# 3.1 Operational Amplifiers

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```3.1 Operational
Amplifiers
• properties of an ideal amplifier
• equivalent circuit and performance of a real
operational amplifier
• three example circuits
P voltage follower circuit - used as an
impedance buffer
P non-inverting amplifier circuit - works by
voltage feedback
P inverting amplifier circuit - works by current
feedback
• Bode plot showing the dependence of gain on
frequency
3.1 : 1/8
Ideal Amplifiers
• operational amplifiers evolved from the field of analog
computation where they were designed to perform mathematical
operations
• they are currently used as building blocks in constructing
electronic instrumentation
• they are available as integrated circuits and cost just a few
dollars - the circuit detail at the transistor level can be ignored
• properties of an ideal amplifier (op-amps come close!)
P an infinite input impedance that draws no current from the
preceding circuit
P a zero output impedance so that a voltage divider is not
formed with the following circuit
P an infinite gain so that the smallest signal can be amplified
to a useful level
P respond to any frequency
3.1 : 2/8
Equivalent Circuit and Performance
inverting
input
+ 15 V
• the signal is connected to one or
both inputs
!
• any current passing between the
Rout
two inputs will cause a voltage,
RS
GVS !
VS, across RS
+
• VS is amplified by a factor of G
+
to create Vout
Vout = -GVS
• when the signal is connected
noninverting
! 15 V
between the common and
input
inverting inputs, the output is the
circuit common
negative of the input
• when the signal is connected between the common and noninverting inputs, the output is the same sign as the input
• typical performance
P open loop gain, G, of &times;104 to &times;109
P effective input impedance (given by RSG) of 109 to 1015 Ω
P effective output impedance (given by Rout/G) of &lt; 1 Ω
P frequency response into the megahertz domain
3.1 : 3/8
Op-Amps with Negative Feedback
There are two equivalent methods
for determining how Vout depends
upon the input signal.
circuit
V!
circuit
!
VS = 0
V+
1. Using voltage: Vout will adjust
itself so that V- = V+. This
makes VS = 0.
+
V out
if
circuit
2. Using current: Vout will adjust
itself so that if = iin. This makes
iS = 0.
!
i in
iS = 0
+
V out
3.1 : 4/8
Voltage Follower
A voltage follower is often used as
an impedance buffer between a
high Z source and low Z circuit.
The voltage approach can be used.
In order that VS = 0, it is necessary
that Vout = Vin. Thus the output
voltage follows the input voltage.
!
VS
+
V out
high
Z
V in
Note that the above relationship is an approximation since
Vin + VS = Vout.
Vin + VS = Vout
Vout
= Vout
G
⎛ G ⎞
= Vin ⎜
⎟
⎝ G −1 ⎠
Vin +
Vout
3.1 : 5/8
for a gain of 104 and
larger the discrepancy
from Vout = Vin is trivial
low
Z
Non-Inverting Amplifier
Rf
The op-amp will increase Vout until V−
equals Vin . At that point VS = 0.
R1
R1
Vin = V− = Vout
R1 + R f
Rf
Vout R1 + R f
=
= 1+
Vin
R1
R1
!
+
V!
Vin
positive attributes
• output voltage is the same sign as the input voltage
• very high input impedance given by G&times;Rs
negative attributes
• the high input impedance will combine with stray capacitance
to limit the amplifier bandwidth
• the non-zero voltage at both inputs stresses the op-amp
3.1 : 6/8
V out
Inverting Amplifier
The op-amp will increase Vout until
if = i1. At that point VS = 0, the +
input is at true ground, and the −
input is at &quot;virtual&quot; ground.
i1 = i f
Vin − 0 0 − Vout
=
R1
Rf
Rf
R1
i1
iS
if
!
V in
VS
+
V out
Rf
Vout
=−
G=
Vin
R1
negative attributes
• output voltage is opposite in sign from the input
• input impedance given by R1 + Rf/G, not G&times;RS
positive attributes
• the low input impedance does not combine with stray
capacitance to limit the bandwidth
• the zero voltage at both inputs maximizes op-amp performance
3.1 : 7/8
Frequency Dependent Gain
A(dB)
741 Operational Amplifier
Bode Plot
The gain curve of an op100
dc gain 86 dB
amp depends upon G
90
80
and the unity gain
70
bandwidth. Draw a
open loop
gain
x100
60
horizontal line at G (dB),
bandwidth
50
x10
and a line with a slope
40
bandwidth
unity gain
of 20 dB/decade upward
30
bandwidth
from the unity gain (0
1.2 MHz
20
dB) bandwidth. Where
10
0
the two lines cross the
0
1
2
3
4
5
6
7
gain is down by 3 dB,
log(f)
just as the filter Bode
plots.
To obtain a Bode plot for a given
amplifier, draw a horizontal line at the
amplifier gain. Where it intersects the
open loop line, the gain is down by 3 dB.
Shown above are lines for &times;10 and &times;100
amplifiers.
3.1 : 8/8
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