Hardware Reference
In-Depth Information
a
b
kR
V in
+
A
V 0
R
V in
V 0
A
(k−1)R
+
R
Fig. 5.1 VOA-based K-gain amplifiers (a) Non-inverting (b) Inverting
A 0 ω p
s
A 0 ω p
s ω t
A
¼
þ ω p
for
ω > ω p
ð
5
:
2
Þ
s
where A 0 is the maximum gain (at DC) and ω p is the pole frequency in radians/sec
with ω t ¼A 0 ω p being the gain-bandwidth-product (GBP) of the op-amp.
By straight forward analysis, it can be shown that the inverting amplifier exhibits
the maximum gain
¼ ω t
k
¼
K and 3-dB bandwidth
þ 1 while the non-inverting
¼ ω k :
amplifier exhibits the maximum gain
¼
+K and 3-dB bandwidth
is fixed, the 3-dB BW also gets
fixed. In other words, increasing the closed loop gain
Thus, in both the cases, the moment the gain
'
K
'
reduces the available
bandwidth and a larger bandwidth can be accomplished only for smaller values of
'
'
K
'
. There is clearly a conflict between the requirement of a larger gain and a larger
bandwidth as the two are interdependent and cannot be met simultaneously.
In the following, we show that when the same configurations are realized with
CCs (as shown in Fig. 5.2a, b ), the gain bandwidth conflict is eliminated and it
becomes possible to design variable gain amplifiers with nearly constant bandwidth
independent of the gain [ 162 ].
A straight forward analysis of the first circuit taking into account the parasitic
Z-port impedance Z p of the CCs which is equal to a parallel RL (Z p ¼
K
'
R p /(1/sC p )
reveals its non-ideal transfer function as:
1
C p R 1
V o
V in ¼
ð 5 : 3 Þ
1
C p
2
1
R p
s
þ
R 2 þ
Similarly, an analysis of the non-inverting configuration reveals:
1
C p
R 1 þ
1
2
R 2
V o
V in ¼ þ
ð
5
:
4
Þ
1
C p
2
1
R p
s
þ
R 2 þ
From the above, it can be easily found that the maximum gains in case of the two
circuits are found to be:
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