Chapter 29 , Feedback Amplifiers¶

Example 29.1 , Page Number 730¶

In :
import math

#Variables

Av = 400.0                     #Voltage gain
beta = 0.1                     #feedback ratio

#Calculation

A1v = Av / (1 + beta * Av)     #Voltage gain with negative feedback

#Result

print "The voltage gain of an amplifier with negative feedback is ",round(A1v,2),"."
The voltage gain of an amplifier with negative feedback is  9.76 .

Example 29.2 , Page Number 730¶

In :
import math

#Variables

Av = 100.0                     #Voltage gain
A1v = 20.0                     #Voltage gain with negative feedback

#Calculation

beta = (Av/A1v - 1) / Av       #feedback ratio

#Result

print "The percentage of the negative feedback is ",beta * 100,"%."
The percentage of the negative feedback is  4.0 %.

Example 29.3 , Page Number 730¶

In :
import math

#Variables

Av = 1000.0                     #Voltage gain
A1v = 10.0                      #Voltage gain with negative feedback

#Calculation

beta = (Av/A1v - 1) / Av        #feedback ratio

#Result

print "The fraction of the output that is feedback to the input is ",beta,"."
The fraction of the output that is feedback to the input is  0.099 .

Example 29.4 , Page Number 730¶

In :
import math

#Variables

V1o = Vo = 12.5                 #Output voltage (in volts)
V1in = 1.5                      #Input voltage with feedback (in volts)
Vin = 0.25                      #Input voltage without feedback (in volts)

#Calculation

Av = Vo / Vin                   #Voltage gain without negative feedback
A1v = V1o / V1in                #Voltage gain with negative feedback
beta = (Av/A1v - 1) / Av        #feedback ratio

#Result

print "The value of voltage gain without negative feedback is ",Av,".\nThe value of voltage gain with negative feedback is ",round(A1v,2),".\nThe value of beta is ",beta,"."
The value of voltage gain without negative feedback is  50.0 .
The value of voltage gain with negative feedback is  8.33 .
The value of beta is  0.1 .

Example 29.5 , Page Number 731¶

In :
import math

#Variables

Av = 60.0                       #Voltage gain
A1v = 80.0                      #Voltage gain with negative feedback

#Calculation

beta = (1 - Av/A1v ) / Av       #feedback ratio
beta1 = 1/Av                    #feedback ratio which causes oscillation

#Result

print "Value of feedback ratio is ",round(beta,3),".\nThe percentage of feedback which causes oscillation is ",round(beta1 * 100,1),"%."
Value of feedback ratio is  0.004 .
The percentage of feedback which causes oscillation is  1.7 %.

Example 29.6 , Page Number 732¶

In :
import math

#Variables

A1v = 100.0                      #Voltage gain with negative feedback
Vin = 50.0 * 10**-3              #Input voltage without feedback (in volts)
V1in = 0.6                       #Input voltage with feedback (in volts)

#Calculation

V1o = A1v * V1in                 #Output voltage with feedback (in volts)
Vo = V1o                         #Output voltage without feedback (in volts)
Av = Vo / Vin                    #Voltage gain without feedback
beta = (Av/A1v - 1) / Av         #feedback ratio

#Result

print "The value of voltage gain without feedback is ",Av,".\nThe value of voltage gain with feedback is ",A1v,"."
The value of voltage gain without feedback is  1200.0 .
The value of voltage gain with feedback is  100.0 .

Example 29.7 , Page Number 733¶

In :
import math

#Variables

Av = 800.0                                 #Voltage gain
beta = 0.05                                #Feedback ratio
dAvbyAv = 20.0                             #Percentage change in open loop gain

#Calculation

dA1vbyA1v = 1 / (1 + beta*Av)*dAvbyAv      #Percentage change in closed loop gain

#Result

print "The percentage change in closed loop gain is ",round(dA1vbyA1v,1),"%."
The percentage change in closed loop gain is  0.5 %.

Example 29.8 , Page Number 733¶

In :
import math

#Variables

A1v = 100.0                            #Voltage gain with feedback
dA1vbyA1v = 0.01                       #Percentage change in closed loop gain
dAvbyAv = 0.20                         #Percentage change in open loop gain

#Calculation

betamultAvplus1 = dAvbyAv/dA1vbyA1v    #Product of feedback ratio and voltage ratio plus one
Av = A1v * betamultAvplus1             #Voltage gain without feedback
beta = betamultAvplus1 / Av            #Feedback ratio

#Result

print "The value of Av is ",Av,".\nThe value of beta is ",beta,"."
The value of Av is  2000.0 .
The value of beta is  0.01 .

Example 29.9 , Page Number 735¶

In :
import math

#Variables

Av = 100.0                    #Voltage gain without feedback
BW = 200.0 * 10**3            #Bandwidth without feedback (in Hertz)
beta = 0.05                   #Feedback ratio
BWn = 1.0 * 10**6             #New bandwidth without feedback (in Hertz)

#Calculation

BW1 = (1 + beta*Av) * BW      #Bandwidth with feedback (in Hertz)
A1v = Av/(1 + beta*Av)        #Voltage gain with feedback
beta1 = (BWn/BW - 1)/Av       #Amount of feedback required

#Result

print "The new bandwidth is ",BW1 * 10**-3," kHz.\nThe new gain is ",round(A1v,1),"."
print "Amout of feedback required when BW = 1MHz is ",beta1 * 100,"%."
The new bandwidth is  1200.0  kHz.
The new gain is  16.7 .
Amout of feedback required when BW = 1MHz is  4.0 %.

Example 29.10 , Page Number 735¶

In :
import math

#Variables

Av = 1500.0                      #Voltage gain
BW = 4.0 * 10**6                 #Bandwidth wihtout feedback (in Hertz)
A1v = 150.0                      #Voltage gain with feedback

#Calculation

beta = (Av/A1v -1) / Av          #Feedback ratio
BW1 = (1 + beta*Av) * BW         #Bandwidth with feedback (in Hertz)

#Result

print "The value of feedback factor is ",beta * 100,"%.\nThe value of bandwidth with feedback is ",BW1 * 10**-6," MHz."
The value of feedback factor is  0.6 %.
The value of bandwidth with feedback is  40.0  MHz.

Example 29.11 , Page Number 736¶

In :
import math

#Variables

Rin = 4.2 * 10**3                    #Input resistance (in ohm)
Av = 220.0                           #Voltage gain without feedback
beta = 0.01                          #Feedback ratio
f1 = 1.5 * 10**3                     #Cut off frequency without feedback (in Hertz)
f2 = 501.5 * 10**3                   #Cut off frequency with feedback (in Hertz)

#Calculation

R1i = (1 + beta * Av) * Rin          #Input resistance of feedback amplifier (in ohm)
f11 = f1 / (1 + beta * Av)           #New cut off frequency without feedback (in Hertz)
f21 = (1 + beta * Av) * f2           #New cut off frequency with feedback (in Hertz)

#Result

print "The value of input resistance with feedback is ",R1i * 10**-3," kilo-ohm.\nNew cut off frequency without feedback is ",round(f11)," Hz.\nNew cut off frequency with feedback is ",f21 * 10**-3,"  kHz."
The value of input resistance with feedback is  13.44  kilo-ohm.
New cut off frequency without feedback is  469.0  Hz.
New cut off frequency with feedback is  1604.8   kHz.

Example 29.12 , Page Number 737¶

In :
import math

#Variables

Av = 1000.0                           #Voltage gain without feedback
beta = 0.01                           #Feedback ratio
f1 = 50.0                             #Cut off frequency without feedback (in Hertz)
f2 = 200.0 * 10**3                    #Cut off frequency with feedback (in Hertz)
D = 0.05                              #Distortion

#Calculation

A1v = Av / (1 + beta * Av)            #Voltage gain with feedback
f11 = f1 / (1 + beta * Av)            #New cut off frequency without feedback (in Hertz)
f21 = (1 + beta * Av) * f2            #New cut off frequency with feedback (in Hertz)
D1 = D/(1 + beta * Av)                #New Distortion

#Result

print "Voltage gain with feedback is ",round(A1v,1),".\nf11 is ",round(f11,1)," Hz.\nf21 is ",f21 * 10**-6," MHz.\nDistortion with feedback is ",round(D1 * 100,2),"%."
Voltage gain with feedback is  90.9 .
f11 is  4.5  Hz.
f21 is  2.2  MHz.
Distortion with feedback is  0.45 %.

Example 29.13 , Page Number 737¶

In :
import math

#Variables

Av = 100.0                      #Voltage gain without feedback
N = 0.8                         #Reduction in noise

#Calculation

beta = ((1 - N)**-1  - 1)/Av    #feedback ratio
A1v = Av / (1 + beta * Av)      #Voltage gain with feedback

#Result

print "Percentage of negative feedback is ",beta * 100,"%.\nVoltage gain with feedback is ",A1v,"."
Percentage of negative feedback is  4.0 %.
Voltage gain with feedback is  20.0 .

Example 29.14 , Page Number 739¶

In :
import math

#Variables

Av = 300.0                    #Voltage gain without feedback
Ri = 1.5 * 10**3              #Input resistance (in ohm)
Ro = 50.0 * 10**3             #Output resistance (in ohm)
beta = 1.0/15.0               #feedback ratio

#Calculation

A1v = Av/ (1 + beta*Av)       #Voltage gain with feedback
R1i = (1 + beta* Av)* Ri      #Input resistance with feedback (in ohm)
R1o = Ro/(1 + beta * Av)      #Output resistance with feedback (in ohm)

#Result

print "Voltage gain with feedback is ",round(A1v,1),".\nInput resistance with feedback is ",R1i * 10**-3," kilo-ohm.\nOutput resistance with feedback is ",round(R1o * 10**-3,1)," kilo-ohm."
Voltage gain with feedback is  14.3 .
Input resistance with feedback is  31.5  kilo-ohm.
Output resistance with feedback is  2.4  kilo-ohm.

Example 29.15 , Page Number 741¶

In :
import math

#Variables

hfe = 100.0                              #hfe
hie = 2.0 * 10**3                        #hie (in ohm)
Re1 = 100.0                              #Emitter resistance (in ohm)
R1 = 15.0 * 10**3                        #Resistance (in ohm)
R2 = 5.6 * 10**3                         #Resistance (in ohm)
Rc = 470.0                               #Collector resistance (in ohm)

#Calculation

Ai = hfe                                 #Current gain
Av = Ai * Rc / hie                       #Voltage gain
Ri = (R1*R2*hie)/(R1*R2+R2*hie+R1*hie)   #Input resistance (in ohm)
beta = Re1 / Rc                          #feedback ratio
A1v = Av / (1 + beta * Av)               #Voltage ratio with feedback
R1i = Ri*(1 + beta * Av)                 #Input resistancewith feedback (in ohm)

#Result

print "Voltage gain without feedback is ",Av,".\nInput resistance without feedback is ",round(Ri)," kilo-ohm.\nVoltage gain with feedback is ",round(A1v,2),".\nInput resistance with feedback is ",round(R1i,1)," kilo-ohm."

#Slight variation due to higher precision.
Voltage gain without feedback is  23.5 .
Input resistance without feedback is  1342.0  kilo-ohm.
Voltage gain with feedback is  3.92 .
Input resistance with feedback is  8051.1  kilo-ohm.

Example 29.16 , Page Number 743¶

In :
import math

#Variables

hfe = 99.0                             #hfe
hie = 2.0 * 10**3                      #hie (in ohm)
Rc = 22.0 * 10**3                      #Load resistor of frist stage (in ohm)
R4  = 100.0                            #Emitter resistance of first stage (in ohm)
R1 = 220.0 * 10**3                     #Biasing resistor of second stage (in ohm)
R2 = 22.0 * 10**3                      #Biasing resistor of second stage (in ohm)
R1c = 4.7 * 10**3                      #Load resistance of second stage (in ohm)
R3 = 7.8 * 10**3                       #Feedback resistor from collector of second stage to emitter of first stage (in ohm)

#Calculation

Ri = hie                               #Input resistance of first stage (in ohm)
Ro1 = (1/Rc + 1/R1 + 1/R2 + 1/hie)**-1 #Output resistance of first stage (in ohm)
Ri2 = hie                              #Input resistance of second stage (in ohm)
Ro2 = R1c * (R3 + R4)/(R1c + R3 + R4)  #Output resistance of second stage (in ohm)
Av1 = hfe * Ro1 / hie                  #Voltage gain of first stage
Av2 = hfe * Ro2 / hie                  #Voltage gain of second stage
Av = Av1 * Av2                         #Overall voltage gain without feedback
beta = R4 / (R3 + R4)                  #Feedback ratio
Ri1 = Ri*(1 + beta*Av)                 #Input resistance with feedback (in ohm)
R1o2 = Ro2 / (1 + beta * Av)           #Output resistance with feedback (in ohm)
A1v = Av / (1 + beta * Av)             #Overall voltage gain with feedback

#Result

print "Voltage gain without feedback is ",round(Av,1),".\nInput resistance of first stage without feedback is ",Ri * 10**-3," kilo-ohm.\nInput resistance of second stage without feedback is ",Ri2 * 10**-3," kilo-ohm.\nOutput resistance of first stage without feedback is ",round(Ro1 * 10**-3,2)," kilo-ohm.\nOutput resistance of second stage without feedback is ",round(Ro2 * 10**-3,2)," kilo-ohm ."
print "Voltage gain with feedback is ",round(A1v,1),".\nInput resistance with feedback is ",round(Ri1 * 10**-3,2)," kilo-ohm.\nOutput resistance with feedback is ",round(R1o2 * 10**-3,3)," kilo-ohm."

#Calculation error in book about value of Av.
Voltage gain without feedback is  12126.0 .
Input resistance of first stage without feedback is  2.0  kilo-ohm.
Input resistance of second stage without feedback is  2.0  kilo-ohm.
Output resistance of first stage without feedback is  1.68  kilo-ohm.
Output resistance of second stage without feedback is  2.95  kilo-ohm .
Voltage gain with feedback is  78.5 .
Input resistance with feedback is  308.99  kilo-ohm.
Output resistance with feedback is  0.019  kilo-ohm.