1. Crosstalk
Calculation and SLEM

2. 2
Topics
 Crosstalk and Impedance
 Superposition
 Examples
 SLEM
Crosstalk Calculation

3. 3
Cross Talk and Impedance
Impedance is an electromagnetic parameter
and is therefore effected by the
electromagnetic environment as shown in
the preceding slides.
In the this second half, we will focus on
looking at cross talk as a function of
impedance and some of the benefits of
viewing cross talk from this perspective.
Crosstalk Calculation

4. 4
Using Modal Impedance’s for
Calculating Cross Talk
 Any state can be described as a
superposition of the system modes.
 Points to Remember:
Each mode has an impedance and velocity
associated with it.
In homogeneous medium, all the modal
velocities will be equal.
Crosstalk Calculation

5. Super Positioning of Modes
5
For a two line case, there are two modes
Even Mode Switching Odd Mode Switching
Line 1 Line 2
Even States , Rising Edge
½ Even
Mode
V 0.5 V 0.5
Single Bit States 0 , 0 Odd Time Time
Falling Edge
Odd States
, 0 No Change
½ Odd
Mode
V 0.5 V
-0.5
Don’t Care State 0 0 (Line stays high or low, Time
Time
no transition occurs)
+
Digital States that can occur = Single
bit state
V
1.0
V
in a 2 conductor system Time Time
Total of 9 states Crosstalk Calculation

6. 6
Two Coupled Line Example
Calculate the waveforms for two coupled lines when one is driven from
the low state to the high and the other is held low.
30[Ohms] 50[inches]
S=10mils W=7mils
t=1.5 mils
H=4.5 mils Er=4.5
Input Output?
Line A
V
V ? V ?
Line A
Time
Time Time
Line B
V
1.0 V ? V ?
Line B
Time Time
Time
At Driver At Receiver
Crosstalk Calculation

7. Two Coupled Line Example
7
(Cont..)
First one needs the [L] and [C] matrices and then I need the modal
impedances and velocities.
The following [L] and [C] matrices were created in HSPICE.
30[Ohms] 50[inches]
S=10mils W=7mils
t=1.5 mils
H=4.5 mils Er=4.5
 Sanity Check:
The odd and even
velocities are the same
Lo = 3.02222e-007 Zodd 38.0 [Ohms]
3.34847e-008 3.02222e-007 Vodd 1.41E+08 [m/s]
Co = 1.67493e-010 Zeven 47.5 [Ohms]
-1.85657e-011 1.67493e-010 Veven 1.41E+08 [m/s]
Crosstalk Calculation

8. 8
Two Coupled Line Example (Cont..)
Now I deconvolve the the input voltage into the even
and odd modes:
Line A Line B
Case i Case ii
½ Even V 0.5 V 0.5
Mode
Time Time This allows one to
solve four easy
Case iii Case iv problems and
½ Odd Mode V V 0.5
-0.5 Time
simply add the
Time
solutions together!
= Single bit 1.0
V V
state
Time Time
Line A Line B
Crosstalk Calculation

9. 9
Two Coupled Line Example (Cont..)
Case i and Case ii 50[inches]
30[Ohms]
are really the same:
A 0.5[V] step into a
Zeven=47.5[Ω] Line A Line B
line:
Td=len*Veven=8.98[ns] Case i Case ii
V 0.5 V 0.5
Vinit=0.5[V]*Zeven/(Zeven+30[Ohms])
Time Time
Vinit=.306[V]
Vrcvr=2*Vinit=.612[V] Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]
Driver (even) Receiver (even) Veven 1.41E+08 [m/s]
0.612[V] 0.612[V]
0.306[V] 0.306[V]
0.000[V] 0.000[V]
0.0[ns] 9.0[ns] 0.0[ns] 9.0[ns]
Crosstalk Calculation

10. 10
Two Coupled Line Example (Cont..)
Case iii is -0.5[V] 50[inches]
30[Ohms]
step into a
Zodd=38[Ω] line:
Line A
Td=len*Vodd=8.98[ns] V Case iii
Vinit=-0.5[V]*Zodd/(Zodd+30[Ohms])
-0.5
Vinit=-.279[V] Time
Vrcvr=2*Vinit=-.558[V]
Zodd 38.0 [Ohms]
Driver (odd) Receiver (odd) Vodd 1.41E+08 [m/s]
0.558[V] 0.558[V] Zeven 47.5 [Ohms]
0.279[V] 0.279[V] Veven 1.41E+08 [m/s]
9.0[ns] 9.0[ns]
0.000[V] 0.000[V]
-.279[V] -.279[V]
-.558[V] -.558[V]
Crosstalk Calculation

11. 11
Two Coupled Line Example (Cont..)
Case iv is 0.5[V] 50[inches]
30[Ohms]
step into a
Zodd=38[Ω] line:
Line B
Td=len*Vodd=8.98[ns]
V
Case iv
0.5
Vinit=0.5[V]*Zodd/(Zodd+30[Ohms])
Vinit=.279[V] Time
Vrcvr=2*Vinit=.558[V]
Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]
Driver (odd) Receiver (odd) Veven 1.41E+08 [m/s]
0.558[V] 0.558[V]
0.279[V] 0.279[V]
0.000[V] 0.000[V]
0.0[ns] 9.0[ns] 0.0[ns] 9.0[ns]
Crosstalk Calculation

12. 12
Two Coupled Line Example (Cont..)
Line A (Driver) Line B (Driver)
.306+.279=.585[V]
1.0[V] 1.0[V]
.306-.279=.027[V]
0.5[V] 0.5[V]
0.0[V] 0.0[V]
9.0[ns] 9.0[ns]
-0.5[V] -0.5[V]
-1.0[V] -1.0[V]
Driver (odd)
Line A (Receiver) Line B (Receiver) (even)
Driver
0.558[V]
1.0[V] 1.0[V] 0.612[V]
0.279[V] 6.12-.558=
Driver (even) 9.0[ns]
.0539[V] Driver (odd)
0.5[V] 0.5[V] 0.306[V]
0.000[V]
0.612[V] 0.558[V]
0.0[V] 0.0[V] 0.000[V]
-.279[V]
0.306[V] 0.279[V] 0.0[ns] 9.0[ns]
9.0[ns] 9.0[ns]
-0.5[V] -.558[V] -0.5[V]
0.000[V] 0.000[V]
-1.0[V]
0.0[ns] 9.0[ns] -1.0[V] .612+.558=1.17[V]
0.0[ns] 9.0[ns]
Crosstalk Calculation

13. 13
Two Coupled Line Example (Cont..)
Simulating in HSPICE results are identical to
the hand calculation:
embebed
ustrip
L 3.02E-07
Lm 3.35E-08
C 1.67E-10
Cm 1.86E-11
Zodd 38.004847
Vodd 1.41E+08
Zeven 47.478047
Veven 1.41E+08
Tdelay 8.98E-09
Rin 30
Odd [V] 0.5
Even [V] 0.5
Vinit(odd) 0.2794275
Vinit(even) 0.3063968
sum 0.5858243
diff 0.0269693
2xodd 0.558855
2x(odd+even) 1.1716485
2x(even-odd) 0.0539386
Crosstalk Calculation

14. 14
Assignment1
 Use PSPICE and perform previous
simulations
Crosstalk Calculation

15. 15
Super Positioning of Modes
Continuing with the 2 line case, the following [L] and [C]
matrices were created in HSPICE for a pair of microstrips:
S=10mils W=7mils
t=1.5 mils
H=4.5 mils Er=4.5  Note:
The odd and even velocities
are NOT the same
Lo = 3.02222e-007 Zodd=47.49243354 [Ohms]
3.34847e-008 3.02222e-007 Vodd=1.77E+08[m/s]
Co = 1.15083e-010 Zeven=54.98942739 [Ohms]
-4.0629e-012 1.15083e-010 Veven=1.64E+08 [m/s]
Crosstalk Calculation

16. 16
Microstrip Example
The solution to this problem follows the same
approach as the previous example with one
notable difference.
The modal velocities are different and result in
two different Tdelays:
Tdelay (odd)= 7.19[ns]
Tdelay (even)= 7.75[ns]
This means the odd mode voltages will arrive at
the end of the line 0.56[ns] before the even mode
voltages
Crosstalk Calculation

17. 17
Microstrip Cont..
HSPICE Results:
Single Bit switching, two coupled microstrip example
ustrip
L 3.02E-07
Lm 3.35E-08
C 1.15E-10
Cm 4.06E-12
Zodd 47.492434
Vodd 1.77E+08
Zeven 54.989427
Veven 1.64E+08
Td(odd) 7.19E-09
Td(even) 7.75E-09
Rin 30
Odd [V] 0.5
Even [V] 0.5
Vinit(odd) 0.3064327
Vinit(even) 0.3235075
sum 0.6299402
diff 0.0170747
2xodd 0.6128654
2x(odd+even) 1.2598803
2x(even-odd) 0.0341495
Crosstalk Calculation

18. 18
HSPICE Results of Microstrip
Vodd 176724383
Veven
length[in]
163801995.6
50 The width of the pulse is calculated from the mode
length[m]
delay odd
1.27
7.18633E-09
velocities. Note that the widths increases in 567[ps]
delay even
delta[sec]
7.75326E-09
5.66932E-10
increments with every transit
Calculation
Crosstalk Calculation
567[ps] 1134[ps] 1701[ps] 2268[ps]

19. 19
Assignment 2 and 3
 Use PSPICE and perform previous
simulations
Crosstalk Calculation

20. 20
Modal Impedance’s for
more than 2 lines
 So far we have looked at the two line
crosstalk case, however, most practical
busses use more than two lines.
 Points to Remember:
For ‘N’ signal conductors, there are ‘N’ modes.
There are 3N digital states for N signal
conductors
Each mode has an impedance and velocity
associated with it.
In homogeneous medium, all the modal velocities
will be equal.
Any state can be described as a superposition of
the modes Crosstalk Calculation

21. 21
Three Conductor Considerations
Even States , Rising Edge
2 Bit Even States 0, 0,0 ,0 … Odd
Falling Edge
Single Bit States 0 0,0 0, , … 0 No Change
2 Bit Odd States 0, 0,0 ,0 … (Line stays high or low,
no transition occurs)
Odd States
,
The remaining states can be fit into the 1 and 2 bits cases for 27 total cases
There are 3N digital states for N signal conductors
Crosstalk Calculation

22. 22
Three Coupled Microstrip Example
S=10mils S=10mils
t=1.5 mils
H=4.5 mils W=7mils Er=4.5
From HSPICE:
Lo = 3.02174e-007
3.32768e-008 3.01224e-007
9.01613e-009 3.32768e-008 3.02174e-007
Co = 1.15088e-010
-4.03272e-012 1.15326e-010
-5.20092e-013 -4.03272e-012 1.15088e-010
Crosstalk Calculation

23. 23
Three Coupled Microstrip Example
Using the approximations gives: Actual modal info:
56.887 Z[1,1,1]=59.0[Ohms]
2 .L1 , 2
Zeven
L2 , 2
.Ut Zeven = 58.692
C2 , 2 2 . C1 , 2 Zmode = 50.355
Z[1,-1,1]=44.25[Ohms]
46.324
2 .L1 , 2
Zodd
L2 , 2
.Ut Zodd = 43.738
2 . C1 , 2
1.609.10
C2 , 2 8
Veven
1.0 Modal velocities v = 1.718.108
L2 , 2 2 1 , 2 . C2 , 2
.L 2 . C1 , 2
1.789.10
8
. 8
Veven = 1.59210
Vodd
1.0 The three mode vectors
L2 , 2 2 1 , 2 . C2 , 2
.L 2 . C1 , 2 0.53 0.707 0.467
Tv = 0.663 1.52410 15 0.751
.
.
Vodd = 1.85610
8
0.53 0.707 0.467
The Approx. impedances and velocities are pretty close to
the actual, but much simpler to calculate.
Crosstalk Calculation

24. 24
Three Coupled Microstrip Example
Single Bit Example: HSPICE Result
Crosstalk Calculation

25. 25
Points to Remember
 The modal impedances can be used to hand
calculate crosstalk waveforms
 Any state can be described as a
superposition of the modes
 For ‘N’ signal conductors, there are ‘N’
modes.
 There are 3N digital states for N signal
conductors
 Each mode has an impedance and velocity
associated with it.
 In homogeneous medium, all the modal
velocities will be equal.
Crosstalk Calculation

26. 26
Crosstalk Trends
Key Topics:
Impedance vs. Spacing
SLEM
Trading Off Tolerance vs. Spacing
Crosstalk Calculation

27. 27
Impedance vs Line Spacing
•As we have seen in the preceding sections,
1) Cross talk changes the impedance of the line
2) The further the lines are spaced apart the the
less the impedance changes
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
120
Impedance[Ohms]
100
80
60
40
20
0
5 10 15 20
Edge to Edge Spacing [mils]
Z even states Z single bit states Z odd states
Crosstalk Calculation

28. 28
Single Line Equivalent Model (SLEM)
 SLEM is an approximation that allows
some cross talk effects to be
modeled without running fully coupled
simulations
 Why would we want to avoid fully
coupled simulations?
Fully coupled simulations tend to be time
consuming and dependent on many
assumptions
Crosstalk Calculation

29. 29
Single Line Equivalent Model (SLEM)
 Using the knowledge of the cross talk
impedances, one can change a single
transmission line’s impedance to approximate:
Even, Odd, or other state coupling
Equiv to
Zo=90[Ω]
30[Ohms]
Even State
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
Coupling
120
Impedance[Ohms]
100
80
60
Zo=40[Ω]
Equiv to
30[Ohms]
40
Odd State
20
0 Coupling
5 10 15 20
Edge to Edge Spacing [mils]
Z even states Z single bit states Z odd states
Crosstalk Calculation

30. 30
Single Line Equivalent Model (SLEM)
 Limitations of SLEM
SLEM assumes the transmission line is in a
particular state (odd or even) for it’s entire
segment length
This means that the edges are in perfect phase
It also means one can not simulate random bit patterns
properly with SLEM (e.g. Odd -> Single Bit -> Even
state)
The edges maybe in
phase here, but not here V1
Time
V2
1 1
2 2 Time
3 3
V3
Three coupled lines, two with serpentining Time
Crosstalk Calculation

31. 31
Single Line Equivalent Model (SLEM)
 How does one create a SLEM model?
There are a few ways
Use the [L] and [C] matrices along with the
approximations
Use the [L] and [C] matrices along with Weimin’s
MathCAD program
Excite the coupled simulation in the desired state and
back calculate the equivalent impedance (essentially
TDR the simulation)
L2 , 2 2 .L1 , 2
Zeven .Ut
C2 , 2 2 . C1 , 2
L2 , 2 2 .L1 , 2
Zodd .Ut
C2 , 2 2 . C1 , 2 Vinit=Vin(Zstate/(Rin+Zstate))
Crosstalk Calculation

32. Trading Off Tolerance vs. Spacing
32
 Ultimately in a design you have to
create guidelines specifying the
trace spacing and specifying the
tolerance of the motherboard
impedance
i.e. 10[mil] edge to edge spacing with
10% impedance variation
 Thinking about the spacing in
terms of impedance makes this
much simpler
Crosstalk Calculation

33. 33
Trading Off Tolerance vs. Spacing
 Assume you perform simulations with no
coupling and you find a solution space with an
impedance range of
Between ~35[Ω] to ~100[Ω]
Two possible 65[Ω] solutions are
15[mil] spacing with 15% impedance tolerance
10[mil] spacing with 5% impedance tolerance
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
120
Impedance[Ohms]
100
80
60
40
20
0
5 10 15 20
Edge to Edge Spacing [mils]
Z even states Z single bit states Z odd states
Crosstalk Calculation

34. 34
Reducing Cross Talk
 Separate traces farther apart
 Make the traces short compared to the rise time
 Make the signals out of phase
Mixing signals which propagate in opposite directions may
help or hurt (recall reverse cross talk!)
 Add Guard traces
One needs to be careful to ground the guard traces
sufficiently, otherwise you could actually increase the
cross talk
At GHz frequency this becomes very difficult and should
be avoided
 Route on different layers and route orthogonally
Crosstalk Calculation

35. 35
In Summary:
 Cross talk is unwanted signals due to
coupling or leakage
 Mutual capacitance and inductance between
lines creates forward and backwards
traveling waves on neighboring lines
 Cross talk can also be analyzed as a change
in the transmission line’s impedance
 Reverse cross talk is often the dominate
cross talk in a design
(just because the forward cross talk is small or zero, does not
mean you can ignore cross talk!)
 A SLEM approach can be used to budget
impedance tolerance and trace spacing
Crosstalk Calculation