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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

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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 cable

that 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:

generator conductor

receptor conductor

reference conductor

near end terminal

far end terminal

Figure 1

The goal of crosstalk analysis is the prediction of the near and far end

terminal voltages from the knowledge of the line characteristics.

There are two main kinds of analysis


This analysis applies to many kinds of three-conductor transmission

lines. Some examples are:

receptor

wire

receptor

wire

generator

wire

generator

wire

reference wire

reference conductor (ground plane)

(a)

(b)

generator conductor

receptor conductor

receptor

wire

shield

reference

conductor

reference conductor

generator

wire

(d)

(c)

Figure 2


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 line

and write the corresponding transmission line equations.

It turns out that by using a matrix notation, the transmission line

equations for a multi-conductor line resemble those for an ordinary

two-conductor transmission line.


Let us consider the equivalent circuit of a length of a three-conductor

transmission line.

Figure 3

The transmission line equations are:

(1)

(2)



Per-unit-length parameters three-conductor

We will consider only structures containing wires; PCB-like structures

can 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:

(9)

and

(10)


The elements of the L matrix are found under the assumption of wide

separation of the wires. In this condition the current distribution around

the 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.

surface

1m

+

Figure 4

(11)


Then we consider a three-wire configuration: of wide

Figure 5

For this configuration we can write:

(12)

or

(13)


Using the result of (11), we obtain of wide

(14)

(15)

(16)

And from these elements, we obtain the capacitance using

the relationship:

(17)


Frequency-domain solution of wide

Consider the following circuit:

+

+

Three-conductor

line

+

+

-

-

-

-

-

Figure 6

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.:

(18)


Under these assumptions, the near end voltage simplifies to: of wide

(19)

and the far end voltage becomes:

(20)

In (19) and (20)

(21)

and

(22)

(23)


The meaning of (19) and (20) is that for electrically short and weakly

coupled lines the voltage due to the crosstalk are a linear combination

of 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 significant

coupling results at the lower frequencies. This phenomenon is called

common-impedance coupling.

Time-domain solution: exact solutions are more difficult to derive for

multiple transmission lines, so we will not consider them.


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