CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

i in
v in
– ( gm1 + gs1)vin g m2 v A
3.3 A Low-Voltage Transimpedance Amplifier 60
By combining Equations (3.11) and (3.12), we obtain the dc transimpedance gain
The input resistance is obtained by simply applying KCL to the input terminal
which combined with Equation (3.11) gives
(3.14)
The output resistance can be determined by applying a test current at the output as
shown in Figure 3.16. From this circuit come the two relationships,
and the resulting output resistance is
vA
g m3 v A
Figure 3.15 Simplified DC small-signal circuit of low-voltage preamplifier.
R in
v out
--------
i in
(3.16)
(3.17)
vx 1 + gm2 R f
Rout = ---- =
-------------------------- . (3.18)
ix gm2 + gm3 While the preamplifier’s dc characteristics can be derived quite easily, the opti-
mization of the design requires a deeper understanding of the frequency response of
the circuit which is much more complex. Figure 3.17 plots the simulated frequency
responses of four implementations of the proposed preamplifier using different tran-
R f
v out
gm3 R f – 1
= – -------------------------- . (3.13)
gm2 + gm3 iin = gm2v A + ( gm1 + gs1)vin vin gm3 ----- ------------------------- ( gm1 + gs1) . (3.15)
gm2 + gm3 1 –
= =
i in
ix = gm2v A + gm3v A
vx = vA – gm2v AR f