Chapter 5- BJT AC Analysis

Example-5.1 Page No-256

In [45]:
#from the given figure:
Vcc=12                #supply voltage in volts
Vbe=0.7               #base emitterv voltage in volts
Rb=470.0              #base resistor in kohm
B=101
Rc=3.0                #collector resistor in kohm
ro=50.0               #resistance in kohm

#calculation:
print "\nCase-I"
#Case-I 
Ib=(Vcc-Vbe)/Rb       #base current in microA
Ie=(B+1)*Ib              #emitter current in mA
re=26/Ie                 #resistance in ohm
X=B*re
X=X/1000
Zi=(Rb*X)/(Rb+X)   #input resistance in kohm
Zo=Rc                    #resistance in kohm
Av=-Rc/re                 #voltage gain

print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av*1000,2)


#Case-II(ro=50kohm)
Zo=(ro*Rc)/(ro+Rc)         #output  resistance in kohm
Av=-Zo/re                 #voltage gain

print "\nCase-II"
print "Output resistance=",round(Zo,2),"kohm"
print "Voltage gain=",round(Av*1000,2)

Case-I
re= 10.6 ohm
Input resistance= 1.07 kohm
Output resistance= 3.0 kohm
Voltage gain= -282.96

Case-II
Output resistance= 2.83 kohm
Voltage gain= -266.95

Example-5.2 Page No-259

In [46]:
#from the given figure:
Vcc=22                #supply voltage in volts
Vbe=0.7               #base emitter voltage in volts
R1=56.0                #resistor in kohm
R2=8.2                 #resistor in kohm
B=90.0
Rc=6.8                #collector resistor in kohm
Re=1.5                #emitter resistance in kohm

#calculations:
#Case-I

Vb=(R2*Vcc)/(R1+R2)     #Base voltage in volts
Ve=Vb-Vbe               #Emitter voltage in volts
Ie=Ve/Re                #Emitter current in mA
re=26/Ie                #in ohm
R=(R1*R2)/(R1+R2)         #in ohm
X=B*re
X=X/1000
Zi=(R*X)/(R+X)            #input resistance in kohm
Zo=Rc                     #output resistance in kohm
Av=-Rc/re                 #voltage gain
print 
print "Case-I"
print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av*1000,2)

#Case-II
Zo=(Rc*ro)/(Rc+ro)        #output resistance in kohm
Av=-Zo/re                 #voltage gain

print "\nCase-II"
print "Output resistance=",round(Zo,2),"kohm"
print "Voltage gain=",round(Av*1000,2)

Case-I
re= 18.48 ohm
Input resistance= 1.35 kohm
Output resistance= 6.8 kohm
Voltage gain= -367.89

Case-II
Output resistance= 5.99 kohm
Voltage gain= -323.85

Variation in answer is due to different precision value taken at each step of the answer

Example-5.3 Page No-263

In [47]:
#from the given figure:
Vcc=20                #supply voltage in volts
Vbe=0.7               #base emitter voltage in volts
Rb=470.0              #Base resistor in kohm
B=120.0
Rc=2.2                #collector resistor in kohm
Re=0.56               #emitter resistance in kohm
ro=40                 #in kohm

#calculations:

Ib=(Vcc-Vbe)/(Rb+(B+1)*Re)     #base current in microA
Ie=(B+1)*Ib                    #emitter current in mA
re=26/Ie                       #in ohm

Zb=B*(re+Re*1000)
Zb=Zb/1000
Zi=(Rb*Zb)/(Rb+Zb)             #input resistance in kohm
Zo=Rc                          #output resistance in kohm
Av=-(B*Rc)/Zb                  #voltage gain

print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av,2)

re= 5.99 ohm
Input resistance= 59.34 kohm
Output resistance= 2.2 kohm
Voltage gain= -3.89

Example-5.4 Page No-265

In [48]:
#from the calculation of example 5.3:
re=5.99                    #resistance in ohm
Rb=470.0                   #Base resistor in kohm
B=120.0
Rc=2.2                #collector resistor in kohm

#Calculation:
Zb=B*re/1000
Zi=(Rb*Zb)/(Rb+Zb)             #input resistance in kohm
Zo=Rc                          #output resistance in kohm
Av=-Rc/re                      #voltage gain

print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi*1000,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av*1000,2)

re= 5.99 ohm
Input resistance= 717.7 kohm
Output resistance= 2.2 kohm
Voltage gain= -367.28

Example-5.5 Page No-266

In [50]:
#from the given figure:
Vcc=16                #supply voltage in volts
Vbe=0.7               #base emitter voltage in volts
R1=90.0               #resistor in kohm
R2=10.0               #resistor in kohm
B=210.0
Rc=2.2                #collector resistor in kohm
Re=0.68               #emitter resistance in kohm
ro=50                 #resistance in kohm

#Calculations:

Vb=(R2*Vcc)/(R1+R2)     #Base voltage in volts
Ve=Vb-Vbe               #Emitter voltage in volts
Ie=Ve/Re                #Emitter current in mA
re=26/Ie                #in ohm
Rb=(R1*R2)/(R1+R2)         #in ohm
X=B*Re
#X=X/1000
Zi=(Rb*X)/(Rb+X)         #input resistance in kohm
Zo=Rc                     #output resistance in kohm
Av=-Rc/Re                 #voltage gain
 
print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av,2)

re= 19.64 ohm
Input resistance= 8.47 kohm
Output resistance= 2.2 kohm
Voltage gain= -3.24

Example-5.6 Page No-266

In [58]:
#from the answers obtained in example-5.5
re=19.64
B=210
X=B*re
X=X/1000
Zi=(Rb*X)/(Rb+X)          #input resistance in kohm
Zo=Rc                     #output resistance in kohm
Av=-Rc/re                 #voltage gain

print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av*1000,2)

re= 19.64 ohm
Input resistance= 2.83 kohm
Output resistance= 2.2 kohm
Voltage gain= -112.02

Example-5.8 Page No-272

In [60]:
#from the given figure:
alpha=0.98          #constant 
ro=1                #resistance in Mohm
Rc=5                #collector resistance in kohm
Re=1                #emitter resistance in kohm
Vee=2               #emitter voltage in volts
Vcc=8               #collector voltage in volts
Vbe=0.7             #base emitter voltage in volts

#calculations:

Ie=(Vee-Vbe)/Re      #emitter current in mA
re=26/Ie             #in ohm
Re=Re*1000           #emitter resistance in ohm
Zi=(Re*re)/(Re+re)   #input resistance in ohm
Zo=Rc                #output resistance in kohm
Av=Rc/re             #voltage gain


print "re=",round(re,2),"ohm"
print "Input resistance=",round(Zi,2),"kohm"
print "Output resistance=",Zo,"kohm"
print "Voltage gain=",round(Av*1000,2)

re= 20.0 ohm
Input resistance= 19.61 kohm
Output resistance= 5 kohm
Voltage gain= 250.0

Example-5.11 Page No-284

In [2]:
#from the given question:
Rc=3                #collector resistance in kohm
Rl=4.7              #emitter resistance in kohm
re=10.71            #resistance in ohm
Zi=1.07             #input impedance in kohm
Rs=0.3              #source resistance in kohm

#calculation:
X=(Rc*Rl)/(Rc+Rl)       #temporary variable
Avl=(-X/re)*1000        #voltage gain with load
Avs=(Zi*Avl)/(Zi+Rs)    #voltage gain with source impedance
Zo=Rc

print "Avl=",round(Avl,2)
print "Avs=",round(Avs,2)
print "Zi=",Zi,"kohm"
print "Zo=",Zo,"kohm"

Avl= -170.98
Avs= -133.54
Zi= 1.07 kohm
Zo= 3 kohm

Example-5.12 Page No-293

In [5]:
#from the given question:
Avnl=-280           #no load voltage gain
Rl=4.7              #emitter resistance in kohm
Zi=1.07             #input impedance in kohm
Rs=0.3              #source resistance in kohm
Zo=3                 #output impedance in kohm

#calculation:

print "a.)"
Avl=(Avnl*Rl)/(Zo+Rl)       #voltage gain with load
print "Avl=",round(Avl,2)


print "\nb.)"
X=(Avnl*Rl)/(Zo+Rl)       #temporary variable
Avs=(Zi*X)/(Zi+Rs)        #gain with source impedance
print "Avs=",round(Avs,2)

a.)
Avl= -170.91

b.)
Avs= -133.48

Example-5.17 Page No-300

In [29]:
#from the given figure:
Vcc=18                       #supply voltage in volts
Rb=3.3                       #base resistance in Mohm
B=8000
Vbe=1.6                      #base emitter volateg in volts
Re=390                       #emitter resistance in ohm


#calculatons:
X=B*Re                       #temporary volateg
X=X/1000000
Ib=(Vcc-Vbe)/(Rb+X)          #base current in microA
Ie=(B+1)*Ib                  #emitter current in mA
Ve=Ie*Re                     #emitter voltage in volts
Ve=Ve/1000
Vb=Ve/1000+Vbe               #base voltage in volts
Vc=Vcc                       #collector voltage in volts

print "Base current=",round(Ib,2),"microA"
print "Emitter current=",round(Ie/1000,2),"mA"
print "Emitter voltage=",round(Ve/1000,2),"V"
print "Base voltage=",round(Vb,2),"V"
print "Collector voltage=",Vc,"V"

Base current= 2.6 microA
Emitter current= 20.83 mA
Emitter voltage= 8.12 V
Base voltage= 9.72 V
Collector voltage= 18 V

Variation in answer is due to difference in precision of values taken at each step of the answer

Example-5.18 Page No-308

In [54]:
#from the given figure:
Vcc=18                       #supply voltage in volts
Rb=2.0                       #base resistance in Mohm
B1=140
B2=180
Rc=75.0                       #emitter resistance in ohm
Vbe1=0.7                      #base emitter voltage in Volts

#calculations:
X=B1*B2*Rc                          #temporary variable
X=X/1000000
Ib1=(Vcc-Vbe1)/(Rb+X)               #base current in Q1 in microA
Ib2=B1*Ib1                          #base current in Q2 in mA
Ie1=Ic1=Ib2
Ic2=B2*Ib2                          #collector current in Q2 in mA
Ic=Ie1+Ic2                          #current through in Resistance Rc in mA
G=(round((Ic/1000),2)*Rc)/1000       #temporary variable
Ve1=Vcc-G                            #emitter voltage in volts in Q1
Vb1=Ve1-Vbe1                         #base voltage in Q1 in volts

print "Base current in Q1=",round(Ib1,2),"microA"
print "Base current in Q2=",round(Ib2/1000,2),"mA"
print "Collector current in Q2=",round(Ic2/1000,2),"mA"
print "Current through in Resistance Rc=",round(Ic/1000,2),"mA"
print "Emitter voltage in Q1=",round(Ve1,2),"V"
print "Base voltage in Q1=",round(Vb1,2),"V"

Base current in Q1= 4.45 microA
Base current in Q2= 0.62 mA
Collector current in Q2= 112.07 mA
Current through in Resistance Rc= 112.69 mA
Emitter voltage in Q1= 9.55 V
Base voltage in Q1= 8.85 V