TDR/TDT Analysis by Crosstalk in Single and Differential Meander Delay Lines for High Speed PCB Applications

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1 TDR/TDT Analysis by Crosstalk in Single and Differential Meander Delay Lines for High Speed PCB Applications Gawon Kim, Dong Gun Kam, and Joungho Kim Dept. of EECS, KAIST Korea Advanced Institute of Science and Technology Daejeon, Korea Abstract Meander (serpentine) delay lines are generally used for controlling the skew of the traces in high-speed Printed Circuit Board (PCB) applications. They consist of equal-length unit lines closely packed to each other. However the meander lines deteriorate the total time delay and the waveform distortion in the end of the lines, since each unit line is tightly coupled. In this paper, to predict accurate Time-Domain Reflectometry/Time- Domain Transmit (TDR/TDT) waveforms by crosstalk in the single and differential meander line, simple TDR/TDT equations are proposed in point of the signal integrity. The proposed TDR/TDT waveform equations are verified by using TDR/TDT measurements in the single and differential meander delay lines. efficient design method to predict the signal distortion caused by meander delay line. Keywords-crosstalk; meander; delay; serpentine; differential line; Time-Domain Reflectometry; TDR; Time-Domain Transmit; TDT I. INTRODUCTION Nowadays, as electrical devices become more and more mobile, the integration density in package or Printed Circuit Board (PCB) is higher, and the size of the PCB in electrical devices gets smaller. However the data transferred between chips or packages are required to have a fixed time delay to minimize the skew of the data. At that case, the delay transmission lines are certainly needed but they can not consider the shape of simple lines due to the space limitation. Consequently one popular design is the meander (serpentine) delay line that consists of equal-length unit lines closely packed to each other. Noise by Crosstalk become important design issues of delay line having small room in modern high-speed digital systems. Then, the capacitive and inductive coupling occur between unit lines of the meander delay line and they cause the near-end and far-end crosstalk [1-2]. The induced Crosstalks in meander delay line distort Time- Domain Reflectometry/Time-Domain Transmit (TDR/TDT) waveforms as shown Figure 1 [3-4]. Figure 1 shows the top view of the motherboard of laptop personal computer, including single meander delay line design. Many computation methods for the meander delay line have been intensively studied because simulations should be preceded before meander delay line design [5-6]. In practical situations, PCB designers would prefer to have a simple and Figure 1. TDR/TDT waveforms in signle meander delay line Furthermore differential signaling has become a popular choice for multi-gigabit digital applications, offering superior immunity to common mode noise such as crosstalk and simultaneous switching noise [7]. The meander delay lines have been recently employed in differential signaling; it is named differential meander delay line. However previous works for the differential meander delay line have not been enough to accurately calculate the TDR/TDT waveforms [8]. In this paper, the TDR/TDT waveforms are analyzed in single and differential meander line and simple TDR/TDT equations are proposed to predict crosstalk due to meander delay line. II. TDR/TDT ANALYSIS BY CROSSTALK IN SINGLE MEANDER DELAY LINES Figure 2 shows general single meander delay line. Single meander delay line has three design parameters; those are the time delay of unit line and a space between unit lines, and the number of unit lines. Because the line width and the height of PCB (Printed Circuit Board) are determined by characteristic impedance, they are excluded from design parameters of single meander delay line. Surely if the space between unit lines becomes larger and larger, the induced crosstalk is lower and lower, but it is improper in the design goal, compact design X/06/$20.00 (c)2006 IEEE 657

2 Hence space between unit lines is suitably as small as occurring coupling mechanism. When the step pulse travels from the start point of each unit line, the rising edge induces far-end crosstalks and near-end crosstalks on adjacent unit lines [2]. At that time, the far-end crosstalks named F1, F2_1, F2_2, and F3 are propagated in input direction. Figure 4 represents generation points of the farend crosstalks and the TDR waveform in single meander line with 3 unit lines. It is noted that the far-end crosstalks affects only the TDR waveform. Figure 2. General Single Meander Delay Line Analysis of TDR/TDT waveforms in the single meander delay line is explained by giving a simple example, that is, single meander line with 3 unit lines as shown Figure 3. The step pulse is induced in the start of input at initial time. Assume that the crosstalk upward of second is ignored and length of bending line is ignored. TD is a time delay of one unit line. (a) Generation Points of the far-end crosstalks (b) TDT waveform Figure 5. TDT waveform Analysis in signle meander line with 3 unit lines, TD means the time delahy of one unit line Figure 3. Single meander delay line with 3 unit lines (a) Generation points of the far-end crosstalks The near-end crosstalks named N1, N2_1, N2_2, and N3 travel to the direction of the end of meander delay line. Figure 5 describes generation points of the near-end crosstalks and the TDT waveform in the single meander line with 3 unit lines. It should be also noted that TDT waveform is affected only the near-end crosstalk to the contrary of the TDR waveform. As described above, the TDR/TDT waveforms of single meander delay line contained the effects of the far-end crosstalks and the near-end crosstalks. The total TDR waveform is composed of the step pulse and 2 times far-end crosstalks at each 2TD. The magnitude of far-end crosstalk is determined by far-end crosstalk coefficient that is calculated from coupled line structure [2]. The total TDT waveform is formed the transmitted step pulse and the near-end crosstalks. The near-end crosstalk has the magnitude depending heavily on the number of unit lines, N, and occurs before and after arrival of the transmitted step pulse during 2TD. Hence the general TDR/TDT equations are proposed in single meander lines. In single meander line with N unit lines, the proposed equation of TDR waveform is represented as: TDR waveform of single meander line (b) TDR waveform Figure 4. TDR waveform Analysis in signle meander line with 3 unit lines, TD means the time delahy of one unit line N = V h u( t) kfext δ( t 2nTD) (1) n=1 In single meander line with N unit lines, the equation of TDT waveform is depicted as: X/06/$20.00 (c)2006 IEEE 658

3 TDT waveform of single meander line u = Vh + ( t N TD) ( N 1) k [ u( t ( N 2) TD) u( t ( N + 2) TD) ] where TD: Time delay of one unit line k : A near-end crosstalk coefficient k : A far-end crosstalk coefficient FEXT N: The number of unit lines δ (t) : Delta pulse u () t : Unit step pulse III. DIFFERENTIAL TDR/TDT ANALYSIS BY CROSSTALK IN DIFFERENTIAL MEANDER DELAY LINES Turning now to the differential meander delay line, the TDR/TDT waveform in differential meander delay line are analyzed through same process in single meander delay line. Earlier than the TDR/TDT waveform analysis of a differential meander delay line, the crosstalk in differential pair should be considered. (a) The differential meander line with 1 turn (2) Figure 6 (a) represents the differential meander delay line with 1 turn. In port 2, the falling edge induces the near-end crosstalk at port 1 and port 3 with near-end crosstalk coefficient, k, as described Figure 6 (b). The near-end crosstalk coefficient is represented by equation (3) [1]. k 1 C = 4 C m L + m 11 L 11 While, a reflection waveform is generated due to impedance mismatching in port 1, as shown in Figure 6 (c). An impedance of the differential transmission lines matches the differential impedance equals 100Ω; that is the odd-mode impedance matches 50Ω. Because of the impedance of single line is not 50Ω, the reflection waveform generates according to the reflection coefficient relating with an impedance of source and the characteristic impedance of single line. k R where (3) Z single 50Ω = (4) Z + 50Ω single L Z signle = (5) C Z L C L L C + C odd M odd = = = 50 ' odd M The magnitude of near-end crosstalk and that of reflection waveform exactly matches as calculation using equation (4). Therefore the effect of crosstalk can be ignored in differential pair. Consequently the crosstalks in differential meander delay line can be considered only between same-polar lines that are opposite to each other having same voltages not differential voltages. As it were, the TDR/TDT analysis in the differential meander line is similar to that in the single meander line as shown in Figure 7. Also assume that the crosstalk upward of second is ignored and line length of bending is ignored. TD is a time delay of one unit line. Ω (6) (b) The near-end crosstalk by falling edge in point B (a) Differential meander delay line with 1 turn (c) Reflection waveform due to impedance mismatching Figure 6. The differential meander line with 1 turn (b) Alternating with single meander line with 2 unit lines Figure 7. Analysis process of differential meander delay line with 1 turn X/06/$20.00 (c)2006 IEEE 659

4 Analysis of the differential TDR/TDT waveforms in the differential meander lines are explained by giving example as the differential meander line with 1 turn. Because the crosstalk in differential pair, having differential voltages, can be ignored, the rising edge in port 1 is not affected by crosstalk and it will arrive at port 3. However the falling edge encounters same polar coupling lines, it will be affected by crosstalk. The two inner meander lines are same-polar lines; therefore they are regarded as the single meander line with 2 unit line. The waveforms at each port of differential meander delay line with 1 turn are depicted in Figure 8. (a) Differential meander delay line with N turns (b) Differential TDR waveform (a) Waveforms at each port (c) Differential TDT waveform (b) Differential TDR waveform (c) Differential TDT waveform Figure 8. Differential TDR/TDT waveforms in differential meander line with 1 turn In differential signaling, differential signals are detected as the difference between differential signals. Differential TDR waveform is found from the difference between waveforms at port 1 and port 2 as shown in Figure 8 (b). And the differential TDT waveform is also found from the difference between waveforms at port 3 and port 4 as represented in Figure 8 (c). Figure 9 (a) shows general differential meander delay line with N turns. The differential TDR waveform is composed of the step pulse and 1 times far-end crosstalk at each 2TD. The differential TDT waveform is formed from the transmitted step pulse and the near-end crosstalk. The near-end crosstalk has a magnitude depending heavily on the number of turns, N, and occurs before and after arrival of the transmitted step pulse during 2TD. Figure 9. Differential TDR/TDT waveforms in differential meander delay line with N turns Figure 9 (b) and (c) represent generalized differential TDR/TDT waveforms. Consequently, in differential meander line with N turns, the proposed equation of differential TDR waveform is represented as: Differential TDR equation N = V h u( t) + kfext δ( t 2nTD) (7) n=1 In differential meander line with N turns, the proposed equation of differential TDT waveform is depicted as: Differential TDT equation u = Vh + ( t ( N +1) TD) N k [ u( t ( N 1) TD) u( t ( N + 3) TD) ] where TD: Time delay of one unit line k : A near-end crosstalk coefficient k : A far-end crosstalk coefficient FEXT N: The number of turns δ (t) : Delta pulse u () t : Unit step pulse (8) X/06/$20.00 (c)2006 IEEE 660

5 IV. VERIFICATION BY USING TDR/TDT MEASUREMENTS IN SINGLE AND DIFFERENTIAL MEANDER LINES First, the proposed TDR/TDT equations are verified by using TDR/TDT measurements in single meander lines. The TDR/TDT waveforms of single meander delay line with 4 unit lines will be predicted as depicted by Figure 10 (b) and (c). The magnitude of far-end crosstalk is -128mV and that of near-end crosstalk is 25.7mV using equation (1) and (2). Figure 11 represents the measured TDR/TDT waveforms of DUT shown in Figure 10 (a). The magnitude of the first far-end crosstalk is mV and that of the first near-end crosstalk is 25.68mV. It is found that prediction using proposed equations agree with the results of measurement very well. (a) Single meander line with 8 unit lines (a) Single meander line with 4 unit lines (b) Prediction of TDR waveform using proposed equation (b) Prediction of TDR waveform using proposed equation (c) Prediction of TDT waveform using proposed equation (c) Prediction of TDT waveform using proposed equation Figure 10. Prediction of TDR/TDT waveforms in single meander line with 4 unit lines Figure 12. Prediction of TDR/TDT waveforms in single meander line with 8 unit lines Also the single meander delay line with 8 unit lines is considered as represented in Figure 12. The magnitude of farend crosstalk is -128mV and that of near-end crosstalk is 60mV using TDR/TDT equation (1) and (2). (a) Measurement result of TDR waveform (a) Measurement result of TDR waveform (b) Measurement result of TDT waveform Figure 11. Measurement results of TDR/TDT waveforms in single meander line with 4 unit lines (b) Measurement result of TDT waveform Figure 13. Measurement results of TDR/TDT waveforms in single meander line with 8 unit lines X/06/$20.00 (c)2006 IEEE 661

6 Figure 13 shows the measured TDR/TDT waveforms of DUT shown in Figure 12 (a). The magnitude of the first far-end crosstalk is mV and that of the first near-end crosstalk is 45.95mV. It is found that prediction using proposed equations agree with the results of measurement on the whole. However prediction of TDR waveform using TDR equation as Figure 13 (a) is that each far-end crosstalk has equal magnitude, but, it became smaller as time passes. Decreasing of the far-end crosstalk in measured TDR waveform has three reasons. First reason is due to ignore upward of the 2 nd crosstalk. Second reason is that length by bending line is ignored. The last reason is due to an increase of rising time in source step pulse not ideal step pulse. Second, let s consider the differential meander delay line. The differential TDR/TDT waveforms using equations (7) and (8) as proposed in chapter Ⅲ are compared with measured TDR/TDT waveforms and verified in differential meander delay lines. Figure 14 (a) shows the differential meander delay line with 1 turn. As depicted by Figure 14 (b), the differential TDR/TDT waveforms are predicted by using proposed equation (7) and (8) and Figure 15 shows the measured differential TDR/TDT waveforms of DUT of Figure 14 (a). It is also found that prediction using proposed differential TDR/TDT equations agree with the results of measurement on the whole. Some difference is mentioned above. (b) Measurement result of differential TDT waveform Figure 15. Measurement of TDR/TDT waveforms in differential meander delay line with 1 turn V. CONCLUSION In this paper, the TDR/TDT waveforms affected by crosstalk have been analyzed in single meander line and the equations of TDR/TDT waveforms have proposed. Furthermore, we have analyzed the differential TDR/TDT waveforms in the differential meander line, and the proposed differential TDR/TDT waveform equations are verified by using the TDR/TDT measurements in both single and differential meander lines. The prediction of TDR/TDT waveforms by using proposed equations shows a good correlation with the TDR/TDT measurements. REFERENCES (a) Differential meander line with 1 turn (b) Prediction of TDR/TDT using proposed equation Figure 14. Prediction of TDR/TDT waveforms in differential meander delay line with 1 turn [1] K. C. Gupta, et al., "Microstrip Lines and Slotlines", 2nd ed., John Wiely & Sons, Inc., 2000, Ch. 3. [2] Stephen H. Hall, et al., "High-Speed Digital System Design", Norwood, MA: Artech House, Inc., 1996, Ch. 8. [3] Ruey-Beei Wu and Fang-Lin Chao, "Laddering Wave in Serpentine Delay Line", IEEE Trans. on Components, Packaging, and Manufacturing Technology, Vol. 18, No. 4, 1995, pp [4] Ruey-Beei Wu., "Flat Spiral Delay Line Design with Minimum Crosstalk Penalty", IEEE Trans. on Components, Packaging, and Manufacturing Technology, Vol. 19, No. 2, 1996, pp [5] Barry J. Rubin, "Study of Meander Line Delay in Circuit Boards", IEEE Trans. on Microwave Theory and Techniques, Vol. 48, No. 9, 2000, pp [6] Omar M. Ramahi, "Analysis of Conventional and Novel Delay Lines: A Numerical Study", Journal of Applied Computational Electromagnetic Society, Vol. 18, No. 3, 2003, pp [7] D. Kam, et al., Twisted Differential Line Structure on High-Speed Printed Circuit Boards to Reduce Crosstalk and Radiated Emission, IEEE Trans. On Advanced Packaging, Vol. 27, No. 4, Nov. 2004, pp. 590~596. [8] Wei-De Guo, et al., "Comparison between Flat Spiral and Serpentine Differential Delay Lines on TDR and TDT", IEEE 13th Topical Meeting, Electrical Performance of Electronic Packaging, 2004, pp [9] William J. Dally, John W. Poulton, "Digital Systems Engineering", Cambridge University Press, 1998, Ch. 6. (a) Measurement result of differential TDR waveform X/06/$20.00 (c)2006 IEEE 662