EE 350
PROBLEM SET 11
DUE: 17 December 2007
Reading assignment: Lathi Chapter 7, Sections 7.1 and 7.2
Recitation sections meet the week of December 3.
Problem 55:
(20 points)
The gain of an openloop operational amplifier is frequency dependent as shown in Figure 1. Assume that the transfer function
A
d
(
s
) has a single real pole at
s
=

ω
1
and that
A
o
is the DC gain
A
d
(
s
) =
A
o
s/ω
1
+ 1
,
where both
A
o
and
ω
1
are positive real numbers.
1. (3 points) Sketch the Bode plot of the openloop frequency response function
V
o
(
ω
)
/V
d
(
ω
) of the operational amplifier.
What is the 3 dB bandwidth of the openloop response?
2. (1 point)The gain bandwidth (GBW) product is the product of the DC gain and the 3 dB bandwidth.
What is the
GBW product of the openloop operational amplifier?

+
+

+

+

A
(s) V (s)
d
d
V (s)
o
d
V (s)
Figure 1: Operational amplifier with frequency dependent gain.
Using the operational amplifier model in Figure 1, the noninverting amplifier in Figure 2(a) can be represented by the
block diagram in Figure 2(b).
R
1
R
2
i
V (s)
V (s)
o
V (s)
o
i
V (s)
(b)
+
+

+
(a)
K
+



Σ
V (s)
d
Α
ο
/ω
+1
s
1
Figure 2: (a) Noninverting amplifier configuration. (b) Equivalent block diagram.
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3. (2 point) What is the value of
K
in terms of
R
1
and
R
2
?
4. (2 points) Calculate the transfer function
V
o
(
s
)
/V
i
(
s
) of the noninverting amplifier circuit.
5. (1 point) Is the system described by
V
o
(
s
)
/V
i
(
s
) boundedinput boundedoutput stable?
6. (3 points) Sketch the Bode plot of the frequency response function
V
o
(
ω
)
/V
i
(
ω
) of the noninverting amplifier. What
is the 3 dB bandwidth of the noninverting amplifier response?
7. (1 point) Calculate the GBW of the noninverting amplifier.
How does it compare to the GBW of the openloop
operational amplifier?
8. (2 point) For the noninverting amplifier circuit, calculate the transfer function
V
d
(
s
)
/V
i
(
s
) using the block diagram
representation in Figure 2(b). In the limit as
A
o
as approaches infinity, what is
V
d
(
s
)?
Now consider what happens when the output of the operational amplifier is connected to the noninverting input of the
operational amplifier as shown in Figure 3(a). Using the model in Figure 1, the circuit in Figure 3(a) is represented
using the block diagram in Figure 3(b).
R
1
R
2
i
V (s)
V (s)
o
V (s)
o
i
V (s)
(b)
+
+
(a)
K


Σ
V (s)
d
Α
ο
/ω+1
s
1
+

+

Figure 3: (a) Operational amplifier circuit. (b) Equivalent block diagram.
9. (2 point) What is the value of
K
in terms of
R
1
and
R
2
?
10. (2 point) Calculate the transfer function
V
o
(
s
)
/V
i
(
s
) of the circuit.
11. (1 point) Based on the result in part 10, is the circuit in Figure 3(a) BIBO stable?
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 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB
 Amplifier, Frequency, Operational Amplifier, Signal Processing, LTI system theory, Nyquist plot

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