Chapter 3: An Op-Amp with Negative Feedback

Example 3.1

In [1]:
#Example 3.1
#Compute the following parameters of voltage-series feedback amplifier
#Af,Ri,Ro,fF,VooT

from __future__ import division #to perform decimal division

#Variable declaration
R1=1000     #Resistance in ohms
Rf=10000    #Feedback Resistance in Ohms 
A=200000    #Open-loop voltage gain
Ri=2*10**6  #Input resistance without feedback
Ro=75       #Output resistance without feedback
fo=5        #Break frequency of an Op-amp
Vsat=13     #Saturation voltage

#calculation
B=R1/(R1+Rf)       #Gain of the feedback circuit
Af=A/(1+A*B)       #Closed-loop voltage gain
RiF=Ri*(1+A*B)     #Input resistance with feedback
RoF=Ro/(1+A*B)     #Output resistance with feedback
fF=fo*(1+A*B)      #Bandwidth with feedback
VooT=Vsat/(1+A*B)  #Total output offset voltage with feedback

#Result
print "Closed-loop voltage gain is",round(Af,2)
print "Input resistance with feedback is",round(RiF/10**9,2),"Giga Ohm"
print "Output resistance with feedback is",round(RoF*10**3,2),"mOhm"
print "Bandwidth with feedback is",round(fF/10**3,2),"KHz"
print "Total output offset voltage with feedback is ",round(VooT*10**3,3),"mV"

Closed-loop voltage gain is 11.0
Input resistance with feedback is 36.37 Giga Ohm
Output resistance with feedback is 4.12 mOhm
Bandwidth with feedback is 90.91 KHz
Total output offset voltage with feedback is  0.715 mV

Example 3.2

In [2]:
#Example 3.2
#Compute the following parameters of voltage follower circuit of figure 3-7
#Af,Ri,Ro,fF,VooT

from __future__ import division #to perform decimal division

#Variable declaration
R1=1000     #Resistance in ohms
Rf=10000    #Feedback Resistance in Ohms 
A=200000    #Open-loop voltage gain
Ri=2*10**6  #Input resistance without feedback
Ro=75       #Output resistance without feedback
fo=5        #Break frequency of an Op-amp
Vsat=13     #Saturation voltage
B=1         #Gain of the feedback circuit of voltage follower

#calculation

Af=A/(1+A*B)       #Closed-loop voltage gain
RiF=Ri*(1+A*B)     #Input resistance with feedback
RoF=Ro/(1+A*B)     #Output resistance with feedback
fF=fo*(1+A*B)      #Bandwidth with feedback
VooT=Vsat/(1+A*B)  #Total output offset voltage with feedback

#Result
print "Closed-loop voltage gain is",round(Af)
print "Input resistance with feedback is",round(RiF/10**9),"Giga Ohm"
print "Output resistance with feedback is",round(RoF*10**3,3),"mOhm"
print "Bandwidth with feedback is",round(fF/10**6,2),"MHz"
print "Total output offset voltage with feedback is ",round(VooT*10**6,3),"uV"

Closed-loop voltage gain is 1.0
Input resistance with feedback is 400.0 Giga Ohm
Output resistance with feedback is 0.375 mOhm
Bandwidth with feedback is 1.0 MHz
Total output offset voltage with feedback is  65.0 uV

Example 3.3

In [14]:
#Example 3.3
#Compute the following parameters of inverting amplifierof figure 3-8
#Af,Ri,Ro,fF,VooT

from __future__ import division #to perform decimal division

#Variable declaration
R1=470       #Resistance in ohms
Rf=4.7*10**3 #Feedback Resistance in Ohms 
A=200000     #Open-loop voltage gain
Ri=2*10**6   #Input resistance without feedback
Ro=75        #Output resistance without feedback
fo=5         #Break frequency of an Op-amp
Vsat=13      #Saturation voltage


#calculation

K=Rf/(R1+Rf)         #Voltage attenuation factor
B=R1/(R1+Rf)         #Gain of the feedback circuit
Af=-A*K/(1+A*B)      #Closed-loop voltage gain
X=Rf/(1+A)
RiF=R1+(X*Ri)/(X+Ri) #Input resistance with feedback
RoF=Ro/(1+A*B)       #Output resistance with feedback
fF=fo*(1+A*B)/K      #Bandwidth with feedback
VooT=Vsat/(1+A*B)    #Total output offset voltage with feedback

#Result
print "Closed-loop voltage gain is",round(Af)
print "Input resistance with feedback is",round(RiF),"Ohm"
print "Output resistance with feedback is",round(RoF*10**3,2),"mOhm"
print "Bandwidth with feedback is",round(fF/10**3),"kHz"
print "Total output offset voltage with feedback is ",round(VooT*10**3,3),"mV"

Closed-loop voltage gain is -10.0
Input resistance with feedback is 470.0 Ohm
Output resistance with feedback is 4.12 mOhm
Bandwidth with feedback is 100.0 kHz
Total output offset voltage with feedback is  0.715 mV

Example 3.4

In [3]:
%matplotlib inline

from __future__ import division #to perform decimal division
from matplotlib.pyplot import ylabel, xlabel, title, plot, show
import matplotlib.pyplot as plt
import math
import numpy as np
#Variable declaration
R1=470       #Resistance in ohms
Rf=4.7*10**3 #Feedback Resistance in Ohms 
A=200000     #Open-loop voltage gain
vin=1        #input voltage in Volts



#calculation
K=Rf/(R1+Rf)         #Voltage attenuation factor
B=R1/(R1+Rf)         #Gain of the feedback circuit
Af=-A*K/(1+A*B)      #Closed-loop voltage gain
vo=Af*vin            #output voltage

x=np.arange(0,4*math.pi,0.1)
y=-5*np.sin(x)
plt.plot(x,y)
plt.ylabel('vo')
plt.xlabel('t')
plt.title(r'$output voltage$')
plt.show()
#Result
print "Output voltage is",round(vo),"V peak to peak"

Output voltage is -10.0 V peak to peak

Example 3.5_a & 3.5_b

In [4]:
#Example 3.5_a & 3.5_b
#For the circuit of figure 3_14,R1=R2=1 kilo ohm and the opamp is 741 IC.
#a) What are the gain and input resistance of the amplifier?
#b) Calculate output voltage vo if vx=2.7 V pp and vy=3 V pp sine waves at 100 Hz



from __future__ import division #to perform decimal division

#Variable declaration
R1=1000       #Resistance in ohms
R2=1000       #Resistance in ohms
Rf=10*10**3   #Feedback Resistance in Ohms
R3=10*10**3
vx=2.7        #input voltage in Volts
vy=3          #input voltage in Volts


#calculation
#part a
AD=-Rf/R1     #voltage gain
RiFx=R1       #Input resistance of inverting amplifier
RiFy=R2+R3    #Input resistance of noninverting amplifier
#part b
vxy=vx-vy
vo=AD*vxy     #output volatage

#Result
print "Voltage gain is",AD
print "Input resistance of inverting amplifier is",RiFx/10**3,"kilo ohms"
print "Input resistance of noninverting amplifier is",round(RiFy/10**3),"kilo ohms"
print "Output voktage is",vo,"V peak to peak at 100 Hz"

Voltage gain is -10.0
Input resistance of inverting amplifier is 1.0 kilo ohms
Input resistance of noninverting amplifier is 11.0 kilo ohms
Output voktage is 3.0 V peak to peak at 100 Hz

Example 3.6_a & 3.6_b

In [5]:
#Example 3.6_a & 3.6_b
#For the differential amplifier of figure 3_16, R1=R3=680 ohm, Rf=R2=6.8 Kilo ohm
#vx=-1.5 V pp, vy=-2 V pp sine waves at 1 KHz and the opamp is 741 IC.
#a) What are the gain and input resistance of the amplifier?
#b) Calculate output voltage of the amplifier.(Assume vooT=0V)



from __future__ import division #to perform decimal division

#Variable declaration
R1=680       #Resistance in ohms
R2=6800      #Resistance in ohms
Rf=6800      #Feedback Resistance in Ohms
R3=680
Ri=2*10**6   #Open loop input resistance of the opamp
vx=-1.5      #input voltage in Volts
vy=-2        #input voltage in Volts
A=200000     #openloop gain


#calculation
#part a
AD=1+Rf/R1           #voltage gain
B=R2/(R2+R3)
RiFy=Ri*(1+A*B)      #Input resistance of first stage amplifier
B=R1/(R1+Rf)
RiFx=Ri*(1+A*B)          #Input resistance of second stage amplifier
#part b
vxy=vx-vy
vo=AD*vxy     #output volatage

#Result
print "Voltage gain is",AD
print "Input resistance of first stage amplifier is",round(RiFy/10**9),"Giga ohms"
print "Input resistance of second stage amplifier is",round(RiFx/10**9,1),"Giga ohms"
print "Output voLtage is",vo,"V peak to peak at 1 KHz"

Voltage gain is 11.0
Input resistance of first stage amplifier is 364.0 Giga ohms
Input resistance of second stage amplifier is 36.4 Giga ohms
Output voLtage is 5.5 V peak to peak at 1 KHz