CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

4.5 Analyzing Transistor Circuits 103
Either by substituting Equation (4.18) into (4.17) or simply by noting that the cur-
rent i out is forced to flow through , we obtain
(4.19)
By finding an expression for in terms of , we can now solve the output resis-
tance
– gm1v
x
0A
(4.20)
Equation (4.20) tells us that the output impedance of a cascode current mirror is
enhanced by roughly ( 1 + gm2r ds2)
times that of a simple current mirror. Apart
from providing the correct algebraic result, however, nodal analysis provides little
else in terms of understanding this circuit. Nodal analysis gives no insight into the
feedback mechanism; the ( 1 + gm2r ds2)
term resembles the common feedback
expression ( 1 + Aβ)
but it is unclear how we can relate the two expressions, and
why an additional term appears in the answer.
v x
Trying to analyze this circuit using topology-based feedback analysis is chal-
lenging; comprised of only a single dependent current source and two resistors, it is
v out
i out
r ds1
r ds2
Figure 4.28 Small-signal circuit for determining output resistance
of cascode current mirror.
R out
r ds2
v x
vout -------iout
v x
r ds2
=
i out r ds2
i out
≡ = rds1 + rds2 + gm1r ds1rds2 = rds2 + ( 1 + gm1r ds2)rds1
≈ ( 1 + gm1r ds2)rds1