Crosstalk

Crosstalk is the electromagnetic coupling between conductors that are close to each other.

Crosstalk is an EMC concern because it deals with the design of a system that does not interfere with itself.

Crosstalk is may affect that radiated/conducted emission of a product if, for example, an internal cable passes close enough to another cablethat exists the product.

Crosstalk occurs if there are three or more conductors; many of the notions learnt for two-conductor transmission lines are easily transferred to the study of multi-conductor lines.

Crosstalk in three-conductor lines

Consider the following schematic:

SR

LR

FERNER )(tVNE )(tVFE

)(tVFE)(tVNE

),( tzVG ),( tzIG

),( tzVG ),( tzIG

reference conductor

generator conductor

receptor conductor

near end terminal far end terminal

The goal of crosstalk analysis is the prediction of the near and far endterminal voltages from the knowledge of the line characteristics.

There are two main kinds of analysis

crosstalkdomain frequency

crosstalkdomain - time

Figure 1

This analysis applies to many kinds of three-conductor transmission lines. Some examples are:

receptorwire

reference wire

generatorwire

receptorwire

generatorwire

reference conductor (ground plane)

GV

receptorwire

referenceconductor

shield

generatorwire

Gθ

)(tVFE

generator conductor

receptor conductor

reference conductor

Figure 2

(a) (b)

(c) (d)

As in the case of two-conductor transmission lines, the knowledge of the per-unit length parameters is required. The per-unit length parameters may be obtained for some of the configurations shown as long as:

1) the surrounding medium is homogeneous;2) the assumption of widely spaced conductors is made.

Assuming that the per-unit-length parameters are available, we can consider a section of length of a three-conductor transmission lineand write the corresponding transmission line equations.

It turns out that by using a matrix notation, the transmission lineequations for a multi-conductor line resemble those for an ordinarytwo-conductor transmission line.

z

Let us consider the equivalent circuit of a length of a three-conductortransmission line.

The transmission line equations are:

),(),(),(

),(),(),(

tzVt

CtzVGtzIz

tzIt

LtzIRtzVz

(1)

(2)

zrtzI GG ),( zIG

Figure 3

zr 0

z

The meaning of the symbols used in (1) and (2) is:

(4) ),(

),(),((3)

),(

),(),(

tzI

tzItzI

tzV

tzVtzV

R

G

R

G

and

)6(

)5( 00

00

Rm

mG

G

G

ll

llL

rrr

rrrR

mRm

mmG

mRm

mmG

ccc

cccL

ggg

gggG

(7)

(8)

Per-unit-length parameters

We will consider only structures containing wires; PCB-like structurescan only be investigated using numerical methods.

The internal parameters such as rG, rR, r0 do not depend from the

configuration, if the wires are widely separated. Therefore we only need to compute the external parameters L and C.

It is important to keep in mind that for a homogeneous medium surrounding the wires, two important relationships hold:

10

01LCCL

and

10

01LGGL

(9)

(10)

The elements of the L matrix are found under the assumption of wideseparation of the wires. In this condition the current distribution aroundthe wire is essentially uniform.

We recall a previous result for the magnetic flux that penetrates a surface of unit length limited by the edges at radial distance and as in the following.

1R

12 RR

1

20 ln2 R

RI

(11)

+2R

1R

1R

surface1m I

Figure 4

Then we consider a three-wire configuration:

For this configuration we can write:IL (12)

or

R

G

Rm

mG

R

G

I

I

ll

ll

(13)

wGr

wRr

0wr

GRd

Gd

Rd

G R Figure 5

Using the result of (11), we obtain

0

2

0

0

00 ln2

ln2

ln2 wwG

G

w

G

wG

GG rr

drd

rd

l

(14)

0

2

0 ln2 wwG

RR rr

dl

(15)

0

0

0

00 ln2

ln2

ln2 wwG

RG

w

R

GR

Gm rr

ddrd

rd

l

(16)

And from these elements, we obtain the capacitance usingthe relationship:

1 LC (17)

Frequency-domain solution

Consider the following circuit:

The closed form expression for the near and far end voltages and are very complex so we will introduce additional simplifications: 1) the line is electrically short at the frequency of interest; 2) the generator and receptor circuits are weakly coupled, i.e.:

1RG

m

lll

K (18)

NEV

FEV

Three-conductor line

SR

NERNER VV ˆ)0(ˆ

+

-

+

-

)0(GV)0(ˆ

GI)0(ˆ

RI

SV

FER VLV ˆ)(ˆ +

- - -

FER

FER

+

)(ˆ LVG

)(ˆ LIG

)(ˆ LI R

z0z Lz Figure 6

Under these assumptions, the near end voltage simplifies to:

DCDC Gm

FENE

FENEGm

FENE

NENE VLcj

RRRR

ILljRR

RV ˆˆ

Den1ˆ (19)

and the far end voltage becomes:

DCDC Gm

FENE

FENEGm

FENE

FEFE VLcj

RRRR

ILljRR

RV ˆˆ

Den1ˆ (20)

In (19) and (20)

)1)(1(Den RG jj (21)and

LS

LSmg

LS

GG RR

RRLcc

RRLl

)( (22)

FENE

FENEmg

FENE

RR RR

RRLcc

RRLl

)( (23)

The meaning of (19) and (20) is that for electrically short and weaklycoupled lines the voltage due to the crosstalk are a linear combinationof the inductance lm and capacitance cm between the two circuits.

In addition, inductive coupling is dominant for low-impedance loads(high currents), whereas capacitive coupling is dominant for high-impedance loads (low currents).

It turns out that (we skip the proof) if losses are included a significantcoupling results at the lower frequencies. This phenomenon is calledcommon-impedance coupling.

Time-domain solution: exact solutions are more difficult to derive formultiple transmission lines, so we will not consider them.