Digital Signal Processing Reference
In-Depth Information
9.1 HIGH-FREQUENCY VOLTAGE AND CURRENT WAVES
As a prerequisite to describing network theory, it is required to understand how
voltage and current waves propagating on an interconnect will interact with dif-
ferent loads. Many of these concepts were covered partially in Chapter 3 when
lattice diagrams and the reflection coefficient at an impedance junction were dis-
cussed. In this chapter we build on those concepts to calculate the reflection
coefficient looking into a network, such as a transmission line terminated in a
load that is not equal to the characteristic impedance. Similarly, the impedance
looking into a terminated network is also calculated. These concepts are important
for the development of network theory.
9.1.1
Input Reflection into a Terminated Network
The reflection coefficient looking into a network with a finite electrical length
is different from the reflection coefficient looking into an impedance junction
because it has a phase component that will change with electrical length and
frequency. Equation (3-102) from Section 3.5.1 defines the reflection coefficient
looking into an impedance junction:
v
r
v
i
=
Z
02
−
Z
01
≡
(3-102)
Z
02
+
Z
01
where
v
r
and
v
i
are the reflected and incident voltage values, respectively. In
the case of equation (3-102) the reflection occurs immediately, so there is zero
phase delay between the incident and reflected waves. However, consider the case
shown in Figure 9-1, where there is a significant distance between the point where
the reflection is being evaluated and the impedance discontinuity. The reflection
coefficient at the load,
(z
=
0
)
, can be calculated with equation (3-102):
R
l
−
Z
0
R
l
+
Z
0
0
=
However, consider
(z
=−
l)
, which is the reflection coefficient looking into
the input of the network. After a signal is driven onto the network, the reflection
will not arrive back at the input until the signal propagates down the network,
reflects off the impedance discontinuity at
z
=
0 (defined by
0
), and propagates
back to the source. Depending on when the reflections arrive at the receiver, the
incident and reflected waves will combine at specific frequencies and interact
either constructively or destructively. If the incident and reflected waves interact
destructively, the reflection coefficient will be minimized (and vice versa). This
means that
the reflection coefficient looking into the network will be influenced by
propagation delay, characteristic impedance, termination impedance, length, and
frequency
.
Search WWH ::
Custom Search