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					Crosstalk

Overview and Modes
                                             2


Overview
 What is Crosstalk?

 Crosstalk Induced Noise

 Effect of crosstalk on transmission line
  parameters

 Crosstalk Trends

 Design Guidelines and Rules of Thumb
               Crosstalk Overview
Crosstalk Induced Noise
                                          3




     Key Topics:
     Mutual Inductance and capacitance
     Coupled noise
     Circuit Model
     Transmission line matrices




                   Crosstalk Overview
Mutual Inductance and Capacitance
                                                                          4




  Crosstalk is the coupling of energy from one line
   to another via:
         Mutual capacitance (electric field)
         Mutual inductance (magnetic field)


     Mutual Capacitance, Cm                      Mutual Inductance, Lm

                      Zo
                                                             Zo
                                     Zo
                                                                     Zo
                                    far                             far
                     Cm


                                                        Lm


    Zs               near
                                                             near
                                          Zs
                Zo
                                                   Zo

                            Crosstalk Overview
                                                             5


Mutual Inductance and Capacitance
“Mechanism of coupling”
     The circuit element that represents this
       transfer of energy are the following familiar
       equations
                   dI                           dV
        VLm    Lm                  I Cm    Cm
                   dt                           dt
     The mutual inductance will induce current on the
       victim line opposite of the driving current (Lenz’s
       Law)

     The mutual capacitance will pass current through
       the mutual capacitance that flows in both
       directions on the victim line
                          Crosstalk Overview
                                                                               6


Crosstalk Induced Noise
“Coupled Currents”
   The near and far end victim line currents sum to
     produce the near and the far end crosstalk
     noise       Zo
                                                            Zo
                                      Zo
                                                                          Zo
                                      far                                far

                              ICm
                                                       Lm          ILm

      Zs              near                                  near
                                            Zs
                 Zo
                                                  Zo




           I near  I Cm  I Lm         I far  I Cm  I Lm

                             Crosstalk Overview
                                                                       7


Crosstalk Induced Noise
“Voltage Profile of Coupled Noise”
 Near end crosstalk is always positive
      Currents from Lm and Cm always add and flow into the
      node
 For PCB’s, the far end crosstalk is “usually”
   negative
      Current due to Lm larger than current due to Cm
      Note that far and crosstalk can be positive
                                              Zo
                                                                 Zo

                                                             Far End
                        Driven Line

                                                      Un-driven Line
                                                         “victim”


                       Zs                  Near End
              Driver                  Zo


                               Crosstalk Overview
                                                                                                    8


Graphical Explanation
 Time = 0        Near end crosstalk pulse at T=0 (Inear)
                                                                                 ~Tr    Near end
     V                                                                                  crosstalk
                                                     Zo
                                                                        TD

               Far end crosstalk pulse at T=0 (Ifar)
Time= 1/2 TD                                                         ~Tr

                                                                           2TD
  V
         Zo
                                                                                       far end
                                                    Zo                                 crosstalk


Time= TD
 V
         Zo                                              Zo    Far end of current
                                                               terminated at T=TD


Time = 2TD
 V
                                                                Near end current
                                                          Zo
                                                                terminated at T=2TD
         Zo

                               Crosstalk Overview
                                                                                                                           9


Crosstalk Equations                                                                                   TD

                                          Zo                                 Vinput  LM CM 
                                                                        A              
 Terminated Victim                                          Zo                 4  L     C 
                                                                                            
                                                         Far End          TD  X LC
                Driven Line

                                                 Un-driven Line          Vinput X LC  LM CM 
                                                                   B                L  C 
                                                    “victim”                  2Tr                                    A
                                                                                                                           B
               Zs                    Near End
    Driver                      Zo
                                                                                                     Tr    ~Tr    Tr
                                                                   TD
                                                                                                          2TD
      Far End                        Zo

     Open Victim
                                                                                                   Vinput  LM C M 
                                                                                                A            
                                                                                                     4  L      C 
                                                      Far End
             Driven Line                                                                                          
                                               Un-driven Line
                                                  “victim”                              A                   1
                                                                                            B         B      C
                                                                                                C           2
          Zs                     Near End
 Driver                    Zo                                      Tr    ~Tr    ~Tr        Vinput X LC  LM C M 
                                                                                       C              L  C 
                                                                                                  Tr           
                                                                        2TD
                                                      Crosstalk Overview
                                                                                                        10


Crosstalk Equations                                                            TD



   Near End Open Victim
                                                           Vinput  LM C M 
                             Zo
                                                      A              
                                                Zo           2  L     C 
                                            Far End
                                                                                                A       C
            Driven Line                                  Vinput  LM C M 
                                                      C                                           B
                                     Un-driven Line        4  L     C 
                                        “victim”
                                                                               Tr    Tr    Tr
                                                      Vinput X LC  LM C M 
           Zs             Near End             B                 L  C          2TD
  Driver                                                   2Tr            
                                                                                     3TD




      The Crosstalk noise characteristics are
           dependent on the termination of the victim line


                                          Crosstalk Overview
Creating a Crosstalk Model                                                                   11



“Equivalent Circuit”

 The circuit must be distributed into N segments as
     shown in chapter 2
                             C12
           Line 1                  Line 2                                  L12
                                                                K
                C1G                     C2G                               L11L22
  L11(1)                           L11(2)                             L11(N)
                                                            Line 1

                    C1G(1)                         C1G(2)                          C1G(N)

K1                            K1                                     K1        C12(n)
              C12(1)                          C12(2)

                                                            Line 2

  L22(1)             C2G(1)        L22(2)              C2G(2)         L22(N)            C2G(N)
                                       Crosstalk Overview
Creating a Crosstalk Model                                 12



“Transmission Line Matrices”

 The transmission line Matrices are used to
  represent the electrical characteristics

 The Inductance matrix is shown, where:
     LNN = the self inductance of line N per unit length
     LMN = the mutual inductance between line M and N


                           L11       L12 ... L1N 
                          L          L22         
      Inductance Matrix =  21                    
                                                 
                                                 
                           LN 1              LNN 


                       Crosstalk Overview
Creating a Crosstalk Model                                  13



“Transmission Line Matrices”
 The Capacitance matrix is shown, where:
     CNN = the self capacitance of line N per unit length
     where:
              C NN  C NG   Cm utuals

     CNG = The capacitance between line N and ground
     CMN = Mutual capacitance between lines M and N
                              C11    C12   ...   C1 N 
                             C       C22              
     Capacitance Matrix =     21                      
                                                      
                                                      
                             C N 1               C NN 


 For example, for the 2 line circuit shown earlier:
                  C11  C1G  C12
                      Crosstalk Overview
                                                                               14


                                 Example
Calculate near and far end crosstalk-induced noise magnitudes and sketch the
waveforms of circuit shown below:



            v
                 R1                           R2
Vsource=2V, (Vinput = 1.0V), Trise = 100ps.
Length of line is 2 inches. Assume all terminations are 70 Ohms.
Assume the following capacitance and inductance matrix:

           9.869nH      2.103nH 
L / inch = 
           2.103nH      9.869nH 
                                 

            2.051 pF    0.239 pF 
C / inch = 
           0.239 pF     2.051 pF 
                                  
                                                      L11   9.869nH
The characteristic impedance is:               ZO                   69.4
                                                      C11   2.051 pF
Therefore the system has matched termination.

The crosstalk noise magnitudes can be calculated as follows:
                                 Crosstalk Overview
                                                                                                                 15



                                Example (cont.)
 Near end crosstalk voltage amplitude (from slide 12):
                                    Vinput  L12 C12  1V             2.103nH 0.239 pF 
                            Vnear                                9.869nH  2.051 pF   0.082V
                                      4  L11 C11  4                                    

  Far end crosstalk voltage amplitude (slide 12):
          Vinput ( X LC )  L12 C12  1V * 2inch * 9.869nH * 2.051 pF          2.103nH 0.239 pF 
V far                    L C 
                                                                             9.869nH  2.051 pF   0.137V
                                                                                                  
                2Trise     11   11              2 *100 ps                                       

     The propagation delay of the 2 inch line is:
                 TD  X LC  2inch * (9.869nH * 2.051nH  0.28ns
                                    200mV/div




                   Thus,


                                                Crosstalk Overview
                                                   100ps/div
                                                16


Effect of Crosstalk on
Transmission line Parameters
     Key Topics:
     Odd and Even Mode Characteristics
     Microstrip vs. Stripline
     Modal Termination Techniques
     Modal Impedance’s for more than 2 lines
     Effect Switching Patterns
     Single Line Equivalent Model (SLEM)



                    Crosstalk Overview
                                                                    17


Odd and Even Transmission Modes
  Electromagnetic Fields between two driven coupled lines will
   interact with each other
  These interactions will effect the impedance and delay of the
   transmission line
  A 2-conductor system will have 2 propagation modes
       Even Mode (Both lines driven in phase)
       Odd Mode (Lines driven 180o out of phase)

           Even Mode




            Odd Mode




  The interaction of the fields will cause the system electrical
   characteristics to be directly dependent on patterns
                          Crosstalk Overview
Odd Mode Transmission                                                                       18




 Potential difference between the conductors lead to an
  increase of the effective Capacitance equal to the mutual
  capacitance
       +1       -1                                +1        -1

                           Electric Field:                                Magnetic Field:
                           Odd mode                                       Odd mode



 Because currents are flowing in opposite directions, the total
  inductance is reduced by the mutual inductance (Lm)

                                                                        dI      d ( I )
            Drive (I)                                  V         V  L  Lm
                                                                         dt       dt
      Induced (-ILm)                                   I                     dI
                          Induced (ILm)      Lm                   ( L  Lm)
                                                                             dt

             Drive (-I)                                -I
                             Crosstalk Overview
Odd Mode Transmission                                                         19


“Derivation of Odd Mode Inductance”

                                         I1           L11
 Mutual Inductance:
          Consider the circuit:                      + V1 -          Lm
                                                                k
                                         I2          + V2 -          L11L22
                 dI 1     dI
          V1  LO      Lm 2
                 dt        dt                         L22
                 dI       dI
          V2  LO 2  Lm 1
                  dt       dt

Since the signals for odd-mode switching are always opposite, I1 = -I2 and
V1 = -V2, so that: V  L dI 1  L d ( I 1 )  ( L  L ) dI 1
                     1    O         m            O          m
                           dt        dt                    dt
                           dI      d ( I 2 )              dI
                    V2  LO 2  Lm             ( LO  Lm ) 2
                            dt        dt                    dt
Thus, since LO = L11 = L22,
                     Lodd  L11  Lm  L11  L12

Meaning that the equivalent inductance seen in an odd-mode environment
is reduced by the mutual inductance.
                                Crosstalk Overview
Odd Mode Transmission                                                        20


  “Derivation of Odd Mode Capacitance”
                                                       V2
Mutual Capacitance:
          Consider the circuit:              C1g             Cm

      C1g = C2g = CO = C11 – C12             C2g        V2

So,             dV1      d (V1  V2 )               dV      dV
        I1  CO      Cm               (C O  C m ) 1  C m 2
                 dt           dt                     dt      dt
                dV       d (V2  V1 )               dV       dV
        I 2  CO 2  C m               (C O  C m ) 2  C m 1
                 dt           dt                      dt      dt
And again, I1 = -I2 and V1 = -V2, so that:
                 dV1      d (V1  (V1 ))                 dV
        I 1  CO      Cm                  (C1g  2C m ) 1
                  dt            dt                         dt
                 dV2      d (V2  (V2 ))                  dV
        I 2  CO      Cm                   (C O  2C m ) 2
                  dt             dt                         dt
Thus,      Codd  C1g  2Cm  C11  Cm
 Meaning that the equivalent capacitance for odd mode switching increases.
                                  Crosstalk Overview
Odd Mode Transmission                                               21


“Odd Mode Transmission Characteristics”


 Impedance:
 Thus the impedance for odd mode behavior is:
                           Lodd   L11  L12
                 Z odd         
                           Codd   C11  C12
                 ( Note : Z differential  2 Z odd ) Explain why.

  Propagation Delay:
 and the propagation delay for odd mode behavior is:


         TDodd  LoddCodd  ( L11  L12 )(C11  C12 )



                           Crosstalk Overview
Even Mode Transmission                                                                        22




 Since the conductors are always at a equal potential, the
    effective capacitance is reduced by the mutual capacitance
                  +1          +1                                      +1        +1
Electric Field:                                     Magnetic Field:
Even mode                                           Even mode




 Because currents are flowing in the same direction, the total
    inductance is increased by the mutual inductance (Lm)
                                                                             dI      d (I )
                  Drive (I)                                 V         V L       Lm
                                                                             dt       dt
          Induced (ILm)                                     I                     dI
                               Induced (ILm)       Lm                  ( L  Lm)
                                                                                  dt

                  Drive (I)                                 I
                                   Crosstalk Overview
Even Mode Transmission                                                                 23



Derivation of even Mode Effective Inductance

                                                                 L11
  Mutual Inductance:                                       I1
              Again, consider the circuit:                      + V1 -        Lm
                                       dI     dI                         k
                                V1  LO 1  Lm 2           I2   + V2 -        L11L22
                                       dt      dt
                                       dI     dI                 L22
                                V2  LO 2  Lm 1
                                        dt     dt
Since the signals for even-mode switching are always equal and in the same
direction so that I1 = I2 and V1 = V2, so that:
          dI1      d ( I1 )               dI
   V1  LO     Lm           ( LO  Lm ) 1
          dt         dt                   dt
          dI       d (I 2 )                dI
   V2  LO 2  Lm             ( LO  Lm ) 2
           dt         dt                   dt

  Thus,        Leven  L11  Lm  L11  L12

  Meaning that the equivalent inductance of even mode behavior increases
  by the mutual inductance.
                                      Crosstalk Overview
Even Mode Transmission                                                24



Derivation of even Mode Effective Capacitance
                                                           V2
Mutual Capacitance:
             Again, consider the circuit:            C1g         Cm

                                                 C2g        V2
          dV1      d (V1  V1 )      dV
  I 1  CO     Cm               CO 1
           dt          dt             dt
          dV       d (V2  V2 )       dV
  I 2  CO 2  C m                CO 2
           dt           dt             dt


 Thus,          Ceven  C0  C11  Cm


 Meaning that the equivalent capacitance during even mode behavior
 decreases.


                                Crosstalk Overview
Even Mode Transmission                                     25


“Even Mode Transmission Characteristics”

Impedance:
 Thus the impedance for even mode behavior is:

                          Leven   L11  L12
                 Z even        
                          Ceven   C11  C12

 Propagation Delay:
 and the propagation delay for even mode behavior is:


         TDeven  LevenCeven  ( L11  L12 )(C11  C12 )




                          Crosstalk Overview
                                                                         26


Odd and Even Mode Comparison for
Coupled Microstrips
                                Even mode (as seen on line 1)
    Input waveforms
                                                Impedance difference


          V1
                                             Odd mode (Line 1)
                                           Line 1          Probe point

                    v1
                         v2                Line2


    V2         Delay difference due to modal velocity differences



                      Crosstalk Overview
Microstrip vs. Stripline Crosstalk                               27



Crosstalk Induced Velocity Changes

 Chapter 2 defined propagation delay as T   r
                                             pd
                                                   c
 Chapter 2 also defined an effective dielectric constant that
  is used to calculate the delay for a microstrip that accounted
  for a portion of the fields fringing through the air and a
  portion through the PCB material

 This shows that the propagation delay is dependent on the
  effective dielectric constant

 In a pure dielectric (homogeneous), fields will not fringe
  through the air, subsequently, the delay is dependent on the
  dielectric constant of the material




                       Crosstalk Overview
Microstrip vs. Stripline Crosstalk                                 28



Crosstalk Induced Velocity Changes

 Odd and Even mode electric fields in a microstrip
  will have different percentages of the total field
  fringing through the air which will change the
  effective Er
      Leads to velocity variations between even and odd
Microstrip E field patterns                +1   -1
          +1      +1
  Er=1.0                                                  Er=1.0

  Er=4.2                                                  Er=4.2




 The effective dielectric constant, and subsequently
  the propagation velocity depends on the electric
  field patterns
                      Crosstalk Overview
Microstrip vs. Stripline Crosstalk                                   29



Crosstalk Induced Velocity Changes

 If the dielectric is homogeneous (I.e., buried microstrip or
   stripline) , the effective dielectric constant will not change
   because the electric fields will never fringe through air

Stripline E field patterns
           +1      +1                        +1   -1

                                                            Er=4.2
  Er=4.2




 Subsequently, if the transmission line is implemented in a
   homogeneous dielectric, the velocity must stay constant
   between even and odd mode patterns


                        Crosstalk Overview
Microstrip vs. Stripline Crosstalk                                   30



    Crosstalk Induced Noise

 The constant velocity in a homogeneous media (such
     as a stripline) forces far end crosstalk noise to be
     zero TDodd  TDeven
             ( L11  L12 )(C11  C12 )  ( L11  L12 )(C11  C12 )
            L12C11  L11C12   L11C12  L12C11
           L12 C12
              
           L11 C11
 Since far end crosstalk takes the following form:
                                       Vinput X LC  L12 C12 
      Crosstalk ( far _ stripline)                       0
                                            2Tr     L11 C11 
    Far end crosstalk is zero for a homogeneous Er
                              Crosstalk Overview
Termination Techniques                                                      31



    Pi and T networks
 Single resistor terminations described in chapter 2
     do not work for coupled lines
    3 resistor networks can be designed to terminate
     both odd and even modes

T Termination                           Odd Mode     +1   R1

                                        Equivalent
                    R1    R3                         -1   R2

                    R2                                    Virtual Ground
                                                          in center
                  -1
                                                                     2R3
     R1  R2  Z odd                   Even Mode     +1    R1
                                       Equivalent
     R3  Z even  Z odd 
          1                                          +1
                                                                      2R3
                                                                R2
          2              Crosstalk Overview
Termination Techniques                                           32



 Pi and T networks

 The alternative is a PI termination
PI Termination
                                                            R1
                     R1

                                  Odd Mode
                                               +1    ½ R3
                     R3
                                  Equivalent
                                               -1    ½ R3

                      R2                                    R2
             -1

                                                    +1      R1
  R1  R2  Z even                Even Mode
                                  Equivalent        +1      R2
          Z evenZ odd
  R3  2
         Z even  Z oddCrosstalk Overview

				
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