RadioScience. Dominant factors of electromagnetic interference problems of asymmetrical and equi-distance differential-paired lines

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1 RadioScience RESEARCH ARTICLE Special Section: 2013 Hiroshima International Symposium on Electromagnetic Theory Dominant factors of electromagnetic interference problems of asymmetrical and equi-distance differential-paired lines Yoshiki Kayano 1 and Hiroshi Inoue 2 1 Department of Electrical and Electronic Engineering, Akita University, Akita, Japan, 2 Akita Study Center, The Open University of Japan, Akita, Japan Key Points: The paper focuses on differential-paired lines with equi-distance routing Characteristics and dominant imbalance and radiation factor is identified The validity of the equivalent circuit model was demonstrated Supporting Information: Readme Figure S1 Figure S2 Figure S3 Figure S4a Figure S4b Figure S5a Figure S5b Figure S5c Figure S5d Figure S6a Figure S6b Figure S7a Figure S7b Figure S7c Figure S8 Figure S9a Figure S9b Figure S9c Figure S10a Figure S10b Figure S10c Figure S11 Text S1 Correspondence to: Y. Kayano, kayano@gipc.akita-u.ac.jp Citation: Kayano, Y., and H. Inoue (2015), Dominant factors of electromagnetic interference problems of asymmetrical and equi-distance differential-paired lines, Radio Sci., 50, , doi:. Received 30 APR 2014 Accepted 8 JAN 2015 Accepted article online 11 JAN 2015 Published online 10 FEB 2015 Abstract Multichannel differential signaling scheme is one of the key technologies for modern electronics systems. For actual system, the ideal balance or symmetrical topology cannot be established, and hence, an imbalance component is excited. To provide the basic considerations for electromagnetic (EM) radiation from practical asymmetrical differential-paired lines structure with equi-distance routing, in which the same-length paired lines are used in high-speed board/lsi layout design, in this paper we newly attempt to clarify the characteristics and to identify dominant imbalance and EM radiation factor from asymmetrical differential-paired lines, by a physics-based model. The frequency response of EM radiation from asymmetrical differential-paired lines can be identified using the physics-based model. The physics-based model is constructed with an equivalent circuit model to calculate current distribution, and radiation model based on Hertzian dipole antenna. It is validated by comparing the predicted results with finite difference time domain simulation. This paper reported the basic characteristics of imbalance component of differential-paired lines with asymmetrical equi-distance routing and demonstrates the dominant factor of imbalance component and EM radiation successfully. 1. Introduction By advancement of electronics information and communication technologies, computerization, and internationalization of society, there has been a remarkable progress in our social life. The major application area for the practical use of radio frequency (RF) signals is wireless transmission of information [Dazey and Koons, 1982; Caorsi et al., 2001;Culhaoglu et al., 2014]. On the other hand, undesired electromagnetic (EM) waves that can cause interference or noise in various electronic and electrical devices such as radio receivers and telephone communications. The spectrum became more crowded due to the increased demand for data transmission. Radio interferences from electrical apparatus began to appear as a major problem in the dense electronic world. Almost all electronic functions were being implemented digitally because of increased switching speed and miniaturization of the integrated circuits. Furthermore, the noise interference disturbance from a digital signal to an analog signal in a printed circuit board (PCB) is enormous problem. Multichannel differential signaling scheme is one of the key technologies for modern electronics systems. Differential signaling techniques such as low-voltage differential signaling (LVDS) are widely used to establish a high-speed digital propagation with low electromagnetic interference (EMI) [Hall et al., 2000; Johnson and Graham, 2003]. In actual differential-paired lines, there are the nonideal symmetrical topology, discontinuity of the differential-mode (DM) impedance of the differential-paired lines, and the skew and distortion of the output waveform at the signal driver. Hence, unintentional imbalance components between voltages traveling the differential-paired lines deteriorate signal integrity (SI) and intensify EMI. So far, the imbalance and EM radiation from differential-paired lines have been extensively studied by many authors. In addition, the possible reasons for imbalance in differential-paired lines have been proposed and discussed in terms of signal integrity, radiated emission, and susceptibility. Reference [Grassi et al., 2013] has discussed the phenomenon of mode conversion as the basis of radiated emissions and radiated susceptibility of differential-paired lines terminated with not-perfectly balanced loads. The phenomena, which causes issues both in terms of radiated emissions and susceptibility, are concerned with the possible imbalance affecting the line terminal networks, whose behavior may differ from the ideal one in the specific frequency range of interest. Hence, there are two different mechanisms of mode conversion: due to the asymmetrical structure (layout) and due to the imbalanced termination. For the later mechanism, the filtering structure, taper bend discontinuities and meander delay line have KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 111

2 Figure 1. (a g) Geometry of PCB under study (in millimeters). been proposed to improve and compensate the SI [Wu et al., 2005; Shiue et al., 2006; Gazdaetal., 2010; Chang et al., 2012; Shiue et al., 2012; Sejima et al., 2012]. These studies has analyzed the specific case of imbalance with desired asymmetrical cross section and demonstrated that signal integrity issues is improved as long as the two traces have the same length (so-called equi-distance routing). But the papers have mainly focused on SI issue. Therefore, general study for predicting and suppressing EMI as well as establishment of signal integrity over a broadband are required. The previous studies have demonstrated that although equi-distance routing is suitable for the improvement of SI issues, it is not considered for the suppression of the far-field potential radiation [Kayano and Inoue, 2010, 2011]. For mitigation of EMI problems underlying differential-paired lines, the identification of the dominant factors which generate the imbalance component should be an important issue in order to quantify the relationship between the EMI and the configurations at the design stage for practical applications. To provide the basic considerations for EM radiation from practical asymmetrical differential-paired lines structure with equi-distance routing, in which the same-length paired lines are used in high-speed board/lsi layout design, in this paper we newly attempt to clarify the characteristics and to identify dominant imbalance and EM radiation factor from asymmetrical differential-paired lines, by a physics-based model. The main goal of this study is to clarify the characteristics and dominant imbalance KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 112

3 and radiation factor of such PCBs. First, the PCB geometries used in the study are described in section 2. The model under study is based on typical layout of differential-paired lines with different and equi-distance routing. The model is simple to investigate the complicated radiation mechanism, and the model results in generalized point of views. In section 3, the mixed-mode scattering parameters and EM radiation are measured and calculated. Then, the imbalance component on the differential-paired lines is discussed. In section 4, a physics-based model to identify and quantify the far-electric fields at 3 m Figure 2. Frequency response of S dd21. is proposed. The physics-based model for prediction is based on (1) an equivalent circuit to calculate the current distribution on the differential-paired lines and (2) a radiation model to calculate the far electric field. The dominant radiation factor is identified. Section 5 is conclusions. 2. PCB Geometry Under Study The differential-paired lines with different layouts were prepared for the discussion as typical different and equi-distance routing. The geometries of the PCBs under study are illustrated in Figure 1. Figure 1a is a basic symmetrical structure as the ideally balanced case, called Balanced ; Figure 1b is an asymmetrical structure due to differences in bend and length, called Different length (n=0) ; Figures 1c 1e are asymmetrical topology with equi-distance and different bend routing region, called Equi-distance (n = 1, 2, and 3) where the n is the number of the bend routing region. The PCB has two layers, with the upper layer for the signal trace and the lower layer for the reference (ground) plane, as shown in Figure 1f. The size of the microstrip line structure used for the test model is l = 137 mm (length), w = 100 mm (width), and h = 1.53 mm (thickness) for the dielectric substrate with a permittivity of ε r = 4.5. Two traces with l t = 100 mm for the Balanced case, width w t = 1.9 mm, and spacing s are located on the surface of the dielectric substrate. The trace length of the equi-distance (n =1,2,3) is the equi-length 148 mm. As the focuses in this paper are on the imbalance component generated by asymmetrical topologies, the relatively wide separation s = 1.0 mm is selected so that an imbalanced component due to the asymmetrical structure is the dominant fact of the EM radiation compared with that due to the waveform distortion of the output of the LVDS driver. Balanced case has a symmetrical differential-paired lines with the differential mode impedance Z DM = 100 Ω. Figure 3. Frequency response of S cd Imbalance Component on Differential-Paired Lines 3.1. Evaluation of Mixed-Mode S Parameter The frequency responses of mixed-mode scattering parameters are shown in Figures 2 and 3. The solid and dashed lines show the measured results from the network analyzer with four ports, and the finite difference time domain (FDTD) calculated results, respectively. Figure 2 shows the frequency response of S dd21, which is defined as the transmission coefficient of the differential mode. The S dd21 for the Different length (n = 0) is deteriorated compared with that of the other models. The deterioration above 5 GHz is due to a dielectric loss of FR-4 material. KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 113

4 Figure 3 shows the frequency response of S cd21, which is defined as the conversion from differential mode (balance component) to common mode (imbalance component). The measured and calculated results are in good agreement. S cd21 is dramatically increased by the different lengths of Line 1 and Line 2. The resonant and antiresonant frequencies of Different length n =0 correspond to the phase differences due to the different lengths of Lines 1 and 2 [Kayano et al., 2011]. On the other hand, the equi-distance routing can suppress the S cd21. However, the S cd21 in the Equi-distance (n = 1, 2, and 3) cases cannot be suppressed completely even if the geometric length of each line is the same. The S cd21 is increased as the number of bend region is increased. In addition, there is difference of slope of the frequency response at lower frequencies (up to 1 GHz). The frequency responses of S cd21 in the n = 0, 2, and 3 case follow a slope of 6 db/octave. The fact indicates that the dominant factor of generation of imbalance component in the n =0,2, and 3 is difference of the traveling path between Lines 1 and 2 due to the EM coupling. On the other hand, the frequency responses of S cd21 in the n = 1 case follow a slope of 12 db/octave. Figure 4. Frequency response of s parameter. Equi-distance (a) (n =1)and(b)(n =3). In order to identify the dominant generation factor of the imbalance component, the single-end s parameters for the n = 1 and n = 3 cases are measured. The single-end s parameters is related to mixed-mode s parameter: S cd21 = S 21 S 43 + S 41 S 23 (1) 2 There are two factors of contribution to mode conversion from DM to common-mode (CM): one is the difference of the transmission coefficients of Line 1 and Line 2 (S 21 S 43 ), and other is the difference of the far-end cross talk (S 41 S 23 ). Figures 4a and 4b show frequency responses of s parameters for the n = 1 and n = 3 cases, respectively. Figure 4a clearly demonstrates that the dominant factor of generation of imbalance component for the n = 1 case is difference of the far-end cross talk due to the asymmetrical geometry. Consequently, since frequency responses of magnitude and phase difference between far-end cross talk S 41 and S 23 are 6 db/octave, the frequency response of imbalance component at lower frequency follows 12 db/octave. In Figure 4b, the results clearly demonstrate that the dominant factor of generation of imbalance component at lower frequencies is the phase difference of propagation signal (transmission coefficient) between the differential-paired lines, due to difference of net propagation path results from EM coupling in bend region. At higher frequencies, the dominant factor is difference of the far-end cross talk due to the asymmetrical geometry Evaluation of Magnetic Near Field To understand the details of the imbalanced component S cd21, spatial distributions of the magnetic near field on the differential-paired lines are one specific measures. The differential-paired lines are driven by an LVDS driver (NS DS90LV047A) connected to a crystal oscillator (3.3 V amplitude and 25.0 MHz oscillation frequency). The differential-paired lines are terminated with 100 Ω surface mount technology (SMT) resistor as bridge termination at the end of the lines, Port 2. The magnetic near fields, H x and H y, were measured KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 114

5 with 1 mm step using a loop-coil type magnetic near-field probe [Yamaguchi and Arai, 1996] with a 250 μm spatial resolution and were calculated as H. Figure 5 shows the magnetic near-field H distribution at about 2.0 mm above the surface of the differential-paired lines at 1 GHz (fortieth harmonic component). The magnetic near field is mainly distributed on each trace, Line 1 and Line 2, because of differential signaling. The magnetic field strength at the higher frequency, 1000 MHz, is no longer constant. The magnetic field is concentrated in bend region. Such imbalance distribution generates a CM current and may result in significant radiation as a CM dipole Results and Discussion on Radiated Emission Experiments are performed to discuss the correlation between imbalance component and EM Radiation from the PCB. The far electric field radiated from the PCB was measured in an anechoic chamber with a Bi-Log antenna ( MHz). In the coordinate system, φ is the counterclockwise angle in the x-y plane measured from the positive x axis, and θ is the angle from the positive z axis. The differential paired lines are driven by an LVDS driver (NS DS90LV047A), and a crystal oscillator with 3.3 V amplitude and 25.0 MHz oscillation frequency. The crystal oscillator, LVDS driver, and battery are installed on the reverse side and are covered with a shield box (thin-sheet copper). The differential paired line is terminated with 100 Ω SMT resistor. The PCB was placed on a wooden table. The distance between the PCB and the antenna was 3 m. In this experiment, horizontal component E φ at (φ, θ) = (90,90 ): E x and vertical component E θ at (φ, θ) = (90,90 ): E z are chosen as certain measurement point, in order to identify dominant EM radiation factor. Although the EMI regulation is defined as the maximum EMI emission at any possible point of 3 m (or 10 m) sphericalsurface, result of the far electric field at certain point is suitable for discussion on identification of dominant factor and contribution of each factor. Figure 5. Magnetic field distribution at 2.0 mm above the paired lines at 1 GHz. The measured far electric fields are shown in Figure 6. Figures 6a and 6b are horizontal component and vertical component, respectively. The measured results which are smaller than the noise floor level are omitted in Figure 6. The radiation in the Different length (n = 0) is the largest in all five layouts. The radiations in the Equi-distance cases are relatively large compared with the radiation in the Balanced. In addition, the KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 115

6 Figure 6. Measured frequency responses of the far electric field. (a) Horizontal component and (b) vertical component. radiation from the Equi-distance (n = 1) case is not smaller compared with that from the Equi-distance (n = 2, 3) cases. This fact does not correspond to the characteristics of imbalance component evaluated from the S cd21. Although equi-distance routing is suitable for improvement of SI issues, it is not effective in suppressing the EMI. More importantly, the result indicates that only the measurement of S cd21 is insufficient for predicting the EM radiation. Figure 7 shows the angle pattern of the far electric field in the Equi-distance routing case at 350 MHz. In reference Kayano et al. [2011], the horizontal component in Balanced results from CM radiation driven as a half-wavelength dipole antenna, and hence, the angle pattern seems like a bidirectional-sinusoidal pattern. The vertical component in Balanced is due to the DM loop antenna with directivity at φ = 0 and 180.However, both horizontal and vertical components in Equi-distance radiate omnidirectionally, and the angle patterns are more complex. It is difficult to identify the dominant radiation factor by using the simple dipole and/or loop type antennas. So far, three factors could be possible factors why equi-distance does not suppress EMI [Kayano et al., 2011]. (1) There is a region of even-mode current propagation due to the asymmetric layout. The even mode causes significant CM current and radiation as a CM dipole. (2) The spacing between the differential-paired lines becomes wider. Then, the cancelation treatment for EM radiation at the observation point deteriorates dramatically. (3) The differential-paired lines are routed close to the edge of the PCB in the model layout [Kayano et al., 2004; Xiao et al., 2004], and hence, the CM current due to the finite impedance of the ground plane increases. The measured results do not allow us to distinguish the particular radiation component from each of mentioned above factors, these consequences indicate that the equi-distance routing does not work as an effective treatment for suppressing EMI. In section 4, it is newly attempt to identify the dominant radiation factor by using the physics-based model. 4. Identifying Frequency Response of Radiated Emission 4.1. Physics-Based Modeling Identifying and predicting the dominant component at a certain frequency band are a very important subject for mitigating EMI problems in high-speed electronic designs. In order to discuss and identify the dominant factor of EM radiation due to equi-distance routing layout, this paper focuses on Factors (1) and (2), which are independent of the size of PCB. The impact of Factor (3) can be estimated by reference [Kayano et al., 2004; Xiao et al., 2004]. For instance, when the differential-paired lines offset from the center exceeds 25% of the half of the ground plane (l b = 24 mm), Factor (3) increases to approximately 26 db. Now, the PCB with infinite ground plane, in which the Factor (3) can be neglected, is considered as the model under discussion. The physics-based model for identifying and quantifying frequency response of the EM radiation from an asymmetrical differential-paired lines on an infinite ground plane has been proposed [Kayano and Inoue, 2011, 2012, 2013]. As the methodologies of analyzing far electric field (radiated emission) have been studied for many years, the far electric field can be obtained by integrating the current distribution over the surface of the radiator [Kraus, 1988]. Hence, the physics-based model for prediction is KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 116

7 based on (1) an equivalent circuit to calculate the current distribution on the differential-paired lines and (2) a radiation model to calculate the far electric field. In general, a far electric field is obtained by integrating equivalent electric and magnetic current distributions on a closed surface S surrounding the PCB and by using the near to far-field transformation. Equivalent electric and magnetic currents on the closed surface S are given by J S = n H (2) M S = E n. (3) Then, far electric fields are given by E θ (ω) = j k 0 e jk 0 R ( ) Z0 N 4π R θ L φ (4) E φ (ω) = j k 0 e jk 0 R ( ) Z0 N 4π R φ + L θ, (5) where k 0 and Z 0 are wave number and characteristic impedance in free space, respectively, and R is distance from origin O to far zone point P. The radiation vector N and L are defined as ( ) N (ω) = J S ω, R e jk 0R R ds (6) S L (ω) = S M S ( ω, R ) e jk 0 R R ds, (7) Figure 7. Angle pattern of the far electric field measured at 350 MHz. θ =90 and φ =0to 360. E φ (H): horizontal component, E θ (V): vertical component. where R is the unit vector to the far zone point, and R is the vector to the source point of integration [Luebbers et al., 1991]. Since the differential-paired lines used in this study have no multilayer planes and slot, the term of the magnetic current are disregarded: proposed model is based on Hertzian dipole antenna. And hence, the far electric field can be obtained from electric current distribution on the differential-paired lines including image currents. Figure 8 shows cross-sectional view of arrangement of electric current including image currents. The current distribution is calculated by the equivalent circuit model. The equivalent circuit model to calculate the current distribution is consisted of cascade connection of coupled microstrip line and microstrip line region. The differential-paired lines used in this study has two kinds of cross-sectional schemes: coupled microstrip line and microstrip line. First, the structure is divided into plural regions as shown in Figure 9. The entire circuit diagram to calculate the current distribution. Equi-distance (n=1) is divided into five coupled microstrip line regions (n1a, n1b, n1c, n1d, and n1e) and four microstrip line regions (n1f, n1g, n1h, and n1i). Equi-distance (n=2) is divided into ten coupled microstrip line regions (n2a, n2b, n2c, n2d, n2e, n2f, n2g, n2h, n2i, and n2j) and two microstrip line regions (n2k and n2l). Equi-distance (n = 3) is divided fourteen coupled microstrip line regions (n3a n3n) and two microstrip line regions (n3o and n2p). Each region can be modeled by cascade arrangement of previous lossless equivalent circuit model. The length of the unit section Δl is determined so that it is smaller than λ g /20, that is 0.25 mm, KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 117

8 Figure 8. Cross-sectional view of arrangement of electric current. where the λ g is the wavelength of the highest frequency of interest (26.5 GHz). The circuit parameters are calculated from 2-D-field solver. Finally, the behavior of the entire geometry is obtained by connecting all regions together. Consequently, the equivalent circuit analysis reveals the contributions of each region for identification and quantification Identification of Dominant Radiation Factor Calculated results by the equivalent circuit model in the cases of Equi-distance (n = 1, 2, and 3) are shown in Figure 10 with the full-wave (FDTD) simulation as a benchmark. The source voltage is 0 dbm (107 dbμv) in the entire frequency range. Therefore, the far electric field is identical to the radiation efficiency. The calculated results by the equivalent circuit model and FDTD modeling except magnitudes at resonant frequencies are in good agreement within 3 db. The good agreement between the equivalent circuit model and FDTD results indicates the validity of the equivalent circuit model and the proposed approach. The total far electric field up to 1 GHz is dominated by the radiated component from region n1c for the n = 1 case, n2c for the n = 2 case, and n3c for the n = 3. There results indicate that the factor (1) is the dominant radiation factor at lower frequencies. The second radiation factor is the radiated component from regions b (the factor (2)). Although the maximum radiated angle depends on the layout and frequency, these results demonstrate that once the phase difference of propagation signal between the differential-paired lines arises, a cancelation treatment of differential signaling for EM radiation at observation point will be deteriorated dramatically, and hence, EM radiation increases. This is a significant problem of design of a meander delay line for high-speed clock distribution. The expected guideline for PCB design is to place to equi-routing near the phase-difference region whenever possible from viewpoint of EMI. Figure 9. The entire circuit diagram to calculate the current distribution. To identify the details of the dominant radiation factor and quantify the design guideline, the relationship between cross-sectional scheme of differential-paired lines with imbalance component and the far electric field is discussed by using a 2-D scheme of the physics-based model. Figure 11 shows the relationship between s c and normalized radiation α of E theta (0, 0) at 1 GHz, where the s c is the spacing between the centers of differential-paired lines, s c = s + w t + w t = 2.9 mm in 2 2 regions n1a, n1c, and n1e, and s c = 26.9 mm in regions n1b and n1d, and normalized radiation α is defined as the ratio of EM radiation from differential-paired lines to EM radiation from single-ended line. For the ideal differential signaling case, as the spacing s c between differential-paired lines decreases, α decreases. However, for the imbalance condition (phase-difference δ is not ideally differential signaling) cases, α is not varied with s c. In addition, as the phase-difference δ becomes in-phase, α increases dramatically. The difference of α for the ideal differential signaling case between s c = 2.9 mm and s c = 26.9 mm is about 20 db, that is the impact of the factor (2). On the other hand, the difference of α for the s c = 2.9 mm between δ = 180 and 0 is about 30 db, that is the impact of the factor (1) and larger than impact KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 118

9 Figure 10. Contribution of each region to total radiated emission. KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 119

10 of the factor (2). As the results, although S cd21 measured at the end of the paired lines with equi-distance routing is better, even-mode current in region before equi-distance routing causes EM radiation strongly. Even if equi-distance routing is suitable for the improvement of SI issues, it is not enough for the suppression of the far-field potential radiation. Figure 11. The relationship of spacing s c between the centers of differential-paired lines and normalized radiation α of E θ at 1GHz. Consequently, using the physics-based model, frequency response of the EM radiation from an asymmetrical differential-paired lines on an infinite ground plane can be identified and quantified. More importantly, the proposed physics-based model can identify the dominant radiation mechanisms. Identifying the dominant radiation mechanisms facilitates the mitigation of EMI problems in PCBs. 5. Conclusions This paper reported the basic characteristics of imbalance component of differential-paired lines with asymmetrical equi-distance routing and demonstrates the dominant factor of imbalance component and EM radiation successfully. The main objective of this paper is to provide basic considerations for the dominant factor of imbalance component and EM radiation from asymmetrical differential-paired lines with equi-distance routing. The imbalance components and EM radiation from asymmetrical differential-paired lines with equi-distance routing were investigated experimentally and with numerical modeling. Although the geometric length of each line is the same, the imbalance component and EM radiation cannot be suppressed completely. The dominant factor of the EM radiation from equi-distance routing can be identified using the proposed model. The validity of the equivalent circuit model was demonstrated by comparing the predicted results with FDTD simulation. The results indicate that the S cd21 is not a single evaluator for predicting the EM radiation. The equivalent circuit model provides enough flexibility for different geometric parameters and can be used to develop physical insights and design guidelines. Basic consideration and physical insight gained from simple model can be applied to many kinds of practical model, and the mitigation of electromagnetic compatibility problem would be taken place significantly. Future directions include study of engineering implications and development of design guidelines. Acknowledgments Data supporting all figures are available as in supporting information. The authors sincerely thank to Yasunori Tsuda and Akita Industrial Technology Center, for their support of measurements, and Cyberscience Center, Tohoku University, for their support with computer resources. This research was supported by JSPS KAKENHI (grant-in-aid for Young Scientists (B), grant ). References Caorsi, S., M. Donelli, A. Massa, and M. Pastorino (2001), A numerical approach for the evaluation of the nonlinear effects on the attenuation constant in high-temperature superconducting transmission lines, Radio Sci., 36(6), , doi: /2000rs Chang, C. H., R. Y. Fang, and C. L. Wang (2012), Bended differential transmission line using compensation inductance for common-mode noise suppression, IEEE Trans. Compon. Packag. Manuf. Technol., 2(9), Culhaoglu, A. E., A. V. Osipov, and P. Russer (2014), Imaging by a double negative metamaterial slab excited with an arbitrarily oriented dipole, Radio Sci., 49, 68 79, doi: /2013rs Dazey, M. H., and H. C. Koons (1982), Characteristics of a power line used as a VLF antenna, Radio Sci., 17(3), , doi: /rs017i003p Gazda, C., D. V. Ginste, H. Rogier, R. B. Wu, and D. D. Zutter (2010), A wideband common-mode suppression filter for bend discontinuties in differential signaling using tightly coupled microstrips, IEEE Trans. Adv. Packag., 33(4), Grassi, F., G. Spadacini, and S. A. Pignari (2013), The concept of weak imbalance and its role in the emissions and immunity of differential lines, IEEE Trans. Electromagn. Compat., 55(6), Hall, S., G. W. Hall, and J. A. McCall (2000), High-Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices, John Wiley, New York. Johnson, H., and M. Graham (2003), High-Speed Signal Propagation: Advanced Black Magic, Prenticel Hall, N. J. Kayano, Y., and H. Inoue (2010), Identifying EM radiation from a printed-circuit board driven by differential-signaling, Trans. Jpn. Inst. Electron. Packag., 3(1), Kayano, Y., and H. Inoue (2011), A study on characteristics of EM radiation from strip line structure, Radio Sci., 46, RS0F06, doi: /2011rs Kayano, Y., and H. Inoue (2013), Identifying dominant factor of EM radiation from asymmetrical differential-paired lines with equi-distance routing, in Proceedings of URSI International Symposium on Electromagnetic Theory (EMTS), pp , IEEE, Hiroshima, Japan. KAYANO AND INOUE American Geophysical Union. All Rights Reserved. 120

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