# Crosstalk

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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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