![Page 1: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/1.jpg)
Operational Amplifiers:
• An operational amplifier (op-amp) are used in analog electronic design for– Amplification– Analog filtering– Buffering– Threshold detection
![Page 2: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/2.jpg)
Basic Electric CircuitsOperational Amplifiers
inverting input
noninverting inputoutput
V-
V+
The basic op amp with supply voltage included is shownin the diagram below.
-V Vout V
![Page 3: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/3.jpg)
Basic Electric CircuitsOperational Amplifiers
In most cases only the two inputs and the output areshown for the op amp. However, one should keep inmind that supply voltage is required, and a ground.The basic op amp without a ground is shown below.
Outer op amp diagram.
![Page 4: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/4.jpg)
Basic Electric CircuitsOperational Amplifiers
A model of the op amp, with respect to the symbol, isshown below.
V1
V2
_
+
Vd Ri
Ro
AVd
Vo
Op Amp Model.
![Page 5: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/5.jpg)
Basic Electric CircuitsOperational Amplifiers
The previous model is usually shown as follows:
Ri
Ro
AVd
_
+
Vd
V1
V2
Vo
+
_
![Page 6: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/6.jpg)
Basic Electric CircuitsOperational Amplifiers
Application: As an application of the previous model,consider the following configuration. Find Vo as a function of Vin and the resistors R1 and R2.
+
_
R2
R1
+
_
+
_
Vin Vo
![Page 7: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/7.jpg)
Basic Electric CircuitsOperational Amplifiers
In terms of the circuit model we have the following:
Ri
Ro
AVi
_
+
ViVin Vo
+
_
+
_
R1
R2
ab
Total op amp schematic for voltagegain configuration.
![Page 8: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/8.jpg)
Basic Electric CircuitsOperational Amplifiers
Ri
Ro
AVi
_
+
ViVin Vo
+
_
+
_
R1
R2
ab
Circuit values are:R1 = 10 k R2 = 40 k Ro = 50 A = 100,000 Ri = 1 meg
![Page 9: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/9.jpg)
Basic Electric CircuitsOperational Amplifiers
We can write the following equations for nodes a and b.
(1)
(2)
( )10 1 40
( )5040
i oin i i
i oo i
V VV V Vk meg k
V VV AVk
![Page 10: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/10.jpg)
Basic Electric CircuitsOperational Amplifiers
Simplifying 1
inio VVV 10012625 (3)
Simplifying 2
010410005.4 95 io VxVx (4)
![Page 11: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/11.jpg)
Basic Electric CircuitsOperational Amplifiers
From Equations 3 and 4 we find;
ino VV 99.3
Fortunately, we are not required to do elaborate circuitanalysis, as above, to find the relationship between theoutput and input of an op amp. Simplifying the analysisis our next consideration.
(5)
![Page 12: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/12.jpg)
Basic Electric CircuitsOperational Amplifiers
For most all operational amplifiers, Ri is 1 meg orlarger and Ro is around 50 or less. The open-loop gain, A, is greater than 100,000.
Ideal Op Amp:The following assumptions are made for the ideal op amp.
i
o
RohmsinputInfinite
RohmsoutputZero
AgainloopopenInfinite
;.3
0;.2
;.1
![Page 13: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/13.jpg)
Basic Electric CircuitsIdeal Op Amp:
_
+ ++
++
_
__ _
Vi
V1
V2 = V1Vo
i1
i2
= 0
= 0
(a) i1 = i2 = 0: Due to infinite input resistance.
(b) Vi is negligibly small; V1 = V2.
Ideal op amp.
![Page 14: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/14.jpg)
Basic Electric CircuitsIdeal Op Amp:
Find Vo in terms of Vin for the following configuration.
+
_
R2
R1
+
_
+
_
Vin Vo
Gain amplifier op amp set-up.
![Page 15: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/15.jpg)
Basic Electric CircuitsIdeal Op Amp:
+
_
R2
R1
+
_
+
_
Vin Vo
a
Vi
Writing a nodal equation at (a) gives;
21
)(RVV
RVV oiiin
(6)
![Page 16: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/16.jpg)
Basic Electric CircuitsIdeal Op Amp:
21
)(RVV
RVV oiiin
With Vi = 0 we have;
With R2 = 4 k and R1 = 1 k, we have
ino VV 4 Earlierwe got ino VV 99.3
(7)
inVRRV1
20
![Page 17: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/17.jpg)
Basic Electric CircuitsIdeal Op Amp:
Example : Consider the op amp configuration below. Find V0
+
+
+
_
__
3 VVin
6 k
1 k
V0
a
Assume Vin = 5 V
![Page 18: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/18.jpg)
Basic Electric CircuitsOperational Amplifiers
+
+
+
_
__
3 VVin
6 k
1 k
V0
a
At node “a” we can write;
kV
k)V( in
63
13 0
From which; V0 = -51 V (op amp will saturate)
solution
![Page 19: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/19.jpg)
Operational Amplifiers
Summing Amplifier
Example : Given the following, Find V0:Rfb
R1
R2
V2
V1V0
a
fbRV
RV
RV 0
2
2
1
1 (11)
![Page 20: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/20.jpg)
Example continued
Equation 11 can be expressed as;
2
21
10 V
RR
VRR
V fbfb (12)
If R1 = R2 = Rfb then,
210 VVV (13)
Therefore, we can add signals with an op amp.
![Page 21: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/21.jpg)
Basic Electric CircuitsOperational Amplifiers
Example : The non-inverting op amp. Consider the following:
R0
Rfb
V0V2_
+
+
_
a
![Page 22: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/22.jpg)
Basic Electric CircuitsOperational Amplifiers
Writing a node equation at “a” gives;
20
0
02
0
02
0
2
1
,
11
0)(
VRR
V
giveswhich
RRV
RV
so
RVV
RV
fb
fbfb
fb
![Page 23: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/23.jpg)
Basic Electric CircuitsOperational Amplifiers
Example: Non-inverting Input.Find V0 for the following op amp configuration.
+
_
+
+
_
_ 4 V
2 k
6 k
5 k
10 k
V0
a
Vx
33
![Page 24: –Amplification –Analog filtering –Buffering –Threshold](https://reader034.vdocuments.us/reader034/viewer/2022042623/626494a2b760c91d0a2ef44b/html5/thumbnails/24.jpg)
Basic Electric CircuitsOperational Amplifiers
The voltage at Vx is found to be 3 V.
Writing a node equation at “a” gives;
0105
0
k
)VV(k
V xx
orVVV x 930