1) An op-amp inverting amplifier circuit produces an output voltage that is equal to the negative of the input voltage multiplied by the feedback resistor divided by the input resistor. 2) An op-amp non-inverting amplifier produces an output voltage that is equal to the input voltage multiplied by the feedback resistor divided by the input resistor plus the input voltage. 3) An op-amp summing amplifier adds multiple input voltages together by taking advantage of the op-amp's high input impedance, treating each input separately and summing them at the output.

1. By
P.SIVA NAGENDRA REDDY

2. Slide 7
Inverting Op-Amp
V1
R1
Rf
Vo



3. Notice the output formula is similar to Inverting Amplifier, but they are not the same.
Non inverting Amplifier
V1)
R1
Rf
1(Vo 

4. Summing Amplifier
Because the op-amp has a high input impedance the multiple inputs are treated as separate inputs.






 3
3
f
2
2
f
1
1
f
V
R
R
V
R
R
V
R
R
Vo

5. Differential Amplifier Using Op Amp
v v 
1
1
1
v v
i
R


I/P Current to op amp is zero
0
1
2
v v
i
R
 

+
-
1R
2R
1v
ovv
v
1i
1i
2v
1R
2R
2
2
1 2
R
v v
R R
 

01
1 2
v vv v
R R
 

2 2
1 2 2 0
1 2 1 2
1 2
R R
v v v v
R R R R
R R
 
 


6. Differential Amplifier Using Op Amp
+
-
1R
2R
1v
ovv
v
1i
1i
2v
1R
2R
2 2
1 2 2 0
1 2 1 2
1 2
R R
v v v v
R R R R
R R
 
 

 
2
2 2 2
0 1 2 2
1 1 2 1 1 2
R R R
v v v v
R R R R R R
   
 
2 2 2
0 1 2
1 1 2 1
1
R R R
v v v
R R R R
 
    
  
 2
0 2 1
1
R
v v v
R
 

7. The Unity-Gain Amplifier or “Buffer”
• This is a special case of the non-inverting amplifier, which is also
called a voltage follower, with infinite R1 and zero R2.
Hence Av = 1.
• It provides an excellent electrical isolation while maintaining the
signal voltage level.
• The “ideal” buffer requires no input current and can drive any
desired load resistance without loss of signal voltage.
• Such a buffer is used in many sensor and data acquisition system
applications.

8. 1o
F
i
v
A
v
 
i ov v v v   
+
-
ov
v
v
iv
o
F
i
v
A
v

i ov v v v   
Closed-loop voltage gain
Used as a "line driver" that transforms a high input impedance (resistance) to a
low output impedance. Can provide substantial current gain.
Unity-Gain Buffer

9. Ideal Integrator

10. Since the inverting input is at virtual ground
dt
dv
Ci o
2 
R
v
i in
1 
Applying KCL at the inverting input
i1+i2 = 0
0
R
v
dt
dv
C ino

)initial(vdtv
RC
1
v oino  

11. Ideal Differentiator Circuit

12. dt
dv
Ci in
1 
R
v
i o
2 
i1+i2 = 0
0
R
v
dt
dv
C oin

dt
dv
RCv in
o 
Since the inverting input is at virtual ground
Applying KCL at the inverting input
Differentiators are avoided in practice as they amplify noise
Op-Amp Differentiator Cont…

13. Instrumentation Amplifier
Combines 2 non-inverting amplifiers
with the difference amplifier to provide
higher gain and higher input
resistance.
Gain can be varied by varying single
resistor R1
)
b
va(v
3
4v 
R
R
o
b
v
2
i)
1
i(2
2
iav  RRR
1
2
2
v
1
v
i
R


)
2
v
1
(v
1
21
3
4v 














R
R
R
R
o
NOTE
Ideal input resistance is infinite
because input current to both op
amps is zero. The CMRR is
determined only by Op Amp 3.

14. Ideal Op-Amp Analysis
To analyze an op-amp feedback circuit:
• Assume no current flows into either input terminal
• Assume no current flows out of the output terminal
• Constrain: V+ = V-

15. Inverting Amplifier Analysis
virtual ground

16. Non-Inverting Amplifier
Analysis

17. Op-Amp Buffer
Vout = Vin
Isolates loading effects
A
High output
impedance
B
Low input
impedance

18. Op-Amp Differentiator

19. Op-Amp Integrator

20. Op-Amp Summing Amplifier

21. Op-Amp Differential
Amplifier
If R1 = R2 and Rf = Rg:

22. Applications of Op-Amps
Filters
Types:
•Low pass filter
•High pass filter
•Band pass filter
•Cascading (2 or more filters connected
together) R2
+
-
+
V0
__
+ Vcc
- Vcc
-
+
R1
C
Low pass filter
Low pass filter Cutoff
frequency 
Low pass filter transfer
function

23. Applications of Op-Amps Electrocardiogram (EKG) Amplification
 Need to measure difference in voltage from lead 1 and lead
2
 60 Hz interference from electrical equipment

24. Applications of Op-Amps
 Simple EKG circuit
 Uses differential
amplifier to cancel
common mode signal
and amplify differential
mode signal
 Realistic EKG circuit
 Uses two non-inverting
amplifiers to first
amplify voltage from
each lead, followed by
differential amplifier
 Forms an
“instrumentation
amplifier”