I/O CIRCUITS AND MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 466

diagram. In practice, drawing a Bergeron diagram with better than 5mV, 0.5mA
accuracy is difficult, which limits its use primarily to initial, first-order estimates.

11.6.1 Theory and method
The Bergeron diagram works by using Kirchhoff's circuit laws at the connections
between the transmission line and the transmitter and receiver components,
along with the current versus voltage relationships. For the transmission line,
the current and voltage are related by Ohm's law. The linear transmitter and
receiver models that we used in our previous example also obey Ohm's law,
although nonlinear models will obey the more complex relationships described
by equations (11-1) and (11-4). The Bergeron diagram also works with nonlinear
transceivers, as we show in the next section.
In describing the theory behind the Bergeron diagram, we use the generalized
circuit shown in Figure 11-22 with a rising signal. We start at the steady state
prior to the rising transition. Under steady-state conditions a lossless transmission
line is a short circuit, so that the output of the transmitter is connected effectively
directly to the receiver. In our discussion here, when we refer to the transmitter
and receiver we mean the equivalent circuits for each, as shown in Figure 11-22.
At steady state, we know that the current flowing out of the equivalent circuit for
the transmitter is equal to the current flowing into the equivalent circuit for the
receiver from Kirchhoff's current law. From Kirchhoff's voltage law we know
that the voltage at the output of the transmitter equivalent circuit is equal to
the voltage at the input of the receiver equivalent circuit. We also know that
the relationship between the current and voltage at the output of the transmitter
follows Ohm's law, as does the current-voltage relationship at the input of the

V DD

V TT

R Tx,hi

R TT

i

t = 0

Z 0 , t d

R TX,lo

V TT v V DD

R TT R TX,lo R Tx,hi

i i

i

v

v

Transmitter pull-up Transmitter pull-down Receiver

Figure 11-22 General linear circuit for Bergeron analysis.