Biomedical Engineering Reference
In-Depth Information
Taking
L
D
and
L
C
into account, the gain equation of the LNA becomes
v
out
v
in
=
F
(
s
)
g
m
s
(
C
p
+
−
C
gs
)
ω
t
L
s
(
R
L
+
sL
L
)(1
+
s
2
L
D
C
gd3
)
∗
1)
.
(4)
s
2
(
L
L
+
sL
L
)(
s
2
L
D
C
gd3
+
1
+
sR
L
C
gd3
+
L
D
)
C
gd3
+
C
gb2
(
R
L
+
Comparing two gain equations, it can be concluded that adding the peaking inductors
has resulted in removal of one of amplifier's dominant poles which was located at
M
2
's drain.
This has been done by breaking parasitic capacitance of this node, (
C
db2
+
C
gd3
),
into two smaller capacitors. From another point of view, if the step response of
this circuit is considered, then isolating the buffer stage from the cascode stage and
splitting these two capacitors from each other, results in a much smaller capacitance
to be charged and discharged every cycle. This means shorter transient time in the
time domain or wider bandwidths in the frequency domain.
Figure
14
shows the pole-zero analysis and the effect of adding
L
D
. Based on
this plot,
L
D
should be designed in a way such that undesired poles and zeros will
be removed. In this work,
L
D
was designed in such a way that the added poles are
located at 7.4 and 9.2 GHz and zeros at 5.9 (twin) and 7.6 GHz. The pole at 7.4
GHz and the zero at 7.6 GHz are close enough to approximately cancel each other's
effect and consequently would not have any significant effect on the gain curves.
In contrast, the zero at 5.9 GHz, which is a twin zero, not only prevents the gain
from decreasing at higher frequencies, but it also results in an increase of the gain
amplitude for frequencies beyond 5.9 GHz. This increase will continue until the
next twin pole at 9.2 GHz, which stops the gain increment and causes a decrease in
the gain until the end of bandwidth. Although the gain amplitude and bandwidth is
improved significantly, the gain is still not very flat.
Figure
15
shows the gain curves in different stages of design. Figure
15
aisthe
original design without any additional inductances, Fig.
15
b shows the effect of
adding
L
D
and Fig.
15
c the effect of both
L
D
and
L
C
. The problem with flatness
is basically due to the parasitics generated by the cascode stage. The addition of an
inductor between the gain and cascode stages will help to improve the gain flatness.
In fact,
L
C
, together with
C
gd1
and
C
gs2
, can form a wideband
-section LC network.
As a result, it can resonate with the capacitors to produce broadband operation for
the LNA. Figure
14
b shows that adding
L
C
has caused three sets of poles to be
relocated and also one set of poles to be generated. Among the three poles that have
been displaced, two of them do not have a significant effect. The first is a pole at 8.3
GHz which is moved to 8.1 GHz and the other one is the pole which is moved from
7.5 to 7.9 GHz. In contrast, the third pole displacement is moving the undesirable
pole out of the band and it is very effective in improving the gain curve. This pole
is moved from 8.94 to 10.9 GHz. The most important effect of
L
C
is the pole which
is generated at 6.13 GHz. This pole is designed to be very close to the twin-zero
generated due to the addition of
L
D
, and it can cancel one of the zeros. As a result,
π
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