CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

2.5 An Overview of Signal-Flow Graphs 36
network β. The signal-flow graph represents the pair of equations
from which we obtain the familiar expression
x 1
x 1
x 1
x 2
x 1
t 12
t a
t b
t 13
t 23
t 12
x 2
x 2
x 3
(2.9)
(2.10)
(2.11)
In contrast to Equations (2.8) and (2.11), most textbooks have a plus rather than
minus sign, a result of adopting a convention whereby the feedback signal is sub-
tracted rather than added back to the input node. Since the difference is only one of
convention, we will continue with our existing convention in order to remain consis-
tent with the signal-flow graph algebra. The quantities L and Aβ are commonly
known as the loop gain.
x 2
t 23
t 34
t 23
t 24
x 3
=
Ax 2
x2 = βx3 + kx1 x 3
----
x 1
x 3
x 4
kA
= -----------------
1 – Aβ
x 3
x 4
t a
t b
≡ x 1 x 2
a)
≡
b)
c)
x 1
x 1
+
t 12 t 23
x 3
≡ x 3
d)
x 2
≡ x 1
t 12 t 23
t 12 t 24
t 13 t 34
t 23 t 34
Figure 2.18 Four elementary equivalences of signal-flow graphs.
x 3
x 4