Biomedical Engineering Reference
In-Depth Information
However, since the target signal is in the low frequency range, we can take advantage
of this characteristic to implement the embedded band-pass filter function. Ignoring
the channel length modulation and transistor body effect, the drain current of
NM
1
−
4
can be given as:
V
B
+
V
th
2
β
2
W
L
V
in
2
I
1
=
−
(7)
V
B
−
V
th
2
β
2
W
L
V
in
2
−
I
2
=
(8)
β
2
W
L
(
V
B
−
V
th
)
2
I
3
=
I
4
=
(9)
The squarer output voltage can be expressed as:
β
4
W
L
v
in
R
load
V
out
=
I
out
·
R
load
=
(
I
1
+
I
2
−
I
3
−
I
4
)
·
R
load
=
(10)
where ß is the transistor constant,
R
load
represents the equivalent total loading resis-
tance at the output of the squarer. From (Eq.
10
), it can be observed that, besides
using larger transistors for the transconductance stage, increasing the squarer load
resistance is another efficient way to boost the squarer output voltage. At low fre-
quency,
R
load
is limited by the squarer output resistance, since the squarer output is
connected to the gate of next stage which has very high input impedance. The output
resistance of proposed squarer can be expressed as:
1
r
o
,
NM
5
g
m
,
NM
5
·
r
o
,
NM
1
R
load
≈
r
o
,
PM
1
||
+
·
(11)
2
where
r
o
is the transistor output resistance and
g
m
is the transistor transconductance.
The large
R
load
together with the parasitic capacitance and the input capacitance of
the next stage will form a band-pass filter to suppress the low-frequency and high-
frequency NBI components after the squaring operation. The optimized R
load
should
be the one that maximizes the squarer output voltage without significantly filtering
the down-converted Gaussian envelope component by the squarer .
Analog Baseband
The block diagram of VGA and comparator is shown in Fig.
8
. The VGA consists
of a three-stage fixed gain (12 dB) and a variable gain stage (
15-15 dB). Coarse
gain tuning is achieved by selecting the number of fixed gain stages to use. Fine gain
tuning is varied by controlling the current ratio in the variable gain stage to achieve
resolution of 1 dB/step. The output of the VGA is then connected to a limiting
amplifier which output full-swing pulse to the digital baseband. In order to ensure
−
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