# Chapter 18: Operational amplifiers

### Example 1, page no. 279

In :
from __future__ import division
import math
#initializing  the  variables:
Vi2  =  2.45;#  in  Volts
Vi1  =  2.35;#  in  Volts
A0  =  120;#  open-loop  voltage  gain

#calculation:
Vo  =  A0*(Vi2  -  Vi1)

#Results
print  "\n\n  Result  \n\n"
print  "\n  the  output  voltage  is  ",round(Vo,2),"  V"


Result

the  output  voltage  is   12.0   V

### Example 2, page no. 281

In :
from __future__ import division
import math
#initializing  the  variables:
Vg  =  150E3;#  differential  voltage  gain
CMRR  =  90;#  in  dB

#calculation:
CMG  =  Vg/(10**(CMRR/20))

#Results
print  "\n\n  Result  \n\n"
print  "\n  common-mode  gain  is  ",round(CMG,2)


Result

common-mode  gain  is   4.74

### Example 3, page no. 282

In :
from __future__ import division
import math
#initializing  the  variables:
Vg  =  120;#  differential  voltage  gain
Vi  =  3;#  in  Volts
Vo  =  0.024;#  in  Volts

#calculation:
CMG  =  Vo/Vi
CMRR  =  20*(1/2.303)*math.log(Vg/CMG)

#Results
print  "\n\n  Result  \n\n"
print  "\n  common-mode  gain  is  ",round(CMG,3),"  and  CMRR  is  ",round(CMRR,2),"  dB"


Result

common-mode  gain  is   0.008   and  CMRR  is   83.51   dB

### Example 4, page no. 283

In :
from __future__ import division
import math
#initializing  the  variables:
Rf  =  2000;#  in  ohms
Ri  =  1000;#  in  ohms
Vi1  =  0.4;#  in  Volts
Vi2  =  -1.2;#  in  Volts

#calculation:
Vo1  =  -1*Rf*Vi1/Ri
Vo2  =  -1*Rf*Vi2/Ri

#Results
print  "\n\n  Result  \n\n"
print  "\n  output  voltage  when  the  input  voltage  is  0.4V  is  ",round(Vo1,2),"  V "
print   " and  when  the  input  voltage  is  -1.2V  is  ",round(Vo2,2),"  V"


Result

output  voltage  when  the  input  voltage  is  0.4V  is   -0.8   V
and  when  the  input  voltage  is  -1.2V  is   2.4   V


### Example 5, page no. 283

In :
from __future__ import division
import math
#initializing  the  variables:
Ii  =  100E-9;#  in  Amperes
T  =  20;#  in  °C
Rf  =  1E6;#  in  ohms
Ri  =  10000;#  in  ohms

#calculation:
A  =  -1*Rf/Ri
Vos  =  Ii*Ri*Rf/(Ri+Rf)

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  voltage  gain  is  ",round(A,2),""
print  "\n  (b)output  offset  voltage  is  ",round(Vos*1000,2),"  mV"
print  "\n  (c)The  effect  of  input  bias  current  can  be  minimised  by  ensuring  "
print  "that  both  inputs have the  same  driving  resistance."
print  "This  means  that  a  resistance  of  value  of  9.9  kohm  (from  part  (b))  "
print   "should  be  placed  between  the  non-inverting  (+)  terminal  and  earth."


Result

(a)the  voltage  gain  is   -100.0

(b)output  offset  voltage  is   0.99   mV

(c)The  effect  of  input  bias  current  can  be  minimised  by  ensuring
that  both  inputs have the  same  driving  resistance.
This  means  that  a  resistance  of  value  of  9.9  kohm  (from  part  (b))
should  be  placed  between  the  non-inverting  (+)  terminal  and  earth.


### Example 6, page no. 284

In :
from __future__ import division
import math
#initializing  the  variables:
Vg  =  40;#  in  dB
bf  =  5000;#  in  Hz
Ri  =  10000;#  in  ohms

#calculation:
A  =  10**(Vg/20)
Rf  =  A*Ri
f  =  A*bf

#Results
print  "\n\n  Result  \n\n"
print  "\n  the  voltage  gain  is  ",round(A,2),",  Rf  =  ",round(Rf/1000,2),"kohm  and  frequency  =  ",round(f/1000,2),"  kHz"


Result

the  voltage  gain  is   100.0 ,  Rf  =   1000.0 kohm  and  frequency  =   500.0   kHz

### Example 7, page no. 286

In :
from __future__ import division
import math
#initializing  the  variables:
Vi  =  -0.4;#  in  Volts
R1  =  4700;#  in  ohms
R2  =  10000;#  in  ohms

#calculation:
A  =  1  +  (R2/R1)
Vo  =  A*Vi

#Results
print  "\n\n  Result  \n\n"
print  "\n(a)  the  voltage  gain  is  ",round(A,2),""
print  "\n(b)  output  voltageis  ",round(Vo,2),"  V"


Result

(a)  the  voltage  gain  is   3.13

(b)  output  voltageis   -1.25   V

### Example 8, page no. 287

In :
from __future__ import division
import math
#initializing  the  variables:
V1  =  0.5;#  in  Volts
V2  =  0.8;#  in  Volts
V3  =  1.2;#  in  Volts
R1  =  10000;#  in  ohms
R2  =  20000;#  in  ohms
R3  =  30000;#  in  ohms
Rf  =  50000;#  in  ohms

#calculation:
Vo  =  -1*Rf*(V1/R1  +  V2/R2  +  V3/R3)

#Results
print  "\n\n  Result  \n\n"
print  "\n  output  voltageis  ",round(Vo,2),"  V"


Result

output  voltageis   -6.5   V

### Example 10, page no. 289

In :
from __future__ import division
import math
from scipy import integrate
#initializing  the  variables:
Vs  =  -0.75;#  in  Volts
R  =  200000;#  in  ohms
C  =  2.5E-6;#  in  Farads
t  =  0.1;#  in  secs

#calculation:
f = lambda x,a : a*1
y, err = integrate.quad(f, 0, 0.1, args=(-0.75,))
Vo  =  (-1/(C*R))*y

#Results
print  "\n\n  Result  \n\n"
print  "\n  output  voltage  is  ",Vo,"  V"


Result

output  voltage  is   0.15   V

### Example 11, page no. 290

In :
from __future__ import division
import math
#initializing  the  variables:
V1a  =  0.005;#  in  Volts
V2a  =  0;#  in  Volts
V1b  =  0;#  in  Volts
V2b  =  0.005;#  in  Volts
V1c  =  0.05;#  in  Volts
V2c  =  0.025;#  in  Volts
V1d  =  0.025;#  in  Volts
V2d  =  0.05;#  in  Volts
R1  =  10000;#  in  ohms
R2  =  10000;#  in  ohms
R3  =  100000;#  in  ohms
Rf  =  100000;#  in  ohms

#calculation:
Vo1  =  -1*Rf*V1a/R1
Vo2  =  (R3/(R2+R3))*(1  +  (Rf/R1))*V2b
Vo3  =  -1*Rf*(V1c-V2c)/R1
Vo4  =  (R3/(R2+R3))*(1  +  (Rf/R1))*(V2d-V1d)

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)output  voltage  is  ",round(Vo1,2),"  V"
print  "\n  (b)output  voltage  is  ",round(Vo2,2),"  V"
print  "\n  (c)output  voltage  is  ",round(Vo3,2),"  V"
print  "\n  (d)output  voltage  is  ",round(Vo4,2),"  V"


Result

(a)output  voltage  is   -0.05   V

(b)output  voltage  is   0.05   V

(c)output  voltage  is   -0.25   V

(d)output  voltage  is   0.25   V