Class20 CrosstalkII Calculations
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Transcript of Class20 CrosstalkII Calculations
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Crosstalk
Calculation and SLEM
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Crosstalk Calculation
Topics
Crosstalk and Impedance
Superposition
Examples
SLEM
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Crosstalk Calculation
Cross Talk and Impedance
Impedance is an electromagnetic parameterand is therefore effected by theelectromagnetic environment as shown inthe preceding slides.
In the this second half, we will focus on
looking at cross talk as a function ofimpedance and some of the benefits ofviewing cross talk from this perspective.
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Crosstalk Calculation
Using Modal Impedances forCalculating Cross Talk
Any state can be described as asuperposition of the system modes.
Points to Remember:Each mode has an impedance and velocityassociated with it.
In homogeneous medium, all the modalvelocities will be equal.
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Crosstalk Calculation
Super Positioning of Modes
Positive
Going
Voltage
Negative
Going
Voltage
Odd Mode Switching
Positive
Going
Voltage
Positive
Going
Voltage
Even Mode Switching
Even States
Single Bit States
Rising Edge
Falling Edge
0 No Change(Line stays high or low,
no transition occurs)
Odd States
,0 , 0
,Dont Care State 0 0
Digital States that can occur
in a 2 conductor systemTotal of 9 states
= Single
bit stateV
Time
V
Time
1.0
Line 1 Line 2
Even
Mode
Odd
Mode
0.5V
Time
0.5V
Time
0.5V
Time
-0.5
V
Time
For a two line case, there are two modes
+
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Crosstalk Calculation
Two Coupled Line Example (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.
Lo = 3.02222e-007
3.34847e-008 3.02222e-007
Co = 1.67493e-010
-1.85657e-011 1.67493e-010
Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]
Veven 1.41E+08 [m/s]
H=4.5 mils
t=1.5 mils
W=7mils
Er=4.5
S=10mils
Sanity Check:
The odd and even
velocities are the same
30[Ohms] 50[inches]
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
Now I deconvolve the the input voltage into the even
and odd modes:
= Single bit
stateV
Time
V
Time
1.0
Line A Line B
Even
Mode
Odd Mode
0.5V
Time
0.5V
Time
0.5V
Time
-0.5
V
Time
Line A Line B
This allows one tosolve four easy
problems and
simply add the
solutions together!
Case i Case ii
Case iii Case iv
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]Veven 1.41E+08 [m/s]
30[Ohms] 50[inches]Case i and Case iiare really the same:
A 0.5[V] step into a
Zeven=47.5[ ] line:Line A Line B
0.5V
Time
0.5V
Time
Case i Case iiTd=len*Veven=8.98[ns]Vinit=0.5[V]*Zeven/(Zeven+30[Ohms])
Vinit=.306[V]
Vrcvr=2*Vinit=.612[V]
0.000[V]
Driver (even)
0.0[ns] 9.0[ns]
0.306[V]
0.612[V]
0.000[V]
Receiver (even)
0.0[ns] 9.0[ns]
0.306[V]
0.612[V]
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]Veven 1.41E+08 [m/s]
30[Ohms] 50[inches]Case iii is -0.5[V]step into a
Zodd=38[ ] line:
Line A
Td=len*Vodd=8.98[ns]Vinit=-0.5[V]*Zodd/(Zodd+30[Ohms])
Vinit=-.279[V]
Vrcvr=2*Vinit=-.558[V]
Driver (odd)
0.000[V]9.0[ns]
0.279[V]
0.558[V]
-.558[V]
-.279[V]
Receiver (odd)
0.000[V]9.0[ns]
0.279[V]
0.558[V]
-.558[V]
-.279[V]
-0.5
V
Time
Case iii
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
Zodd 38.0 [Ohms]
Vodd 1.41E+08 [m/s]
Zeven 47.5 [Ohms]Veven 1.41E+08 [m/s]
30[Ohms] 50[inches]Case iv is 0.5[V]step into a
Zodd=38[ ] line:
Td=len*Vodd=8.98[ns]Vinit=0.5[V]*Zodd/(Zodd+30[Ohms])
Vinit=.279[V]
Vrcvr=2*Vinit=.558[V]
0.000[V]
Driver (odd)
0.0[ns] 9.0[ns]
0.279[V]
0.558[V]
0.000[V]
Receiver (odd)
0.0[ns] 9.0[ns]
0.279[V]
0.558[V]
0.5V
Time
Line B
Case iv
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
Line A (Receiver)
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
6.12-.558=
.0539[V]
Line B (Driver)
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
.306+.279=.585[V]
Line B (Receiver)
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
.612+.558=1.17[V]
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
Line A (Driver)
.306-.279=.027[V]
0.000[V]
Driver (even)
0.0[ns] 9.0[ns]
0.306[V]
0.612[V]
Driver (odd)
0.000[V]9.0[ns]
0.279[V]
0.558[V]
-.558[V]
-.279[V]
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
Line A (Driver)
.306-.279=.027[V]
0.000[V]
Driver (odd)
0.0[ns] 9.0[ns]
0.279[V]
0.558[V]
0.000[V]
Driver (even)
0.0[ns] 9.0[ns]
0.306[V]
0.612[V]
Line B (Driver)
0.0[V]
0.5[V]
1.0[V]
-1.0[V]
-0.5[V]9.0[ns]
.306+.279=.585[V]
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Crosstalk Calculation
Two Coupled Line Example (Cont..)
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] 0.5Vinit(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
Simulating in HSPICE results are identical to
the hand calculation:
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Crosstalk Calculation
Assignment1
Use PSPICE and perform previoussimulations
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Crosstalk Calculation
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:
Lo = 3.02222e-007
3.34847e-008 3.02222e-007
Co = 1.15083e-010
-4.0629e-012 1.15083e-010
Zodd=47.49243354 [Ohms]Vodd=1.77E+08[m/s]
Zeven=54.98942739 [Ohms]
Veven=1.64E+08 [m/s]
H=4.5 mils
t=1.5 mils
W=7mils
Er=4.5
S=10mils
Note:
The odd and even velocities
are NOT the same
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Crosstalk Calculation
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
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Crosstalk Calculation
Microstrip Cont..
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
HSPICE Results:
Single Bit switching, two coupled microstrip example
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Crosstalk Calculation
HSPICE Results of MicrostripVodd 176724383
Veven 163801995.6
length[in] 50
length[m] 1.27delay odd 7.18633E-09
delay even 7.75326E-09
delta[sec] 5.66932E-10
The width of the pulse is calculated from the mode
velocities. Note that the widths increases in 567[ps]increments with every transit
567[ps] 1134[ps] 1701[ps] 2268[ps]
Calculation
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Crosstalk Calculation
Modal Impedances formore than 2 lines
So far we have looked at the two linecrosstalk case, however, most practicalbusses use more than two lines.
Points to Remember:For N signal conductors, there are N modes.There are 3N digital states for N signalconductorsEach mode has an impedance and velocity
associated with it.In homogeneous medium, all the modal velocitieswill be equal.Any state can be described as a superposition of
the modes
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Crosstalk Calculation
Three Conductor Considerations
Even States
Single Bit States
Rising Edge
Falling Edge
0 No Change
(Line stays high or low,
no transition occurs)
2 Bit Even States
2 Bit Odd States
Odd States
,
, , ,0
0
000
0 000, , ,0,0 0
,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
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Crosstalk Calculation
Three Coupled Microstrip Example
Zmode
56.887
50.355
46.324
v
1.609108
1.718108
1.789108
Tv0.53
0.663
0.53
0.707
1.5241015
0.707
0.467
0.751
0.467
Using the approximations gives: Actual modal info:
ZevenL
2 22 L
1 2
C2 2
2 C1 2
Ut Zeven 58.692
ZoddL
2 22 L
1 2
C2 2
2 C1 2
Ut Zodd 43.738
Veven1.0
L2 2
2 L1 2
C2 2
2 C1 2
Vodd1.0
L2 2
2 L1 2
C2 2
2 C1 2
Veven 1.592108
Vodd 1.856108
Modal velocities
The three mode vectors
Z[1,-1,1]=44.25[Ohms]
Z[1,1,1]=59.0[Ohms]
The Approx. impedances and velocities are pretty close to
the actual, but much simpler to calculate.
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Crosstalk Calculation
Three Coupled Microstrip ExampleSingle Bit Example: HSPICE Result
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Crosstalk Calculation
Points to Remember
The modal impedances can be used to handcalculate crosstalk waveforms
Any state can be described as asuperposition of the modes
For N signal conductors, there are Nmodes.
There are 3N digital states for N signalconductors
Each mode has an impedance and velocityassociated with it.
In homogeneous medium, all the modalvelocities will be equal.
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Crosstalk Calculation
Crosstalk Trends
Key Topics:
Impedance vs. Spacing
SLEM
Trading Off Tolerance vs. Spacing
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Crosstalk Calculation
Impedance vs Line Spacing
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
0
20
40
60
80
100
120
5 10 15 20Edge to Edge Spacing [mils]
Impedance[Ohms]
Z single bit states Z odd statesZ even states
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
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Crosstalk Calculation
Single Line Equivalent Model(SLEM)
SLEM is an approximation that allowssome cross talk effects to bemodeled without running fully coupledsimulations
Why would we want to avoid fullycoupled simulations?
Fully coupled simulations tend to be time
consuming and dependent on manyassumptions
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Crosstalk Calculation
Single Line Equivalent Model(SLEM)
Using the knowledge of the cross talkimpedances, one can change a singletransmission lines impedance to approximate:
Even, Odd, or other state coupling
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
0
20
40
60
80
100
120
5 10 15 20Edge to Edge Spacing [mils]
Impedance[O
hms]
Z single bit states Z odd statesZ even states
30[Ohms] Zo=90[ ]
30[Ohms] Zo=40[ ]
Equiv to
Even State
Coupling
Equiv to
Odd State
Coupling
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Crosstalk Calculation
Single Line Equivalent Model(SLEM) Limitations of SLEM
SLEM assumes the transmission line is in aparticular state (odd or even) for its entiresegment length
This means that the edges are in perfect phase
It also means one can not simulate random bit patternsproperly with SLEM (e.g. Odd -> Single Bit -> Evenstate)
The edges maybe in
phase here, but not here
Three coupled lines, two with serpentining
V2
Time
V1
Time
V3
Time
1
2
3
1
2
3
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Crosstalk Calculation
Single Line Equivalent Model(SLEM) How does one create a SLEM model?
There are a few waysUse the [L] and [C] matrices along with theapproximations
Use the [L] and [C] matrices along with WeiminsMathCAD program
Excite the coupled simulation in the desired state andback calculate the equivalent impedance (essentially
TDR the simulation)
Zeven
L2 2
2 L1 2
C2 2
2 C1 2
Ut
ZoddL
2 22 L
1 2
C2 2
2 C1 2
UtVinit=Vin(Zstate/(Rin+Zstate))
32T di Off T l S i
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Crosstalk Calculation
Trading Off Tolerance vs. Spacing
Ultimately in a design you have to
create guidelines specifying thetrace spacing and specifying thetolerance of the motherboard
impedancei.e. 10[mil] edge to edge spacing with10% impedance variation
Thinking about the spacing interms of impedance makes thismuch simpler
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Crosstalk Calculation
Trading Off Tolerance vs. Spacing
Assume you perform simulations with no
coupling and you find a solution space with animpedance range ofBetween ~35[W] to ~100[W]
Two possible 65[W] solutions are
15[mil] spacing with 15% impedance tolerance10[mil] spacing with 5% impedance tolerance
Impedance Variation for a Three Conductor Stripline
(Width=5[mils])
0
20
40
60
80
100
120
5 10 15 20Edge to Edge Spacing [mils]
Impedance[O
hms]
Z single bit states Z odd statesZ even states
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Crosstalk Calculation
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 mayhelp or hurt (recall reverse cross talk!)
Add Guard tracesOne needs to be careful to ground the guard traces
sufficiently, otherwise you could actually increase thecross talkAt GHz frequency this becomes very difficult and shouldbe avoided
Route on different layers and route orthogonally
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Crosstalk Calculation
In Summary:
Cross talk is unwanted signals due to
coupling or leakage Mutual capacitance and inductance between
lines creates forward and backwardstraveling waves on neighboring lines
Cross talk can also be analyzed as a changein the transmission lines impedance
Reverse cross talk is often the dominatecross talk in a design
(just because the forward cross talk is small or zero, does notmean you can ignore cross talk!)
A SLEM approach can be used to budgetimpedance tolerance and trace spacing