IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 129

τ d = 250 ps

v s

75 Ω

50 Ω A

0-2 V

(a)

3

t r = 10 ps

2

t r = 250 ps

1 t r = 500 ps

t r = 750 ps

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

Time, ns

(b)

Figure 3-38 (a) Underdriven transmission line; (b) example of how increased rise and
fall times mask the reflections.

connectors tend to be inductive. This makes it necessary to understand how
these reactive elements affect the reflections in a transmission-line system. In
this section we briefly introduce the effect that capacitors and inductors have on
reflections.

Reflection from a Capacitive Load When a transmission line is terminated in a
reactive element such as a capacitor, the shape of the waveforms at the driver
and the load will be dependent on the value of the capacitor, the characteristic
impedance of the transmission line, and any resistive terminations that may be
present. Essentially, a capacitor is a time-dependent load that will look initially
like a short circuit when the signal reaches the capacitor and will then look like
an open circuit after the capacitor is fully charged. Let's consider the reflection
coefficient at time t = τ d (the delay of the transmission line). At time t = τ d ,
which is the time when the signal has propagated down the line and has reached
the capacitive load, the capacitor will not be charged and will look like a short
circuit. As described earlier in the chapter, a short circuit will have a reflection
coefficient of

−

1. This means that the initial wave of magnitude v i will be

− v i , yielding an initial voltage of
0 V. The capacitor will then begin to charge at a rate dependent on τ , which is the
time constant of an RC circuit, where C is the termination capacitor value and
R is the characteristic impedance of the transmission line. Once the capacitor is
fully charged, the reflection coefficient will be 1 since the capacitor will resemble
an open circuit. Equation (3-108), which is the step response of a simple network
with a time constant τ , approximates the voltage at the end of a transmission

reflected off the capacitor with a magnitude of