Digital Signal Processing Reference
In-Depth Information
R
1
R
2
i
(
t
)
Isolation
amplifier
v
(
t
)
v
1
(
t
)
L
1
v
2
(
t
)
L
2
Figure 2.36
Cascade connection of two
circuits.
illustrated with the cascade connection of two
RL
circuits in Figure 2.36. The equation
of the current
i
(
t
) in the first circuit is independent of the second circuit, provided
that the isolation amplifier has a very high input impedance (usually, a good ap-
proximation). For this case, the current into the input terminals of the amplifier is
negligible compared with
i
(
t
), and the system characteristics of the first circuit are
not affected by the presence of the second circuit. If the isolation amplifier is re-
moved, and affect the voltage across and the system model for as a
function of
v
(
t
) changes. When we draw an interconnection of systems, such as in
Figures 2.34 and 2.35, the implicit assumption is made that the characteristics of all
systems are unaffected by the presence of the other systems.
An example illustrating the interconnection of systems will now be given.
R
2
L
2
L
1
,
v
1
(t)
Interconnections for a system
EXAMPLE 2.16
Consider the system of Figure 2.37. Each block represents a system, with a number given to
identify the system. The circle with the the multiplication of the two input
signals. We can write the following equations for the system:
symbol * denotes
y
3
(t) = y
1
(t) + y
2
(t) = T
1
[x(t)] + T
2
[x(t)]
and
y
4
(t) = T
3
[y
3
(t)] = T
3
(T
1
[x(t)] + T
2
[x(t)]).
Thus,
y(t) = y
4
(t) * y
5
(t) = [T
3
(T
1
[x(t)] + T
2
[x(t)])]T
4
[x(t)].
(2.56)
This equation denotes only the interconnection of the systems. The mathematical model of
the total system depends on the mathematical models of the individual systems.
y
1
(
t
)
y
3
(
t
)
y
4
(
t
)
1
3
x
(
t
)
y
2
(
t
)
y
(
t
)
2
y
5
(
t
)
4
Figure 2.37
System for Example 2.16.
