CHAPTER 9 : TRANSISTOR BIASING¶
Example 9.1: Page number 195-196¶
In [1]:
#Variable declaration
V_CC=6.0; #Collector supply voltage
R_C=2.5; #Collector load in kΩ
#Calculations
#(i)
#For faithful amplification Vce (collector-emitter voltage)> 1V for Si transistor.
V_CE_max=1; #Maximum allowed collector-emitter voltage for faithful amplification, in V.
V_Rc_max=V_CC-V_CE_max; #maximum voltage drop across collector load in V.
I_C_max=V_Rc_max/R_C; #Maximum allowed collector current in mA
#(ii)
IC_min_zero_signal=I_C_max/2; #Minimum zero signal collector current in mA
#Results
print("The maximum allowed collector current during application of signal for faithful amplification = %d mA."%I_C_max);
print("The minimum zero signal collector current required = %d mA."%IC_min_zero_signal);
Example 9.2: Page number 196¶
In [2]:
#Variable declaration
VCC=13.0; #Collector supply voltage in V
V_knee=1.0; #Knee voltage in V
R_C=4.0; #Collector load in kΩ
rate_IC_VBE=5.0; #Rate of change of collector current IC with base-emitter voltage VBE in mA/V.
beta=100.0; #base current amplification factor
#Calculations
V_Rc_max=VCC-V_knee; #Maximum allowed voltage across collector load in V
I_C_max=V_Rc_max/R_C; #Maximum allowed collector current in mA
I_B_max=I_C_max/beta; #Maximum base current in mA
I_B_max=I_B_max*1000; #Maximum base current in 𝜇A
V_B_max=I_C_max/rate_IC_VBE; #Maximum base voltage signal in V
V_B_max=V_B_max*1000; #Maximum base voltage signal in mV
#Results
print("Maximum base current =%d 𝜇A."%I_B_max);
print("Maximum input signal voltage =%d mV."%V_B_max);
Example 9.3: Page number 200-201¶
In [3]:
#Variable declaration
VCC=9.0; #Colector supply voltage in V
VBB=2.0; #Base supply voltage in V
R_B=100.0; #Base resistor's resistance in kΩ
R_C=2.0; #Collector load in kΩ
beta=50.0; #base current amplification factor
#Calculations
#Case (i):
#Applying Kirchhoff's law to the input circuit
#We get, IB*RB +VBE =VBB.
#Neglecting the small base-emitter voltage, we get:
I_B=VBB/R_B; #Base current in mA
I_C=beta*I_B; #Collector current in mA
print("Collector current = %dmA"%I_C);
#Applying Kirchhoff's law to the output ciruit
#We get, IC*RC + VCE= VCC.
#From the above equation, we get:
V_CE=VCC-I_C*R_C; #Collector emitter voltage in V
print("Collector emitter voltage =%dV."%V_CE);
#Case (ii):
R_B=50.0;
I_B=VBB/R_B;
I_C=beta*I_B;
V_CE=VCC - I_C*R_C;
print("The new operating point for base resistor RB=50 kΩ is, VCE=%dV and IC=%dmA."%(V_CE,I_C));
Example 9.4: Page number 201-202¶
In [5]:
%matplotlib inline
import matplotlib.pyplot as plt
#variable declaration
beta=100.0; #base current amplification factor
VCC=6.0; #Collector suply voltagein V
VBE=0.7 #Base emitter voltage in V
R_B=530.0; #Base resistor's resistance in kΩ .
R_C=2.0; #Collector resistor's resistance in kΩ .
#Calculation
#D.C load line equation : VCE=VCC-IC*RC;
#Calculating maximum VCE ,by IC=0;
I_C_Vce_max=0; #Collector current for maximum collector-emitter voltage, in mA
VCE_max=VCC;-I_C_Vce_max*R_C; #Maximum collector-emitter voltage in V
#Calculating maximum collector current IC,by VCE=0;
V_CE_IC_max=0; #Collector-emitter voltage for maximum collector current, in V
I_C_max=(VCC-V_CE_IC_max)/R_C; #Maximum collector current in mA
#Operating point:
#For input circuit, applying Kirchhoff's law, We get,
#VCC=IB*RB + VBE.
#From the above equation,
IB=(VCC-VBE)/R_B; #Base current in mA
IC=beta*IB; #Collector current
#From the output circuit, applying Kirchhoff's law, we get:
VCE=VCC-IC*R_C; #Collector-emitter voltage in V
#Stability factor
SF=beta+1;
#Result
print("Operating point: VCE= %dV and IC=%d mA"%(VCE,IC));
print("Stability factor= %d."%SF);
#plot
limit = plt.gca()
limit.set_xlim([0,10])
limit.set_ylim([0,5])
VCE=[i for i in range(0,(int)(VCC+1))]; #Plot variable for V_CE
IC=[((VCC-i)/(R_C)) for i in (VCE[:])]; #Plot variable for I_C
p=plt.plot(VCE,IC);
plt.xlabel("VCE(V)");
plt.ylabel("IC(mA)");
plt.title("d.c load line");
plt.show(p);
Example 9.5: Page number 202¶
In [6]:
#Variable declaration
VCC=12.0; #Collector supply voltage in V
beta=100.0; #base current amplification factor
I_C_zero_signal=1.0; #zero signal collector current in mA
VBE=0.3; #Base-emitter voltage of Ge transistor in V
#calculations
#Case(i)
I_B_zero_signal=I_C_zero_signal/beta; #Zero signal base current in mA
#applying the Kirchhoff's law along input circuit:
#We get, VCC=IB*RB +VBE
#From the above equation we get,
R_B=(VCC-VBE)/I_B_zero_signal; #Required base resistor's resistance in kΩ
print("Value of base resistor for operating the given Ge transistor at zero signal IC=1mA is = %d kΩ"%R_B);
#Case(ii)
beta=50;
I_B=(VCC-VBE)/R_B; #Base current of another transistor with beta=50, in mA
I_C_zero_signal=beta*I_B; #Zero signal collector current for beta=50 , in mA
print("The new value of zero signal collector current =%.1fmA"%I_C_zero_signal);
Example 9.6:Page number 202-203¶
In [8]:
#Variable declaration
VCC=10.0; #Collector supply voltage in V
VBE=0; #Base emitter voltage in V(considering itas zero due to it's small value)
R_B=1.0; #Base resistor's resistance in MΩ
R_C=2.0; #Collector resistor's resistance in kΩ
R_E=1.0; #Emitter resistor's resistance in kΩ
beta=100.0; #Base current amplification factor
#Calculations
#using Kirchhoff's law in the input circuit, we get:
#VCC=IB*RB +VBE +IE*RE
#Since, IE=(beta +1)*I_B
#From the above equation we get:
I_B=round((VCC-VBE)/((beta + 1)*R_E + R_B*1000),4); #Base current in mA
I_C=round(beta*I_B,2); #Collector current in mA
I_E=I_B+I_C; #Emitter current in mA
#Result
print("Base current =%.4f mA"%I_B);
print("Collector current =%.2f mA"%I_C);
print("Emitter current =%.3f mA"%I_E);
Example 9.7: Page number 203-204¶
In [9]:
#Variable declaration
VCE=8.0; #Collector-emitter voltage at operating point in V
IC=2.0; #Colector current at operating point in mA
VCC=15.0; #Collector supply voltagein V
beta=100.0; #base current amplification factor
VBE=0.6; #base emitter voltage in V
#Calculations
#Applying Kirchhoff's law along the output circuit,
#we get, VCC=VCE+IC*RC.
#So, from above equation we get:
RC=(VCC-VCE)/IC; #Collector resistor's resistance in kΩ .
IB=IC/beta; #Base current in mA
#Applying Kirchhoff's law along the input circuit,
#we get, VCC=IB*RB + VBE
#So, from the above equation:
RB=(VCC-VBE)/IB; #Base resistor's resistance in kΩ .
#Results
print("Collector load =%.1f kΩ ."%RC);
print("Base resistor=%d kΩ ."%RB);
Example 9.8: Page number 204¶
In [10]:
#Variable declaration
VCC=12.0; #Collector supply voltage in V
VBE=0.7; #Base-emitter voltage in V
RB=100.0; #Base resistor's resistance in kΩ
RC=560.0; #Collector resistor's resistance in Ω
beta_25=100.0; #base current amplification factor at 25 degree celsius
beta_75=150.0; #base current amplification factor at 25 degree celsius
#Calculations
#Applying Kirchhoff's law along input circuit, we get
#VCC=IB*RB+VBE
IB=(VCC-VBE)/RB; #Base current at 25 degree celsius, in mA
#For temperature 25 degree celsius
IC_25=beta_25*IB; #Collector current at 25 degree celsius, in mA
#Applying Kirchhoff's alw at the output circuit,
#we get: VCC=IC*RC + VCE
#From the above equation,
VCE_25=round(VCC-(IC_25/1000)*RC,2); #Collector emitter voltage at 25 degree celsius, in V
#For temperature 75 degree celsius
IC_75=round(beta_75*IB,0); #Collector current at 75 degree celsius, in mA
#Applying Kirchhoff's alw at the output circuit,
#we get: VCC=IC*RC + VCE
#From the above equation,
VCE_75=round(VCC-(IC_75/1000)*RC,2); #Collector emitter voltage at 75 degree celsius, in V
change_IC=(IC_75-IC_25)*100.0/IC_25; #percentage change in collector current
change_VCE=(VCE_75-VCE_25)*100.0/VCE_25; #Percentage change in collector-emitter voltage
#Results
print("The percentage change in collector current =%d%%"%change_IC);
print("The percentage change in collector-emitter voltage =%.1f%%"%change_VCE);
Example 9.10: Page number 205¶
In [11]:
#Variable declaration
VCE_max=20.0; #Maximum collector-emitter voltage in V
VBE=0.7; #Base-emitter voltage in V
IC_max=8.0; #Maximum collector current in mA
IB=40.0; #Base current in microampere
#Calculations
#During cut off state the collector-emitter voltage is maximum and equal to collector supply voltage
VCC=VCE_max; #Collector supply voltage in V
#Maximum collector current IC_max=collector supply voltage(VCC)/collector load(RC)
#Collector load(RC)=VCC*IC_max
RC=VCC/IC_max; #Collector load in kΩ .
#Applying Kirchhoff's law along input circuit,
#we get, VCC=IB*RB +VBE.
#From the above equation, we get:
RB=(VCC-VBE)/(IB/1000); #Base resistor's resistance in kΩ .
#Results
print("Collector supply voltage = %dV"%VCC);
print("Collector load=%.1f kΩ ."%RC);
print("Base resistor's resistance=%.1f kΩ ."%RB);
Example 9.12: Page number 208¶
In [12]:
#Variable declaration
VCC=20.0; #Collector supply voltage in V
VEE=-20.0; #Emitter supply voltage in V
RB=100.0; #Base resistor's resistance in kΩ
RC=4.7; #Collector resistor's resistance in kΩ
RE=10.0; #Emitter resistor's resistance in kΩ
VBE=0.7; #Base-emitter voltage in V
beta=85.0; #Base current amplification factor
#Calculations
#Applying Kirchhoff's voltage law along the base-emitter circuit (input circuit),
#we get,IB*RB +IE*RE +VBE -VEE=0.
#Since IB=IC/beta and IC~IE,
#(IE/beta)*RB + IE*RE + VBE + VEE =0.
IE=(-VEE-VBE)/(RE + RB/beta); #Emitter current in mA
IC=IE; #Collector current (approximately equal to emitter current) in mA
#Applying Kirchhoff's law from VCC till collector terminal,
#we get, VCC - IC*RC =VC
VC=VCC-IC*RC; #voltage at collector terminal in V
#Applying Kirchhoff's law from emitter terminal to VEE
#we get, VE -IE*RE =VEE
VE=VEE + IE*RE; #Voltage at emitter treminal in V
VCE=VC-VE; #Collector-emitter voltage in V
#Results
print("The collector current = %.2f mA"%IC);
print("The emitter current = %.2f mA"%IE);
print("The voltage at collector terminal = %.1f V"%VC);
print("The collector-emitter voltage = %.1f V"%VCE);
Example 9.13: Page number 208-209¶
In [13]:
#Variable declaration
VCC=20.0; #Collector supply voltage in V
VEE=-20.0; #Emitter supply voltage in V
RB=100.0; #Base resistor's resistance in kΩ
RC=4.7; #Collector resistor's resistance in kΩ
RE=10.0; #Emitter resistor's resistance in kΩ
beta1=85.0; #Base current amplification factor for case 1
beta2=100.0; #Base current amplification factor for case 1
VBE_1=0.7; #Base emitter voltage for case 1 in V
VBE_2=0.6; #Base emitter voltage for case 2 in V
#Calculations
#For beta=85 and VBE=0.7,
#As calculated in the previous question,
IC_1=1.73; #Collector current in mA.
VCE_1=14.6; #Collector-emitter voltage in V.
#For case (ii)
#beta=100 and VBE=0.6
#Applying Kirchhoff's voltage law along the base-emitter circuit (input circuit),
#we get,IB*RB +IE*RE +VBE -VEE=0.
#Since IB=IC/beta and IC~IE,
#(IE/beta)*RB + IE*RE + VBE +VEE =0.
IE_2=round((-VEE-VBE_2)/(RE + RB/beta2),2); #Emitter current in mA
IC_2=IE_2; #Collector current (approximately equal to emitter current) in mA
#Applying Kirchhoff's law from VCC till collector terminal,
#we get, VCC - IC*RC =VC
VC=round(VCC-IC_2*RC,1); #voltage at collector terminal in V
#Applying Kirchhoff's law from emitter terminal to VEE
#we get, VE -IE*RE =VEE
VE=round(VEE + IE_2*RE,1); #Voltage at emitter treminal in V
VCE_2=VC-VE; #Collector-emitter voltage in V
change_IC= (IC_2-IC_1)*100/IC_1; #%age change in collector current
change_VCE=(VCE_2-VCE_1)*100/VCE_2; #%age change in collector-emitter voltage
#Results
print("Percentage change in collector current =%.1f%%"%change_IC);
print("Percentage change in collector-emitter voltage =%.1f%%"%change_VCE);
Example 9.14: Page number 210¶
In [14]:
#Variable declaration
VCC=20.0; #Collector supply voltage in V
VBE=0.7 #Base-emitter voltage in V
RB=100.0; #Base resistor's resistance in kΩ
RC=1.0; #Collector resistor's resistance in kΩ
beta=100.0; #base current amplification factor
#Calculations
#Applying Kirchhoff's law along input circuit,
#we get, VCC -IC*RC -IB*RB -VBE=0.
#since IC= beta*IB,
#We get,
IB=(VCC-VBE)/(RB + beta*RC); #Base current in mA
IC=beta*IB; #Collector current in mA
#Applying Kirchhoff's law along the output circuit,
#we get, VCC-VCE - IC*RC=0.
#From the above equation,
VCE=VCC-IC*RC; #Collector emitter voltage in V
#Results
print("The operating point : VCE=%.2fV and IC=%.2fmA."%(VCE,IC));
Example 9.15: Page number 210-211¶
In [15]:
#Variable declaration
VCC=12.0; #Collector supply voltage in V
VBE=0.3; #Base emitter voltage in V
IC=1.0; #Collector current in mA
VCE=8.0; #Collector emitter voltage in V
beta=100.0; #Base current amplification factor
#Calculations
#Case(i)
#Applying Kirchhoff's law along the output circuit,
#we get, VCC-IC*RC-VCE=0.
#from the above equation we get,
RC=(VCC-VCE)/IC; #Collector load in kilo ohm
IB=IC/beta; #Base current in mA
#Applying Kirchhoff's law along input circuit
#we get, VCC-VBE-(beta*IB*RC)-IB*RB=0.
#From the above equation we get,
RB=round((VCC-VBE-beta*IB*RC)/IB,0); #Base resistor's resistance in kΩ
#Results
print("The resistance value of base resistor=%d kΩ and collector load= %d kΩ."%(RB,RC));
#Case(ii)
beta=50;
#Applying Kirchhoff's law along input circuit,
#we get, VCC -IC*RC -IB*RB -VBE=0.
#since IC= beta*IB,
#We get,
IB=(VCC-VBE)/(RB + beta*RC); #Base current in mA
IC=beta*IB; #Collector current in mA
#Applying Kirchhoff's law along the output circuit,
#we get, VCC-VCE - IC*RC=0.
#From the above equation,
VCE=round(VCC-IC*RC,1); #Collector emitter voltage in V
#Results
print("The operating point : VCE=%.1fV and IC=%.1fmA."%(VCE,IC));
Example 9.16 : Page number 211¶
In [16]:
#Variable declaration
VCE=2.0; #Collector-emitter voltage at operating point in V
VBE=0.7; #Base-emitter voltage in V
IC=1.0; #Collector current at operating point in mA
beta=100.0; #Base current amplification factor
#Calculations
IB=IC/beta; #Base current in mA
#As, VCE=VCB +VBE
#we get,
VCB=VCE-VBE; #Collector-base voltage in V
RB=VCB/IB; #Base resistor's resistance in kΩ
#Results
print("Value of base resistor's resistance=%d kΩ."%RB);
Example 9.17 : Page number 211-212¶
In [17]:
#Variable declaration
VCC=12.0; #Collector supply voltage in V
VBE=0.7 #Base-emitter voltage in V
RB=400.0; #Base resistor's resistance in kΩ
RC=4.0; #Collector resistor's resistance in kΩ
RE=1.0; #Emitter resistor's resistance in kΩ
beta=100.0; #Base current amplification factor
#Calculations
#Applying Kirchhoff's law along outut circuit,
#we get, VCC -(IC+IB)*RC -IB*RB -VBE - IE*RE=0.
#since IC= beta*IB, IC+IB ~ IC and IE~IC,
#We get, VCC - IC*RC -(IC/beta)*RB -VBE - IE*RE
IC=(VCC-VBE)/(RB/beta + RC + RE); #Collector current current in mA.
IE=IC; #Emitter current in mA
#Applying Kirchhoff's law along the output circuit,
#we get, VCC-VCE - IC*RC -IE*RE=0. (IE~IC)
#From the above equation,
VCE=VCC-IC*(RC+RE); #Collector emitter voltage in V
#Results
print("The operating point : VCE=%.1fV and IC=%.2fmA."%(VCE,IC));
Example 9.18 : Page number 212¶
In [18]:
#Variable declaration
VCC=10.0; #Collector supply voltage in V
RB=100.0; #Base resistor's resistance in kΩ
RC=10.0; #Collector resistor's resistance in kΩ
RE=0; #Emitter resistor's resistance in kΩ
VBE=0.7; #Base-emitter voltage in V
beta=100.0; #Base current amplification factor
#Calculations
#Applying Kirchhoff's law along outut circuit,
#we get, VCC -(IC+IB)*RC -IB*RB -VBE - IE*RE=0.
#since IC= beta*IB, IC+IB ~ IC and IE~IC,
#We get, VCC - IC*RC -(IC/beta)*RB -VBE - IE*RE
IC=(VCC-VBE)/(RC +RB/beta + RE); #Collector current in mA
#Applying Kirchhoff's law along the output circuit,
#we get, VCC-VCE - IC*RC =0. (IE~IC)
#From the above equation,
VCE=VCC-IC*RC; #Collector-emitter voltage in V
#Results
print("The d.c bias values are: VCE=%.2fV and IC=%.3fmA"%(VCE,IC));
Example 9.19: Page number 214-215¶
In [19]:
%matplotlib inline
import matplotlib.pyplot as plt
#Variable declaration
VCC=15.0; #Collector supply voltage in V
R1=10.0; #Resistor R1's resistance in kΩ
R2=5.0; #Resistor R2's resistance in kΩ
RC=1.0; #Collector resistor's resistance in kΩ
RE=2.0; #Emitter resistor's resistance in kΩ
VBE=0.7; #Base-emitter voltage in V
#Calculations
#Applying Kirchhoff's law along output circuit
#VCE=VCC-IC*(RC+RE);
#IC=0, for VCE_max
VCE_max=VCC; #Maximum collector-emitter voltage in V
#VCE=0, for IC_max
IC_max=VCC/(RC+RE); #Maximum collector current in mA
#Operating point
V2=(VCC*R2)/(R1+R2); #Voltage across R2 resistor V
IE=(V2-VBE)/RE; #Emitter current in mA
IC=IE; #Collector current(Approx. equal to emitter current) in mA
VCE=VCC-IC*(RC+RE); #Collector-emitter voltage in V
#Results
print("Collector-emitter voltage at operating point=%.2fV"%VCE);
print("Collector current at operating point = %.2fmA"%IC);
#plot
limit = plt.gca()
limit.set_xlim([0,20])
limit.set_ylim([0,6])
VCE=[i for i in range(0,(int)(VCC+1))]; #Plot variable for V_CE
IC=[((VCC-i)/(RC+RE)) for i in (VCE[:])]; #Plot variable for I_C
p=plt.plot(VCE,IC);
plt.xlabel("VCE(V)");
plt.ylabel("IC(mA)");
plt.title("d.c load line");
plt.show(p);
Example 9.20: Page number 215-216¶
In [20]:
#Variable declaration
VCC=15.0; #Collector supply voltage in V
R1=10.0; #Resistor R1's resistance in kΩ .
R2=5.0; #Resistor R2's resistance in kΩ .
RC=1.0; #Collector resistor's resistance in kΩ .
RE=2.0; #Emitter resistor's resistance in kΩ .
VBE=0.7; #Base-emitter voltage in V
#Calculations
#Using Thevenin's Theorem for replacing circuit consisting of VCC,R1,R2
E0=(VCC*R2)/(R1+R2); #Thevenin's voltage in V
R0=(R1*R2)/(R1+R2); #Thevenin's equivalent resistance in kΩ .
#Applying Kirchhoff' law along thevenin's equivalent circuit,
#E0=IB*R0+VBE+IE*RE;
#Since IE~IC and IC=beta*IB
#IC=(E0-VBE)/(R0/beta +RE);
IC=(E0-VBE)/RE; #(Since R0/beta << RE) collector current in mA
VCE=VCC-IC*(RC+RE); #Collector emitter voltage in V
#Results
print("Collector-emitter voltage at operating point=%.2fV"%VCE);
print("Collector current at operating point = %.2fmA"%IC);
Example 9.21: Page number 216-217¶
In [21]:
#Variable declaration
VCC=12.0; #Collector supply voltage in V
RE=1.0; #Emitter resistor, kΩ .
R1=50.0; #Resistor R1, kΩ .
R2=10.0; #Resistor R2, kΩ .
#Calculations
#(i)
VBE=0.1; #Base-emitter voltage in V
V2=(VCC*R2)/(R1+R2); #Voltage drop across resistor R2, V
IE=(V2-VBE)/RE; #Emitter current in mA
print("(i)Emitter current= %.1fmA"%IE);
#(ii)
VBE=0.3; #Base-emitter voltage in V
V2=(VCC*R2)/(R1+R2); #Voltage drop across resistor R2, V
IE=(V2-VBE)/RE; #Emitter current in mA
print("(ii)Emitter current= %.1fmA"%IE);
Example 9.22: Page number 217¶
In [22]:
#Variable declaration
VCC=20.0; #Collector supply voltage, V
R1=10.0; #Resistor R1, kΩ
R2=10.0; #Resistor R2, kΩ .
RC=1.0; #Collector resistor, kΩ .
RE=5.0; #Emitter resistor, kΩ .
#Calculations
V2=(VCC*R2)/(R1+R2); #Voltage drop across resistor R2, V
#Applying kirchhoff's law from base terminal to emitter resistor
#V2=VBE+IE*RE
#VBE is neglected due to its small value
IE=V2/RE; #Emitter current in mA
IC=IE; #Collector current (approx. equal to emitter current), mA
#Applying Kirchhoff's law along output circuit
VCE=VCC-IC*(RC+RE); #Collector-emitter voltage , V
VC=VCC-IC*RC; #Voltage at collector terminal,V
#Results
print("Emitter current =%dmA"%IE);
print("Collector-emitter voltage=%dV"%VCE);
print("Collector terminal's voltage=%dV"%VC);
Example 9.23: Page number 219-220¶
In [23]:
#Variable declaration
VCC=12.0; #Collector supply voltage, V
VBE=0.7; #Base-emitter voltage, V
beta=50; #Base current amplification factor
R1=150; #Resistor R1, kΩ .
R2=100; #Resistor R2, kΩ .
RC=4.7; #Collector resistor, kΩ .
RE=2.2; #Emitter resistor, kΩ .
#Calculations
#Using Thevenin's theorem, calculating Thevenin's voltage and resistance
E0=(VCC*R2)/(R1+R2); #Thevenin's voltage, V
R0=(R1*R2)/(R1+R2); #Thevenin's resistance, kΩ .
#Applying Kirchhoff' law along thevenin's equivalent circuit,
#E0=IB*R0+VBE+IE*RE;
#Since IE~IC and IC=beta*IB
IB=round((E0-VBE)/(R0+beta*RE),3); #Base current in mA
IC=round(beta*IB,1); #Collector current, mA
#Applying Kirchhoff's law along the output circuit
VCE=VCC-IC*(RC+RE); #Collector-emitter voltage, V
S=(beta+1)*(1+R0/RE)/(beta +1+R0/RE); #Stability factor
#Results
print("Operating point : VCE= %.2fV and IC=%.1fmA"%(VCE,IC));
print("Stability factor=%.1f"%S);
Example 9.24 : Page number 220¶
In [24]:
#Variable declaration
VCC=15.0; #Collector supply voltage, V
VBE=0.7; #Base-emitter voltage , V
beta=100.0; #Base current amplification factor
R1=6.0; #Resistor R1, kΩ .
R2=3.0; #Resistor R2, kΩ .
RC=470.0; #Collector resistor, Ω.
RE=1.0; #Emitter resistor, kΩ .
#Calculations
#Using Thevenin's theorem, calculating Thevenin's voltage and resistance
E0=(VCC*R2)/(R1+R2); #Thevenin's voltage, V
R0=(R1*R2)/(R1+R2); #Thevenin's resistance, kΩ .
#Applying Kirchhoff' law along thevenin's equivalent circuit,
#E0=IB*R0+VBE+IE*RE;
#Since IE~IC and IC=beta*IB
IB=round((E0-VBE)/(R0+beta*RE),3); #Base current in mA
IC=round(beta*IB,1); #Collector current, mA
#Applying Kirchhoff's law along the output circuit
VCE=VCC-IC*(RC/1000+RE); #Collector-emitter voltage, V
S=(beta+1)*(1+R0/RE)/(beta +1+R0/RE); #Stability factor
#Results
print("Operating point : VCE= %.2fV and IC=%.1fmA"%(VCE,IC));
print("Stability factor=%.2f"%S);
Example 9.25 : Page number 221-222¶
In [25]:
#Varaible declaration
VCC=9; #Collector supply voltage, V
VCE=3; #Collector-emitter voltage, V
VBE=0.3; #Base-emitter voltage in V
RC=2.2; #Collector resistor , kΩ .
IC=2; #Collector current, mA
beta=50.0; #Base current amplification factor
#Calculations
IB=IC/beta; #Base current in mA
#According to given relation, I1=10*IB
I1=IB*10; #Current through the resistor R1, mA
#I1=VCC/(R1+R2), .'s LAW
R1_R2_sum=VCC/I1; #Sum of the resistor's R1 and R2, kΩ (OHM'S LAW).
#Applying Kirchhoff's law along the output circuit
#VCC=IC*RC+VCE+IE*RE
#IC~IE
RE=(VCC-IC*RC-VCE)/IC; #Emitter resistor, kΩ .
RE=round(RE*1000,0); #Emittter resistor, Ω .
IE=IC; #Emittter current(approximately equal to collector current), mA
VE=IE*(RE/1000); #Voltage at emitter terminal (OHM's LAW), V
V2=VBE+VE; #Voltage drop across resistor R2, V
R2=V2/I1; #Resistor R2,(OHM's LAW), kΩ .
R1=R1_R2_sum-R2; #Resistor R1, kΩ .
#Results
print("RE=%d Ω., R1=%.2f kΩ . and R2=%.2f kΩ ."%(RE,R1,R2));
Example 9.26 : Page number 222¶
In [26]:
#Variable declaration
VCC=16.0; #Collector supply voltage, V
R2=20.0; #Resistor R2, kΩ
RE=2.0; #Emitter resistor, kΩ
VCE=6.0; #Collector-emitter voltage, V
IC=2.0; #Collector current , mA
VBE=0.3; #Base-emitter voltage,V
alpha=0.985; #Current amplification factor
#Calculations
beta=alpha/(1-alpha); #Base current amplificatioon factor
IE=IC; #Emitter current, mA
IB=IC/beta; #Base current, mA
VE=IE*RE; #Emitter voltage,(OHM's LAW) V
V2=VBE+VE; #Voltage drop across resistor R2,(Kirchhoff's law) V
V_R1=VCC-V2; #Voltage drop across resistor R1, V
I1=V2/R2; #Current through resistor R2 an R1,(OHM's LAW) mA
R1=V_R1/I1; #Resistor R1,(OHM's LAW) kΩ
V_RC=(VCC-VCE-VE); #Voltage across collector resistor, V
RC=V_RC/IC; #Collector resistor,(OHM's LAW) kΩ
#Results
print("R1=%.1f kΩ and RC=%d kΩ."%(R1,RC));
Example 9.27 :Page number 222-223¶
In [27]:
#Variable declaration
VCC=15.0; #Collector supply voltage, V
R1=10.0; #Resistor R1, kΩ
R2=5.0; #Resistor R2, kΩ
RC=1.0; #Collector resistor, kΩ
RE=2.0; #Emitter resistor, kΩ
VBE=0.7; #Base-emitter voltage, V
beta=100; #Base current amplification factor
#Calculations
#Using Thevenin's theorem, calculating Thevenin's voltage and resistance
E0=(VCC*R2)/(R1+R2); #Thevenin's voltage, V
R0=(R1*R2)/(R1+R2); #Thevenin's resistance, kΩ
#Applying Kirchhoff' law along Thevenin's equivalent circuit,
#E0=IB*R0+VBE+IE*RE;
#Since IE~IC and IB=IE/beta,
IE=(E0-VBE)/(R0/beta + RE); #Emitter current , mA
#Calculations
print("The exact value of emitter current in the circuit = %.2fmA."%IE);
Example 2.28: Page number 223-224¶
In [28]:
#Variable declaration
IE=2.0; #Emitter current, mA
IB=50.0; #Base current, mA
VCC=10.0; #Collector supply voltage, V
VBE=0.2; #Base-emitter voltage, V
R2=10.0; #Resistor R2, kΩ
RE=1.0; #Emitter resistance, kΩ
#Calculations
#Applying Kirchhoff's law from the base to the emitter resistor,
V2=VBE+IE*RE; #Voltage at base terminal, V
I2=V2/R2; #Current through the resistor R2, mA
I1=I2+IB/1000; #Current through the resistor R2, mA
V1=VCC-V2; #Voltage drop across the resistor R2
R1=V1/I1; #Resistor R1, kΩ
#Results
print("The value of the resistor R1=%.2f kΩ."%R1);
Example 9.30 :Page number 225-226¶
In [29]:
#Variable declaration
VCC=8.0; #Collector supply voltage, V
RB=360.0; #Base resistor, kΩ
RC=2.0; #Collector resistor, kΩ
VBE=0.7; #Base-emitter voltage, V
beta=100.0; #base current amplification factor
#Calculations
IC_max=VCC/RC; #Maximum collector current, mA
VCE_max=VCC; #Maximum collector voltage, V
#Operating point
#Applying Kirchhoff's law along the input circuit
IB=(VCC-VBE)/RB; #Base current, mA
IC=beta*IB; #Collector current, mA
#Kirchhoff' law along the output circuit
VCE=VCC-IC*RC; #Collector-emitter voltage, V
#Results
print("VCE=%.2fV, is approximately half of VCC=%dV \n therefore it is mid-point biased."%(VCE,VCC));
Example 9.31: page number 226¶
In [30]:
#Variable declaration
VCC=10.0; #Collector supply voltage, V
VBE=0.7; #Base-emitter voltage, V
beta=50.0; #Base current amplification factor
R1=12.0; #Resistor R1, kΩ
R2=2.7; #Resistor R2, kΩ
RC=620.0; #Collector resistor, Ω
RE=180.0; #Emitter resistor, Ω
#Calculations
#Voltage divder rule across R1 and R2
V2=round((VCC*R2)/(R1+R2),2); #Voltage drop across resistor R2, V
IE=round(((V2-VBE)/RE)*1000,2); #Emitter current, mA
IC=IE; #Collector current(Approximately equal to emitter current), mA
print("IC~IE=%.2fmA."%IC);
#Applying Kirchhoff's law along the output circuit
VCE=VCC-(IC/1000)*(RC+RE); #Collector-emitter voltage, V
#Results
print("VCE=%.2fV, is approximately half of VCC=%dV \n therefore it is mid-point biased."%(VCE,VCC));
Example 9.32 : Page number 227¶
In [31]:
from math import sqrt
#Variable declaration
VCC=10.0; #Collector supply voltage, V
IC=10.0; #Collector current, mA
VBE=0.7; #Base-emitter voltage, V
R1=1.5; #Resistor R1, kΩ
R2=680.0; #Resistor R2, Ω
RC=260.0; #Collector resistor, Ω
RE=240.0; #Emitter resistor, Ω
beta_min=100; #Minimum value of base current amplification factor
beta_max=400; #Maximum value of base current amplification factor
#Calculations
#Voltage divder rule across R1 and R2
V2=round((VCC*R2/1000)/(R1+R2/1000),2); #Voltage drop across resistor R2, V
IE=round((V2-VBE)/(RE/1000),0); #OHM' LAW, Emitter current, mA
IC=IE; #Collector current(approx. equal to emitter current),mA
beta_avg=sqrt(beta_min*beta_max); #Average value of base current amplification factor
IB=IE/(beta_avg +1); #Base current, mA
IB=IB*1000; #Base current, 𝜇A
#Results
print("Base current= %.2f 𝜇A"%IB);
Example 9.33 : Page number 227-228¶
In [32]:
#Variable declaration
VEE=12.0; #Emitter supply voltage, V
RC=1.5; #Collector resistor, kΩ
RB=120.0; #Base resistor kΩ
RE=510.0; #Emitter resistor, Ω
VBE=0.7; #Base-emitter voltage, V
beta=60.0; #Base current amplification factor
#Calculations
#Applying Kirchhoff's voltage law,
#IB*RB - VBE - IE*RE +VEE=0
#Since IE~IC and IC=beta*IB,
IB=(VEE-VBE)/(RB + beta*RE/1000); #Base current , mA
IC=round(beta*IB,1); #Collector current, mA
#Applying Kirchhoff's voltage law along output circuit,
VCE=VEE-IC*(RC + RE/1000); #Collector-emitter voltage, V
#Results
print("Operating point : VCE= %.2fV and IC=%.1fmA."%(VCE,IC));
Example 9.34 : Page number 228-229¶
In [33]:
from math import floor
#Variable declaration
VEE=9.0; #Emitter supply voltage, V
RC=1.2; #Collector resistor, kΩ
RB=100.0; #Base resistor ,kΩ
VBE=0.7; #Base-emitter voltage, V
beta=45.0; #Base current amplification factor
#Calculations
#Applying Kirchhoff's voltage law,
#IB*RB + VBE=VEE
#Since IE~IC and IC=beta*IB,
IB=round((VEE-VBE)/RB,3); #Base current , mA
IC=floor(beta*IB*100)/100; #Collector current, mA
#Applying Kirchhoff's voltage law along output circuit,
VCE=VEE-IC*RC; #Collector-emitter voltage, V
#Results
print("Operating point : VCE= %.2fV and IC=%.2fmA."%(VCE,IC));
Example 9.35 : Page number 229¶
In [34]:
#Variable declaration
VCC=16.0; #Collector supply voltage, V
VBE=0.7; #Base-emitter voltage, V
IC=1.0; #Collector current, mA
VCE=6.0; #Collector-emitter voltage, V
beta=150.0; #Base current amplification factor
#Calculations
#For a good design, VE=VCC/10;
VE=VCC/10; #Emitter terminal's voltage, V
#OHM's Law
#And, taking IE~IC
RE=VE/IC; #Emitter resistor, kΩ
#Applying Kirchhoff's voltage law alog output circuit:
#VCC=IC*RC + VCE + VE
RC=(VCC-VCE-VE)/IC; #Collector resistor, kΩ
V2=VE+VBE; #Voltage drop across resistor R2,V
#From the relation I1=10*IB
R2=(beta*RE)/10; #Resistor R2, kilo ohm
#From voltage divider rule across R1 and R2,
#V2=(VCC*R2)/(R1+R2)
R1=(VCC-V2)*R2/V2; #Resistor R1, kΩ
#Results
print("RE=%.1f kΩ , RC=%.1f kΩ, R1=%.0f kΩ and R2=%d kΩ."%(RE,RC,R1,R2));
Example 9.36 : Page number 230-231¶
In [35]:
#Variable declaration
ICBO=5.0; #Collector to base leakage current, microampere
beta=40.0; #Base current amplification factor
IC_zero_signal=2.0; #Zero signal collector current, mA
op_temp=25.0; #operating temperature, degree celsius
temp_risen=55.0; #Temperature risen, degree celsius
temp_ICBO_doubles=10.0; #Temperature after which ICBO doubles, degree celsius
#Calculations
#(i)
ICEO=(beta+1)*ICBO; #Collector to emitter leakage current, microampere
#(ii)
Number_of_times_ICBO_doubled=(temp_risen - op_temp)/temp_ICBO_doubles; #Number of times ICBO doubles
ICBO_final=ICBO*2**Number_of_times_ICBO_doubled; #Final value of collector to base leakage current, microampere
ICEO_final=ICBO_final*(beta + 1); #Final value of collector to emitter leakage current, microampere
IC_zero_signal_55=(ICEO_final/1000) +IC_zero_signal; #Zero signal collector current at 55 degree celius
change=(IC_zero_signal_55-IC_zero_signal)*100/IC_zero_signal; #Percentage change in zero signal collector current
#Result
print("(i) The percentage change in the zero signal collector current=%.0f%%. "%change)
#(iii)
#For the silicon transistor
ICBO=0.1; #Collector to base leakage current, microampere
ICEO=(beta+1)*ICBO; #Collector to emitter leakage current, microampere
Number_of_times_ICBO_doubled=(temp_risen - op_temp)/temp_ICBO_doubles; #Number of times ICBO doubles
ICBO_final=ICBO*2**Number_of_times_ICBO_doubled; #Final value of collector to base leakage current, microampere
ICEO_final=ICBO_final*(beta + 1); #Final value of collector to emitter leakage current, microampere
IC_zero_signal_55=(ICEO_final/1000) +IC_zero_signal; #Zero signal collector current at 55 degree celius
change=(IC_zero_signal_55-IC_zero_signal)*100/IC_zero_signal; #Percentage change in zero signal collector current
#Result
print("(ii) The percentage change in the zero signal collector current=%.1f%%. "%change)
Example 9.37 : Page number 231¶
In [36]:
#Variable declaration
ICBO=0.02 #Collector to base leakage current, 𝜇A
alpha=0.99; #Current amplification factor
IE=1.0; #Emitter current, mA
op_temp=27.0; #operating temperature, degree celsius
temp_risen=57.0; #Temperature risen, degree celsius
temp_ICBO_doubles=6.0; #Temperature after which ICBO doubles, degree celsius
#Calculations
Number_of_times_ICBO_doubled=(temp_risen - op_temp)/temp_ICBO_doubles; #Number of times ICBO doubles
ICBO_55=ICBO*2**Number_of_times_ICBO_doubled; #collector to base leakage current at 55 degree celsius, 𝜇A
IC=alpha*IE + ICBO_55/1000; #Collector current, mA
IB=IE-IC; #Base current, mA
IB=IB*1000; #Base current,𝜇A
#Results
print("Base current at 57 degree celsius=%.1f 𝜇A "%IB);