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
Key Topics:
Mutual Inductance and capacitance
Coupled noise
Circuit Model
Transmission line matrices
Crosstalk Overview
3
Mutual Inductance and Capacitance
 Crosstalk is the coupling of energy from one line
to another via:
Mutual capacitance (electric field)
Mutual inductance (magnetic field)
Mutual Inductance, Lm
Mutual Capacitance, Cm
Zo
Zo
Zo
Zo
far
far
Cm
Lm
near
Zs
Zo
near
Zs
Zo
Crosstalk Overview
4
Mutual Inductance and Capacitance
“Mechanism of coupling”
 The circuit element that represents this
transfer of energy are the following familiar
equations
VLm
dI
 Lm
dt
I Cm
dV
 Cm
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
5
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
ILm
Lm
near
Zs
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
Driver
Near End
Zo
Crosstalk Overview
8
Graphical Explanation
Time = 0
Near end crosstalk pulse at T=0 (Inear)
~Tr
V
Zo
Near end
crosstalk
TD
Far end crosstalk pulse at T=0 (Ifar)
~Tr
Time= 1/2 TD
2TD
V
Zo
far end
crosstalk
Zo
Time= TD
V
Zo
Zo
Far end of current
terminated at T=TD
Time = 2TD
V
Zo
Zo
Crosstalk Overview
Near end current
terminated at T=2TD
9
Crosstalk Equations
TD
Zo
Terminated Victim
A
Zo
Vinput  LM CM 

4  L
C 
TD  X LC
Far End
Driven Line
Un-driven Line
“victim”
B
Vinput X LC  LM CM 
 L  C 
2Tr


A
B
Zs
Near End
Driver
Zo
Tr
~Tr
Tr
TD
2TD
Far End
Open Victim
Zo
Vinput  LM C M 
A

4  L
C 
Far End
Driven Line
Un-driven Line
“victim”
A
B
Zs
Driver
B
C
1
C
2
Near End
Zo
Tr
~Tr
2TD
Crosstalk Overview
~Tr
Vinput X LC  LM C M 
C
 L  C 
Tr
10
Crosstalk Equations
TD
Near End Open Victim
A
Zo
Zo
Vinput  LM C M 

2  L
C 
Far End
Driven Line
Un-driven Line
“victim”
Zs
Driver
Near End
B
Vinput X LC  LM C M 
 L  C 
2Tr


B
Tr
Tr
Tr
2TD
3TD
 The Crosstalk noise characteristics are
dependent on the termination of the victim line
Crosstalk Overview
C
A
Vinput  LM CM 
C

4  L
C 
Creating a Crosstalk Model
11
“Equivalent Circuit”
 The circuit must be distributed into N segments as
shown in chapter 2
C12
Line 2
Line 1
C1G
C2G
C1G(1)
K1
K
L11(2)
L11(1)
C12(1)
L12
L11L22
Line 1
L11(N)
C1G(N)
C1G(2)
K1
K1
C12(2)
C12(n)
Line 2
L22(1)
C2G(1)
L22(2)
C2G(2)
Crosstalk Overview
L22(N)
C2G(N)
Creating a Crosstalk Model
“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
L
Inductance Matrix =  21


 LN 1
L12 ...
L22
Crosstalk Overview
L1N 




LNN 
12
Creating a Crosstalk Model
“Transmission Line Matrices”
 The Capacitance matrix is shown, where:
CNN = the self capacitance of line N per unit length
where:
CNN  CNG   Cmutuals
CNG = The capacitance between line N and ground
CMN = Mutual capacitance between lines M and N
Capacitance Matrix =
 C11
C
 21


CN 1
C12
C22
...
C1N 




CNN 
 For example, for the 2 line circuit shown earlier:
C11  C1G  C12
Crosstalk Overview
13
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
2.103nH 
9.869nH 
 2.051 pF
0.239 pF
0.239 pF 
2.051 pF 
L / inch = 
C / inch = 
The characteristic impedance is:
ZO 
L11
9.869nH

 69.4
C11
2.051 pF
Therefore the system has matched termination.
The crosstalk noise magnitudes can be calculated as follows:
Crosstalk Overview
14
15
Example (cont.)
Near end crosstalk voltage amplitude (from slide 12):
Vnear
Vinput  L12 C12  1V




4  L11 C11  4
 2.103nH 0.239 pF 
 9.869nH  2.051 pF   0.082V


Far end crosstalk voltage amplitude (slide 12):
V far 
Vinput ( X LC )  L12 C12  1V * 2inch * 9.869nH * 2.051 pF

 

2Trise
L
C
2 *100 ps
11 
 11
 2.103nH 0.239 pF 

  0.137V

 9.869nH 2.051 pF 
The propagation delay of the 2 inch line is:
Thus,
200mV/div
TD  X LC  2inch * (9.869nH * 2.051nH  0.28ns
Crosstalk
Overview
100ps/div
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
16
Odd and Even Transmission Modes
17
 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:
Odd mode
Magnetic Field:
Odd mode
 Because currents are flowing in opposite directions, the total
inductance is reduced by the mutual inductance (Lm)
V
Drive (I)
Induced (-ILm)
Induced (ILm)
Lm
Drive (-I)
Crosstalk Overview
I
-I
dI
d ( I )
V  L  Lm
dt
dt
dI
 ( L  Lm)
dt
Odd Mode Transmission
19
“Derivation of Odd Mode Inductance”
L11
I1
Mutual Inductance:
+ V1
+ V2 -
Consider the circuit:
I2
dI 1
dI
 Lm 2
dt
dt
dI
dI
V2  LO 2  Lm 1
dt
dt
V1  LO
k
Lm
L11 L22
L22
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
C1g = C2g = CO = C11 – C12
C2g
So,
Cm
V2
dV1
d (V1  V2 )
dV
dV
 Cm
 (C O  C m ) 1  C m 2
dt
dt
dt
dt
dV2
d (V2  V1 )
dV
dV
I 2  CO
 Cm
 (C O  C m ) 2  C m 1
dt
dt
dt
dt
I1  CO
And again, I1 = -I2 and V1 = -V2, so that:
dV1
d (V1  (V1 ))
dV
 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
I1  CO
Thus,
Codd  C1g  2C m  C11  Cm
Meaning that the equivalent capacitance for odd mode switching increases.
Crosstalk Overview
Odd Mode Transmission
“Odd Mode Transmission Characteristics”
Impedance:
Thus the impedance for odd mode behavior is:
Z odd
Lodd
L11  L12


Codd
C11  C12
( Note : Z differential  2 Z odd ) Explain why.
Propagation Delay:
and the propagation delay for odd mode behavior is:
TDodd  Lodd Codd  ( L11  L12 )(C11  C12 )
Crosstalk Overview
21
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
Magnetic Field:
Even mode
Electric Field:
Even mode
 Because currents are flowing in the same direction, the total
inductance is increased by the mutual inductance (Lm)
V
Drive (I)
Induced (ILm)
Induced (ILm)
Lm
Drive (I)
I
I
Crosstalk Overview
dI
d (I )
 Lm
dt
dt
dI
 ( L  Lm)
dt
V L
Even Mode Transmission
23
Derivation of even Mode Effective Inductance
Mutual Inductance:
I1
Again, consider the circuit:
dI
dI
V1  LO 1  Lm 2
dt
dt
dI
dI
V2  LO 2  Lm 1
dt
dt
L11
+ V1
I2
+ V2 -
k
Lm
L11 L22
L22
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
 Lm
 ( LO  Lm ) 1
dt
dt
dt
dI
d (I2 )
dI
V2  LO 2  Lm
 ( LO  Lm ) 2
dt
dt
dt
V1  LO
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
dV1
d (V1  V1 )
dV
 Cm
 CO 1
dt
dt
dt
dV
d (V2  V2 )
dV
I 2  CO 2  C m
 CO 2
dt
dt
dt
C2g
Cm
V2
I 1  CO
Thus,
Ceven  C0  C11  Cm
Meaning that the equivalent capacitance during even mode behavior
decreases.
Crosstalk Overview
Even Mode Transmission
“Even Mode Transmission Characteristics”
Impedance:
Thus the impedance for even mode behavior is:
Z even
Leven
L11  L12


Ceven
C11  C12
Propagation Delay:
and the propagation delay for even mode behavior is:
TDeven  Leven Ceven  ( L11  L12 )(C11  C12 )
Crosstalk Overview
25
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
V2
Line2
Delay difference due to modal velocity differences
Crosstalk Overview
26
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
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
30
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
R1
R3
Odd Mode
Equivalent
+1
R1
-1
R2
R2
Virtual Ground
in center
-1
R1  R2  Z odd
1
R3  Z even  Z odd 
2
Crosstalk Overview
Even Mode
Equivalent
+1
2R3
R1
+1
R2
2R3
Termination Techniques
32
Pi and T networks
 The alternative is a PI termination
PI Termination
R1
R1
R3
-1
Odd Mode
Equivalent
+1
½ R3
-1
½ R3
R2
R2
Even Mode
R1  R2  Z even
Equivalent
Z even Z odd
R3  2
Z even  Z oddCrosstalk Overview
+1
+1
R1
R2