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 twoconductor transmission lines are easily
transferred to the study of multiconductor lines.
Crosstalk in threeconductor 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 threeconductor 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 twoconductor transmission lines, the knowledge
of the perunit length parameters is required. The perunit 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 perunitlength parameters are available, we can
consider a section of length of a threeconductor transmission line
and write the corresponding transmission line equations.
It turns out that by using a matrix notation, the transmission line
equations for a multiconductor line resemble those for an ordinary
twoconductor transmission line.
Let us consider the equivalent circuit of a length of a threeconductor
transmission line.
Figure 3
The transmission line equations are:
(1)
(2)
The meaning of the symbols used in (1) and (2) is:
and
(7)
(8)
Perunitlength parameters
We will consider only structures containing wires; PCBlike 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 threewire configuration:
Figure 5
For this configuration we can write:
(12)
or
(13)
Using the result of (11), we obtain
(14)
(15)
(16)
And from these elements, we obtain the capacitance using
the relationship:
(17)
Frequencydomain solution
Consider the following circuit:
+
+
Threeconductor
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:
(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 lowimpedance 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
commonimpedance coupling.
Timedomain solution: exact solutions are more difficult to derive for
multiple transmission lines, so we will not consider them.