CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

4.5 Analyzing Transistor Circuits 98
shows for an npn device, the redirection of electrons from the base to the collector
by virtue of the transconductance element.
i scb
i scb
g m
Z ||
b re Z ||
b rπ – gm
v b
1 ⁄ re – gm+ 1 ⁄ re – gm
v b
1 ⁄ rπ+ gm Z ||
c ro 1 ⁄ ro gm + 1 ⁄ ro Z || e r || e ro Figure 4.21 Corresponding signal-flow graphs for the two small-signal
models shown in Figure 4.20.
The SFG for MOS transistors can be derived in the same manner. Although the
MOS transistors can also be modeled with both the T-model and the hybrid-π
model, the hybrid-π model as shown in Figure 4.22 better reflects the physical oper-
ation of the device because the gate is explicitly shown as an open circuit. With the
T-model, the gate appears to be connected to the voltage-controlled current source
and the source resistance, and it is only the exact relationship between these two ele-
ments that ensures the gate current remains zero. The body effect can been incorpo-
i scc
i sce
a) T-model
1 ⁄ rπ i sce
i scc
b) Hybrid-π model
Z ||
c ro 1 ⁄ ro gm + 1 ⁄ ro Z ||
e r ||
π ro – gm
v c
v e
v c
v e