# CHAPTER 04 - THE TRANSISTOR AT LOW FREQUENCY¶

## Example E1 - Pg 105¶

In [1]:
# Exa 4.1
import math
# Given data
R1 = 100.*10.**3.;# in ohm
R2 = 10.*10.**3.;# in ohm
h_fe = 50.;
h_oe = 1./40.;# in ohm
R_L = 5.*10.**3.;# in ohm
R_S= 5.*10.**3;# in ohm
h_ie = 1.1*10.**3.;# in ohm
h_re = 2.5*10.**-4.;
R_B = (R1*R2/(R1+R2));# in ohm
A_I = (-h_fe)/(1 + h_oe*R_L);
print '%s %.2f %s' %("The internal current gain is",A_I,"\n");
#Internal input impedance, Zi = Vbe/Ib or
Zi = (h_ie + h_re*A_I*R_L);# in ohm
Zi= Zi*10.**-3.;# in k ohm
print '%s %.2f %s' %("The internal input impedance in k ohm is",Zi,"\n");
Zi= Zi*10.**3.;# in ohm
#Internal voltage gain, Av = Vce/Vbe or
Av = (A_I*R_L)/Zi;
print '%s %.2f %s' %("The internal voltage gain is",Av,"\n");
Ri =round(R_B*Zi/(R_B+Zi));# in ohm
Ri= Ri*10**-3;# in k ohm
print '%s %.2f %s' %("The overall input impedance in k ohm is",Ri,"\n");
Ri= Ri*10**3;# in ohm
# V_S= I_i*R_S+v_be or
VS_by_vbe= Ri/(Ri+R_S);
Avs= Av*VS_by_vbe;
print '%s %.2f %s' %("The overall voltage gain is : ",Avs,"\n")
# R_B*(I_i-I_b)= Zi*I_b or
I_bBYI_i= R_B/(R_B+Zi);
A_IS= A_I*I_bBYI_i;
print '%s %.2f %s' %("The overall current gain is : ",A_IS,"\n")
Rdesh_S= R_B*R_S/(R_B+R_S);# in ohm
Rdesh_S= 3220
I_bByVce= -h_re/(h_ie+Rdesh_S);
Yo= h_oe-h_fe*h_re/(h_ie+Rdesh_S)*10**3;
Zo= 1/Yo;
print '%s %.2f %s' %("The Output impedance in ohm is : ",Zo,"\n")

The internal current gain is -0.40

The internal input impedance in k ohm is 1.10

The internal voltage gain is -1.80

The overall input impedance in k ohm is 0.98

The overall voltage gain is :  -0.30

The overall current gain is :  -0.35

The Output impedance in ohm is :  45.24



## Example E2 - Pg 107¶

In [2]:
# Exa 4.2
import math
# Given data
V_CC = 15.;# in V
R_L = 10.;# in k ohm
Rf = 200.;# in k ohm
R_S = 5.;# in k ohm
Rf2 = Rf;# in k ohm
h_fe = 50.;
V_S= 10.*10.**-3.;# in V
h_oe = 1./40.;# in k ohm
R_L = (R_L*Rf2)/(R_L+Rf2);# in k ohm
Ai = -h_fe/(1.+h_oe*R_L);
print '%s %.2f %s' %("The internal current gain is",Ai,"\n");
#Zi = Vbe/Ib = h_ie +Ai*h_re*R_L;
h_ie = 1.1;# in k ohm
h_re = 2.5*10.**-4.;
Zi = h_ie +Ai*h_re*R_L;# in k ohm
print '%s %.2f %s' %("The internal input impedance in k ohm is",Zi,"\n");
#A_V = Vce/Vbe = (Ai*R_L)/Zi;
A_V = (Ai*R_L)/Zi;
print '%s %.2f %s' %("The internal voltage gain is",A_V,"\n");
Rf1= Rf/(1-A_V)
# Rf1 = Rf/(1-A_V);# in k ohm
#Ri = Vi/Ii = Vbe/Ii = (Rf1*Zi)/(Rf1+Zi);
Ri = (Rf1*Zi)/(Rf1+Zi);# in k ohm
print '%s %.2f %s' %("The overall input impedance in k ohm is",Ri,"\n");
#A_VS = Vo/V_S or
A_VS = A_V*(Ri/(R_S+Ri));
print '%s %.2f %s' %("The overall voltage gain is",A_VS,"\n");
#A_IS = I_L/Ii or
A_IS = (Rf2/(Rf2+R_L))*Ai*(Rf1/(Rf1+Zi));
print '%s %.2f %s' %("The overall current gain is",A_IS,"\n");
Rdesh_S= Rf1*R_S/(Rf1+R_S);# in k ohm
Yo= h_oe-h_re*h_fe/(h_ie+Rdesh_S);# in mho
Zo= 1/Yo;# in ohm
print '%s %.2f %s' %("The output impedance in ohm is : ",Zo,"\n")
Zdesh_o= Rf2*Zo/(Rf2+Zo);# in ohm
print '%s %.2f %s' %("The overall output impedance in ohm is : ",Zdesh_o,"\n");
Vo= V_S*abs(A_VS);# in V
Vo= Vo*10**3;# in mV
print '%s %.2f %s' %("The magnitude of output voltage in mV is : ",Vo,"\n")

The internal current gain is -40.38

The internal input impedance in k ohm is 1.00

The internal voltage gain is -383.14

The overall input impedance in k ohm is 0.34

The overall voltage gain is -24.58

The overall current gain is -13.17

The output impedance in ohm is :  58.66

The overall output impedance in ohm is :  45.36

The magnitude of output voltage in mV is :  245.85



## Example E3 - Pg 108¶

In [3]:
# Exa 4.3
import math
# Given data
h_ic = 2.;# in k ohm
h_fc = -51.;
h_oc = 25.*10.**-6.;# in ohm
h_rc= 1.;
V_CC = 20.;# in V
R1 = 10.;# in k ohm
R2 = 10.;# in k ohm
R_S = 1.;# in k ohm
R_E = 5.;# in k ohm
R_B= 5.;# in k ohm
R_L= 5.;# in k ohm
# (i) Current Gain
Ai = (-h_fc)/(1.+h_oc*R_E*10.**3.);
print '%s %.2f %s' %("The current gain is",Ai,"\n");
# (ii) Input impedance
Zi = h_ic*10**3 + h_rc*Ai*R_E*10**3;# in ohm
Zi = Zi * 10**-3;# in k ohm
print '%s %.2f %s' %("The input impedance in k ohm is",Zi,"\n");
# (iii) Voltage Gain
A_V = (Ai*R_L*10**3)/(Zi*10**3);
A_V = 1;# (approx)
print '%s %.2f %s' %("The voltage gain is",A_V,"\n");
# (iv) Overall Input Impedance
Z_IS = (R_B*Zi)/(R_B+Zi);# in k ohm
print '%s %.2f %s' %("The overall input impedance in k ohm is",Z_IS,"\n");
# (v) Overall voltage gain
A_VS = (A_V*Zi)/(Zi+R_S);
print '%s %.2f %s' %("The overall voltage gain is",A_VS,"\n");
# (vi) Overall current gain
A_IS =Ai*(R_B/(R_B+Zi));
print '%s %.2f %s' %("The overall current gain is",A_IS,"\n");
# (vii) Output impedance
RdasS = (R_S*R_B)/(R_S+R_B);# in k ohm
Yo = h_oc - ( (h_fc*h_rc)/(h_ic*10.**3.+RdasS*10.**3.) );# in mho
Zo = 1./Yo;# in ohm
print '%s %.2f %s' %("The output impedance in ohm is",Zo,"\n");

The current gain is 45.33

The input impedance in k ohm is 228.67

The voltage gain is 1.00

The overall input impedance in k ohm is 4.89

The overall voltage gain is 1.00

The overall current gain is 0.97

The output impedance in ohm is 55.48



## Example E4 - Pg 110¶

In [4]:
# Exa 4.4
# Given data
h_ie = 1.1;# in k ohm
h_re = 2.5*10.**-4.;
h_fe = 50.;
h_oe = 25.*10.**-6.;# in A
V_CC = 15.;# in V
R1 = 20.;# in k ohm
R_C = 2.;# in k ohm
R2 = 10.;# in k ohm
R_S = 1.;# in k ohm
R_E = 1.;# in k ohm
# (i) Current Gain
Ai = -h_fe/(1. + h_oe*R_C*10.**3.);
print '%s %.2f %s' %("The current gain is",Ai,"\n");
# (ii) Input impedance
Zi = (h_ie*10**3) + (h_re*Ai*R_C*10**3);#in ohm
Zi = Zi * 10**-3;# in k ohm
print '%s %.2f %s' %("The input impedance in k ohm is",Zi,"\n");
# (iii) Voltage gain
A_V = (Ai*R_C)/Zi;
print '%s %.2f %s' %("The voltage gain is",A_V,"\n");
# (iv) Overall input impedance
R_B = (R1*R2)/(R1+R2);# in k ohm
Z_IS = (Zi*R_B)/(Zi+R_B);# in k ohm
print '%s %.2f %s' %("The overall input impedance in k ohm is",Z_IS,"\n");
# (v) Overall voltage gain
A_VS = A_V * (Z_IS/(Z_IS+R_S));
print '%s %.2f %s' %("The overall voltage gain is",A_VS,"\n");
# (vi) Overall current gain
A_IS =Ai*(R_B/(R_B+Zi));
print '%s %.2f %s' %("The overall current gain is",A_IS,"\n");

The current gain is -47.62

The input impedance in k ohm is 1.08

The voltage gain is -88.50

The overall input impedance in k ohm is 0.93

The overall voltage gain is -42.56

The overall current gain is -41.00



## Example E5 - Pg 111¶

In [5]:
# Exa 4.5
# Given data
h_ie = 1.1;# in k ohm
h_oe = 25.;# in A/V
h_oe = h_oe * 10.**-6.;# in A/V
h_fe = 50.;
h_re = 2.5*10.**-4.;
R_L = 1.6;# in ohm
R_S = 1.;# in k ohm
V_CC = 15.;# in V
# (i) Current Gain
Ai = -h_fe/(1. + (h_oe*R_L));
print '%s %.2f %s' %("The current gain is",Ai,"\n");
# (ii) Input impedance
Zi = (h_ie*10**3) + (h_re*Ai*R_L);# in ohm
Zi= Zi*10**-3;# in k ohm
print '%s %.2f %s' %("The input impedance in k ohm is",Zi,"\n");
Zi= Zi*10**3;# in ohm
# (iii) Voltage gain
A_V = Ai*R_L/Zi;
print '%s %.2f %s' %("The voltage gain is",A_V,"\n");
# (iv) Power gain
A_P = Ai*A_V;
print '%s %.2f %s' %("The power gain is",A_P,"\n");

The current gain is -50.00

The input impedance in k ohm is 1.10

The voltage gain is -0.07

The power gain is 3.64



## Example E6 - Pg 112¶

In [6]:
# Exa 4.6
# Given data
h_fe = 150.;
Beta_dc = h_fe;
h_ie = 1.*10.**3.;# in ohm
h_re = 0;
h_oe = 0;
V_CC = 18.;# in V
V_BE= 0.7;# in V
R1 = 100.*10.**3.;# in ohm
R2 = 50.*10.**3.;# in ohm
R_C = 1.*10.**3.;# in ohm
R_E = 0.5*10.**3.;# in ohm
V_Th = (V_CC/(R1+R2))*R2;# in V
R_Th =(R1*R2)/(R1+R2);# in ohm
# V_Th - I_B*R_Th - V_BE - (1+Beta)*-I_B*R_E = 0;
I_B = (V_Th-V_BE)/( R_Th + (1+Beta_dc)*R_E);# in A
#I_C = I_CQ = Beta*I_B;
I_C = Beta_dc*I_B;# in A
I_CQ = I_C;# in A
I_CQ= I_CQ*10.**3.;# in mA
print '%s %.2f %s' %("The value of I_CQ in mA is",I_CQ,"\n");
I_E = (1+Beta_dc)*I_B;# in mA
# V_CC - I_C*R_C - V_CE - I_E*R_E = 0;
V_CE = V_CC - (I_C*R_C) - (I_E*R_E);# in V
print '%s %.2f %s' %("The value of V_CE in V is",V_CE,"\n");
R_L =R_C;# in ohm
Ai = -h_fe/(1+(h_oe*R_L));
print '%s %.2f %s' %("The current gain is ",Ai,"\n");
Zi = h_ie + h_re*Ai*R_L;# in ohm
Zi= Zi*10**-3;# in k ohm
print '%s %.2f %s' %("The input impedance in k ohm is",Zi,"\n");
Zi= Zi*10**3;# in ohm
A_V = Ai*(R_L/Zi);
print '%s %.2f %s' %("The voltage gain is",A_V,"\n");
R_B= (R1*R2)/(R1+R2);# in ohm
Z_IS =(Zi*R_B)/(Zi+R_B);# in ohm
Z_IS= Z_IS*10**-3;# in kohm
print '%s %.2f %s' %("The overall input impedance in k ohm is",Z_IS,"\n");
Z_IS= Z_IS*10**3;# in ohm
A_VS =A_V*(Z_IS/Z_IS);
print '%s %.2f %s' %("The overall voltage gain is",A_VS,"\n");
A_IS =Ai * (R_B/(R_B+Zi));
print '%s %.2f %s' %("The overall current gain is",A_IS,"\n");

The value of I_CQ in mA is 7.30

The value of V_CE in V is 7.02

The current gain is  -150.00

The input impedance in k ohm is 1.00

The voltage gain is -150.00

The overall input impedance in k ohm is 0.97

The overall voltage gain is -150.00

The overall current gain is -145.63