I/O CIRCUITS AND MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 468

− 1 /Z 0 and 1 /Z 0 , until it approaches steady state. So we see that the Berg-

eron is simply a graphical technique for repeatedly solving the simultaneous
equations arising from circuit laws that describe the transient voltage and current
signals at both ends of a transmission line. We now illustrate the application of
the technique to a system with nonlinear transceiver characteristics.

Example 11-4 Bergeron Diagram with Nonlinear Transceivers In this example
we analyze the falling edge for the circuit shown in Figure 11-23, which uses a
CMOS push-pull transmitter with no termination at the receiver end. The system
relies on the output impedance of the transmitter to provide source termination,
and the transistors are sized to provide a 50- output impedance to match the
target impedance of the transmission line. The load-line plot shows the nonlinear
transistor behavior discussed in Section 11.2.1. The load line for the receiver is
simply a zero-current (infinite-impedance) line that represents the open circuit
at that end. We know that the characteristic impedance of the transmission lines
may vary by up to 20% due to manufacturing tolerances. Thus, for our example

we choose a 60- characteristic impedance for the transmission line. With this
information, we step through the analysis as follows:

±

1. The Bergeron diagram begins at the load-line intersection of the transmitter
pull-up and the receiver. The potential and current are 2.5 V and 0mA,
respectively.
2. From that point we draw the load line for a transmission line with slope
equal to 0 . 0167 − 1 ( − 1 / 60 ) , extending it until it intersects the nonlin-

ear curve for the transmitter pull-down device at 0.80 V and 28.3 mA, which
are the initial values at the transmitter after the falling-edge transition.
3. Draw a load line from the previous point, with slope equal to 0 . 0167 − 1
until it intersects with the receiver load line at i =

−

0, which gives the volt-

age at the receiver ( 0 . 90 V) after the first incident wave reaches it. A sim-

ple means of checking the result at this point is to consider the magnitudes
of the incident and reflected voltage waves. The incident-wave magnitude
is equal to 0.80 V

−

− 2.50 V, or − 1 . 70 V. The reflected wave is also equal to

50

Tx pull-down

40

30

20

i

10

Rx

0

60 Ω , 1 ns

− 10

− 20

− 30

Tx pull-up

− 40

− 50

− 1.0 − 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

v out (V)

Figure 11-23 Push-pull transmitter circuit and nonlinear i - v characteristics.