I/O CIRCUITS AND MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 462

2.5 V 2.5 V

v

i

12.5 Ω 75 Ω

12.5 Ω

i

i

0.0 V

v v

v − 2.5 V = (12.5 Ω ) i v (12.5 ) i 2.5 V − v = (75 Ω ) i

= Ω

(a) (b) (c)

Tx Pull-Down

200

0)
(0.357 V, 28.6 mA)

Tx ( t <

100

Rx

0

− 100

− 200

Tx Pull-Up

− 300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Voltage [V]
(d)

Figure 11-19 Equivalent circuits and voltage-current expressions for Example 11-3:
(a) transmitter pull-up; (b) transmitter pull-down; (c) receiver; (d) load-line plot.

where v 0 and i 0 are the steady-state voltage and current for the system when
driven low. The slope of the line is negative because the rising-edge transition
causes current to flow from the transmitter into the transmission line, while we
have defined positive current as flowing from the line back into the transmitter.
The transmitter also follows Ohm's law, so that the intersection between the
transmission line and the transmitter pull-up lines gives the initial voltage and
current at the transmitter for the rising edge. Figure 11-20a illustrates this, giving
an initial voltage and current of 2.357 V and

11.4mA.
The next step is to draw another load line for the transmission line. The line
starts at the previous point (2.357 V,

−

11.4 mA), has a slope equal to 1 /Z 0 ,
and extends until it intersects with the load line for the receiver, as shown in
Figure 11-20b. This gives us the voltage and current at the receiver after the
first propagation delay, and comprehends both the initial and reflected waves.
It works because we are again satisfying simultaneous Ohm's law expressions
for the transmission line and the receiver, while taking into account the previous
voltage and current levels. Ohm's law gives us the relationships that allow us to
solve for the signal values given the constraints imposed by Kirchhoff's circuit
laws. Since the transmission line is connected to the receiver, Kirchhoff's circuit

−