Information Technology Reference
In-Depth Information
To reduce the Miller effect experienced by the gate-drain capacitances of the input
transistors M
9
and M
12
, a capacitive cancellation technique [13] is used. This is
implemented using transistor M
23
and M
24
acting as capacitances. This technique has
been used to increase the bandwidth of multistage amplifiers in wideband circuits
[14]. The principle here is that the Miller capacitances due M
23
and M
24
are negative
because of their cross-connections. Thus they cancel the Miller capacitances due to
the gate-drain capacitances of M
9
and M
12
, and thus significantly reduce the net Miller
capacitances, and hence achieve wide-band performance. Also, note that the two
currents I
C2
and I
C1
from the control circuit in Fig. 1 are mirrored to M
13
and M
14
.
Since the transconductance is a function of the bias current, the gain variation is
obtained by controlling the bias currents of the input-pair (M
9
and M
12
) and the loads
(M
10
and M
11
). Therefore, the differential gain of the VGA cell shown in Fig. 3 is:
g
(
W
/
L
)
I
m
−
M
9
,
12
M
9
,
12
C
2
A
=
=
(5)
v
g
(
W
/
L
)
I
m
−
M
10
,
11
M
10
,
11
C
V
DD
M
15
M
16
M
7
M
8
V
out-
V
out+
C
p
M
23
M
24
V
out+
V
i
n+
V
in-
V
ou
t-
M
9
M
10
M
11
M
12
M
17
M
18
M
19
M
20
V
ref
I
C2
I
C1
V
bias
V
b
ias
C
2
C
1
M
14
M
21
M
22
M
13
V
SS
(VGA Cell circuit)
(Common-mode feedback circuit [2])
Fig. 3.
Amplifying block Schematic
From (4) and (5), the differential gain in terms of the control voltage V
C
can be
expressed as
2
I
V
o
c
+
1
+
(
)
(
)
2
V
−
V
(
W
/
L
K
V
−
V
dd
TH
M
12
dd
TH
A
=
*
(6)
v
2
(
W
/
L
M
10
,
11
I
V
o
c
+
1
−
(
)
(
)
2
V
−
V
K
V
−
V
dd
TH
dd
TH
In this equation, by adjusting the bias current I
O
, the gain can be controlled. For the I
O
value corresponding to k = 0.12, the circuit yields more than 60 dB gain variation.
