Chapter 08 : The Transistor at Low Frequency

Example 8.2, Page No 251

In [1]:
import math
#initialisation of variables
Rl=10.0   #in K
Rs=1.0        #in K
hie=1.1       #in K
hre=2.5*(10**-4) 
hfe=50.0
hoe=25*(10**-3)            #in K^-1

#Calculations
Ai= -hfe/(1+(hoe*Rl))                     #Current Gain or Current Amplification
print("Ai= %.2f  " %Ai)

Ri = hie + (hre*Rl*Ai)
print("Ri= %.2f K" %Ri)

Av=(Ai*Rl)/Ri            #Voltage Gain
print("Av= %.2f  " %Av)

Avs=(Av*Ri)/(Ri+Rs)            #Overall Voltage Gain taking source resistance into account
print("Avs= %.2f  " %Avs)

Ais=(Ai*Rs)/(Ri+Rs)           #Overall current gain taking source resistance into account
print("Ais= %.2f  " %Ais)

#Results
Yo=hoe-((hfe*hre)/(hie+Rs))          #Admittance
print("Yo= %.2f K^-1 " %Yo)

Zo = 1.0/Yo          #Impedence
print("Zo= %.2f K " %Zo)

Ai= -40.00  
Ri= 1.00 K
Av= -400.00  
Avs= -200.00  
Ais= -20.00  
Yo= 0.02 K^-1 
Zo= 52.50 K

Example 8.3, Page No 251

In [2]:
import math

#initialisation of variables

#Yo = I/Vo
#When current in a short circuit placed across the output terminals and V is the open circuit voltage
print('When current in a short circuit placed across the output terminals and V is the open circuit voltage')
print('I = -hf*I1=-(hf*Vs)/(Rs+hi)')
#Applying KVL
print('Vs = I1*(Rs+hi)+hr*V = -ho*V*(Rs+hi)/hf+hr*V')
print('or')
print('V = -(hf*Vs/(Rs+hi))/(ho-hf*hr(Rs+hi))')

When current in a short circuit placed across the output terminals and V is the open circuit voltage
I = -hf*I1=-(hf*Vs)/(Rs+hi)
Vs = I1*(Rs+hi)+hr*V = -ho*V*(Rs+hi)/hf+hr*V
or
V = -(hf*Vs/(Rs+hi))/(ho-hf*hr(Rs+hi))

Example 8.4 Page No 252

In [3]:
import math

#initialisation of variables

hie=1.1#in K
hre=2.5*(10^-4)
hfe=50
hoe=25*(10^-3)#in K^-1
r=200#in K
Rs=10#in K
Ri=1#in K
Rl=10#in K

#Calculations
rl=(r*Rs)/(r+Rs)#in K

Ai = -hfe/(1+(hoe*rl))#Current Gain
print("Ai =  %.2f " %Ai)

Ri = hie + (hre*Ai*rl)
print("Ri =  %.2f K" %Ri)

Av=(Ai*rl)/Ri#Voltage Gain
print("Av = %.2f " %Av)

k = r/(1-Av)
ri = (Ri*k)/(Ri+k)
print("ri =  %.2f K" %ri)


#Results
Avs = Av*(ri/(ri+Rs))#Overall voltage Gain taking Source resistance into account
print("Avs = %.2f " %Avs)

ai = Avs*((ri+Rs)/Rl)
print("ai = -I2/I1 =  %.2f " %ai)

Ai =  0.00 
Ri =  1.10 K
Av = 0.00 
ri =  1.09 K
Avs = 0.00 
ai = -I2/I1 =  0.00

Example 8.5, Page No 254

In [4]:
import math
#initialisation of variables

hie = 2#in K
hfe = 50
hre = 6*(10^-4)
hoe = 25*(10^-3)#in K^-1
hic=2#in K
hfc=-51
hrc=1
hoc=25*(10^-3)#/in K^-1
Re2=5#in K
Rs=1#in K
Rc1=5#in K

#The Second Stage

#Calculations
Rl = Re2
Ai2 = -hfc/(1+(hoc*Re2))#Current Gain in @nd Transistor
print("Ai2 = %.2f " %Ai2)

Ri2 = hic + (hrc*Ai2*Re2)
print("Ri2 = %.2f K" %Ri2)

Av2 = (Ai2*Re2)/Ri2#Voltage Gain in 2nd Transistor
print("Av2 = %.2f " %Av2)

#The First Stage

Rl1 = (Rc1*Ri2)/(Rc1+Ri2)
print("Rl1 = %.2f K" %Rl1)


Ai1 = -hfe/(1+(hoe*Rl1))#Current Gain in 1st Transistor
print("Ai1 = %.2f " %Ai1)

Ri1 = hie + (hre*Ai1*Rl1)
print("Ri1 = %.2f K" %Ri1)

Av1 = (Ai1*Rl1)/Ri1#Voltage Gain in 1st Transistor
print("Av1 = %.2f " %Av1)

print('The output Admittance of Transistor')
Yo1 = hoe - ((hfe*hre)/(hie+Rs))
print("Yo= %.2f K^-1 " %Yo)

Ro1 = 1/Yo1

#Output Impedence of First Stage
print('Output Impedence of First Stage')
ro1 = (Ro1*Rc1)/(Ro1+Rc1)
print("ro1= %.2f K " %ro1)
rs2 = ro1

Yo2 = hoc - ((hfc*hrc)/(hic+rs2))
print("Yo2= %.2f K^-1 " %Yo2)

A1 = (Ai2*Ai2*Rc1)/(Ri2+Rc1)#Overall Current gain
print("A1 = %.2f " %A1)

Av = Av2*Av1#Overall Voltage Gain
print("Voltage Gain Av = %.2f " %Av)
print(Av,' = Av=')


#Results
Avs = (Av*Ri1)/(Ri1+Rs)#Overall Voltage gain with Source Impedence
print("Overall Voltage gain taking Source Impedence into account = Avs = %.2f " %Avs)

Ai2 = -1.00 
Ri2 = -3.00 K
Av2 = 1.00 
Rl1 = -8.00 K
Ai1 = -1.00 
Ri1 = -478.00 K
Av1 = -1.00 
The output Admittance of Transistor
Yo= 0.02 K^-1 
Output Impedence of First Stage
ro1= 0.00 K 
Yo2= -199.00 K^-1 
A1 = 2.00 
Voltage Gain Av = -1.00 
(-1, ' = Av=')
Overall Voltage gain taking Source Impedence into account = Avs = -2.00

Example 8.6 Page No 257

In [5]:
import math
#initialisation of variables
hie = 2#in K
hfe = 50
hre = 6*(10^-4)
hoe = 25*(10^-3)#in K^-1
hic=2#in K
hfc=-51
hrc=1
hoc=25*(10^-3)#/in K^-1
Re2=5#in K
Rs=5#in K
Rc1=5#in K

#Calculations
#For the CC output Stage
print('For the CC output Stage')
Rl = Re2
Ai2 = 1+ hfe#Current gain in 2nd Transistor
print("Ai2= %.2f " %Ai2)
Ri2 = hie+((1+hfe)*Rl)
print("Ri2= %.2f K" %Ri2)
Av2=1-(hie/Ri2)#voltage gain in 2nd transistor
print("Av2= %.2f " %Av2)

#For the CE input Stage
print('For the CE input Stage')

Ai1=-hfe#Current gain in 1st transistor
Ri1 = hie
print("Ai1= %.2f " %Ai1)
Rl1=(Rc1*Ri2)/(Rc1+Ri2)
print("Rl1= %.2f K" %Rl1)
Av1=(Ai1*Rl1)/Ri1#Voltage gain in 1st transistor
print("Av1= %.2f " %Av1)
ro1=Rc1
Ro2 = (hie+Rs)/(1+hfe)
ro2=(Ro2*Rl)/(Ro2+Rl)
print("Effective Source Impedence = %.2f k" %ro2)

Av = Av1*Av2#Overall voltage gain

#Results
print("Overall Voltage Gain= %.2f k" %Av)
Ai = Ai1*Ai2*(Rc1/(Rc1+Ri2))#Overall current Gain
print("Overall Current Gain= %.2f k" %Ai)

For the CC output Stage
Ai2= 51.00 
Ri2= 257.00 K
Av2= 1.00 
For the CE input Stage
Ai1= -50.00 
Rl1= 4.00 K
Av1= -100.00 
Effective Source Impedence = 0.00 k
Overall Voltage Gain= -100.00 k
Overall Current Gain= 0.00 k