE.    time (72 ps/div) time (72 ps/div) V (40 mv/div) (b) (a) V (40 mv/div)           Figure 9. 3D view (a) and layout (unit cell) (b) of the common-mode suppression filter based on rectangular patches connected to the ground plane through meandered inductive strips. The metallic regions in (b) are indicated in gray.   ( a ) ( b ) TOP BOTTOM             Figure 10. Lumped element equivalent circuit model (unit cell) of a differential microstrip line loaded with rectangular patches connected to the ground plane by inductive strips (a), equivalent circuit model for the common mode (b), and equivalent circuit model for the differential mode (c). The nomenclature used for the different elements is the one of [24], different than the one used in Fig. 6.    Ground plane s L p C p C s L s L s L p L 4 s C 4 s C p L 2 s C 2 s C p L s L p C s L s L p C s L ( a ) ( b ) ( c )