Module 5: Advanced Transmission Lines Topic 3: Crosstalk OGI EE564 Howard Heck © H. Heck 2008 Section 5.3

Transmission Line Basics Analysis Tools Metrics & Methodology Where Are We? Introduction Transmission Line Basics Analysis Tools Metrics & Methodology Advanced Transmission Lines Losses Intersymbol Interference (ISI) Crosstalk Frequency Domain Analysis 2 Port Networks & S-Parameters Multi-Gb/s Signaling Special Topics © H. Heck 2008 Section 5.3

Contents Introduction Circuit Models Effective Impedance and Velocity Mutual Inductance Mutual Capacitance Effective Impedance and Velocity Coupling Matrices Noise Coupling On Passive Lines Coupling Coefficient Forward and Backward Crosstalk Crosstalk on Passive Lines – Example Implementation Considerations Homogeneous and Non-Homogeneous Media Printed Circuit Boards Minimization Techniques Lossy Lines Summary References © H. Heck 2008 Section 5.3

Introduction Recall the T.E.M. mode single line: Two adjacent lines have two possible T.E.M. modes: Even mode – excited in phase with equal amplitudes. Odd mode – driven 180º out of phase with equal amplitudes. E E H H Even Mode Odd Mode © H. Heck 2008 Section 5.3

Crosstalk can have the following impacts: Introduction #2 In general, for a system of n transmission lines, there are n possible TEM modes. When the fields from adjacent transmission line interact with each other, we get crosstalk. Crosstalk can have the following impacts: The characteristics (Z0, vp) of the driven lines are altered. Noise is coupled onto passive lines. © H. Heck 2008 Section 5.3

Circuit Model Single line (lossless): 2 coupled lines: The mutual inductance, Lm, causes the current in line 1 to induce a voltage on line 2 : [5.3.1] The mutual capacitance, Cm, causes the voltage on line 1 to induce a current in line 2 : [5.3.2] © H. Heck 2008 Section 5.3

Mutual Inductance [5.3.3] [5.3.4] If the lines are driven in even mode, . Then [5.3.5] [5.3.6] If the lines are driven in odd mode, . Then [5.3.7] [5.3.8] Effective inductances: © H. Heck 2008 Section 5.3

Mutual Capacitance [5.3.9] [5.3.10] Even mode, . Then [5.3.11] [5.3.12] Odd mode, . Then [5.3.13] [5.3.14] Recall the even mode field diagram. Some fringing fields are lost due to overlap between electrical field lines. So, even mode capacitance is less than the total capacitance of a single PCB trace. In a multi-conductor PCB, the effective capacitances obey the relationship, , where C0 is the total capacitance of the line. © H. Heck 2008 Section 5.3

Effective Impedance and Velocity [5.3.15] Recall: [5.3.16] Even mode: [5.3.17] [5.3.18] Odd mode: [5.3.19] [5.3.20] Since and , we get: What about vp? Typically, for microstrips. Since all fields are contained within the dielectric medium, there is no effect on np for striplines. © H. Heck 2008 Section 5.3

Coupling Matrices Capacitance: [5.3.21] Total capacitance (C0 + Cm) 12 Capacitance: [5.3.21] Total capacitance (C0 + Cm) where Mutual capacitance (Cm) Note, Cii is the total capacitance capacitance (sum of capacitance to ground plus mutual capacitances). Mathematically : and © H. Heck 2008 Section 5.3

Coupling Matrices #2 Inductance: [5.3.22] where L11 and L22 are self inductances L12 and L21 are mutual inductances Recall even and odd modes: Apply the matrices to the even and odd mode equations: [5.3.23] [5.3.24] [5.3.25] [5.3.26] where C0 = Cs1 (total capacitance to ground) © H. Heck 2008 Section 5.3

Coupling Matrics – n Line System Inductance matrix: Lii = self inductance of line i Lij = mutual inductance between lines i and j Capacitance matrix: Cii = total capacitance seen by line i = capacitance of conductor i to ground plus all mutual capacitances to other lines. Cij = mutual capacitance between conductors i and j © H. Heck 2008 Section 5.3

Effective Impedance & Velocity Again The effective inductance and capacitance can be calculated using the matrices for arbitrary switching patterns. For lines switching in-phase (even mode), inductances add, capacitances subtract. For lines switching out-of-phase (odd mode), inductances subtract, capacitances add. From this, the effective impedance and propagation velocity can be approximated. © H. Heck 2008 Section 5.3

Lossless Example Network: PCB trace cross-section: LC matrices: 60 W Coupling Line 1 Line 2 Network: PCB trace cross-section: LC matrices: 0.005" 0.0007" 0.0074" 0.002" e r = 4.0 © H. Heck 2008 Section 5.3

Lossless Example #2 Out-of-Phase Coupled Model Single Line Eq. Model -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 time [ns] voltage [V] -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 time [ns] voltage [V] R1 0.981V 1.000V D 0.939V 1.000V R 0.996V D2 0.138V 0.003V D1 0.862V 0.997V R2 0.019V 0.000V 1.93ns 1.912ns © H. Heck 2008 Section 5.3

Lossless Example #3 In-Phase Coupled Model Single Line Eq. Model 1.100V 1.001V R1 0.990V 1.000V R2 D2 2 4 6 8 time [ns] -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 voltage [V] 1.95ns -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 time [ns] voltage [V] D R 1.039V 0.998V 1.000V 1.97ns © H. Heck 2008 Section 5.3

Noise Coupling Mechanism Z V S L m C 2IC I C I C I L IC + IL IC - IL Current IC flows through the mutual capacitance from the driven line to the victim line. IC splits into equal components traveling forward & backward in the victim line. Lm induces current IL traveling backward on the victim line. The total backward current is IC + IL. The total forward current is IC – IL. © H. Heck 2008 Section 5.3

Coupling Coefficients The capacitive coupling coefficient is the ratio of the mutual capacitances to the total capacitance: [5.3.37] The inductive coupling coefficient is the ratio of the mutual inductances to the self inductance of the transmission line: [5.3.38] We can rewrite the coupling coefficient from equation [5.3.36] in terms of the capacitive and inductive coupling coefficients: [5.3.39] © H. Heck 2008 Section 5.3

Forward & Backward Crosstalk We have seen that TEM modes cause forward & backward coupled waves. How does that show up as noise at the ends of the network? Noise currents (IC and IL) are proportional to the edge rate of the signal (dV/dt). IC has 2 equal components traveling in opposite directions. IL has 1 component traveling backward. Noise voltages VL has a backward component with the same polarity as VC and a forward component which has the opposite polarity from VC. Therefore, VL subtracts from VC in the forward direction, but adds to VC in the backward direction. © H. Heck 2008 Section 5.3

Far End (Forward) Crosstalk Forward coupling coefficient: [5.3.40] where: td is the transmission line propagation delay per unit length which equals 1/vp (propagation velocity). Recall and . Then [5.3.41] © H. Heck 2008 Section 5.3

Far End (Forward) Crosstalk #2 Far end crosstalk noise: [5.3.42] where: l is the coupled line length and [5.3.43] Substitute: [5.3.44] [5.3.45] Pulse width of the noise: [5.3.46] © H. Heck 2008 Section 5.3

Near End (Backward) Crosstalk Backward Coupling Coefficient: [5.3.47] Near End Crosstalk Noise: Non-saturated [5.3.48] Saturated Near end crosstalk pulse width: [5.3.49] © H. Heck 2008 Section 5.3

Near End vs. Far End Crosstalk The magnitude of the backward (near end) crosstalk coefficient is greater than that of forward (far end) crosstalk. The pulse width of backward crosstalk is greater than that of forward crosstalk. Why do we care about near end crosstalk? © H. Heck 2008 Section 5.3

Crosstalk Noise Example Using the coupled lines from the even/odd mode example: 2 4 6 8 time [ns] -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 voltage [V] D1 R1 D2 R2 0.119V -0.490V 0.981V 1.000V 1.93ns 3.86ns © H. Heck 2008 Section 5.3

Crosstalk Noise Example #2 The forward coupled pulse: appears at the receiver at the same time as the driven signal. has the opposite polarity from the driven signal. has a pulse width equal to the rise time of the signal The backward coupled noise pulse: appears at the driver as soon as the driven signal propagates onto the coupled lines. has the same polarity as the driven signal. has a pulse width of twice the prop delay. 2 4 6 8 time [ns] -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 voltage [V] D1 R1 D2 R2 0.119V -0.490V 0.981V 1.000V 1.93ns 3.86ns © H. Heck 2008 Section 5.3

Crosstalk in Homogenous Media Relationship between inductive & capacitive coupling matrices: [5.3.50] Where I is the identity matrix. Therefore, . Relationship of KC and KL: From it follows that .  KC = KL. Forward Crosstalk: [5.3.51] Backward Crosstalk: [5.3.52] © H. Heck 2008 Section 5.3

Crosstalk on Non-Homogeneous Media Relationship between inductive & capacitive coupling matrices: Relationship of KC and KL:  KC  KL Forward Crosstalk: Backward Crosstalk: © H. Heck 2008 Section 5.3

Crosstalk in Printed Circuit Boards w s t h 1 2 e r Param Xtalk er   t   w  s  h  What other parts of the interconnect can act as sources of crosstalk? © H. Heck 2008 Section 5.3

Techniques for Minimizing Crosstalk In general, striplines have less crosstalk than microstrips, due to the presence of the second reference plane. This is not always true. To design a stripline to the same impedance as a microstrip may require you to increase h for the stripline. This can actually cause the crosstalk to be higher for the stripline. Increase s: For speeds of 100 MHz or higher: s  2w For speeds of 200 MHz or higher: s  3w Decrease h: For 133 MHz & higher: h  w. © H. Heck 2008 Section 5.3

Techniques for Minimizing Crosstalk #2 Limit the coupled trace length. Remember, crosstalk can occur between adjacent layers, too. Keep adjacent layers far apart. Route lines on adjacent layers orthogonally, if possible. Add “shielding”: Route “guard” traces between signal traces on PCBs. Be careful with this one. You must tie use vias to connect the guard traces to the adjacent reference layer at frequent points. Lots of ground I/O in connectors and packages. Use resistor packs instead of resistor networks. V TT S 1 4 3 2 5 7 6 V TT S 1 4 3 2 © H. Heck 2008 Section 5.3

Crosstalk noise travels in both directions. Summary Crosstalk arises from mutual capacitance and inductance between transmission lines. Crosstalk alters the impedance and propagation velocity of transmission lines, and creates noise on quiet lines. Crosstalk can be expressed in terms of the ratios of mutual capacitance to the total capacitance and mutual inductance to the self inductance. Crosstalk noise travels in both directions. © H. Heck 2008 Section 5.3

References S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1st edition. H. Johnson and M. Graham, High-Speed Signal Propagation: Advanced Black Magic, Chapters 2 & 3, Prentice Hall, 2003, 1st edition, ISBN 0-13-084408-X. W. Dally and J. Poulton, Digital Systems Engineering, Chapters 4.3 & 11, Cambridge University Press, 1998. H.B.Bakoglu, Circuits, Interconnections, and Packaging for VLSI, Addison Wesley, 1990. © H. Heck 2008 Section 5.3

References #2 H. Johnson and M. Graham, High Speed Digital Design: A Handbook of Black Magic, PTR Prentice Hall, 1993. R. Poon, Computer Circuits Electrical Design, Prentice Hall, 1st edition, 1995. R.E. Matick, Transmission Lines for Digital and Communication Networks, IEEE Press, 1995. “Line Driving and System Design,” National Semiconductor Application Note AN-991, April 1995. K.M. True, “Data Transmission Lines and Their Characteristics,” National Semiconductor Application Note AN-806, February 1996. © H. Heck 2008 Section 5.3

Noise Coupling from an Impedance Point of View Coupling occurs when the initial wave travelling on the active line reaches point z. The noise waves are the sum of the even and odd propagation modes. We can derive a coupled noise coefficient as a function of the even and odd mode impedances. © H. Heck 2008 Section 5.3

Noise Coupling #2 Define coupling coefficient: [5.3.1a] At z: [5.3.2a] Substitute: [5.3.4a] Use Ohm’s law: [5.3.5a] [5.3.6a] Substitute: [5.3.7a] Apply KCL at z: [5.3.8a] [5.3.9a] Substitute: [5.3.10a] © H. Heck 2008 Section 5.3