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OPERATIONAL AMPLIFIERS
Ho Kyung Kim, Ph.D.
hokyung@pusan.ac.kr
School of Mechanical Engineering
Pusan National University
Basic Experiment and Design of Electronics
Outline
• Ideal Op-amp
• Inverter
• Non-inverter
• Difference
• Integrators
• Differentiators
• Active rectifiers
2
• Let us consider, CD player (source) + Amplifier + Speakers (load)
Ideal Op-Amp
Equivalent source circuit that
the amplifier sees from its input port
Equivalent load resistance
seen from the output port of the amplifier
)()( tAvtv SL
• Amplification factor depends upon
– the source and load impedances
– the input and output resistance of the amplifier
• The given amplifier would perform differently with different loads or sources
• What are the desirable characteristics of the amplifier?
– (large input impedance) Rin >> 1
– (small output impedance) Rout << 1 (or Rout = 0)
)(tvRR
Rv S
inS
inin
Lout
LinL
RR
RAvv
S
Lout
L
inS
inL v
RR
R
RR
RAv
amplification factor
Sin vv 1lim
inS
in
R RR
R
in
inL Avv
• Operational amplifier (simply, op-amp)
– is an integrated circuit (IC)
– has a great number of operations such as addition, filtering, and integration
– is found in most measurement and instrumentation applications
• Open-loop model
– an ideal differential amplifier that amplifies the difference between two input voltages
– near-infinite input resistance and very small output resistance
• Rin =
• : AV(OL) = open-loop voltage gain (105 ~ 107)
0ini
)()(
vvAv OLVout
Inverter
inFS iii
S
S
SR
vvi
F
out
FR
vvi
0v
vAvvAv OLVOLVout )()( )(
)(OLV
out
A
vv
F
Sout
OLVSFOLVSF
outSR
Rv
ARRARRvv
)()(
1
/
1
/
1
0ini
KCL;
Ohm's law;
Ground;
Open-loop model;
or
FS ii
FOLV
out
F
out
SOLV
out
S
S
RA
v
R
v
RA
v
R
v
)()(
SOLV
out
FOLV
out
F
out
S
S
RA
v
RA
v
R
v
R
v
)()(
or
inverting amplifier closed-loop gain
• Let us consider the inverting terminal voltage;
• The effect of the feedback connection from output to inverting (noninverting) input is to force the voltage at the inverting (noninverging) input to be equal that at the noninverting (inverting) input ( virtual grounds)
• Useful assumptions for analysis of ideal op-amp with negative feedback
①
②
0)(
OLV
out
A
vv vvor
vv
0ini
Summing amplifier
FN iiii 21
S
S
nR
vi n
F
out
FR
vi
F
outN
n S
S
R
v
R
v
n
n 1
n
n
S
N
n S
Fout v
R
Rv
1
KCL;
Ohm's law;
Non-Inverter
SinSF iiii
S
SR
vi
F
outF
R
vvi
vvv S
S
S
F
Sout
R
v
R
vv
S
F
S
out
R
R
v
v1
Voltage Follower
vv
Svv
outvv
outS vv
Differential Amplifier
2
21
2 vRR
Rv
1
11
R
vvi
2
2R
vvi out
)(
)(
12
1
2
2
211
2
21
2
1
12
vvR
R
vRRR
R
RR
v
R
vRvout
Instrumentation Amplifier
v2
noninverting amp differential amp
1
2
1
2 21
2/1
R
R
R
RA
)(2
1)( 21
1
221 vv
R
R
R
RAvAv
R
Rv FF
out
1
2
21
21
R
R
R
R
vv
vA Fout
V
Integrator
)()( titi FS
S
SS
R
tvi
)(
dt
tdvCti out
FF
)()(
dt
tdvtv
CR
out
S
FS
)()(
1
t
S
FS
out dttvCR
tv ')'(1
)(
KCL;
Ohm's law;
From the definition of a capacitor;
Differentiator
)()( titi FS
dt
tdvCi S
SS
)(
F
out
FR
vti )(
dt
tdvCRtv S
SFout
)()(
KCL;
Ohm's law;
Active low-pass filter
S
FLPF
Z
ZjwA )(
FF
F
F
FFCjwR
R
jwCRZ
1
1| |
SS RZ
FF
SF
S
FLPF
CjwR
RR
Z
ZjwA
1
/)(
FF CR
10
dB 3log202log20log20)( 0 S
F
S
F
dBLPFR
R
R
RjA
cutoff freq. or – 3dB freq.
Active high-pass filter
S
SSjwC
RZ1
FF RZ
SS
SF
S
FHPF
CjwR
CjwR
Z
ZjwA
1)(
S
FHPF
w R
RjwA
)(lim
Active band-pass filter
Analog computer
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