Description of crosstalk between parallel surface conductors. (Microstrip.)

Figure 44 shows a cross section of the lines under discussion.

Figure 45 shows a plan view.

Figure 46 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 .

Propagation is approximately TEM.

If Zo is the characteristic impedance between the lines  , then

v = iZo.

When the signal reaches , the effect of the line  has to be considered.
It has been shown that the mismatch on line A at  is negligible in practical cases for buried lines.
This is also true for surface lines. So voltage and current v, i, continue along the line A past .

However, as with buried lines, when the signal v, i, passes  it must break up into a combination of the two possible TEM modes for a pair of parallel conducting strips above a ground plane. These modes are as previously described for buried conductors.

If the front end  is open circuit, it was shown that the ratio of crosstalk amplitude at  to signal is

.

So as the signal travels down A1 A, a smaller crosstalk voltage step appears at . 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 .

Unlike the case of buried conductors, the magnitude of FX is not the maximum that can appear anywhere on the line . The reason for this is that as surface conductors are in an inhomogeneous medium, the OM signal travels faster than the EM, and so further down the line  the OM signal appears on its own for a time. This is here defined as Differential Crosstalk (DX) and it greatly exceeds FX. In long lines, it reaches an amplitude of approximately , even for widely separated lines.

To reach its maximum amplitude of , the difference in propagation times for the two modes down  must exceed the rise time of the original signal v, i.

In practice, this is not the case, and only a fraction of the maximum possible DX appears[1].

The actual amplitude reached by DX at P2 is equal to

.

In the case of surface lines, the designer should be sure that FX is not excessive and also that DX is not excessive. Both of these are reduced by increasing line spacing. DX is reduced because there is less difference in propagation times for two modes in more widely spaced lines, as we see in Figure 49 [2].

If each line is terminated with its characteristic impedance, at  then reflected DX will be less than FX, and so need not be considered. However, if the lines are terminated in a mismatch, such as short circuits or open circuits, then the OM signal, which arrives first at  will be reflected. On its way back to  it will draw further away from the (now reflected) EM signal. So if the lines are badly terminated, the amplitude reached by the reflected DX when it reaches P will equal

This is double the amplitude reached by DX. However, this is not a practical case, because for reasons of reflections alone not related to crosstalk,  must be terminated properly[3].
So we need only consider the case when  is terminated properly, either by a further length of line  or by a resistor Zo, and there is only a mismatch (short or open) at .
In that case, the incident OM signal will be reflected in two modes, half OM and half EM, and it can be shown that the maximum amplitude of reflected DX will be only about half the maximum DX.

The conclusion is that in practice the problem of reflected DX may be ignored, and one need only consider FX and DX.

The passive line may have two active lines, one on each side of it, so the figure for crosstalk in Figures 48 (graph for stripline crosstalk) and Figure 49 (graph for microstrip crosstalk), should be doubled for worst case design. If P1 is terminated with a resistor equal to Zo, the crosstalk is halved. However, it is safer to ignore this.

Note: The classic oscilloscope photographs of these waveforms taken during
the crucial experiment in the 1960s are at
http://www.ivorcatt.com/emcrosstalk.htm.

[1]
All of this theory applies to buried lines and surface lines in a printed circuit board. However, it also applies to a cableform with two twisted pairs or with two signal lines and one return (ground) line. In the case of a cableform, the theory indicates various important things. (1) FX reaches an easily calculable maximum regardless of length of cable, which is good. (2) DX reaches half the logic signal, which is disastrous. Therefore the dielectric must be consistent, and not a mixture of air and teflon, so that DX disappears.

[2]
Velocity difference is caused by the EM field being concentrated less in (faster) air than the OM signal, so that EM arrives downstream later than OM. However, the two field patterns are more similar to each other with widely spaced lines, so the velocities are more similar, approximating towards the velocity for a single line on its own. (This last point is proved in ref. 15, Fig.39.)

[3]
This is not always true. "Series termination" of logic signal lines is a counter-example. A high speed logic gate might have a 47 ohm series resistor on its output into a 50 ohm line which is open circuit at destination. This system is used to minimise power dissipation, but happens to increase the effect of DX.