# chapter 5: Feed Back¶

## example 5.1, Page No.192¶

In [5]:
#Percentage of output which is fed back
import math
#variable declaration
A=50.0                         #gain(unitless)
Af=10.0                        #gain(unitless)

#calculation

#Formula : Af=A/(1+A*Beta)
Beta=(A/Af-1)/A               #feedback ratio (unitless)

#Result
print("Percentage of output feed back : %.0f%%"%(Beta*100))

Percentage of output feed back : 8%


## example 5.2, Page No.192¶

In [6]:
#Voltage gain and reduction in voltage
import math
#variable declaration
A=1000.0                     #gainWithoutFeedback(unitless)
g_reduce=0.40                #factor by which gain reduced
#Calculations

#Part (i) :
Af=A-A*g_reduce              #gainWithFeedback(unitless)
#Formula : Af=A/(1+A*Beta)
Beta=(A/Af-1)/A           #feedback factor (unitless)

#Part (ii)
Reduction1=((Af-Af_dash)/Af)*100 #% reduction without feedback

#Result
print("At normal collector supply :")
print("with feedback gain reduces by a factor %.2f"%g_reduce)
print("At normal collector supply, Gain with feedback :%.0f "%Af)
print("\nAt reduced power supply :")
print("At Reduced collector supply, Gain with feedback : %.0f"%(math.ceil(Af_dash)))
print("%% reduction in gain without feedback :%.0f%%"%Reduction)
print("%% reduction in gain with feedback :%.0f%%"%Reduction1)
#Note : answer of Af is wrong in the book.

At normal collector supply :
with feedback gain reduces by a factor 0.40
At normal collector supply, Gain with feedback :600

At reduced power supply :
At Reduced collector supply, Gain with feedback : 522
% reduction in gain without feedback :20%
% reduction in gain with feedback :13%


## example 5.3, Page No.192¶

In [11]:
#Gain with feedback factor and feedback voltage
import math
#Variable declaration

A=100.0                           #gain without feedback(unitless)
Beta=1.0/25.0                     #feedback ratio (unitless)
Vi=50.0                           #in mV

#Calculations

#Part (i) :
Af=A/(1+A*Beta)                   #gain with feedback(unitless)

#Part (ii) :
FeedbackFactor=Beta*A            #unitless

#Part (iii) :
Vo_dash=Af*Vi*10**-3             #in volt

#Part (iv) :
FeedbackVoltage=Beta*Vo_dash     #in volt

#Part (v) :
Vi_dash=Vi*(1+Beta*A)            #in mv

#Result
print("(i)\n Gain with feedback :%.0f"%Af)
print("(ii)\n Feedback Factor :%.0f"%FeedbackFactor)
print("(iii)\n Output Voltage in volts :%.0f"%Vo_dash)
print("(iv)\n Feedback Voltage in volts :%.2f"%FeedbackVoltage)
print("(v)\n New Increased Input Voltage in milli volts :%.0f"%Vi_dash)

(i)
Gain with feedback :20
(ii)
Feedback Factor :4
(iii)
Output Voltage in volts :1
(iv)
Feedback Voltage in volts :0.04
(v)
New Increased Input Voltage in milli volts :250


## example 5.4, Page no.193¶

In [3]:
#Bandwidth with negative feedback
import math
#variable declaration
BW=200.0                              #in kHz
A=40.0                                #gain without feedback(in dB)
Beta=5.0                              #negative feedback in %
Beta=Beta/100.0                       #feedback factor

#calculation

#Formula : Af=A/(1+A*Beta)
Af=A/(1+A*Beta)                    #gain with feedback(in dB)
BW_dash=A*BW/Af                    #in kHz

#Result
print("Since gain bandwidth product remains constant, A*BW=Af*BW_dash")
print("New Bandwidth in kHz : %.0f"%BW_dash)

Since gain bandwidth product remains constant, A*BW=Af*BW_dash
New Bandwidth in kHz : 600


## example 5.5, Page No.193¶

In [5]:
#Fraction of output fed back
import math
#variable declaration
A=140.0                     #gain without feedback(unitless)
Af=17.5                     #gain with feedback(unitless)

#Calculations
#Formula : Af=A/(1+A*Beta)
Beta=(A/Af-1)/A             #feedback ratio (unitless)

#Result
print("Fraction of output fed back to input : %.2f or 1/20"%Beta)

Fraction of output fed back to input : 0.05 or 1/20


## example 5.6, Page No.205¶

In [16]:
#Small Change in gain
import math
#variable declaration
A=200.0                           #gain without feedback(unitless)
Beta=0.25                         #fraction ratio(unitless)

#CAlculations
#Given : Normal gain changes by 10 %, it means dA/A=10/100
dABYA=10.0/100.0                  #change in gain
dAfBYAf=(1/(1+Beta*A))*(dABYA)    #change in gain

#Result
print("We have, Af=A/(1+Beta*A).................eqn(1)")
print("\nDifferentiating it with respect to A, we get")
print("\ndAf/dA=((1+Beta*A)-Beta*A)/(1+Beta*A)^2=1/(1+Beta*A)^2")
print("\ndAf=dA/(1+Beta*A)^2.......................eqn(2)")
print("\nDividing eqn(2) by eqn(1),")
print("\ndAf/Af=(dA/((1+Beta*A)^2))*((1+Beta*A)/A)=(1/(1+Beta*A))*(dA/A)")
print("\n\nChange in gain : %.4f"%((math.floor(dAfBYAf*10**4))/10**4))

We have, Af=A/(1+Beta*A).................eqn(1)

Differentiating it with respect to A, we get

dAf/dA=((1+Beta*A)-Beta*A)/(1+Beta*A)^2=1/(1+Beta*A)^2

dAf=dA/(1+Beta*A)^2.......................eqn(2)

Dividing eqn(2) by eqn(1),

dAf/Af=(dA/((1+Beta*A)^2))*((1+Beta*A)/A)=(1/(1+Beta*A))*(dA/A)

Change in gain : 0.0019


## example 5.7, Page No.206¶

In [7]:
#New gain distortion and input voltage
import math
#Variable declaration
A=200.0                               #gain without feedback(unitless)
Dn=10.0                               #Distortion in %
Vi=0.5                                #Initial input voltage in volt
Beta=0.05                             #feedback ratio (unitless)

#Calculations
#Formula : Af=A/(1+A*Beta)
Af=A/(1+A*Beta)                       #gain with feedback(unitless)
Dn_dash=Dn/(1+A*Beta)                 #new distortion in %
InitialOutputVoltage=A*Vi             #in Volt
NewInputVoltage=InitialOutputVoltage/Af

print("New gain :%.3f"%Af)
print("Distortion with negative feedback : %.3f%%"%Dn_dash)
print("Initial Output Voltage in volt:%.0f"%InitialOutputVoltage)
print("New Input Voltage in volts :%.2f"%NewInputVoltage)
#Note :Ans of Af and  NewInputVoltage is not acurate in the book.

New gain :18.182
Distortion with negative feedback : 0.909%
Initial Output Voltage in volt:100
New Input Voltage in volts :5.50


## example 5.8, Page No. 206¶

In [24]:
#Feedback rction voltage and impedence
import math

#variable declaration
A=10000.0                             #gain without feedback(unitless)
Zi=10.0                               #in kOhm
Zo=100.0                              #in Ohm
R1=2.0                                #in Ohm
R2=18.0                               #in Ohm

#calculations

#Part (i) :
Beta=R1/(R1+R2)                     #feedback fraction(unitless)

#Part (ii) :
Af=A/(1+A*Beta)                     #Gain with negative feedback(unitless)

#Part (iii) :
inputVoltge=0.5                     #in mV
outputVoltge=Af*inputVoltge         #in mV

#Part (iv) :
Zif=Zi*(1+Beta*A)                   #in kOhm

#Part (v) :
Zof=Zo/(1+Beta*A)                   #in kOhm

print("(i)\nFeedback Fraction :%.1f"%Beta)
print("\n(ii)\nGain with negative feedback :%.0f"%(math.ceil(Af)))
print("\n(iii)\nOutput Voltage in milli volts :%.0f"%(math.ceil(outputVoltge)))
print("\n(iv)\nInput impedance of feedback amplifier in Mohm : %.2f"%(Zif*10**-3))
print("\n(v)\nOutput impedance with feedback in Ohm : %.1f"%Zof)

(i)
Feedback Fraction :0.1

(ii)
Gain with negative feedback :10

(iii)
Output Voltage in milli volts :5

(iv)
Input impedance of feedback amplifier in Mohm : 10.01

(v)
Output impedance with feedback in Ohm : 0.1


## example 5.9, Page No.207¶

In [26]:
#Voltage gain input and output resistance
import math
#variable declaration
A=200                                #gain without feedback(unitless)
Ri=2                                 #in kOhm
Ro=12                                #in kOhm
Beta=0.02                            #feedbak ratio(unitless)

#Calculation

#Part (i) :
Af=A/(1+A*Beta)                      #gain with feedback(unitless)

#Part (ii) :
Rif=Ri*(1+A*Beta)                    #in kOhm

#Part (ii) :
Rof=Ro/(1+A*Beta)                    #in kOhm

#Result
print("(i)\nGain with Negative Feedback :%.0f"%Af)
print("\n(ii)\nInput resistance with feedback in kOhm :%.0f"%Rif)
print("\n(iii)\nOutput resistance with feedback in kOhm :%.1f"%Rof)

(i)
Gain with Negative Feedback :40

(ii)
Input resistance with feedback in kOhm :10

(iii)
Output resistance with feedback in kOhm :2.4


## example 5.10, Page No.207¶

In [32]:
# Gain wih feedbck in dB
import math
#variable declaration
A=1000.0                       #gain(unitless)
Beta=1.0/20.0                  #feedback ratio (unitless)

#Calculation
#Formula : Af=A/(1+A*Beta)
Af=A/(1+A*Beta)                #gain with feedback(unitless)
Af=20*math.log10(Af)           #in dB

#Result
print("Gain with feedback in dB : %.1f"%Af)

Gain with feedback in dB : 25.8


## example 5.11, page No.208¶

In [34]:
#Bandwidth after feedback
import math
#Variable declarations

A=800.0                               #gain(unitless)
f1=40.0                               #in Hz
f2=16.0                               #in kHz
Beta=2.0/100.0                        #feedback fator (unitless)

#caalculations

#Formula : Af=A/(1+A*Beta)
Af=A/(1+A*Beta)                       #gain with feedback(unitless)
BW=f2*10**3-f1                        #Bandwidth of amplifier in Hz
f1_f=f1/(1+A*Beta)                    #in Hz
f2_f=f2*(1+A*Beta)                    #in kHz
BW_f=f2_f*10**3-f1_f                  #Bandwith after feedback in Hz

#result
print("Voltage gin with feedback : %.0f"%Af)
print("Bandwidth of amplifier in kHz : %.2f"%(BW*10**-3))
print("Bandwith after feedback in KHz : %.0f"%(BW_f*10**-3))

Voltage gin with feedback : 47
Bandwidth of amplifier in kHz : 15.96
Bandwith after feedback in KHz : 272


## example 5.12, Page No.208¶

In [8]:
#Gain and new bandwidth
import math
#Variable declaration
A=100.0                           #gain(unitless)
BW=10.0                           #in Hz
Beta=5.0                          #in %

#Calculations

#Part (i) :
#Formula : Af=A/(1+A*Beta)
Af=A/(1+A*Beta/100.0)            #gain with feedback(unitless)

#Part (ii)
BW_f=BW*(1+A*Beta/100.0)         #Bandwith after feedback in Hz

#Result
print("Voltage gain with feedback :%.2f "%Af)
print("Bandwith with negative feedback in KHz : %.0f"%BW_f)

Voltage gain with feedback :16.67
Bandwith with negative feedback in KHz : 60


## example 5.13, Page No.208¶

In [9]:
#Input resistance and voltage gain
import math
#variable decclaration
hfe=50.0                                #unitless
hie=1.1                                 #in kOhm
hoe=0.0                                 #unitless
hre=0.0                                 #unitless
RL=4.0                                  #in kOhm
Rs=10.0                                 #in kOhm
RB=40.0                                 #in kOhm

#calculation

RLdash=RB*RL/(RB+RL)                    #in Kohm
AV=-hfe*RLdash/hie                      #unitless

#Part (i) ;
Rif=hie*(RB/(1-AV))/(hie+(RB/(1-AV)))   #in kOhm
print("Input resistance with feedback in Ohm : %.0f"%(Rif*1000))
#Part (ii) :
AVf=AV*(Rif/(Rs+Rif))                   #unitless
print("Voltage gain with feedback : %.2f"%((math.ceil(AVf*100))/100))

Input resistance with feedback in Ohm : 197
Voltage gain with feedback : -3.19