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1
Crosstalk is the coupling of energy from one line
to another via:
Mutual capacitance (electric field)
CrosstalkCrosstalk
Mutual inductance (magnetic field)
Zo
Zo
Mutual Capacitance, Cm Mutual Inductance, L^ m
Zo
Zo
far far
Crosstalk Overview
Zs Zo Zs Zo
Cm
Lm
near near
2
The circuit element that represents this
transfer of energy are the following familiar
equations
Mutual Inductance and CapacitanceMutual Inductance and Capacitance
““Mechanism of coupling”Mechanism of coupling”
equations
dt
dI
V L Lm m =
dt
dV
I C
Cm m
The mutual inductance will induce current on the
victim line opposite of the driving current (Lenz’s
Law)
Crosstalk Overview
Law)
The mutual capacitance will pass current through
the mutual capacitance that flows in both
directions on the victim line
3
The near and far end victim line currents sum to
produce the near and the far end crosstalk
noise
Crosstalk Induced NoiseCrosstalk Induced Noise
““Coupled Currents”Coupled Currents”
noise
Zs
Zo
Zo
Zs
Zo
Zo
I (^) Cm Lm
near
far
near
far
I (^) Lm
Crosstalk Overview
Zo
Zs
Zo
near Cm Lm far Cm Lm
I =I +I I =I −I
4
Near end crosstalk is always positive
Currents from Lm and Cm always add and flow into the
node
Crosstalk Induced NoiseCrosstalk Induced Noise
““Voltage Profile of Coupled Noise”Voltage Profile of Coupled Noise”
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
Crosstalk Overview
Driven Line
Un-driven Line “victim”
Driver
Zs
Zo
Near End
7 Creating a Crosstalk ModelCreating a Crosstalk Model
““Equivalent Circuit”Equivalent Circuit”
The circuit must be distributed into N segments as
shown in chapter 2
C 12
L
L 11 (1)
C (1)
L11(2)
C (2)
L 11 (N)
C (N)
C1G C2G
L L
L
K =
Line 1
Line 1 Line 2
Crosstalk Overview
K
L 22 (1)
C1G(1)
C 12 (1)
K
L 22 (2)
C1G(2)
C 12 (2)
C2G(1) C2G(2)
K
L 22 (N)
C1G(N)
C 12 (n)
C2G(N)
Line 2
8
The transmission line Matrices are used to
represent the electrical characteristics
Creating a Crosstalk ModelCreating a Crosstalk Model
““Transmission Line Matrices”Transmission Line Matrices”
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
⎡ N
L L
L L L
11 12 1
Crosstalk Overview
Inductance Matrix =
⎣ N NN
L L
L L
1
21 22
9
The Capacitance matrix is shown, where:
CNN = the self capacitance of line N per unit length
where:
Creating a Crosstalk ModelCreating a Crosstalk Model
““Transmission Line Matrices”Transmission Line Matrices”
∑
C = C + C
CNG = The capacitance between line N and ground
CMN = Mutual capacitance between lines M and N
Capacitance Matrix =
⎡ N
C C
C C C
21 22
∑
NN NG mutuals
C C C
Crosstalk Overview
⎣ N^ NN
C 1 C
11 1 12
C C C
G
For example, for the 2 line circuit shown earlier:
10
Example
Calculate near and far end crosstalk-induced noise magnitudes and sketch the waveforms of circuit shown below:
v
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:
L / inch = ⎥ ⎦
nH nH
nH nH
⎡ 2051 pF^0239 pF ⎤
v
R 1 R 2
Crosstalk Overview
C / inch =
The characteristic impedance is:
Therefore the system has matched termination.
The crosstalk noise magnitudes can be calculated as follows:
pF pF
pF pF
11
11
pF
nH
C
L
Z O
13
Electromagnetic Fields between two driven coupled lines will
interact with each other
These interactions will effect the impedance and delay of the
transmission line
Odd and Even Transmission ModesOdd and Even Transmission Modes
transmission line
A 2-conductor system will have 2 propagation modes
Even Mode (Both lines driven in phase)
Odd Mode (Lines driven 180 o out of phase)
Even Mode
Crosstalk Overview
The interaction of the fields will cause the system electrical
characteristics to be directly dependent on patterns
Odd Mode
14
Potential difference between the conductors lead to an
increase of the effective Capacitance equal to the mutual
capacitance
Odd Mode TransmissionOdd Mode Transmission
Magnetic Field:
Odd mode
Electric Field:
Odd mode
Because currents are flowing in opposite directions, the total
inductance isreduced by the mutual inductance (Lm)
Crosstalk Overview
Drive (I)
Drive (-I)
Induced (-ILm) Induced (I Lm
V
-I
Lm
dt
dI
L Lm
dt
d I
Lm
dt
dI
V L
I
15 Odd Mode TransmissionOdd Mode Transmission
““Derivation of Odd Mode Inductance”Derivation of Odd Mode Inductance”
Mutual Inductance:
Consider the circuit:
dI L
dI V L 1 2
L 11 L 22
L k m =
L 11
I 2
I 1
dt
dI L dt
dI V L
dt
dI L dt
dI V L
O m
O m
2 1 2
1 2 1
= +
= + L 22
Since the signals for odd-mode switching are always opposite, I 1 = -I 2 and
V 1 = -V 2 , so that:
dI L L
d I L
dI V L
dt
dI L L dt
d I L dt
dI V L
O m O m
O m O m
2 2 2 2
1 1 1 1
( )
( )
( )
( )
= −
− = +
= −
− = +
Crosstalk Overview
L (^) odd =L 11 −Lm=L 11 −L 12
dt dt dt
2 O m (O m)
Thus, since L O = L 11 = L22,
Meaning that the equivalent inductance seen in an odd-mode environment
is reduced by the mutual inductance.
16 Odd Mode TransmissionOdd Mode Transmission
““Derivation of Odd Mode Capacitance”Derivation of Odd Mode Capacitance”
Mutual Capacitance:
Consider the circuit:
C2g
C1g Cm
V 2
V 2
CC1g1g = CC2g2g = CCOO = CC 1111 – CC 1212 C2g
So,
dt
dV C dt
dV C C dt
dV V C dt
dV I C
dt
dV C dt
dV C C dt
dV V C dt
dV I C
O m O m m
O m O m m
2 2 1 2 1 2
1 1 2 1 2 1
And again, I 1 = -I 2 and V 1 = -V 2 , so that:
dV C C
dV V C
dV I C
1 1 1 1 ( 2 )
Crosstalk Overview
Codd = C 1 g + 2 Cm=C 11 +C m
dt
dV C C dt
dV V C dt
dV I C
dt
C C
dt
C
dt
I C
O m O m
O m g m
2 2 2 2 2
1 1
Thus,
Meaning that the equivalent capacitance for odd mode switching increases.
19
Even Mode TransmissionEven Mode Transmission
Derivation ofDerivation of even Mode Effective Inductanceeven Mode Effective Inductance
L 11 L 22
L k = m
L 11
I 2
I 1
Mutual Inductance:
Again, consider the circuit:
dI L
dI V LO
1 2 1 = +
L 22
Since the signals for even-mode switching are always equal and in the same
direction so that I 1 = I 2 and V 1 = V 2 , so that:
dt
dI L dt
dI V L
dt
L dt
V L
O m
O m
2 1 2
1
= +
dI L L
dI L
dI V L
dt
dI L L dt
dI L dt
dI V LO m O m
2 2 2
1 1 1 1
( )
( )
( )
( ) = + = +
Crosstalk Overview
Leven =L 11 +Lm=L 11 +L 12
dt
L L dt
L dt
V LO m O m 2 2 2 2 ( )
( ) = + = +
Thus,
Meaning that the equivalent inductance of even mode behavior increases
by the mutual inductance.
20 Even Mode TransmissionEven Mode Transmission
Derivation ofDerivation of even Mode Effective Capacitanceeven Mode Effective Capacitance
Mutual Capacitance:
Again, consider the circuit: C1g
Cm
V 2
V
Ceven = C 0 =C 11 −C m
C2g
V 2
dt
dV C dt
dV V C dt
dV I C
dt
dV C dt
dV V C dt
dV I C
O m O
O m O
2 2 2 2 2
1 1 1 1 1
Thus,
Crosstalk Overview
even 0 11 m
Meaning that the equivalent capacitance during even mode behavior
decreases.
21 Even Mode TransmissionEven Mode Transmission
““Even Mode Transmission Characteristics”Even Mode Transmission Characteristics”
Impedance:
Thus the impedance for even mode behavior is:
11 12
11 12
C C
L L
C
L
Z
even
even even
and the propagation delay for even mode behavior is:
Propagation Delay:
Crosstalk Overview
11 12 11 12
TD L C L L C C
even even even
22
Odd and Even Mode Comparison forOdd and Even Mode Comparison for
Coupled MicrostripsCoupled Microstrips
Input waveforms
Even mode (as seen on line 1)
Input waveforms
Odd mode (Line 1)
v 1
Probe point
Impedance difference
V
Line 1
Crosstalk Overview
v 2
V2 Delay difference due to modal velocity differences
Line
25 Microstrip vs. Stripline CrosstalkMicrostrip vs. Stripline Crosstalk
Crosstalk Induced Velocity ChangesCrosstalk 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
Er=4.
Er=4.
Stripline E field patterns
Crosstalk Overview
Subsequently, if the transmission line is implemented in a
homogeneous dielectric, the velocity must stay constant
between even and odd mode patterns
26 Microstrip vs. Stripline CrosstalkMicrostrip vs. Stripline Crosstalk
Crosstalk Induced NoiseCrosstalk Induced Noise
The constant velocity in a homogeneous media (such
as a stripline) forces far end crosstalk noise to be
zero TD TD
dd
11
12
11
12
12 11 11 12 11 12 12 11
11 12 11 12 11 12 11 12
C
C
L
L
L C LC L C L C
L L C C L L C C
TD TD
odd even
Since far end crosstalk takes the following form:
Crosstalk Overview
( _ )
11
12
11
12
C
C
L
L
T
V X LC
Crosstalk far stripline
r
input
Since far end crosstalk takes the following form:
Far end crosstalk is zero for a homogeneous Er
27 Termination TechniquesTermination Techniques
Pi and T networksPi and T networks
Single resistor terminations described in chapter 2
do not work for coupled lines
3 resistor networks can be designed to terminate
bboth odd and even modes h dd d d
T Termination
R 1
R 2
R 3
Odd Mode
Equivalent
R 1
R
2
Virtual Ground
Crosstalk Overview
in center
Even Mode
Equivalent
R 1
R
2
2R 3
2R
3
odd R = R =Z 1 2
( ) even odd
R = Z −Z
2
1
28 Termination TechniquesTermination Techniques
Pi and T networksPi and T networks
The alternative is a PI termination
PI Termination
Odd Mode
Equivalent
R 1
R 2
R 3
½ R
3
½ R 3
R 1
R
2
Crosstalk Overview
Even Mode
Equivalent
R 1
R 2
even
R = R =Z 1 2
even odd
even odd
Z Z
Z Z R
−
= 2 3
