CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

4.4 Determining Port Impedances 90
Figure 4.12 Final signal-flow graphs for unity-gain circuit showing all voltage
constraints.
The final signal-flow graph can be simplified as shown in Figure 4.13 to high-
light the relationships needed to find the gain and input and output resistances.
The voltage gain can now be easily determined by inspection
It is useful to note that, for the voltage gain, vi is considered an independent source.
Thus, the graph can be opened at node vi using the substitution theorem, and the
feedback path from vo to isci can be disregarded. We can simplify Equation (4.8) by
utilizing the fact that
1 ⁄ ro isci rid 1 ⁄ rid iti vi isco ito i ti
i sci
r id
1 ⁄ rid v x
A v Av
v i
1
----- Av + -----
r id
r ||
id ro Figure 4.13 Simplified SFG from Figure 4.12.
vo ---vi
r id
r o
i to
1 ⁄ rid r o
–
– Av ⁄ ro r ||
id ro 1
----- A ⎛ v⎞
r ||
id ro = ⎜ + ----- ⎟ × ------------------------------------------------
⎝ ⎠ 1 + r || id ro × Av ⁄ ro v o
v o
(4.8)