Chapter 24 , Singly-Stage BJT Amplifiers

Example 24.1 , Page Number 590

In [1]:
import math

#Variables

VCC = 10.0                        #Source voltage (in volts)
RC = 10.0                         #Collector resistance (in kilo-ohm)
RB = 1.0 * 10**3                  #Base resistance (in kilo-ohm)
beta = 100.0                      #Common emitter current gain 
VBE = 0.7                         #Emitter-to-Base Voltage (in volts)

#Calculation

IB = (VCC - VBE) / RB             #Base current (in milli-Ampere)
IC = beta * IB                    #Collector current (in milli-Ampere)
IE = IC                           #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3          #a.c resistance of emitter diode (in kilo-ohm)
R1 = beta * r1e                   #Input resistance looking directly into the base (in kilo-ohm)
Ris = RB * R1/(RB + R1)           #Stage input resistance (in kilo-ohm)
Ro = RC                           #Output resistance (in kilo-ohm)
Av = RC / r1e                     #Voltage gain
    
#Result

print "Input resistance looking into the base is ",round(R1,2)," kilo-ohm.\nInput resistance of the stage is ",round(Ris,3)," kilo-ohm.\nOutput resistance is ",Ro," kilo-ohm.\nVoltage gain is ",Av,"."

#Correction to be done in the book for the formula of Ris in the question.

Input resistance looking into the base is  2.69  kilo-ohm.
Input resistance of the stage is  2.681  kilo-ohm.
Output resistance is  10.0  kilo-ohm.
Voltage gain is  372.0 .

Example 24.2 , Page Number 591

In [2]:
import math

#Variables

Ri = 2.5                         #Input resistance (in kilo-ohm)
Av = 200.0                       #Voltage gain
Vs = 5.0 * 10**-3                #Input signal voltage (in volts)
beta = 50.0                      #Common emitter current gain

#Calculation

IB = Vs / Ri                     #Base current (in milli-Ampere)   
IC = beta * IB                   #Collector current (in milli-Ampere)
Ai = beta                        #Current gain
Ap = Ai * Av                     #Power gain
Gp = 10 * math.log10(Ap)              #dB power gain (in decibel)

#Result

print "The base current is ",IB," mA.\nThe collector current is ",IC," mA.\nThe power gain is ",Ap,".\nThe dB power gain is ",Gp," dB."

#Wrong unit of IB. IB is in micro Ampere but in book it is given in milli-Ampere in solution.
#Also wrong unit in IC.

The base current is  0.002  mA.
The collector current is  0.1  mA.
The power gain is  10000.0 .
The dB power gain is  40.0  dB.

Example 24.3 , Page Number 593

In [3]:
import math

#Variables

VCC = 20.0                       #Source voltage (in volts)
RC = 5.0                         #Collector resistance (in kilo-ohm)
RE = 1.0                         #Emitter resistance (in kilo-ohm)
RB = 100.0                       #Base resistance (in kilo-ohm)
beta = 150.0                     #Common emitter current gain

#Calculation

IC = VCC / (RE + RB/beta)        #Collector current (in milli-Ampere)
IE = IC                          #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3         #a.c. resistance of emitter diode (in kilo-ohm)
Ri = beta * (r1e + RE)           #Input resistance looking directly into the base (in kilo-ohm)
Ris = RB * Ri / (RB + Ri)        #Input resistance of the stage (in kilo-ohm)
Av = RC / RE                     #Voltage gain 
Gp = 10 * math.log10(Av)              #dB power gain (in decibel)

#Result

print "Input resistance looking into the base is ",round(Ri)," kilo-ohm.\nInput resistance of the stage is ",round(Ris)," kilo-ohm.\nVoltage gain is ",Av,".\ndB voltage gain is ",round(Gp)," dB."

Input resistance looking into the base is  150.0  kilo-ohm.
Input resistance of the stage is  60.0  kilo-ohm.
Voltage gain is  5.0 .
dB voltage gain is  7.0  dB.

Example 24.4 , Page Number 595

In [4]:
import math

#Variables

VCC = 12.0                       #Source voltage (in volts)
RC = 10.0 * 10**3                #Collector resistance (in ohm)
RE = 1.0 * 10**3                 #Emitter resistance (in ohm)
RB = 500.0 * 10**3               #Base resistance (in ohm)
beta = 50.0                      #Common emitter current gain

#Calculation

IC = VCC / (RE + RB/beta)        #Collector current (in Ampere)
IE = IC                          #Emitter current (in Ampere)
r1e = 25.0 / IE * 10**-3         #a.c. resistance of emitter diode (in ohm)
Ri = beta * (r1e)                #Input resistance looking directly into the base (in ohm)
Ris = RB * Ri / (RB + Ri)        #Input resistance of the stage (in ohm)
Av = RC / r1e                    #Voltage gain 
AV1 = RC / RE                    #New voltage gain  

#Result

print "Input resistance looking into the base is ",round(Ri)," ohm.\nInput resistance of the stage is ",round(Ris,1)," kilo-ohm.\nVoltage gain is ",round(Av,2),".\nNew Voltage gain is ",AV1,"."

#Slight variations in answers due to high precision.

Input resistance looking into the base is  1146.0  ohm.
Input resistance of the stage is  1143.2  kilo-ohm.
Voltage gain is  436.36 .
New Voltage gain is  10.0 .

Example 24.5 , Page Number 597

In [5]:
import math

#Variables

VCC = 30.0                        #Source voltage (in volts)
RC = 10.0                         #Collector resistance (in kilo-ohm)
RE = 8.2                          #Emitter resistance (in kilo-ohm)
RL = 3.3                          #Load resistance (in kilo-ohm)
beta = 200.0                      #Common emitter current gain
VBE = 0.7                         #Emitter-to-Base Voltage (in volts)
R1 = 47.0                         #Resistance (in kilo-ohm)   
R2 = 15.0                         #Resistance (in kilo-ohm)
Vs = 5.0                          #a.c voltage (in milli-volts)

#Calculation

Vth = VCC * R2 / (R1 + R2)        #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)         #Thevenin's equivalent voltage (in volts)
IE = (Vth - VBE)/(RE + Rth/beta)  #Emitter current (in milli-Ampere)
r1e = 25.0 / IE                   #a.c. resistance of emitter diode (in ohm)     
rL = RC * RL/(RC + RL)            #a.c load seen by the amplifier (in kilo-ohm)     
Av = rL * 10**3 / r1e             #Voltage gain
vo = Av * Vs                      #Output voltage (in volts)
Ri = beta * r1e * 10**-3          #Input resistance looking directly into the base (in ohm)  
Ris = Rth * Ri / (Rth + Ri)       #input resistance of the stage (in ohm)

#Result

print "a.c output voltage is ",round(vo,2)," mV.\nInput impedance for the circuit is ",round(Ris)," kilo-ohm."

#Slight variation in value of vo due to higher precision. 

a.c output voltage is  394.14  mV.
Input impedance for the circuit is  4.0  kilo-ohm.

Example 24.6 , Page Number 599

In [6]:
import math

#Variables

VCC = 10.0                            #Source voltage (in volts)
RC = 5.0                              #Collector resistance (in kilo-ohm)
RE = 1.0                              #Emitter resistance (in kilo-ohm)
beta = 50.0                           #Common emitter current gain
VBE = 0.7                             #Emitter-to-Base Voltage (in volts)
R1 = 50.0                             #Resistance (in kilo-ohm)   
R2 = 10.0                             #Resistance (in kilo-ohm)
Vs = 10.0                             #a.c voltage (in milli-volts)
RS = 600.0 * 10**-3                   #Source resistance (in kilo-ohm)  

#Calculation

Vth = VCC * R2 / (R1 + R2)            #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent voltage (in volts)
IE = (Vth - VBE)/(RE + Rth/beta)      #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3              #a.c. resistance of emitter diode (in kilo-hm)     
Ris = Rth * beta*r1e/(Rth + beta*r1e) #input resistance of the stage (in ohm)
rL = RC * R1/(RC + R1)                #a.c load seen by the amplifier (in kilo-ohm)     
Av = rL / r1e                         #Voltage gain
vin = Vs * Ris / (Ris + RS)           #input voltage (in milli-volts)    
vo = Av * vin                         #Output voltage (in milli-volts)
Avs = Av * vin / Vs                   #Overall voltage gain 

#Result

print "The output voltage is ",round(vo * 10**-3,3)," V.\nThe overall voltage gain is ",round(Avs,2),"."

#Slight variation due to higher precision.

The output voltage is  1.025  V.
The overall voltage gain is  102.5 .

Example 24.7 , Page Number 601

In [7]:
import math

#Variables

VCC = 12.0                            #Source voltage (in volts)
RC = 4.0                              #Collector resistance (in kilo-ohm)
RE = 3.3                              #Emitter resistance (in kilo-ohm)
beta = 120.0                          #Common emitter current gain
VBE = 0.7                             #Emitter-to-Base Voltage (in volts)
R1 = 60.0                             #Resistance (in kilo-ohm)   
R2 = 30.0                             #Resistance (in kilo-ohm)

#Calculation

Vth = VCC * R2 / (R1 + R2)            #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent voltage (in volts)
IE = (Vth - VBE)/(RE + Rth/beta)      #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3              #a.c. resistance of emitter diode (in kilo-hm)
rL = RC                               #Load resistance (in kilo-ohm)
Av = RC / r1e                         #Voltage gain

#Result

print "The voltage gain is ",round(Av,1),"."

#Slight variation due to higher precision.

The voltage gain is  152.3 .

Example 24.8 , Page Number 601

In [8]:
import math

#Variables

VCC = -18.0                           #Source voltage (in volts)
RC = 4.3                              #Collector resistance (in kilo-ohm)
RE = 1.0                              #Emitter resistance (in kilo-ohm)
beta = 200.0                          #Common emitter current gain
VBE = -0.7                            #Emitter-to-Base Voltage (in volts)
R1 = 39.0                             #Resistance (in kilo-ohm)   
R2 = 8.2                              #Resistance (in kilo-ohm)
RL = 3.0                              #Load resistance (in kilo-ohm)

#Calculation

Vth = VCC * R2 / (R1 + R2)            #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent voltage (in volts)
IC = (Vth - VBE)/(RE + Rth/beta)      #Collector current (in milli-Ampere)
IE = -IC                              #Emitter current (in milli-Amper) 
r1e = 30.0/IE * 10**-3                #a.ac resistance (in kilo-ohm)
Ris = Rth * beta*r1e/(Rth + beta*r1e) #input resistance of the stage (in ohm)
rL = RC * RL / (RC + RL)              #a.c. load resistance (in kilo-ohm)     
Av = rL / r1e                         #Voltage gain 

#Result

print "Voltage gain is ",round(Av,1),"."

#printing mistake in book about formula for rL it is in fact rL = RC * RL /(RC + RL).
#Slight variation due to higher precision.

Voltage gain is  138.3 .

Example 24.9 , Page Number 603

In [15]:
import math

#Variables

VCC = 20.0                            #Source voltage (in volts)
RC = 5.7                              #Collector resistance (in kilo-ohm)
RE = 1.0                              #Emitter resistance (in kilo-ohm)
beta = 100.0                          #Common emitter current gain
VBE = 0.7                             #Emitter-to-Base Voltage (in volts)
R1 = 100.0                            #Resistance (in kilo-ohm)   
R2 = 10.0                             #Resistance (in kilo-ohm)
Vs = 10.0 * 10**-3                    #a.c voltage (in volts)
RS = 100.0 * 10**-3                   #Source resistance (in kilo-ohm)  

#Calculation

Vth = VCC * R2 /(R1 + R2)             #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent resistance (in kilo-ohm)
IE = (Vth - VBE)/(RE + Rth/beta)      #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3              #a.c. resistance of emitter diode (in kilo-hm)
Ris = Rth * beta*r1e/(Rth + beta*r1e) #input resistance of the stage (in ohm)
rL = RC                               #Load resistance (in kilo-ohm)
Av = rL / r1e                         #Voltage gain 
vin = Vs * Ris / (Ris + RS)           #input voltage (in milli-volts)    
vo = Av * vin                         #Output voltage (in milli-volts)
Avs = Av * vin / Vs                   #Overall voltage gain 

#Result

print "Av is ",Av,".\nRi is ",round(Ris * 10**3,2)," ohm.\nVo is ",round(vo,2)," V.\nAvs is ",round(Avs,2),"."

#Slight variation due to higher precision.

Av is  233.7 .
Ri is  1923.08  ohm.
Vo is  2.22  V.
Avs is  222.15 .

Example 24.10 , Page Number 604

In [1]:
import math

#Variables

VCC = -18.0                           #Source voltage (in volts)
RC = 4.3                              #Collector resistance (in kilo-ohm)
RE = 1.0                              #Emitter resistance (in kilo-ohm)
beta = 200.0                          #Common emitter current gain
VBE = -0.7                            #Emitter-to-Base Voltage (in volts)
R1 = 39.0                             #Resistance (in kilo-ohm)   
R2 = 8.2                              #Resistance (in kilo-ohm)
RV = 75.0 * 10**-3                    #Resistance (in kilo-ohm)
re = 30.0 * 10**-3                    #Emitter resistance (in kilo-ohm)
RL = 3.3                              #Load resistance (in kilo-ohm)

#Calculation

Vth = VCC * R2 /(R1 + R2)             #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent resistance (in kilo-ohm)
IE = (Vth - VBE)/(RE + Rth/beta)      #Emitter current (in milli-Ampere)
IC = round(IE,2)                      #Collector current (in milli-Ampere) 
VCE = VCC - IC * (RC + RE)            #Collector-to-Emitter voltage (in volts)
r1e = 30.0/abs(IE) * 10**-3           #a.c. resistance (in kilo-ohm)
Ris = Rth * beta*r1e/(Rth + beta*r1e) #input resistance of the stage (in ohm)
rL = RC * RL / (RC + RL)              #Load resistance (in kilo-ohm)
Av = rL / (r1e + RV)                  #Voltage gain 

#Result

print "Voltage gain Av is ",round(Av,1),".\nInput impedance is ,",round(Ris,3)," kilo-ohm.\nVCE is ",VCE," V." 

#Slight variation due to higher precision.

Voltage gain Av is  21.3 .
Input impedance is , 1.856  kilo-ohm.
VCE is  -5.545  V.

Example 24.11 , Page Number 606

In [10]:
import math

#Variables

VCC = 10.0                            #Source voltage (in volts)
RC = 5.0                              #Collector resistance (in kilo-ohm)
rE = 500 * 10**-3                     #Emitter resistance (in kilo-ohm)
beta = 50.0                           #Common emitter current gain
VBE = 0.7                             #Emitter-to-Base Voltage (in volts)
R1 = 50.0                             #Resistance (in kilo-ohm)   
R2 = 10.0                             #Resistance (in kilo-ohm)
Vs = 100.0 * 10**-3                   #a.c voltage (in volts)
RS = 600.0 * 10**-3                   #Source resistance (in kilo-ohm)
RL = 50.0                             #Load resistance (in kilo-ohm)
RE1 = 500.0 * 10**-3                  #Resistance (in kilo-ohm)    

#Calculation

Vth = VCC * R2 /(R1 + R2)             #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)             #Thevenin's equivalent resistance (in kilo-ohm)
RE = RE1 + rE                         #Emitter total resistance (in kilo-ohm)
IE = (Vth - VBE)/(RE + Rth/beta)      #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3              #a.c. resistance (in kilo-ohm)      
Ri = beta * (rE + r1e)                #Input resistance directly into the base (in kilo-ohm)
Ris = Rth * Ri/(Rth + Ri)             #Input resistance of the stage (in kilo-ohm)
rL = RC * RL / (RC + RL)              #a.c. load resistance (in kilo-ohm)
Av = rL/(rE + r1e)                    #Voltage gain
Avs = Av * Ris / (RS + Ris)           #Overall voltage gain
Vo = Avs * Vs                         #Output voltage (in volts)

#Result

print "Input resistance looking directly into the base is ",round(Ri,1)," kilo-ohm.\nInput resistance of the stage is ",round(Ris,2)," kilo-ohm.\nVoltage gain is ",round(Av,3)," .\nOverall voltage gain is ",round(Avs,2)," .\nOutput voltage is ",round(Vo,2),"V."

#Slight variations due to higher precision.
#Vo in the book is not properly calculated. Calculation error in Vo. Vo value should be 0.78 V.

Input resistance looking directly into the base is  26.5  kilo-ohm.
Input resistance of the stage is  6.34  kilo-ohm.
Voltage gain is  8.574  .
Overall voltage gain is  7.83  .
Output voltage is  0.78 V.

Example 24.12 , Page Number 611

In [1]:
import math

#Variables

VCC = 10.0                            #Source voltage (in volts)
RC = 10.0                             #Collector resistance (in kilo-ohm)
alpha = 0.98                          #Common base current gain
VBE = 0.7                             #Emitter-to-Base Voltage (in volts)
Vs = 10.0 * 10**-3                    #a.c voltage (in volts)
RL = 5.1                              #Load resistance (in kilo-ohm)
RE = 20.0                             #Resistance (in kilo-ohm) 
VEE = 10.0                            #Voltage (in volts)

#Calculation

IE = (VEE - VBE) / RE                 #Emitter current (in milli-Ampere)
r1e = 25.0 / IE * 10**-3              #a.c. emitter resistance (in kilo-ohm)
Ri = r1e                              #input resistance looking directly in the emitter (in kilo-ohm)
Ris = RE * r1e / (RE + r1e)           #Input resistance of the stage (in kilo-ohm)  
Ai = alpha                            #Current gain
rL = RC * RL / (RC + RL)              #a.c. load resistance (in kilo-ohm)
Av = rL / r1e                         #Voltage gain
Ap = Av * Ai                          #Power gain
Gp = 10 * math.log10(Ap)                   #Power gain (in decibels)
vin = Vs                              #input voltage (in volts)
Vo = Av * vin                         #Output voltage (in volts)  

#Result

print "The input resistance looking directly into the emitter is ",round(Ri * 10**3,1)," ohm.\nThe input resistance of the stage is ",round(Ris * 10**3,2)," ohm.\nThe current gain is ",Ai," .\nThe voltage gain is ",round(Av,1)," .\nThe power gain is ",round(Ap,2)," .\nThe power gain in decibels is ",round(Gp,1)," dB.\nThe output voltage is ",round(Vo * 10**3)," mV." 

The input resistance looking directly into the emitter is  53.8  ohm.
The input resistance of the stage is  53.62  ohm.
The current gain is  0.98  .
The voltage gain is  62.8  .
The power gain is  61.56  .
The power gain in decibels is  17.9  dB.
The output voltage is  628.0  mV.

Example 24.13 , Page Number 613

In [12]:
import math

#Variables

Rs = 50.0                         #source resistance (in ohm)
IE = 0.465                        #Emitter current (in milli-Ampere)
r1e = 53.8                        #a.c. resistance (in ohm)
Ri = 53.8                         #Input resistance (in ohm)
Ris = 52.4                        #Input resistance of stage (in ohm)
RL = 3.38 * 10**3                 #Load resistance (in ohm)  
Vs = 10.0 * 10**-3                #Input a.c. voltage (in volts)

#Calculation

Avs = RL / (Rs + r1e)             #Overall voltage gain
Av = RL / r1e                     #Voltage gain
vo = Avs * Vs                     #Output a.c. voltage (in volts)
vin = vo / Av                     #input voltage (in volts)

#Result

print "Voltage gain from source to output is ",round(Avs,1)," .\nVoltage gain from emitter to output is ",round(Av,1)," .\nValue of Vin is ",round(vin * 10**3,1)," V." 

Voltage gain from source to output is  32.6  .
Voltage gain from emitter to output is  62.8  .
Value of Vin is  5.2  V.

Example 24.14 , Page Number 617

In [13]:
import math

#Variables

VEE = 10.0                         #Voltage (in volts)
RE = 10.0 * 10**3                  #Emitter resistance (in ohm)     
RB = 100.0 * 10**3                 #Base resistance (in ohm)
beta = 50.0                        #Common emitter current gain
VBE = 0.7                          #Emitter-to-Base Voltage (in volts)

#Calculation

IE = (VEE - VBE)/(RE + RB/beta)    #Emitter current (in Ampere)
r1e = 25.0 / IE * 10**-3           #a.c. resistance (in ohm)
Ri = beta * (RE + r1e)             #Input resistance directly looking into the base (in ohm)
Ris = RB * Ri / (RB + Ri)          #Input resistance of the stage (in ohm)
Ro = r1e                           #Output resistance (in ohm) 
Av = RE / (r1e + RE)               #Voltage gain  

#Result

print "Input resistance looking directly into the base is ",round(Ri * 10**-3,1)," ohm.\nInput resistance of the stage is ",round(Ris * 10**-3 ,1)," ohm.\nOutput resistance is ",round(Ro,1)," ohm.\nVoltage gain is ",round(Av,3)," ." 

Input resistance looking directly into the base is  501.6  ohm.
Input resistance of the stage is  83.4  ohm.
Output resistance is  32.3  ohm.
Voltage gain is  0.997  .

Example 24.15 , Page Number 618

In [14]:
import math

#Variables

beta = 80.0                         #Common emitter current gain
VBE = 0.7                           #Emitter-to-Base Voltage (in volts)
VCC = 15.0                          #Voltage (in volts)
R1 = 20.0 * 10**3                   #Resistance (in ohm)
R2 = 20.0 * 10**3                   #Resistance (in ohm)
Vs = 5.0 * 10**-3                   #a.c voltage (in volts)
RE = 8.2 * 10**3                    #Emitter resistance (in ohm)
RL = 1.5 * 10**3                    #Load resistance (in ohm)
RS = 2.0 * 10**3                    #Source resistance (in ohm)

#Calculation

Vth = VCC * R2 / (R1 + R2)          #Thevenin's voltage (in volts)
Rth = R1 * R2 / (R1 + R2)           #Thevenin's equivalent resistance (in ohm)
IE = (Vth - VBE)/(RE + Rth / beta)  #Emitter resistance (in ohm)
r1e = 25.0 / IE * 10**-3            #a.c resistance of emitter diode (in ohm)
rL = RE * RL /(RE + RL)             #a.c. load resistance (in ohm)
Ri = beta * (rL + r1e)              #Input resistance looking directly into the base (in ohm)
Ris = Rth * Ri / (Rth + Ri)         #Input resistance of the stage (in ohm)
Ro = r1e + (RS*Rth)/(Rth + RS)/beta #Output resistance of the stage (in ohm)
Vin = Vs * (Ris / (RS + Ris))       #Input voltage (in volts)
Vo = Vin                            #Output voltage (in volts)

#Result

print "Value of input resistance looking directly into the base is ",round(Ri * 10**-3)," kilo-ohm.\nValue of input resistance of the stage is ",round(Ris * 10**-3,1)," kilo-ohm.\nOutput resistance is ",round(Ro,1)," ohm.\nA.C. output voltage is ",round(Vo * 10**3,1)," mV." 

Value of input resistance looking directly into the base is  104.0  kilo-ohm.
Value of input resistance of the stage is  9.1  kilo-ohm.
Output resistance is  51.4  ohm.
A.C. output voltage is  4.1  mV.