# Chapter-10 Operational Amplifiers¶

## Example-10.1 Page number-598¶

In [3]:
#from the given circuit:
Vee=9                    #supply in volts
Re=3.3                   #emitter resistance in Kohm
Rc=3.9                   #collector resistance in Kohm
Vcc=9                    #supply voltage in volts

#Calculation:

Ie=(Vee-0.7)/Re           #emitter current in mA
Ic=Ie/2                   #collector current in mA
Vc=Vcc-(Ic*Rc)            #Dc voltage in volts

print "The DC voltage =",round(Vc,1),"V"
print "Collector current=",round(Ic,2),"mA"
print "Emitter current=",round(Ie,1),"mA"
The DC voltage = 4.1 V
Collector current= 1.26 mA
Emitter current= 2.5 mA

## Example-10.2 Page number-601¶

In [12]:
#from the given circuit:
Vee=9                    #supply in volts
Re=43.0                  #emitter resistance in Kohm
Rc=47.0                  #collector resistance in Kohm
Vcc=9                    #supply voltage in volts
Vi=2                     #input voltage in mV

#Calculation:

Ie=((Vee-0.7)/Re)*1000          #emitter current in microA
Ic=Ie/2                         #collector current in microA
Vc=Vcc-((Ic*Rc)/1000)           #Dc voltage in volts
re=(26/Ic)/1000                  #in ohms
A=Rc/(2*re)                     #Ac voltage gain
Vo=(A/1000)*Vi                  #Output ac voltage in volts

print "The Output AC voltage =",round(Vo,1),"mV"
The Output AC voltage = 174.5 mV

## Example-10.3 Page number-603¶

In [2]:
#for the given circuit:
B=75
Rc=47.0                  #collector resistance in Kohm
ri=20                    #in Kohm
Re=43.0                  #emitter resistance in Kohm

#Common mode gain of the given amplifier (A):
A=(B*Rc)/(ri+2*(B+1)*Re)

print "Common mode gain of the given amplifier (A):",round(A,2)
Common mode gain of the given amplifier (A): 0.54

## Example-10.4 Page number-604¶

In [4]:
#for the given circuit:
B=75
Rc=10.0                  #collector resistance in Kohm
ri=11                    #in Kohm
Re=200.0                 #emitter resistance in Kohm

#Common mode gain of the given amplifier (A):
A=(B*Rc)/(ri+2*(B+1)*Re)

print "Common mode gain of the given amplifier (A):",round(A,4)
Common mode gain of the given amplifier (A): 0.0247

## Example-10.5 Page number-610¶

In [7]:
#for the given Inverting circuit:
Vi=2                      #input voltage in volts
Rf=500.0                  #feedback resistance in Kohm
R1=100.0                  #input resistance in Kohm

#Output voltage Vo:
Vo=-(Rf*Vi)/(R1)

print "Output voltage of the inverting amplifier:",round(Vo,2),"V"
Output voltage of the inverting amplifier: -10.0 V

## Example-10.6 Page number-611¶

In [8]:
#for the given non-Inverting circuit:
Vi=2                      #input voltage in volts
Rf=500.0                  #feedback resistance in Kohm
R1=100.0                  #input resistance in Kohm

#Output voltage Vo:
Vo=(1+(Rf/R1))*Vi

print "Output voltage of the non-inverting amplifier:",round(Vo,2),"V"
Output voltage of the non-inverting amplifier: 12.0 V

## Example-10.7(a) Page number-612¶

In [10]:
#for the given summing amplifier circuit:
V1=1                      #input voltage in volts
V2=2                      #input voltage in volts
V3=3                      #input voltage in volts
R1=500.0                  #input resistance in Kohm
R2=1000.0                 #input resistance in Kohm
R3=1000.0                 #input resistance in Kohm
Rf=1000.0                 #feedback resistance in Kohm

#calculation:

X1=(Rf/R1)*V1             #temporary value
X2=(Rf/R2)*V2             #temporary value
X3=(Rf/R3)*V3             #temporary value

#Output voltage Vo:
Vo=-(X1+X2+X3)

print "Output voltage of the Summing amplifier:",round(Vo,2),"V"
Output voltage of the Summing amplifier: -7.0 V

## Example-10.7(b) Page number-612¶

In [11]:
#for the given summing amplifier:
V1=-2                     #input voltage in volts
V2=3                      #input voltage in volts
V3=1                      #input voltage in volts
R1=200.0                  #input resistance in Kohm
R2=500.0                  #input resistance in Kohm
R3=1000.0                 #input resistance in Kohm
Rf=1000.0                 #feedback resistance in Kohm

#calculation:

X1=(Rf/R1)*V1             #temporary value
X2=(Rf/R2)*V2             #temporary value
X3=(Rf/R3)*V3             #temporary value

#Output voltage Vo:
Vo=-(X1+X2+X3)

print "Output voltage of the Summing amplifier:",round(Vo,2),"V"
Output voltage of the Summing amplifier: 3.0 V

## Example-10.8 Page number-616¶

In [14]:
#for the given amplifier circuit:
Vi=1.2*(10**-3)           #input voltage in volts
Rf=150.0                  #feedback resistance in Kohm
R1=2.0                    #input resistance in Kohm

#Output offset voltage Vo:
Vo=((R1+Rf)/R1)*Vi         #in volts
Vo=Vo*1000                 #output voltage in mVolts

print "Output offset voltage of the amplifier:",round(Vo,2),"mV"
Output offset voltage of the amplifier: 91.2 mV

## Example-10.9 Page number-617¶

In [18]:
#for the given amplifier circuit:
Ii=100                   #input current in nA
Rf=150.0                  #feedback resistance in Kohm

#Output offset voltage Vo:
Vo=Ii*(10**-3)*Rf                   #in mVolts

print "Output offset voltage of the amplifier:",round(Vo,2),"mV"
Output offset voltage of the amplifier: 15.0 mV

## Example-10.10 Page number-617¶

In [22]:
#for the given amplifier circuit:
Vi=4.0*(10**-3)           #input voltage in volts
Rf=500.0                  #feedback resistance in Kohm
R1=5.0                    #input resistance in Kohm
Ii=150                    #input current in nA

#Output offset voltage Vo1(due to Vi):
Vo1=((R1+Rf)/R1)*Vi         #in volts
Vo1=Vo1*1000                 #output voltage in mVolts

#Output offset voltage Vo2(due to Ii):
Vo2=Ii*(10**-3)*Rf          #in mVolts

Total=Vo1+Vo2               #in mvolts

print "Output offset voltage due to Vi:",round(Vo1,2),"mV"
print "Output offset voltage due to Ii:",round(Vo2,2),"mV"
print "Total offset voltage of the amplifier:",round(Total,2),"mV"
Output offset voltage due to Vi: 404.0 mV
Output offset voltage due to Ii: 75.0 mV
Total offset voltage of the amplifier: 479.0 mV

## Example-10.11 Page number-618¶

In [23]:
#for the given amplifier:
Ii=5.0                    #input current in nA
Ib=30                     #average input bias current in nA

#calculation:
Ib1=Ib+(Ii/2)             #input bias current at first input in nA
Ib2=Ib-(Ii/2)             #input bias current at second input in nA

print "input bias current at first input:",Ib1,"nA"
print "input bias current at second input:",Ib2,"nA"
input bias current at first input: 32.5 nA
input bias current at second input: 27.5 nA

## Example-10.12 Page number-619¶

In [29]:
#for the given amplifier:
f1=1*(10**6)             #frequency in Hz
Avd=200                  #Gain of the amplifier in V/mV

#cut-off frequency(fc):
fc=f1/(Avd*(10**3))               #cut-off frequency in Hz

print "The cut-off frequency Fc:",fc,"Hz"
The cut-off frequency Fc: 5 Hz

## Example-10.13 Page number-620¶

In [30]:
#from the given question:
Sr=2                       #slew rate in V/microS
Vic=0.5                    #change in input signal(during time t)in volts
t=10                       #time of change of input signal in microS

#calculation:
X=Vic/t                      #rate of change in input signal in V/microS
Acl=Sr/X                     #maximum closed-loop gain

print "Maximum closed loop gain:",Acl
Maximum closed loop gain: 40.0

## Example-10.14 Page number-620¶

In [38]:
#for the given amplifier circuit:
Sr=0.5                    #slew rate in V/microS
Vi=0.02                   #input voltage in volts
Rf=240.0                  #feedback resistance in Kohm
R1=10.0                   #input resistance in Kohm
K=0.48

#calculation:
Acl=Rf/R1                 #closed loop gain
K=Acl*Vi                  #output voltage in volts
x=(Sr/K)*(10**6)          #maximum frequency value in rad/s

if(w<=x):
print "No output distortion"
else:
print "Distortion in output"
No output distortion

## Example-10.15 Page number-621¶

In [43]:
#from the data given in the question:
V=12.0                           #dual power supply in volts
P=500                            #power dissipated in mW

#Curent drawn I:
I=(P/2)/V

print "Current drawn from the power supply:",round(I,2),"mA"
Current drawn from the power supply: 20.83 mA

## Example-10.16 Page number-624¶

In [45]:
#from the given circuit:
Vio=1                     #input voltage in mV
Rf=360.0                  #feedback resistance in Kohm
R1=12.0                   #input resistance in Kohm
Ii=20                     #input current in nA

#Output offset voltage Vo1(due to Vio):
Vo1=((R1+Rf)/R1)*Vio         #in mV

#Output offset voltage Vo2(due to Ii):
Vo2=Ii*(10**-3)*Rf          #in mVolts

Total=Vo1+Vo2               #in mvolts

print "Output offset voltage due to Vi:",round(Vo1,2),"mV"
print "Output offset voltage due to Ii:",round(Vo2,2),"mV"
print "Total offset voltage of the amplifier:",round(Total,2),"mV"
Output offset voltage due to Vi: 31.0 mV
Output offset voltage due to Ii: 7.2 mV
Total offset voltage of the amplifier: 38.2 mV

## Example-10.17 Page number-624¶

In [52]:
#for the 741 Op-amp:
r0=75.0                   #resistance in ohm
A=200*(10**3)             #gain
Rf=360                    #feedback resistor in Kohm
R1=12                     #input resistor in Kohm
B=1.0/30
#calculation:
Acl=-Rf/R1               #(a)Closed loop gain
Zi=R1                    #(b)input impedance in Kohm
Zo=r0/(1+B*A)            #(c)output impedance in ohm

print "Closed loop gain Acl:",Acl
print "Input Impedance Zi:",Zi,"Kohm"
print "Output Impedance Zo=",round(Zo,3),"ohm"
Closed loop gain Acl: -30
Input Impedance Zi: 12 Kohm
Output Impedance Zo= 0.011 ohm

## Example-10.18 Page number-625¶

In [56]:
#from th given characterstics:
f1=1*(10**6)                 #frequency in Hz
Avd=20000                    #large signal amplification

fc=f1/Avd                     #cut-off frequency
print "Cut-off frequency fc:",fc,"Hz"
Cut-off frequency fc: 50 Hz

## Example-10.19 Page number-625¶

In [62]:
#from th given data:
Vi=25*(10**-3)               #input voltage in V
Acl=30                       #closed-loop gain
Sr=0.5                        #slew rate in V/microS

#Calculation:
K=Acl*Vi                      #output gain factor
fm=Sr/(2*3.14*K)               #maximum frequency in kHz

print "maximum frequencyof the input signal:",round(fm*1000,1),"kHz"
maximum frequencyof the input signal: 106.2 kHz

## Example-10.20 Page number-626¶

In [76]:
import math
#from the given figure:
Vcc=12.0                    #supply voltage in volts
Avd=104.0                    #open loop Gain in dB

Avdc=10**(Avd/20)             #open loop voltage gain
print "Open loop voltage gain:",round(Avdc,1)
Open loop voltage gain: 158489.3

## Example-10.21 Page number-628¶

In [82]:
import math
#from the given circuit:
#Differntial mode:
Vo=8.0                       #output voltage in volts
Vd=1*(10**-3)                #input voltage in volts

#Common Mode operation:
Voc=12.0                      #output voltage in mV
Vc=1                          #input voltage in mV

CMRR=20*math.log10(CMRR)      #CMRR in dB

print "Value of CMRR in dB:",round(CMRR,2),"dB"
Value of CMRR in dB: 56.48 dB

## Example-10.22(a) Page number-629¶

In [90]:
#from the given question:
Vi1=150.0                      #first input voltage in microV
Vi2=140.0                      #second input voltage in microV
CMRR=100.0

#Calculation:
Vd=Vi1-Vi2                  #differential voltage in microV
Vc=0.5*(Vi1+Vi2)            #common mode voltage

print "Output voltage of the Op-amp:",round(Vo/1000,2),"mV"
Output voltage of the Op-amp: 45.8 mV

## Example-10.22(b) Page number-629¶

In [92]:
#from the given question:
Vi1=150.0                      #first input voltage in microV
Vi2=140.0                      #second input voltage in microV