CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 164

Recall from Section 4.1 that the elements on the matrix diagonals represent
the self-inductance and total capacitance, respectively, while the off-diagonal
elements represent the mutual terms. Once we obtain the effective inductance and
capacitance, we can calculate the effective impedance and propagation velocity:

L eff ,n
C eff ,n

Z 0 , eff ,n = (4-44)

1
L eff ,n C eff ,n

ν p, eff ,n = (4-45)

We can use equations (4-44) and (4-45) along with the physical length of the
transmission line to analyze or simulate the behavior of any line as a simple
noncoupled line while accounting for the coupling to the other lines in the system.
This technique is best used during the early design phase of a bus, when I/O
transceiver impedances and line-to-line spacing are being chosen. In addition, it
is useful only for signals traveling in the same direction. For signals traveling
in opposite directions, fully coupled simulations are required to comprehend the
effects of crosstalk.
At this point it is important to note that although the SLEM method gives
correct results for systems with two coupled lines, it is an approximation that will
not exactly match the actual modal impedances and velocities for three or more
coupled lines. As such, its use should be restricted to early design exploration
aimed at narrowing down the solution space. Final simulations should always be
done with fully coupled models. The accuracy of the SLEM model (for three
lines) is reasonable for cross sections in which the spacing/height ratio is greater
than 1. When this ratio is less than 1, the SLEM approximation should not be
used. In Section 4.4 we introduce a technique for producing exact solutions to
systems of three or more coupled lines.

4.3.2 Coupled Noise
Before describing the coupled noise mechanism and developing methods to quan-
tify the noise, we need to provide some motivation for doing so. By now it should
be clear that our goal is to transmit interchip digital data signals successfully. In
doing so, we use an active transmitter circuit to drive the data onto the intercon-
nect, where it propagates as an electromagnetic wave to a receiver circuit that
senses the signal and restores it to the appropriate logic level. It is this signal
restoration operation that can be affected by crosstalk noise (as well by any other
sources of noise).
In restoring the signals, the receivers have thresholds for distinguishing
between logic levels. Crossing over a logic threshold will cause the receiver
to switch the output state. Referring to Figure 4-14, we see a voltage transfer
characteristic for an inverting receiver. When a rising input signal crosses v IH ,it
will cause the output of the receiver to switch from high to low. However, noise