Crosstalk Calculation and SLEM. 2 Crosstalk Calculation Topics Crosstalk and Impedance ...

Crosstalk

Calculation and SLEM

Crosstalk Calculation

2

Topics

Crosstalk and ImpedanceSuperpositionExamplesSLEM


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.


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.


5

Super Positioning of Modes

Odd Mode SwitchingEven Mode Switching

Even States

Single Bit StatesRising Edge

OddFalling Edge

0 No Change(Line stays high or low,no transition occurs)

Odd States

,0 , 0

,Don’t Care State 0 0

Digital States that can occur in a 2 conductor system

Total of 9 states

= Single bit state

V

Time

V

Time

1.0

Line 1 Line 2

½ Even Mode

½ Odd Mode

0.5V

Time

0.5V

Time

0.5V

Time

-0.5

V

Time

For a two line case, there are two modes

+


6

Two Coupled Line ExampleCalculate the waveforms for two coupled lines when one is driven from the low state to the high and the other is held low.

H=4.5 mils

t=1.5 milsW=7mils

Er=4.5

S=10mils30[Ohms] 50[inches]

InputV

Time

V

Time

1.0

Line A

Line B

Output?V

Time

?

V

Time

?

Line A

Line B

At Driver At Receiver

V

Time

?

V

Time

?


7

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-007Co = 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 milsW=7mils

Er=4.5

S=10mils

Sanity Check:The odd and even velocities are the same

30[Ohms] 50[inches]


8


Now I deconvolve the the input voltage into the even and odd modes:

= Single bit state

V

Time

V

Time

1.0

Line A Line B

½ Even Mode

½ Odd Mode

0.5V

Time

0.5V

Time

0.5V

Time

-0.5

V

Time

Line A Line B

This allows one to solve four easy problems and simply add the solutions together!

Case i Case ii

Case iii Case iv


9



30[Ohms] 50[inches]

Case i and Case ii are 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]


10



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


11



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


12


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]


13


embebed ustrip

L 3.02E-07Lm 3.35E-08C 1.67E-10Cm 1.86E-11

Zodd 38.004847Vodd 1.41E+08Zeven 47.478047Veven 1.41E+08Tdelay 8.98E-09

Rin 30Odd [V] 0.5Even [V] 0.5Vinit(odd) 0.2794275Vinit(even) 0.3063968sum 0.5858243diff 0.02696932xodd 0.5588552x(odd+even) 1.17164852x(even-odd) 0.0539386

Simulating in HSPICE results are identical to the hand calculation:


14

Assignment1

Use PSPICE and perform previous simulations


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:

Lo = 3.02222e-007 3.34847e-008 3.02222e-007Co = 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 milsW=7mils

Er=4.5

S=10mils

Note:The odd and even velocities are NOT the same


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


17

Microstrip Cont..

ustrip

L 3.02E-07Lm 3.35E-08C 1.15E-10Cm 4.06E-12

Zodd 47.492434Vodd 1.77E+08Zeven 54.989427Veven 1.64E+08Td(odd) 7.19E-09Td(even) 7.75E-09Rin 30Odd [V] 0.5Even [V] 0.5Vinit(odd) 0.3064327Vinit(even) 0.3235075sum 0.6299402diff 0.01707472xodd 0.61286542x(odd+even) 1.25988032x(even-odd) 0.0341495

HSPICE Results:Single Bit switching, two coupled microstrip example


18

HSPICE Results of MicrostripVodd 176724383Veven 163801995.6length[in] 50length[m] 1.27delay odd 7.18633E-09delay even 7.75326E-09delta[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


19

Assignment 2 and 3

Use PSPICE and perform previous simulations


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 conductorsEach 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


21

Three Conductor Considerations

Even States

Single Bit States

Rising Edge Odd

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

0 0 0

0 0 0 0 , , ,

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 conductorsThere are 3N digital states for N signal conductors


22

Three Coupled Microstrip Example

H=4.5 milst=1.5 mils

W=7mils Er=4.5

S=10mils S=10mils

From HSPICE:Lo = 3.02174e-007 3.32768e-008 3.01224e-007 9.01613e-009 3.32768e-008 3.02174e-007Co = 1.15088e-010 -4.03272e-012 1.15326e-010 -5.20092e-013 -4.03272e-012 1.15088e-010


23

Three Coupled Microstrip Example

Zmode

56.887

50.355

46.324

v

1.609108

1.718108

1.789108

Tv

0.53

0.663

0.53

0.707

1.52410 15

0.707

0.467

0.751

0.467

Using the approximations gives: Actual modal info:

ZevenL

2 2 2 L1 2

C2 2 2 C

1 2

Ut Zeven 58.692

ZoddL

2 2 2 L1 2

C2 2 2 C

1 2

Ut Zodd 43.738

Veven1.0

L2 2 2 L

1 2 C

2 2 2 C1 2

Vodd1.0

L2 2 2 L

1 2 C

2 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.


24

Three Coupled Microstrip ExampleSingle Bit Example: HSPICE Result


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.


26

Crosstalk Trends

Key Topics:

Impedance vs. Spacing

SLEM

Trading Off Tolerance vs. Spacing


27

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]

Imp

edan

ce[O

hm

s]

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 line2) The further the lines are spaced apart the the less the impedance changes


28Single 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


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


(Width=5[mils])

0

20

40

60

80

100

120


Imp

edan

ce[O

hm

s]


30[Ohms] Zo=90[]

30[Ohms] Zo=40[]

Equiv to Even State Coupling

Equiv to Odd State Coupling


30


Limitations of SLEMSLEM 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 phaseIt 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

Three coupled lines, two with serpentining

V2

Time

V1

Time

V3

Time

123

123


31


How does one create a SLEM model?

There are a few waysUse the [L] and [C] matrices along with the approximationsUse 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)

ZevenL

2 2 2 L1 2

C2 2 2 C

1 2

Ut

ZoddL

2 2 2 L1 2

C2 2 2 C

1 2

UtVinit=Vin(Zstate/(Rin+Zstate))


32Trading Off Tolerance vs. Spacing

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


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[] to ~100[]Two possible 65[] solutions are

15[mil] spacing with 15% impedance tolerance10[mil] spacing with 5% impedance tolerance


(Width=5[mils])

0

20

40

60

80

100

120


Impe

danc

e[O

hm

s]



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 tracesOne needs to be careful to ground the guard traces sufficiently, otherwise you could actually increase the cross talkAt GHz frequency this becomes very difficult and should be avoided

Route on different layers and route orthogonally


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 and SLEM. 2 Crosstalk Calculation Topics Crosstalk and Impedance ...

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Transcript of Crosstalk Calculation and SLEM. 2 Crosstalk Calculation Topics Crosstalk and Impedance ...