Overview and Modes Crosstalk

Crosstalk

Overview and Modes

2

 What is Crosstalk?

 Crosstalk Induced Noise

 Effect of crosstalk on transmission line parameters

 Crosstalk Trends

 Design Guidelines and Rules of Thumb

Overview

Crosstalk Induced Noise

Key Topics:

 Mutual Inductance and capacitance

Coupled noise

 Circuit Model

 Transmission line matrices

4



Mutual capacitance (electric field) Mutual inductance (magnetic field)

Mutual Inductance and Capacitance Mutual Inductance and Capacitance

Zs

Zo

Zo Zo

Mutual Capacitance, C^m Mutual Inductance, L^m

Zs

Zo Zo

Cm

L^m

near

far

near

far

5

 The circuit element that represents this

transfer of energy are the following familiar equations

Mutual Inductance and Capacitance Mutual Inductance and Capacitance

““Mechanism of coupling”Mechanism of coupling”

dt L dI

V



dt C dV

I



 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

6

 The near and far end victim line currents sum to produce the near and the far end crosstalk noise

Crosstalk Induced Noise Crosstalk Induced Noise

““Coupled Currents”Coupled Currents”

Zs

Zo

Zo Zo

Zs

Zo

Zo Zo

I_Cm

L^m

near

far

near

far I_Lm

Lm Cm

far Lm

Cm

near

I I I I I

I    

7

 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

Crosstalk Induced Noise Crosstalk Induced Noise

““Voltage Profile of Coupled Noise”Voltage Profile of Coupled Noise”

Driven Line

Un-driven Line

“victim”

Driver

Zs

Zo

Zo Zo

Near End

Far End

Graphical Explanation

Graphical Explanation

TD

2TD

~Tr

~Tr

far end crosstalk

Near end crosstalk

V

Time = 2TD

Zo Near end current terminated at T=2TD

V

Time = 0

Zo

Near end crosstalk pulse at T=0 (I_near)

Far end crosstalk pulse at T=0 (I_far)

Zo

Zo

V

Time= 1/2 TD

Zo

V

Time= TD

Zo Far end of current terminated at T=TD

Crosstalk Equations

Crosstalk Equations

Driven Line

Un-driven Line

“victim”

Driver

Zs

Zo

Zo Zo

Near End

Far End

Driven Line

Un-driven Line

“victim”

Driver

Zs

Zo

Zo

Near End

Far End

LC X TD 



 

 C

C L V L

A ^{input M M}

4



 



 C

C L L T

LC X

B V ^{M M}

r input

2

TD

2TD

Tr ~Tr Tr

A B

TD

2TD

Tr ~Tr ~Tr

A B



 

 C

C L

V L

A ^{input M M}

4

C B 2

 1



 



 C

C L

L T

LC X

C V ^{M M}

r input

C

Terminated Victim

Far End Open Victim

Crosstalk Equations

Crosstalk Equations

Driven Line

Un-driven Line

“victim”

Driver

Zs

Zo Zo

Near End

Far End

Near End Open Victim

TD

2TD

Tr Tr Tr

A B

C

3TD



 

 C

C L

V L

A ^{input M M}

2



 



 C

C L L T

LC X

B V ^{M M}

r input

2



 

 C

C L V L

C ^{input M M}

4

 The Crosstalk noise characteristics are

dependent on the termination of the victim line

Creating a Crosstalk Model

Creating a Crosstalk Model

““Equivalent Circuit”Equivalent Circuit”

 The circuit must be distributed into N segments as shown in chapter 2

K1

L₁₁(1)

L₂₂(1)

C_1G(1)

C₁₂(1) K1

L11(2)

L₂₂(2)

C_1G(2) C₁₂(2)

C_2G(2) C_2G(1)

K1

L₁₁(N)

L₂₂(N)

C_1G(N) C₁₂(n)

C_2G(N)

C_1G C_2G

C₁₂

22 11

12

L L

K  L

Line 1

Line 2

Line 1 Line 2

12

 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

Creating a Crosstalk Model Creating a Crosstalk Model

““Transmission Line Matrices”Transmission Line Matrices”

Inductance Matrix =

 

 





 

 





NN N

N

L L

L L

L L

L

1

22 21

1 12

11

...

13

 The Capacitance matrix is shown, where:

CNN = the self capacitance of line N per unit length where:

CNG = The capacitance between line N and ground CMN = Mutual capacitance between lines M and N

Creating a Crosstalk Model Creating a Crosstalk Model

““Transmission Line Matrices”Transmission Line Matrices”

Capacitance Matrix =

















NN N

N

C C

C C

C C

C

1

22 21

1 12

11 ...







NN

C C

C

12 1

11

C C

C 



 For example, for the 2 line circuit shown earlier:

Example

Calculate near and far end crosstalk-induced noise magnitudes and sketch the waveforms of circuit shown below:

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 =

C / inch =

The characteristic impedance is:

Therefore the system has matched termination.



 





nH nH

nH nH

869 . 9 103

. 2

103 . 2 869

. 9



 





pF pF

pF pF

051 . 2 239

. 0

239 . 0 051

. 2







 69.4

051 . 2

869 . 9

11 11

pF nH C

Z_O L

v

R¹ R²

Crosstalk Overview

Example (cont.)

pF V pF nH

nH V

C C L

V L

V_near ^input 0.082

051 . 2

239 . 0 869

. 9

103 . 2 4 1

4 ₁₁

12 11

12  



 



 

 



 



 



pF V pF nH

nH ps

pF nH

inch V

C C L

L T

LC X V V

rise input

far 0.137

051 . 2

239 . 0 869

. 9

103 . 2 100

* 2

051 . 2

* 869 . 9

* 2

* 1 2

) (

11 12 11

12  

 



 





 



 



Near end crosstalk voltage amplitude (from slide 12):

Far end crosstalk voltage amplitude (slide 12):

Thus,

100ps/div

200mV/div

The propagation delay of the 2 inch line is:

ns nH

nH inch

LC X

TD   2 * (9.869 *2.051  0.28

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)

Odd and Even Transmission Modes

Odd and Even Transmission Modes

Even Mode

Odd Mode

18

 Potential difference between the conductors lead to an increase of the effective Capacitance equal to the mutual capacitance

Odd Mode Transmission Odd Mode Transmission

Magnetic Field:

Odd mode Electric Field:

Odd mode

+1 -1 +1 -1



Drive (I) Induced (-I_Lm)

Induced (I_Lm)

V

Lm dt

Lm dI L

dt I Lm d

dt L dI V

) (

) (





 



I

Odd Mode Transmission

Odd Mode Transmission

““Derivation of Odd Mode Inductance”Derivation of Odd Mode Inductance”

12 11

11 L L L

L

L_odd   _m  

Mutual Inductance:

Consider the circuit:

dt L dI dt

L dI V

dt L dI dt

L dI V

m O

m O

1 2

2

2 1

1









22 11L L k  L^m

L¹¹

L²² I²

I¹

+ V² -

+ V¹ -

Since the signals for odd-mode switching are always opposite, I¹ = -I² and V¹ = -V², so that:

dt L dI dt L

I L d

dt L dI V

dt L dI dt L

I L d

dt L dI V

m O

m O

m O

m O

2 2

2 2

1 1

1 1

) ) (

(

) ) (

(



 







 





Thus, since L^O = L¹¹ = L²²,

Meaning that the equivalent inductance seen in an odd-mode environment is reduced by the mutual inductance.

Odd Mode Transmission

Odd Mode Transmission

““Derivation of Odd Mode Capacitance”Derivation of Odd Mode Capacitance”

m m

g

odd C C C C

C  ₁  2  ₁₁ 

Mutual Capacitance:

Consider the circuit:

C^2g

C^1g C^m V²

V²

C^1g = C^2g = C^O = C¹¹

–

So,

dt C dV dt

C dV dt C

V V

C d dt

C dV I

dt C dV dt

C dV dt C

V V C d

dt C dV I

m m

O m

O

m m

O m

O

1 2

1 2

2 2

2 1

2 1

1 1

) ) (

(

) ) (

(





 









 





And again, I¹ = -I² and V¹ = -V², so that:

dt C dV

dt C V V

C d dt

C dV I

dt C dV dt C

V V

C d dt

C dV I

m O

m O

m g

m O

2 2

2 2

2

1 1

1 1

1 1

) 2 )) (

( (

) 2 )) (

( (



 

 





 

 



Thus,

Odd Mode Transmission

Odd Mode Transmission

““Odd Mode Transmission Characteristics”Odd Mode Transmission Characteristics”

Impedance:

Thus the impedance for odd mode behavior is:

) 2

: (

12 11

12 11

odd al

differenti odd odd odd

Z Z

Note

C C

L L

C Z L





 



and the propagation delay for odd mode behavior is:

) )(

( L

L

C

C

C

L

TD



   Propagation Delay:

Explain why.

22



Even Mode Transmission Even Mode Transmission



Drive (I) Induced (I_Lm)

Induced (I_Lm)

V

Lm dt

Lm dI L

dt I Lm d dt

L dI V

) (

) (









I

Electric Field:

Even mode

Magnetic Field:

Even mode

+1 +1

+1 +1

Even Mode Transmission

Even Mode Transmission

Derivation of even Mode Effective Inductance Derivation of even Mode Effective Inductance

12 11

11 L L L

L

L_even   _m  

22 11L L k  L^m

L¹¹

L²² I²

I¹

+ V² -

+ V¹ -

Mutual Inductance:

Again, consider the circuit:

Since the signals for even-mode switching are always equal and in the same direction so that I¹ = I² and V¹ = V², so that:

dt L dI dt

L dI V

dt L dI dt

L dI V

m O

m O

1 2

2

2 1

1









dt L dI dt L

I L d dt L dI V

dt L dI dt L

I L d dt L dI V

m O m

O

m O m

O

2 2

2 2

1 1

1 1

) ) (

(

) ) (

(

















Thus,

Meaning that the equivalent inductance of even mode behavior increases by the mutual inductance.

Even Mode Transmission

Even Mode Transmission

Derivation of even Mode Effective Capacitance Derivation of even Mode Effective Capacitance

m

even C C C

C  ₀  ₁₁ 

Mutual Capacitance:

Again, consider the circuit:

C^2g

C^1g C^m V²

V²

dt C dV dt

V V C d

dt C dV I

dt C dV dt

V V C d

dt C dV I

O m

O

O m

O

2 2

2 2

2

1 1

1 1

1

) (

) (

 





 





Thus,

Meaning that the equivalent capacitance during even mode behavior decreases.

Even Mode Transmission

Even Mode Transmission

““Even Mode Transmission Characteristics”Even Mode Transmission Characteristics”

Impedance:

Thus the impedance for even mode behavior is:

12 11

12 11

C C

L L

C Z L

even even

even



 



and the propagation delay for even mode behavior is:

) )(

( L

L

C

C

C

L

TD



  

Propagation Delay:

Odd and Even Mode Comparison for

Odd and Even Mode Comparison for Coupled Microstrips

Coupled Microstrips

Input waveforms Even mode (as seen on line 1)

Odd mode (Line 1)

v

v

Probe point

Delay difference due to modal velocity differences Impedance difference

V1

V2

Line 1 Line2

Microstrip vs. Stripline Crosstalk

Microstrip vs. Stripline Crosstalk

Crosstalk Induced Velocity Changes Crosstalk Induced Velocity Changes

 Chapter 2 defined propagation delay as

 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

T

c 



Microstrip vs. Stripline Crosstalk

Microstrip vs. Stripline Crosstalk

Crosstalk Induced Velocity Changes 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

+1 +1 +1 -1



Er=4.2 Er=1.0

Er=4.2 Er=1.0

Microstrip E field patterns

Microstrip vs. Stripline Crosstalk

Microstrip vs. Stripline Crosstalk

Crosstalk Induced Velocity Changes Crosstalk Induced Velocity Changes

 Subsequently, if the transmission line is implemented in a homogeneous dielectric, the velocity must stay constant between even and odd mode patterns

 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

+1 +1 +1 -1

Er=4.2 Er=4.2

Stripline E field patterns

Microstrip vs. Stripline Crosstalk

Microstrip vs. Stripline Crosstalk

Crosstalk Induced Noise Crosstalk Induced Noise

 The constant velocity in a homogeneous media (such as a stripline) forces far end crosstalk noise to be zero

11 12 11

12

11 12 12

11 12

11 11

12

12 11

12 11

12 11

12

11

)( ) ( )( )

(

C C L

L

C L C

L C

L C

L

C C

L L

C C

L L

TD TD

























2 0 )

_ (

11 12 11

12

 



 



 



 C

C L

L T

LC X

stripline V far

Crosstalk

r input

Since far end crosstalk takes the following form:

Far end crosstalk is zero for a homogeneous Er

Crosstalk Overview

Termination Techniques

Termination Techniques

Pi and T networks 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

-1

R₁ R₂

R₃

Odd Mode

+1

Equivalent

-1

R₁ R₂

Virtual Ground in center

Even Mode

+1

Equivalent

+1

R₁

R₂ 2R₃

2R₃

Z

R

R





 ^Z

^Z



R  

2 1

3

Termination Techniques

Termination Techniques

Pi and T networks Pi and T networks

 The alternative is a PI termination PI Termination

Odd Mode

+1

Equivalent

-1

R₁

R₂ R₃

-1

½ R₃

½ R₃

Even Mode

+1

Equivalent

+1

R₁ R₂

Z

R

R





odd even

Z R  2 Z

R₁

R₂