Description of crosstalk between parallel buried conductors. (Stripline.)

fig41- Stripline

Figure 41 shows a cross section of the lines under discussion.

fig42- Stripline plan view

Figure 42 shows a plan view.

fig43- Stripline diagammatic view

Figure 43 shows a diagrammatic representation of the same.

In a digital system, a voltage-current step v,i, representing a transition from the FALSE state to the TRUE state, is introduced at .
Lines can be assumed to be lossless and so propagation is TEM.
If  is the characteristic impedance between the lines  , then v= i .

When the signal reaches  , the effect of the line  has to be considered.

If the front end  is open circuit, no current can flow in the line, and the only change in  will be due to the effect of charge moving in a lateral direction across the passive line. This effect may be safely neglected.
If   is shorted, the change in  on line A which occurs at  is a maximum.
However, if the line spacing is such that maximum crosstalk between lines is acceptably low, this effect may also be neglected.

[If  = x ,
then maximum change of  at  is by a factor .
In practice, x<0.1. So  changes by <1%.]

So it may be assumed that the characteristic impedance of a line is not altered significantly by the presence of other lines.

It is not possible for a current voltage signal to travel from  to  and leave the line  unaffected. Two fundamental TEM modes can exist on a pair of parallel conducting strips between parallel ground planes. One mode is called the Even coupled-strip Mode (EM), because the strips are at the same potential and carry equal currents in the same direction. The other mode is called the Odd coupled-strip Mode (OM), because the strips are at equal but opposite potentials and carry equal currents in opposite directions. .

Now the total voltage and current step passing  is v, i, where .
If  is open circuit, the total current passing  is zero.
So if the voltage-current steps continuing down the line  are respectively  for the EM and  for the  OM signal, then

.

Also,

 and .

Since  and , then  .

So the net voltage appearing on the passive line is positive and equals

.

The ratio of crosstalk amplitude to signal is

.

So as the signal travels down  , a smaller crosstalk voltage step appears on the line . The crosstalk that is seen is the small difference between two large signals, whose sum, equal to the original signal v, i, is seen on the driven line A. This crosstalk is here defined as fast Crosstalk (FX), because its full amplitude is reached only if the signal rise time is fast compared to the propagation time down  . The magnitude of the crosstalk so obtained is the maximum that can appear anywhere on the line P, for any values of terminating resistors at  and . It is a good value to use for worst-case design.

Fast Crosstalk (FX) is a flat topped pulse whose rise and fall times equal  for the original signal, and whose width equals twice the propagation time down the passive line.

Slow Crosstalk (SX) is a degenerate case of FX, when the propagation time down the passive line and back is less than  . SX has the triangular (noise spike) shape that we are all familiar with in slower logic.

fig48- Stripline crosstalk graph

Figure 47 Characteristic Impedance of Surface and Buried Conductors.