# Chapter 13 : Feedback Amplifier¶

## Example 13.1, Page No 481¶

In [1]:
import math
#initialisation of variables
Rs=0          #in V
hfe=50.0      #in K
hie=1.1       #in K
hre=0         #in K
hoe=0         #in K

print('We first calculate the effective load Rl1 at the first calculator')
r1=10         #in K
r2=47         #in K
r3=33.0       #in K
r4=1+0.1      #in K

#Calculations
Rl1=(r1*r2*r3*r4)/((r1*r2*r3)+(r1*r2*r4)+(r1*r3*r4)+(r2*r3*r4))
print("Rl1= %.2f K " %Rl1)

print('Similarly for 2nd Transistor')
R1=0.1            #in K
R2=4.7            #in K
Rc1=R1+R2
Rc2=4.7          #in K

Rl2=(Rc1*Rc2)/(Rc1+Rc2)
print("Rl2= %.2f K" %Rl2)

Re=(R1*R2)/(R1+R2)

print('Voltage Gain of Transistor Q1')
Av1 = -(hfe*Rl1)/(hie+((1+hfe)*Re))
print("Av1= %.2f v " %Av1)

print('Voltage Gain of Transistor Q2')
Av2=-(hfe*Rl2)/hie
print("Av2= %.2f v " %Av2)
print('Voltage Gain of two transistors in cascade without feedback')
Av=Av1*Av2
print("Av= %.2f v " %Av)

B=R1/(R1+R2)#beta which is feedback
D=1+(B*Av)

Avf=Av/D
print("Avf= %.2f v " %Avf)

print('Input resistance without external feedback')
Ri=hie+(1+hfe)*Re
print("Ri= %.2f K " %Ri)

Rif=Ri*D

#Results
print("Rif= %.2f K " %Rif)
Ro=Rl2
Rof=Ro/D*1000
print("Rof= %.2f ohm" %Rof)

We first calculate the effective load Rl1 at the first calculator
Rl1= 0.94 K
Similarly for 2nd Transistor
Rl2= 2.37 K
Voltage Gain of Transistor Q1
Av1= -7.74 v
Voltage Gain of Transistor Q2
Av2= -107.94 v
Voltage Gain of two transistors in cascade without feedback
Av= 835.02 v
Avf= 45.39 v
Input resistance without external feedback
Ri= 6.09 K
Rif= 112.10 K
Rof= 129.09 ohm


## Example 13.2a, Page No 484¶

In [2]:
import math

#initialisation of variables
Gmf=-1           #Transconductance in mA/V
D=50.0           #Desensivity
Avf=-4           #Voltage Gain
Rs=1.0           #in K
hfe=150.0
Vt=0.026        #in V

#Calculations
Gm=Gmf*D
print("Gm= %.2f mA/V " %Gm)

#B=-Re, D = 1+B*Gm = 1-B*Gm
Re=(1.0-D)/Gm         #in K

#Results
print("Re= %.2f K " %Re)

Gm= -50.00 mA/V
Re= 0.98 K


## Example 13.2b Page No 484¶

In [3]:
import math

#initialisation of variables
Rc1=3#in K
Rc2=0.5#in K
Re=0.05#in K
Rs=1.2#in K
hfe=50.0
hie=1.1#in K
hre=0
hoe=0

R=Rs

#Calculations
#Ai=-Ic2/Is=-(Ic2/Ib2)*(Ib2/Ic1)*(Ic1/Ib1)*(Ib1/Is)
# -Ic2/Ib2 =- hfe = -50
# Ic1/Ib1 = hfe
#Let Ib2/Ic1 = k
Ri2= hie+((1+hfe)*(Re*R/(Re+R)))
k=-Rc1/(Rc1+Ri2)

r= Rs*(Rs+Re)/(Rs+R+Re)
#Let Ib1/Is = l
l=r/(r+hie)

Ai=(-hfe)*(k)*(hfe)*(l)

B=Re/(Re+R)#beta
D=1+(B*Ai)

Aif=Ai/D

Avf=(Aif*Rc2)/Rs

#To find Rif

Ri=(r*hie)/(r+hie)
Rif=Ri/D

#Results
print("The value of Rif= %.2f ohm " %(Rif*1000))

The value of Rif= 22.63 ohm


## Example 3.2c, Page No 484¶

In [4]:
import math
#initialisation of variables
Gmf=-1     #Transconductance in mA/V
D=50.0     #Desensivity
Avf=-4     #Voltage Gain
Rs=1.0     #in K
hfe=150.0
Vt=0.026    #in V
Gm=Gmf*D

#Calculations
#B=-Re, D = 1+B*Gm = 1-B*Gm
Re=(1-D)/Gm#in K
Rl=Avf/Gmf#in K
# Gm= -hfe/(Rs+hie+Re)
hie= -(hfe/Gm)-Rs-Re
Ri = Rs + hie +Re
Rif = Ri*D

#Results
print("The value of Rif= %.2f K " %Rif)

The value of Rif= 150.00 K


## Example 13.2d Page No 484¶

In [5]:
import math
#initialisation of variables
Gmf=-1       #Transconductance in mA/V
D=50.0       #Desensivity
Avf=-4       #Voltage Gain
Rs=1.0       #in K
hfe=150.0
Vt=0.026     #in V
Gm=Gmf*D

#Calculations
#B=-Re, D = 1+B*Gm = 1-B*Gm
Re=(1-D)/Gm#in K
Rl=Avf/Gmf#in K

# Gm= -hfe/(Rs+hie+Re)
hie= -(hfe/Gm)-Rs-Re
Ri = Rs + hie +Re
Rif = Ri*D
Ic=(hfe*Vt)/hie

#Results
print("Quiscent Collector Current =  %.2f mA " %Ic)

Quiscent Collector Current =  3.82 mA


## Example 13.3a Page No 489¶

In [6]:
import math

#initialisation of variables
Rc1=3#in K
Rc2=0.5#in K
Re=0.05#in K
Rs=1.2#in K
hfe=50.0
hie=1.1#in K
hre=0
hoe=0
R=Rs

#Calculations
#Ai=-Ic2/Is=-(Ic2/Ib2)*(Ib2/Ic1)*(Ic1/Ib1)*(Ib1/Is)
# -Ic2/Ib2 =- hfe = -50
# Ic1/Ib1 = hfe
#Let Ib2/Ic1 = k
Ri2= hie + ((1+hfe)*(Re*R/(Re+R)))
k=-Rc1/(Rc1+Ri2)
r= Rs*(Rs+Re)/(Rs+R+Re)
#Let Ib1/Is = l
l=r/(r+hie)
Ai=(-hfe)*(k)*(hfe)*(l)

print("The value of Ai = %.2f " %Ai)

B=Re/(Re+R)#beta
D=1+(B*Ai)

Aif=Ai/D
print("The value of Aif = %.2f v " %Aif)

Avf=(Aif*Rc2)/Rs

#Results
print("The value of Avf = %.2f v " %Avf)

The value of Ai = 409.55
The value of Aif = 23.56 v
The value of Avf = 9.82 v


## Example 13.3b, Page No 489¶

In [7]:
import math
#initialisation of variables
Rc1=3.0     #in K
Rc2=0.5     #in K
Re=0.05     #in K
Rs=1.2      #in K
hfe=50.0
hie=1.1    #in K
hre=0
hoe=0
R=Rs

#Calculations
#Ai=-Ic2/Is=-(Ic2/Ib2)*(Ib2/Ic1)*(Ic1/Ib1)*(Ib1/Is)
# -Ic2/Ib2 =- hfe = -50
# Ic1/Ib1 = hfe
#Let Ib2/Ic1 = k
Ri2= hie + ((1+hfe)*(Re*R/(Re+R)))
k=-Rc1/(Rc1+Ri2)
r= Rs*(Rs+Re)/(Rs+R+Re)
#Let Ib1/Is = l
l=r/(r+hie)
Ai=(-hfe)*(k)*(hfe)*(l)
B=Re/(Re+R)#beta
D=1+(B*Ai)
Aif=Ai/D
Avf=(Aif*Rc2)/Rs

#To find Rif
Ri=(r*hie)/(r+hie)
Rif=Ri/D

#Results
print("The value of Rif =  %.2f ohm " %(Rif*1000))

The value of Rif =  22.63 ohm


## Example 13.3c Page No 489¶

In [8]:
import math

#initialisation of variables
Rc1=3.0   #in K
Rc2=0.5   #in K
Re=0.05   #in K
Rs=1.2    #in K
hfe=50.0
hie=1.1   #in K
hre=0
hoe=0
R=Rs

#Calculations
#Ai=-Ic2/Is=-(Ic2/Ib2)*(Ib2/Ic1)*(Ic1/Ib1)*(Ib1/Is)
# -Ic2/Ib2 =- hfe = -50
# Ic1/Ib1 = hfe
#Let Ib2/Ic1 = k
Ri2= hie + ((1+hfe)*(Re*R/(Re+R)))
k=-Rc1/(Rc1+Ri2)

r= Rs*(Rs+Re)/(Rs+R+Re)
#Let Ib1/Is = l
l=r/(r+hie)

Ai=(-hfe)*(k)*(hfe)*(l)

B=Re/(Re+R)#beta
D=1+(B*Ai)

Aif=Ai/D

Avf=(Aif*Rc2)/Rs

Ri=(r*hie)/(r+hie)
Rif=Ri/D

rif=(Rif*Rs)/(Rs-Rif)

#Results
print("Resistance with feedback seen by voltage source is %.2f K " %(rif+Rs))

Resistance with feedback seen by voltage source is 1.22 K


## Example 13.3d Page No 489¶

In [9]:
import math
#initialisation of variables
Rc1=3.0        #in K
Rc2=0.5        #in K
Re=0.05        #in K
Rs=1.2         #in K
hfe=50.0
hie=1.1        #in K
hre=0
hoe=0
R=Rs

#Calculations
#Ai=-Ic2/Is=-(Ic2/Ib2)*(Ib2/Ic1)*(Ic1/Ib1)*(Ib1/Is)
# -Ic2/Ib2 =- hfe = -50
# Ic1/Ib1 = hfe
#Let Ib2/Ic1 = k
Ri2= hie + ((1+hfe)*(Re*R/(Re+R)))
k=-Rc1/(Rc1+Ri2)
r= Rs*(Rs+Re)/(Rs+R+Re)
#Let Ib1/Is = l
l=r/(r+hie)
Ai=(-hfe)*(k)*(hfe)*(l)
B=Re/(Re+R)#beta
D=1+(B*Ai)

Aif=Ai/D
Avf=(Aif*Rc2)/Rs
Rof=(Avf*Rs)/Aif

#Results
print("Output Resistance = %.2f K " %Rof)

Output Resistance = 0.50 K


## Example 13.4a Page No 494¶

In [10]:
import math

#initialisation of variables
Rc=4#in K
r=40#in K
Rs=10#in K
hie=1.1#in K
hfe=50
hre=0
hoe=0

#Calculations
#Required Formulae
rc=(Rc*r)/(Rc+r)
R=(Rs*r)/(Rs+r)
Rm=-(hfe*rc*R)/(R+hie)
print("The value of Rm = %.2f K " %Rm)
B=-1/r#in mA/V
D=1+(B*Rm)
Rmf=Rm/D
#Avf = Vo/Vs = Vo/(Is*Rs) = Rmf/Rs
Avf=Rmf/Rs

#Results
print("The value of Avf = %.2f v " %Avf)

The value of Rm = -131.87 K
The value of Avf = -0.10 v


## Example 13.4b , Page No 494¶

In [11]:
import math

#initialisation of variables

Rc=4.0     #in K
r=40.0     #in K
Rs=10.0    #in K
hie=1.1    #in K
hfe=50.0
hre=0
hoe=0

#Calculations
#Required Formulae
rc=(Rc*r)/(Rc+r)
R=(Rs*r)/(Rs+r)
Rm=-(hfe*rc*R)/(R+hie)
B=-1.0/r#in mA/V
D=1+(B*Rm)
Rmf=Rm/D
#Avf = Vo/Vs = Vo/(Is*Rs) = Rmf/Rs
Avf=Rmf/Rs
Ri = (R*hie)/(R+hie)
Rif=Ri/D

#Results
print("The value of Rif = %.2f v " %Rif)

The value of Rif = 0.19 v


## Example 13.4c, Page No 494¶

In [12]:
import math
#initialisation of variables
Rc=4.0    #in K
r=40.0    #in K
Rs=10.0   #in K
hie=1.1   #in K
hfe=50.0
hre=0
hoe=0

#Calculations
#Required Formulae
rc=(Rc*r)/(Rc+r)
R=(Rs*r)/(Rs+r)
Rm=-(hfe*rc*R)/(R+hie)

print("The value of Rm = %.2f v " %Rm)
B=-1/r#in mA/V
D=1+(B*Rm)
Rmf=Rm/D
#Avf = Vo/Vs = Vo/(Is*Rs) = Rmf/Rs
Avf=Rmf/Rs
Ri = (R*hie)/(R+hie)
Rif=Ri/D

#If the input resistance looking to the right of Rs is rif then Rif=(rif*Rs)/(rif+Rs)
rif=(Rif*Rs)/(Rs-Rif)

print("The impedence seen by the voltage source=Rif = %.2f K " %(Rs+rif))
Ro=40.0    #in K
r=40.0     #in K
Rm = -(hfe*r*R)/(R+hie)
Rof=Ro/(1+(B*Rm))
#We are writting Rof' = rof
rof=(Rof*Rc)/(Rof+Rc)

#Results
print("The value of rof =  %.2f K " %rof)

The value of Rm = -159.84 v
The impedence seen by the voltage source=Rif = 10.20 K
The value of rof =  0.73 K