CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

Pole frequencies(MHz)
500
450
400
350
300
250
200
150
100
50
5.2 Developing an Analytic Circuit Model 129
Since the process of optimizing the frequency response involves maximizing the
gain for a desired bandwidth, the gain-bandwidth (GBW) product is a useful figure
of merit because it combines gain and bandwidth into a single quantity. Although
bandwidth and gain can be traded off with feedback, the product of the two is often
fixed for a given topology, bias condition, etc. We can optimize our preamplifier
design through maximizing the GBW. By approximating the bandwidth with ω p1 ,
we can obtain an analytic expression for the GBW from Equations (5.25) and
(5.26):
0
0 5
R (kΩ)
f
10 15
500
450
400
350
300
250
200
150
100
0
20
Figure 5.20 shows the resulting 3-dimensional plot of GBW versus and
(5.30)
while Figure 5.21 presents the same surface in two, 2-dimensional projections
views. Across the design space, we see that the GBW can vary by over an order of
magnitude. We can identify that portion of the design space which meets our band-
width requirement by projecting the bounded region identified in Figure 5.18 onto
the GBW plot. Within this region, we have marked in grey a sub-region that corre-
sponds to an area with the highest GBW.
Pole frequencies(MHz)
50
10
0 −10
20*log (K )
10 cm
Figure 5.19 Two projections of the surface plot in Figure 5.18.
GBW
( gm1 + gs1) ( 1 – gm3 R f )
= ----------------------------------------------------------------------------------------------
Cin + ( gm1 + gs1) ( CL + C f )Rf⁄ K cm
−20
surface —
mesh —
R f
ω p1
ωo K cm