Chapter 12 : Small signal Amplifiers¶

Example 12.1, Page No 474¶

In [1]:
import math
#initialisation of variables

hfe=50.0
hie=1.0*10**3
hib=20.0
f1=100.0
Rc=3.3*10**3

#Calculations
Re=Rc
print(" required capacitance")
Xc2=hib
C2=1/(2*3.14*f1*Xc2)
print(" voltage gain with emitter terminal completely bypassed to ground")
Av=-(hfe*Rc)/hie
print("voltage gain  when f=100")
Av=-(hfe*Rc)/math.sqrt(((hie**2)+((1+hfe)*Xc2)**2))

#Results
print(" voltage gain when C2 is incorrectly selected as Xc2=Re/10")
Avx=-(hfe*Rc)/math.sqrt(((hie**2)+((1+hfe)*(Re/10))**2))
print('The value of Avx= %.2f ' %(Avx))

 required capacitance
voltage gain with emitter terminal completely bypassed to ground
voltage gain  when f=100
voltage gain when C2 is incorrectly selected as Xc2=Re/10
The value of Avx= -9.79


Example 12.2, Page No 477¶

In [2]:
import math

#initialisation of variables

Vcc=24.0
Ve=5.0
Vce=3.0
Rl=120.0*10**3
Vbe=0.7
Rc=Rl/10.0

#Calculations
Vrc=Vcc-Vce-Ve
Ic=Vrc/Rc
Re=Ve/Ic#use 3.9Kohm standard value to make Ic littel less than design level
Re=3.9*10**3
R2=10*Re
I2=(Ve+Vbe)/R2
R1=(Vcc-Ve-Vbe)/I2

#Results
print('The value of R1= %.2f ' %(R1/10**3))

The value of R1= 125.21


Example 12.3 Page No 477¶

In [3]:
import math

#initialisation of variables

hfe=100.0
Ie=1.3*10**-3
f1=100.0
R1=120.0*10**3
R2=39.0*10**3
rs=600.0

#Calculations
Rl=R1
re=(26*10**-3)/Ie
Xc2=re
C2=1/(2*3.14*f1*Xc2)
hie=(1+hfe)*re
Zi=(R1*R2*hie)/(R1*R2+R1*hie+R2*hie)
C1=1/((2*3.14*f1*((Zi+rs)/10)))
C3=1/(2*3.14*f1*((Rc+Rl)/10))

#Results
print('The value of C3= %.2f mf ' %(C3*10**6))

The value of C3= 0.12 mf


Example 12.5, Page No 484¶

In [4]:
import math
#initialisation of variables
rs=600.0
f1=100.0
Yfs=6000.0*10**-6
R1=4.7*10**6
R2=1.0*10**6
Rd=6.8*10**3
Rl=120*10**3

#Calculations
Xc2=1/Yfs
C2=1/(2*3.14*f1*Xc2)
Zi=(R1*R2)/(R1+R2)
C1=1/(2*3.14*f1*(Zi+rs)/10)
C3=1/(2*3.14*f1*(Rd+Rl)/10)

#Calculations
print('The value of C3= %.2f mF' %(C3*10**6))

The value of C3= 0.13 mF


Example 12.7 Page No 489¶

In [5]:
import math
#initialisation of variables

R1=120.0*10**3
R2=39.0*10**3
hie=2.0*10**3
R7=12.0*10**3
Zo=R7
R5=R1
R6=R2
hfe=100.0

#Calculations
R3=R7
Zl=R1
Zi=(R1*R2*hie)/(R1*R2+R1*hie+R2*hie)
Zi2=(R1*R2*hie)/(R1*R2+R1*hie+R2*hie)
Av1=-(hfe*((R3*Zi2)/(R3+Zi2)))/hie
Av2=-(hfe*((R7*Zl)/(R7+Zl)))/hie
Av=Av1*Av2

#Results
print('The value of Av= %.2f ' %(Av))

The value of Av= 44180.12


Example 12.8 Page No 491¶

In [6]:
import math

#initialisation of variables

Ve1=5.0
Vce1=3.0
Vce2=3.0
Vbe=0.7
Vcc=14.0
Rl=40.0*10**3

#Calculations
Vb2=Ve1+Vce1
Vc1=Vb2
Ve2=Vb2-Vbe
Vr5=Vcc-Ve2-Vce2
R5=Rl/10#use 3.9Kohm satandard value
R5=3.9*10**3
Ic2=Vr5/R5
R6=Ve2/Ic2#use 8.2Kohm as standard and recalculate
R6=8.2*10**3
Ic2=Ve2/R6
Vr3=Vcc-Vc1
print(" Ic1>>Ib2 %select Ic1=1mA")
Ic1=1*10**-3
R3=Vr3/Ic1#use standard value as 5.6Kohm and recalculate Ic1 in order ti keep Vb2=8V
R3=5.6*10**3
Ic1=Vr3/R3
R4=Ve1/Ic1
Vr2=Ve1+Vbe
Vr1=Vcc-Ve1-Vbe
R2=10*R4
I2=(Ve1+Vbe)/R2
R1=(Vr1*R2)/Vr2

#Results
print('The value of R1= %.2f kohm' %(R1/10**3))

 Ic1>>Ib2 %select Ic1=1mA
The value of R1= 67.95 kohm


Example 12.9, Page No 493¶

In [7]:
import math
#initialisation of variables

hfe=50.0
re=26.0
R1=68.0*10**3
R2=47.0*10**3
rs=600.0
f1=75.0
R5=3.9*10**3
Rl=40.0*10**3

#Calculations
hie=(1+hfe)*re
Zi=(R1*R2*hie)/(R1*R2+R1*hie+R2*hie)
Xc1=(Zi+rs)/10
C1=1/(2*3.14*f1*Xc1)
Xc2=.65*re
Xc3=Xc2
C2=1/(2*3.14*f1*Xc2)
C3=C2
Xc4=(R5+Rl)/10
C4=1/(2*3.14*f1*Xc4)

#Results
print('The value of C4= %.2f mf' %(C4*10**6))

The value of C4= 0.48 mf


Example 12.10, Page No 494¶

In [8]:
import math
#initialisation of variables

hfe=50.0
hie=1.3*10**3
R3=5.6*10**3
R5=3.9*10**3
Rl=40.0*10**3

#Calculations
Av1=-(hfe*((R3*hie)/(R3+hie)))/hie
Av2=-(hfe*((R5*Rl)/(R5+Rl)))/hie

#Results
print(" overall voltage gain is Av=Av1*Av2")
Av=Av1*Av2
print('The value of Av= %.2f ' %(Av))

 overall voltage gain is Av=Av1*Av2
The value of Av= 5546.20


Example 12.11 Page No 497¶

In [9]:
import math

#initialisation of variables

Vp=100.0*10**-3
Rl=100.0
Vbe=0.7
Vcc=20.0

#Calculations
ip=Vp/Rl
print("select Ie2>ip")
Ie2=2.0*10**-3
Ve1=5.0
Vce1=3.0
Vb2=Ve1+Vce1
Vc1=Vb2
Ve2=Vb2-Vbe
R5=Ve2/Ie2#use 3.3Kohm standard value
R5=3.3*10**3
Ic1=1*10**-3
Vr3=Vcc-Vb2
R3=Vr3/Ic1
R4=Ve1/Ic1#use 4.7Kohm standard value
R4=4.7*10**3
Vb1=Ic1*R4+Vbe
R2=10*R4
R1=((Vcc-Vb1)*R2)/Vr2

#Results
print('The value of R1= %.2f kohm ' %(R1/10**3))

select Ie2>ip
The value of R1= 120.39 kohm


Example 12.12 Page No 498¶

In [10]:
import math
#initialisation of variables

rs=600.0
Ie1=1.0*10**-3
hfe=50.0
R1=120.0*10**3
R2=47.0*10**3
f1=150.0
Ie2=2.0*10**-3
R5=3.3*10**3
R3=12.0*10**3
Rl=100.0

#Calculations
re=26*10**-3/Ie1
hie=(1+hfe)*re
Zi=(R1*R2*hie)/(R1*R2+R1*hie+R2*hie)
Xc1=(Zi+rs)/10
C1=1/(2*3.14*f1*Xc1)#use 6*10**-6 as standard value
Xc2=.65*re
C2=1/(2*3.14*f1*Xc2)
re2=26*10**-3/Ie2
Zo=(R5*(re2+R3/hfe))/(R5+(re2+R3/hfe))
Xc3=.65*(Rl+Zo)
C3=1/(2*3.14*f1*Xc3)

#Results
print('The value of C3= %.2f mf' %(C3*10**6))

The value of C3= 4.88 mf


Example 12.13 Page No 499¶

In [11]:
import math

#initialisation of variables

Ie2=2.0*10**-3
hfe=50.0
R5=3.3*10**3
Rl=100.0
hfc2=51.0
R3=12.0*10**3

#Calculations
re=26*10**-3/Ie2
hic=hfe*re
Zi2=hic+hfc2*((Rl*R5)/(Rl+R5))
Av1=-(hfe*((R3*Zi2)/(R3+Zi2)))/hie
Av2=1.0

#Results
print("overall voltage gain is Av=Av1*Av2")
Av=Av1*Av2
print('The value of Av= %.2f ' %(Av))

overall voltage gain is Av=Av1*Av2
The value of Av= -143.97


Example 12.14, Page No 503¶

In [12]:
import math

#initialisation of variables

vp=50.0*10**-3
Rl=50.0
Ve2=5.0
Vcc=12.0
Vbe=0.7
hFE=70.0
hfe=100.0
R2=120.0*10**3
f1=150.0
R3=150.0*10**3
R1=5.6*10**3
R4=2.2*10**3

#Calculations
ip=vp/Rl
print("select Ie2>ip")
Ie2=2*10**-3
R4=Ve2/Ie2#use standard 2.2Kohm
R4=2.2*10**3
Ie2=Ve2/R4
Ic1=1*10**-3
Vr1=Vcc-(Vbe+Ve2)
R1=Vr1/Ic1#use 5.6kohm and recalculate
R1=5.6*10**3
Ic1=Vr1/R1
Ib1=Ic1/hFE
hie=hfe*(26*10**-3/Ic1)
hie2=hfe*((26*10**-3)/(2.27*10**-3))
Zi1=(R2*hie)/(R2+hie)
Xc1=Zi1/10
C1=1/(2*3.14*f1*Xc1)
Xc2=R3/100
C2=1/(2*3.14*f1*Xc2)
Zo=(((hie2+R1)/hfe)*R4)/(((hie2+R1)/hfe)+R4)
Xc3=Rl+Zo
C3=1/(2*3.14*f1*Xc3)

#Results
print('The value of C3= %.2f mf' %(C3*10**6))

select Ie2>ip
The value of C3= 9.20 mf


Example 12.15, Page No 407¶

In [13]:
import math
#initialisation of variables

Vgsoff=-6.0
Idss=20.0*10**-3
Yfs=4000.0*10**-6
Id=2.0*10**-3
Vcc=20.0
Zi=500.0*10**3
R2=560.0*10**3
Rl=80.0*10**3
Vbe=0.7
Vce=3.0

#Calculations
Vgs=Vgsoff*(1-math.sqrt(Id/Idss))
Vds=(-Vgsoff)+1-(-Vgs)
Vr3=(Vcc-Vds)/2
Vr4=Vr3
R3=Vr4/Id#use 3.9kohm as standard and recalculate Vr3 and Vr4
R4=R3
R4=3.9*10**3
Vr3=Id*R4
Vr4=Vr3
Vr2=Vr4-(-Vgs)
Vr1=Vcc-Vr2
R1=(Vr1*R2)/Vr2
R6=Rl/10
Vr5=Vr3-Vbe
Vr6=Vcc-Vr5-Vce
Ic2=Vr6/R6
R5=Vr5/Ic2

#Results
print('The value of R5= %.2f kohm' %(R5/10**3))

The value of R5= 5.74 kohm


Example 12.16, Page No 508¶

In [14]:
import math
#initialisation of variables

R1=2.7*10**6
R2=560.0*10**3
f1=150.0
Yfs=8000.0*10**-6
Ie=1.2*10**-3
Rl=80.0*10**3
R6=8.2*10**3

#Calculations
Zi=(R1*R2)/(R1+R2)
Xc1=Zi/10
C1=1/(2*3.14*f1*Xc1)
Xc2=.65/Yfs
C2=1/(2*3.14*f1*Xc2)#use 15pF as standard value
re=26*10**-3/Ie
Xc3=.65*re
C3=1/(2*3.14*f1*Xc3)
Xc4=(R6+Rl)/10
C4=1/(2*3.14*f1*Xc4)

#Results
print('The value of C4= %.2f mf' %(C4*10**6))

The value of C4= 0.12 mf


Example 12.17, Page No 509¶

In [15]:
import math
#initialisation of variables

re=22.0
hfe=100.0
R3=3.9*10**3
Yfs=4000*10**-6
R6=8.2*10**3
Rl=80.*10**3

#Calculations
Zi2=hfe*re
Av1=-Yfs*((R3*Zi2)/(R3+Zi2))
Av2=-(hfe*((R6*Rl)/(R6+Rl)))/Zi2

#Results
print("overall voltage is Av=Av1*Av2")
Av=Av1*Av2
print('The value of Av= %.2f ' %(Av))

overall voltage is Av=Av1*Av2
The value of Av= 1902.09


Example 12.18, Page No 516¶

In [16]:
import math
#initialisation of variables

hFE=60.0
hfe=60.0
hie=1.4*10**3
Rl=70.0*10**3
Vce=3.0
Vbe=.7
Vcc=10.0

#Calculations
Rc2=Rl/10#use 6.8Kohm as standard value
Vrc2=Vcc+Vbe-Vce
Ic=Vrc2/Rc2
Ie=Ic
Re=(Vcc-Vbe)/(2*Ie)#use 4.7 as standard value
Re=4.7*10**3
Rb=Vbe/(10*(Ic/hFE))
Rb1=Rb

#Results
print('The value of Rb= %.2f kohm ' %(Rb/1000))

The value of Rb= 3.82 kohm


Example 12.19, Page No 517¶

In [17]:
import math
#initialisation of variables

f1=60.0
Ie=1.13*10**-3
hfe=60.0
Rb=3.9*10**3
Rl=70.0*10**3
Rc=6.8*10**3

#Calculations
re=26*10**-3/Ie#use 20 as standard value
re=20
hie=hfe*re
Zb=2*hie
Zi=(Rb*Zb)/(Rb+Zb)
C1=1/(2*3.14*f1*Zi)
C2=1/(2*3.14*f1*(Rl/10))
Av=(hfe*((Rc*Rl)/(Rc+Rl)))/(2*hie)

#Results
print('The value of Av= %.2f ' %(Av))

The value of Av= 154.95


Example 12.20, Page No 521¶

In [18]:
import math
#initialisation of variables

Vcc=20.0
Rl=90.0*10**3
hfe=50.0
hie=1.2*10**3
hib=24.0
Vce=3
Vce1=Vce
Ve=5.0
Vbe=0.7

#Calculations
Rc=Rl/10#use 8.2kohm as standard value
Rc=8.2*10**3
Vrc=Vcc-Vce-Vce1-Ve
Ic=Vrc/Rc
Re=Ve/Ic
Re=4.7*10**3#use 4.7 as standard value
R3=10*Re
Vb1=Ve+Vbe
I3=Vb1/R3
Vb2=Ve+Vce+Vbe
Vr2=Vb2-Vb1
R2=Vr2/I3
R1=(Vcc-Vb2)/I3

#Results
print('The value of R1= %.2f kohm ' %(R1/1000))

The value of R1= 93.18 kohm


Example 12.21, Page No 522¶

In [19]:
import math
#initialisation of variables

f1=25.0
R2=24.7*10**3
R3=47.0*10**3
hie=1.2*10**3
hib=24.0
Rc=9.0*10**3
Rl=90*10**3

#Calculations
Zi=(R2*R3*hie)/(R2*R3+R2*hie+R3*hie)
C1=1/(2*3.14*f1*(Zi/10))
C2=1/(2*3.14*f1*(hie/10))
C3=1/(2*3.14*f1*hib)
C4=1/(2*3.14*f1*((Rc+Rl)/10))

#Results
print('The value of C4= %.2f mF' %(C4*10**6))

The value of C4= 0.64 mF


Example 12.22, Page No 525¶

In [20]:
import math
#initialisation of variables

hie=1.0
hfe=50.0
hoe=10.0*10**-6
Cc=5*10**-12
Cp=330*10**-12
Lp=75*10**-6
Rw=1.0
Rl=5.0
hfb=50.0
fo=1.0*10**6

#Calculations
fo=1.0/(2.0*3.14*math.sqrt(Lp*(Cp+Cc)))
print("resonance frequency is %3fHz " %fo)
Zp=Lp/((Cp+Cc)*Rw)
Rc=(1.0/hoe)/1000
RL=(Zp*Rc*Rl)/(Rl*Rc+Rc*Zp+Rl*Zp)
RL1=4.7    #as standard value
Av=(hfb*RL1)/hie
print(" voltage gain is %d " %Av)
Qp=7.6
QL=(2*3.14*fo*Lp)/Rw
print("since QL>Qp")
fo=1
B=fo/Qp

#Results
print("bandwidth is %.2f kHz " %(B*10**3))

resonance frequency is 1004586.461587Hz
voltage gain is 235
since QL>Qp
bandwidth is 131.58 kHz


Example 12.23, Page No 528¶

In [21]:
import math
#initialisation of variables
hie=1.0*10**3
hfe=50.0
hoe=10.0*10**-6
Cc=5.0*10**-12
Cp=330.0*10**-12
Lp=75.0*10**-6
Rw=1.0
Rl=5.0*10**3
fo=1.0*10**6
zP=224.0*10**3
rC=100.0*10**3
K=0.015
Ls=50.0*10**-6

#Calculations
RL=(Zp*Rc)/(Rc+Zp)
print("voltage gain from the input to the primary memory winding")
Avp=(hfe*RL)/hie
Vsp=K*math.sqrt(Ls/Lp)
print("overall voltage gain from the input to teh secondary winding")
Av=Avp*Vsp
Qp=Rc/(2*3.14*fo*Lp)
Ql=471
Q=(Ql*Qp)/(Ql+Qp)
B=fo/Q

#Results
print("bandwidth is %.2f kHz " %(B/10**5))

voltage gain from the input to the primary memory winding
overall voltage gain from the input to teh secondary winding
bandwidth is 47.12 kHz


Example 12.24, Page No 530¶

In [22]:
import math
#initialisation of variables

f=1.0*10**6
L2=50.0*10**-6
K=0.015
L1=75*10**-6
rs=5.0
Rw=1.0
Lp=100.0*10**-6
Cp=330.0*10**-12
Cc=5.0*10**-12
Rc=100.0*10**3
hfe=50.0
hie=1.0*10**3

#Calculations
C2=1/(((2*3.14*f)**2)*L2)
M=K*math.sqrt(L1*L2)
Rs=(((2*3.14*f)**2)*(M)**2)/rs
Rp=Rs+Rw
Zp=Lp/((Cp+Cc)*Rp)
Rl=(Zp*Rc)/(Zp+Rc)
print("voltage gain from the input to primary winding")
Avp=(hfe*Rl)/hie
Vsp=12.2*10**-3
Vos=((2*3.14*f)*L2)/rs

#Results
print("overall voltage gain from the input to secondary winding ")
Av=Avp*Vos*Vsp
print('The value of Av= %.2f ' %(Av))

voltage gain from the input to primary winding
overall voltage gain from the input to secondary winding
The value of Av= 1074.71