# Chapter 4 : Transistor Amplifiers¶

## Example : 4.1 - Page No : 105¶

In [48]:
%matplotlib inline
import numpy as np
import pylab as pl
from __future__ import division
#Given data
V_CC = 20 # in V
I_C= 2*10**-3 # in A
I_CQ= I_C # in A
I_E=I_C # in A
R_C = 3 # in k ohm
R_C = R_C * 10**3 # in ohm
R_L = 12 # in k ohm
R_L = R_L * 10**3 # in ohm
R_E = 2 # in k ohm
R_E = R_E * 10**3 # in ohm
V_CE= np.arange(0,20,0.1) # in V
I_C_sat= (V_CC-V_CE)/(R_C+R_E)*10**3 # in mA
pl.plot(V_CE,I_C_sat)
Rac= R_C*R_L/(R_C+R_L) # in ohm
V_CEQ= V_CC-I_CQ*(R_C+R_E) # in V
I_Csat= I_CQ+V_CEQ/Rac # in A
I_Csat=I_Csat*10**3 # in mA
V_CEoff= V_CEQ+I_CQ*Rac # in V
pl.plot([V_CEoff,0],[0,I_Csat], 'r')
pl.xlabel("V_CE in volts")
pl.ylabel("I_C in mA")
pl.plot([0,10],[2,2],'--')
pl.plot([10,10],[0,2],'--')
pl.show()
# Maximum peak output signal
POSmax= I_CQ*Rac # in V
# Peak-to-peak value of output signal
PP_out_sig= 2*POSmax # in V
print "Peak-to-peak value of output signal = %0.1f volts " %PP_out_sig
print "DC and AC load line shown in figure."

Peak-to-peak value of output signal = 9.6 volts
DC and AC load line shown in figure.


## Example : 4.2 - Page No : 106¶

In [24]:
 #Given data
delV_BE = 0.02 # in V
delI_B = 10 # in µA
delI_B = delI_B * 10**-6 # in A
delI_C = 1 # in mA
delI_C = delI_C * 10**-3 # in A
R_C = 5 # in k ohm
R_C = R_C * 10**3 # in ohm
R_L = 10 # in k ohm
R_L = R_L * 10**3 # in ohm
Zin = delV_BE/delI_B # in ohm
Zin= Zin*10**-3 # in k ohm
print "The input impedance = %0.f k ohm " %Zin
Zin= Zin*10**3 # in ohm
Beta = delI_C/delI_B # unit less
print "The current gain = %0.f " %Beta
Rac = (R_C*R_L)/(R_C+R_L) # in ohm
Rac= Rac*10**-3 # in k ohm
print "The AC load resistance = %0.3f k ohm " %Rac
Rac= Rac*10**3 # in ohm
Rin = 2 # in k ohm
Rin = Rin * 10**3 # in ohm
Av = Beta*(Rac/Rin)
print "The voltage gain = %0.1f " %Av
Ai = 100 # unit less
Ap = Av*Ai # unit less
print "The power gain = %0.f " %Ap

The input impedance = 2 k ohm
The current gain = 100
The AC load resistance = 3.333 k ohm
The voltage gain = 166.7
The power gain = 16667


## Example : 4.3 - Page No : 107¶

In [25]:
 #Given data
Alpha = 0.988 # unit less
I_E = 1.2 # in mA
I_E = I_E * 10**-3 # in A
I_CO = 0 # in A
I_C = Alpha*I_E + I_CO # in A
I_B = I_E - I_C # in A
I_B = I_B * 10**6 # in µA
print "The base current = %0.1f µA " %I_B

The base current = 14.4 µA


## Example : 4.4 - Page No : 107¶

In [26]:
 #Given data
I_B = 45 # in µA
I_B = I_B * 10**-6 # in A
I_C = 5.45 # in mA
I_C = I_C * 10**-3 # in A
I_E = I_B+I_C # in A
I_E= I_E*10**3 # in mA
print "The value of I_E = %0.3f mA " %I_E
I_E= I_E*10**-3 # in A
Alpha = I_C/I_E # unit less
print "The value of Alpha = %0.4f " %Alpha
Beta = I_C/I_B # unit less
print "The value of Beta = %0.f " %Beta
I_C = 10 # in mA
I_C = I_C * 10**-3 # in A
I_B = I_C/Beta # in A
I_B = I_B * 10**6 # in µA
print "The required base current = %0.1f µA " %I_B

The value of I_E = 5.495 mA
The value of Alpha = 0.9918
The value of Beta = 121
The required base current = 82.6 µA


## Example : 4.5 - Page No : 112¶

In [27]:
 #Given data
delV_EB = 200 # in mV
delI_E = 5 # in mA
# Dynamic input resistance for CB configuration,
r_in = delV_EB/delI_E # in ohm
print "The dynamic input resistance of transistor = %0.f ohm " %r_in

The dynamic input resistance of transistor = 40 ohm


## Example : 4.6 - Page No : 112¶

In [28]:
from __future__ import division
#Given data
R_L = 4 # in k ohm
R_L = R_L * 10**3 # in ohm
V_across_RL = 3 # in V
I_C = V_across_RL/R_L # in A
I_C = I_C * 10**3 # in mA
Alpha = 0.96 # unit less
I_E = I_C/Alpha # in mA
I_B = I_E - I_C # in mA
print "The base current = %0.2f mA " %I_B

The base current = 0.03 mA


## Example : 4.7 - Page No : 113¶

In [29]:
 #Given data
I_E = 3 # in mA
I_CO = 10 # in µA
I_CO = I_CO * 10**-3 # in mA
Alpha = 0.98 # unit less
I_C = (Alpha*I_E) + I_CO # in mA
print "The collector current = %0.2f mA " %I_C
I_B = I_E - I_C # in mA
print "The base current = %0.2f mA " %I_B

The collector current = 2.95 mA
The base current = 0.05 mA


## Example : 4.8 - Page No : 113¶

In [30]:
 #Given data
I_E = 2 # in mA
I_C = 1.97 # in mA
I_B = I_E-I_C # in mA
print "The base current = %0.2f mA " %I_B
I_CO = 12.5 # in µA
I_CO = I_CO * 10**-3 # in mA
Alpha = (I_C-I_CO)/I_E # unit less
print "The current gain = %0.3f " %Alpha

The base current = 0.03 mA
The current gain = 0.979


## Example : 4.9 - Page No : 116¶

In [31]:
 #Given data
delV_BE = 250 # in mV
delV_BE = delV_BE * 10**-3 # in V
delI_B = 1 # in mA
delI_B = delI_B * 10**-3 # in A
r_in = delV_BE/delI_B # in ohm
print "The dynamic input resistance = %0.f ohm " %r_in

The dynamic input resistance = 250 ohm


## Example : 4.10 - Page No : 116¶

In [32]:
 #Given data
V1 = 10 # in V
V2 = 5 # in V
I1 = 5.8 # in mA
I2 = 5 # in mA
delV_C = V1-V2 # in V
delI_C = I1-I2 # in mA
r_out = delV_C/delI_C # in k ohm
print "The dynamic output resistance = %0.2f k ohm " %r_out

The dynamic output resistance = 6.25 k ohm


## Example : 4.11 - Page No : 117¶

In [33]:
 #Given data
V_CC = 8 # in V
I_CR_C = 0.5 # in V
R_C = 800 # in ohm
V_CE = V_CC - I_CR_C # in V
print "The collector emitter voltage = %0.1f V " %V_CE
I_C = I_CR_C/R_C # in A
Alpha = 0.96 # unit less
Beta = Alpha/(1-Alpha)
I_B = I_C/Beta # in A
I_B = I_B * 10**6 # in µA
print "The Base current = %0.f µA " %I_B

The collector emitter voltage = 7.5 V
The Base current = 26 µA


## Example : 4.12 - Page No : 117¶

In [34]:
 #Given data
I_E = 5 # in mA
I_C = 4.95 # in mA
I_CEO = 200 # in µA
I_B = I_E-I_C # in mA
Beta_dc = I_C/I_B # unit less
print "The value of base current = %0.f µA" %(I_B*10**3)
print "The value of Beta_dc = %0.f " %Beta_dc
Alpha_dc = Beta_dc/(1+Beta_dc) # unit less
I_CBO = I_CEO * (1-Alpha_dc) # in µA
print "The collector-to-base leakage cuurent = %0.f µA " %I_CBO

The value of base current = 50 µA
The value of Beta_dc = 99
The collector-to-base leakage cuurent = 2 µA


## Example : 4.13 - Page No : 117¶

In [35]:
 #Given data
I_B = 25 # in µA
I_B = I_B * 10**-6 # in A
I_CBO = 100 # in nA
I_CBO = I_CBO * 10**-9 # in A
Beta = 100 # unit less
I_C = (Beta*I_B) + ((Beta+1)*I_CBO) # in A
I_C= I_C*10**3 # in mA
print "The value of I_C = %0.2f mA " %I_C
I_C= I_C*10**-3 # in A
I_E = I_C + I_B # in A
I_E= I_E*10**3 # in mA
print "The value of I_E = %0.3f mA " %I_E
I_E= I_E*10**-3 # in A
Alpha = Beta/(1+Beta) # unit less
print "The value of Alpha = %0.2f " %Alpha
I_CEO = I_CBO/(1-Alpha) # in A
I_CEO = round(I_CEO *10**6) # in µA
print "The value of I_CEO = %0.f µA " %I_CEO

The value of I_C = 2.51 mA
The value of I_E = 2.535 mA
The value of Alpha = 0.99
The value of I_CEO = 10 µA


## Example : 4.14 - Page No : 124¶

In [36]:
 #Given data
R1= 4 # in ohm
R2= 8 # in ohm
R3= 8 # in ohm
i1= 1 # in A (assumed)
h11= R1+R2*R3/(R2+R3) # in ohm
print "The value of h11 = %0.f ohm " %h11
i2= -1/2*i1 # in A
h21= i2/i1 # unit less
print "The value of h21 = %0.1f " %h21
v2= 1 # in V (assumed)
i2= v2/(R3+R2) # in A
v1= v2/2 # in V
h12= v1/v2 # unit less
print "The value of h12 = %0.1f " %h12
h22= i2/v2 # in s
print "The value of h22 = %0.4f s " %h22

The value of h11 = 8 ohm
The value of h21 = -0.5
The value of h12 = 0.5
The value of h22 = 0.0625 s


## Example : 4.15 - Page No : 127¶

In [37]:
 #Given data
Ib = 20 # in µA
Ib = Ib * 10**-6 # in A
I_C = 1 # in mA
I_C = I_C * 10**-3 # in A
Vbe = 22 # in mV
Vbe = Vbe * 10**-3 # in V
Vce = 0 # in V
h_ie = Vbe/Ib # in ohm
h_ie = h_ie * 10**-3 # in k ohm
print "The value of h_ie = %0.1f k ohm " %h_ie
h_fe = I_C/Ib # unit less
print "The value of h_fe = %0.f " %h_fe
Ib = 0
Vbe = 0.25 # in mV
Vbe = Vbe * 10**-3 # in V
I_C = 30 # in µA
I_C = I_C * 10**-6 # in A
Vce = 1 # in V
h_re = Vbe/Vce # unit less
print "The value of h_re = %0.1e " %h_re
h_oe = I_C/Vce # in S
h_oe = h_oe * 10**6 # in µS
print "The value of h_oe = %0.f µS " %h_oe

The value of h_ie = 1.1 k ohm
The value of h_fe = 50
The value of h_re = 2.5e-04
The value of h_oe = 30 µS


## Example : 4.16 - Page No : 133¶

In [38]:
 #Given data
h_fe = 50 # unit less
h_ie = 0.83 # in k ohm
h_ie = h_ie * 10**3 # in ohm
h_fb = -h_fe/(1+h_fe) # unit less
print "The current gain = %0.2f " %h_fb
h_ib = h_ie/(1+h_fe) # in ohm
print "The input impedance = %0.2f ohm " %h_ib

The current gain = -0.98
The input impedance = 16.27 ohm


## Example : 4.17 - Page No : 133¶

In [39]:
 #Given data
h_ie = 2600 # in ohm
h_fe = 100
h_re = 0.02*10**-2
h_oe = 5*10**-6 # in S
h_ic = h_ie # in ohm
print "The value of h_ic = %0.f ohm " %h_ic
h_fc = -(1+h_fe)
print "The value of h_fc = %0.f " %h_fc
h_rc = 1 - h_re
h_rc = 1
print "The value of h_rc = %0.f " %h_rc
h_oc = h_oe # in S
print "The value of h_oc = %0.e S " %h_oc

The value of h_ic = 2600 ohm
The value of h_fc = -101
The value of h_rc = 1
The value of h_oc = 5e-06 S


## Example : 4.18 - Page No : 137¶

In [40]:
 #Given data
h_ie = 1000 # in ohm
h_fe = 50 # unit less
h_re = 2.5*10**-4 # unit less
h_oe = 25*10**-6 # in A/V
R_L = 10 # in k ohm
R_L = R_L * 10**3 # in ohm
Rs = 100 # in ohm
Ai = -h_fe/(1 + (h_oe*R_L)) # unit less
print "The current gain = %0.f " %Ai
Rin = h_ie - ( (h_re*h_fe)/(h_oe+(1/R_L)) ) # in ohm
print "The input resistance = %0.f ohm " %Rin
Av = Ai*(R_L/Rin) # unit less
print "The voltage gain = %0.2f " %Av
Ais = Ai * (Rs/(Rin+Rs)) # unit less
Avs = Av*(Rin/(Rin+Rs)) # unit less
Gout = h_oe - ( (h_fe*h_re)/(h_ie+Rs) ) # in S
Rout = 1/Gout # in ohm
Rout = Rout * 10**-3 # in k ohm
print "The output resistance = %0.1f k ohm " %Rout
Ap = Avs*Ais # unit less
print "The power gain = %0.f " %Ap

The current gain = -40
The input resistance = 900 ohm
The voltage gain = -444.44
The output resistance = 73.3 k ohm
The power gain = 1600


## Example : 4.19 - Page No : 137¶

In [41]:
 #Given data
h_ie = 2 # in k ohm
h_ie = h_ie * 10**3 # in ohm
h_re = 2*10**-4 # unit less
h_fe = 50 # unit less
h_oe = 20*10**-6 # in A/V
R_L = 4 # in k ohm
R_L = R_L * 10**3 # in ohm
Rs = 200 # in ohm
Ai = -h_fe/( 1+(h_oe*R_L) ) # unit less
print "The value of Ai = %0.1f " %Ai
Ri = h_ie - ( (h_re*h_fe)/( h_oe+(1/R_L) ) ) # in ohm
print "The value of Ri = %0.f ohm " %Ri
#Av = -h_fe/( (h_oe + (1/R_L))*Rin ) = Ai*(R_L/Rin)
Av = Ai*(R_L/Ri) # unit less
print "The value of Av = %0.2f " %Av
Gout = h_oe - ( (h_fe*h_re)/(h_ie+Rs) ) # in S
Rout = 1/Gout # in ohm
Rout = Rout * 10**-3 # in k ohm
print "The value of Rout = %0.1f k ohm" %Rout
Ais = Ai * (Rs/(Ri+Rs) ) # unit less
Avs = Av * (Ri/(Ri+Rs)) # unit less
Ap = Av*Ai # unit less
print "The value of Ap = %0.1f " %Ap

The value of Ai = -46.3
The value of Ri = 1963 ohm
The value of Av = -94.34
The value of Rout = 64.7 k ohm
The value of Ap = 4367.6


## Example : 4.20 - Page No : 138¶

In [42]:
 #Given data
R_S = 200 # in ohm
R_L = 1200 # in ohm
h_ib = 24 # in ohm
h_rb = 4*10**-4 # unit less
h_fb = -0.98 # unit less
h_ob = 0.6 # in µA/V
h_ob = h_ob * 10**-6 # in A/V
Ai = -h_fb/(1+(h_ob*R_L)) # unit less
print "The current gain = %0.3f " %Ai
Ri = h_ib + (h_rb*Ai*R_L) # in ohm
print "The input impedance = %0.2f ohm " %Ri
Av = round((Ai*R_L)/Ri) # unit less
print "The Voltage gain = %0.f " %Av
Ais = (Ai*R_S)/(Ri+R_S) # unit less
print "The overall current gain = %0.3f " %Ais

The current gain = 0.979
The input impedance = 24.47 ohm
The Voltage gain = 48
The overall current gain = 0.873


## Example : 4.21 - Page No : 144¶

In [43]:
 #Given data
g_m = 2500 # in µS
g_m = g_m * 10**-6 # in S
R_L = 12 # in k ohm
R_L = R_L * 10**3 # in ohm
#Av = -g_m*(r_d||R_D||R_L)
Av = -g_m*R_L
print "The voltage gain = %0.f " %Av

The voltage gain = -30


## Example : 4.22 - Page No : 144¶

In [44]:
 #Given data
R_D = 5 # in k ohm
R_D = R_D * 10**3 # in ohm
r_d = 35 # in k ohm
r_d = r_d * 10**3 # in ohm
miu = 50 # amplifier factor
g_m = miu/r_d # in S
Av = -g_m*( (r_d*R_D)/(r_d+R_D) )
print "The voltage gain = %0.2f " %Av
Rout = (R_D*r_d)/(R_D+r_d) # in  ohm
Rout= Rout*10**-3 # in k ohm
print "The output resistance = %0.3f k ohm " %Rout

The voltage gain = -6.25
The output resistance = 4.375 k ohm


## Example : 4.23 - Page No : 145¶

In [45]:
 #Given data
V_GS = -1.0 # in V
V_DS = 4.0 # in V
I_DS = 1 # in mA
I_DS = I_DS * 10**-3 # in A
I_G = 0 # in A
R_G = 500 # in k ohm
R_G = R_G * 10**3 # in ohm
V_DD = 10 # in V
V_DS = 4 # in V
V_G = I_G*R_G # in V
Vs = V_G-V_GS # in V
R_S = Vs/I_DS # in ohm
R_S= R_S*10**-3 # in k ohm
print "The value of R_S = %0.f k ohm " %R_S
R_S= R_S*10**3 # in ohm
# V_DD = I_DD*R_D + V_DS+ I_DS*R_S = I_DS*(R_D+R_S) + V_DS
R_D = ((V_DD-V_DS)/I_DS)-R_S # in ohm
R_D = R_D * 10**-3 # in k ohm
print "The value of R_D = %0.f k ohm " %R_D

The value of R_S = 1 k ohm
The value of R_D = 5 k ohm


## Example : 4.24 - Page No : 145¶

In [46]:
 #Given data
V_GS = -1 # in V
V_DS = -4 # in V
I_DS = 1 # in mA
I_DS = I_DS * 10**-3 # in A
g_m = 5*10**-3 # in mhos
Rds = 20 # in k ohm
Rds = Rds * 10**3 # in ohm
R_S = 1 # in k ohm
R_S = R_S * 10**3 # in ohm
R_D = 5 # in  k ohm
R_D = R_D * 10**3 # in ohm
#Av = Vout/Vin  = -g_m*(r_d||R_D||R_L) = -g_m*((R_D*Rds)/(R_D+Rds))
Av = -g_m*((R_D*Rds)/(R_D+Rds))
print "The voltage gain = %0.f " %Av
R_G = 500 # in k ohm
R_G  = R_G * 10**3 # in ohm
Rin = R_G # in ohm
Rin= Rin*10**-3 # in k ohm
print "The value of Rin = %0.f k ohm " %Rin
Rin= Rin*10**3 # in ohm
Rout = (R_D*Rds)/(R_D+Rds) # in ohm
Rout= Rout*10**-3 # in k ohm
print "The value of Rout = %0.f k ohm " %Rout

The voltage gain = -20
The value of Rin = 500 k ohm
The value of Rout = 4 k ohm


## Example : 4.25 - Page No : 147¶

In [47]:
 #Given data
R1 = 4 # in M ohm
R2 = 2 # in Mohm
R_G = (R1*R2)/(R1+R2) # in Mohm
Zin = R_G # in Mohm
print "The input impedance = %0.2f Mohm " %Zin
R_S = 2.5 # in k ohm
R_S = R_S * 10**3 # in ohm
R_L = 25 # in k ohm
R_L =  R_L * 10**3 # in ohm
g_m = 2500 # in µS
g_m = g_m * 10**-6 # in S
Zout = (R_S*(1/g_m))/(R_S+(1/g_m)) # in ohm
print "The output impedance = %0.f ohm " %Zout
Av = g_m*((R_S*R_L)/(R_S+R_L))/( 1+g_m*((R_S*R_L)/(R_S+R_L)) ) # unite less
print "The voltage gain = %0.2f " %Av

The input impedance = 1.33 Mohm
The output impedance = 345 ohm
The voltage gain = 0.85