Chapter 4: SMALL SIGNAL AMPLIFIERS-FREQUENCY RESPONSE

Example 4.1,Page number 217

In [3]:
import math

#Variable declaration
Vs=1.               #source voltage(V)
C=100*10**-6        #value of capacitance(uF)  
r1=1                #resistance 1(k ohms)
r2=4                #resistance 2(k ohms)
R=5                 #total resistance,R=r1+r2

#Calculations
Imax=Vs/(r1+r2)*10**3        #maximum current(uA)
fc=1/(2*(math.pi)*C*R)        #critical frequency(Hz) 
                             #As w*C*R=1 and w=2*pi*f
f=10*fc                      #lowest frequency(Hz)

#Results
print"maximum current",Imax,"uA"
print"critical frequency",round((fc/1E+3),3),"Hz"
print"lowest frequency",round((f/1E+3),2),"Hz"

maximum current 200.0 uA
critical frequency 0.318 Hz
lowest frequency 3.18 Hz

Example 4.2,Page number 218

In [1]:
import math

#Variable declaration
C=100*10**-6     #capacitance(uF)
Rg=1.            #galvanometer resistance(k oms)
Rl=4.            #load resistance(k ohms)

#Calculations
Rth=(Rg*Rl)/(Rg+Rl)      #thevinine's equivalent resistance
fc=1/(2*(math.pi)*C*Rth)  #critical frequency(Hz)
f=fc*C                    #lowest frequency(Hz)

#Results
print"lowest frequency at which the point A gets grounded is",round((f/1E-2),1),"Hz"

lowest frequency at which the point A gets grounded is 19.9 Hz

Example 4.3,Page number 220

In [12]:
import math

#Variable declaration
rpi=600               #dynamic junction resistance(ohms)
beta=100              #common emitter current gain
Vs=5.                 #source voltage(V)
Rs=400                #source resistance(ohms)
R=10                  #resistance(k ohms)

#Calculations
Ib=Vs/(Rs+rpi)       #base current(uA)  
Vo=R*beeta*Ib        #output voltage(V)
Rin=rpi              #input resistance(ohms)
Rout=R               #output ewsistance(k ohms)

#Results
print"output voltage is",Vo,"V"
print"input resistance",Rin,"ohms"
print"output resistance",Rout,"k ohms"

output voltage is 5.0 V
input resistance 600 ohms
output resistance 10 k ohms

Example 4.4,Page number 220

In [19]:
#Variable declaration
gm=1.                    #transconductance(mS)
rd=40                    #dynamic drain resistance(k ohms)  
Rd1=40                   #JFET 1 drain resistance(k ohms) 
Rd2=10                   #JFET 2 drain resistance(k ohms) 

#Calculations
Avo=(-gm*((rd*Rd1)/(rd+Rd1)))*(-gm*((rd*Rd2)/(rd+Rd2)))             #voltage gain

#Results
print"Avo is",Avo

Avo is 160.0

Example 4.5,Page number 222

In [24]:
#Variable declaration
beta=125           #common emitter current gain
rpi=2.5            #dynamic junction resistance(k ohms)
rd=40              #dynamic drain resistance(k ohms)   
gm=2               #transconductance(mS) 
Vs=1               #assume,source voltage(V)
Rs=10              #source resistance(k ohms)
Rc=1               #collector resistance(k ohms)
rb=2               #resistance(k ohms)
Vgs=1              #gate to source voltage(V)

#Calculations
#Part a
R=(rd*Rs)/(rd+Rs)      #equivalent resistance(k ohms)
Ib=gm*Vgs*(R/(rpi+R))  #base current(mA)
Vo=beeta*Ib*Rc         #output voltage(V)   
Avo=Vo                 #voltage gain

#Part b
Ib1=Vs/(rb+rpi)        #base current(mA) after interchanging stages of JFET and BJT  
Vgs1=beeta*Ib1*Rc      #gate to source voltage(V) after interchanging stages of JFET and BJT
Vo1=gm*Vgs1*R          #output voltage(V) after interchanging stages of JFET and BJT
Avo1=Vo1               #voltage gain after interchanging stages of JFET and BJT

#Results
print"Avo is",round(Avo,1)
print"Avo1 when BJT and FET stages are reversed is",round(Avo1)

Avo is 190.5
Avo1 when BJT and FET stages are reversed is 444.0

Example 4.6,Page number 226

In [37]:
import math

#Variable declaration
Cc1=1*10**-6                 #coupling capacitor 1(uF)
Cc2=1*10**-6                 #coupling capacitor 2 (uF)  
Rs=10**3                     #source resistance(k ohms)
rpi=2*10**3                  #dynamic junction resistance(k ohms)
Rc=4500                      #collector resistance(ohms)
Rl=9*10**3                   #load resistance(k ohms)
w=100                        #corner frequency(rad/s)

#Calculations
w11=1/(Cc1*(Rs+rpi))                    #corner frequency input circuit (rad/s)
w12=1/(Cc2*(Rc+Rl))                     #corner frequency output circuit(rad/s)
f=w11/(2*(math.pi))                     #lower cutoff frequency(Hz)
Zin=complex((Rs+rpi),-(1/(w*Cc1)))      #input impedance(k ohms)   
Zout=complex(Rc,-(1/(w*Cc2)))           #output impedance(k ohms)   

#Results
print"lower cut-off freq is",round(f),"Hz"
print"Zin",Zin,"ohms"
print"Zout",Zout,"ohms"

lower cut-off freq is 53.0 Hz
Zin (3000-10000j) ohms
Zout (4500-10000j) ohms

Example 4.7,Page number 229

In [3]:
import math

#Variable declaration
Re=Rc=1.5*10**3              #collector resistance(ohms)
Rs=600                       #source resistance(ohms)
Rl=2*10**3                   #load resistance(ohms)  
beeta=100                     #common emitter current gain 
rpi=1*10**3                  #dynamic junction resistance(ohms)
f=50                         #frequency(Hz)

#Calculations
w=2*f*(math.pi)              #corner frequency(rad/s)
CE=1/(w*(Rs+rpi))            #capacitance(uF)
Ce=CE*(beeta+1)              #capacitance(uF)
w11=w/10                     #corner frequency input circuit (rad/s)
w12=w11/20                   #corner frequency output circuit(rad/s)
Cc1=1/(w11*(Rs+rpi))         #coupling capacitor 1(uF)  
Cc2=1/(w12*(Rc+Rl))          #coupling capacitor 2 (uF)  

#Results
print"Ce is",round(Ce/1E-6),"uF"
print"Cc1 is",round(Cc1/1e-6,1),"uF"
print"Cc2 is",round((Cc2/1E-5),2),"uF"

Ce is 201.0 uF
Cc1 is 19.9 uF
Cc2 is 18.19 uF

Example 4.8,Page number 235

In [1]:
import math

#Variable declaration
gm=2.5*10**-3            #transconductance(mS) 
Rd=6*10**3               #drain resistance(ohms)
rd=200*10**3             #dynamic drain resistance(ohms)   
Cc1=Cc2=0.12*10**-6      #coupling capacitors(uF)
Rs=1*10**3               #source resistance(ohms)
Rg=0.1*10**6             #R1||R2  
Cgs=12*10**-9            #gate to source capacitor(pF) 
Cgd=2*10**-9             #gate to drain capacitor(pF)    
Co1=10                   # as Co1=Cl+Cw=10

#Calculations
#Part a
Ro=(rd*Rd)/(rd+Rd)                  #equivalent resistance of rd and Rd(ohms)
Vo=-gm*((rd*Rd)/(rd+Rd))            #as Vgs=Vs
Avo=Vo                              #Avo=Vo/Vs=(-gm*Vs*((rd*Rd)/(rd+Rd)))/Vs=Vo  
    
#Part b
f11=1/(2*(math.pi)*Cc1*(Rs+Rg))

#Part c
Ceq=Cgs+(Cgd*(1+gm*Ro))                    #on application of miller theorem
Co=Co1+Cgd*(1+(1/(gm*Ro)))                 #output capacitance(pF)
f21=1/(2*(math.pi)*Ceq*((Rs*Rg)/(Rs+Rg)))  #input circuit cutoff frequency(MHz)
f22=1/(2*(math.pi)*Co*Ro)*10**3            #output circuit cutoff frequency(MHz)
fH=f22                                     #cutoff frequency of high frequency band(MHz)

#Results
print"a)mid freq gain is",round(Avo,1)
print"b)input circuit cut-off is",round(f11,1),"Hz"
print"c)high freq input cutoff is",round((f21/1E+3),2),"and output cutoff is",round((f22/1E-3),2),"MHz"
print"high freq cut-off is",round((fH/1E-3),2),"MHz"

a)mid freq gain is -14.6
b)input circuit cut-off is 13.1 Hz
c)high freq input cutoff is 3.73 and output cutoff is 2.73 MHz
high freq cut-off is 2.73 MHz

Example 4.9,Page number 238

In [4]:
import math

#Variable declaration
beta=50.              #common emitter current gain 
R1=11.5              #resistance(k ohms)
R2=41.4              #resistance(k ohms)  
Vcc=10.               #supply voltage to collector(V)
Rc=5.                 #collector resistance(k ohms)
Re=1.                 #emitter resistance(k ohms)
Rs=1.                 #source resistance(k ohms)
Vbe=0.7              #base emitter voltage(V)
Rl=10.                #load resistance(k ohms)
Cc1=Cc2=20*10**-6.    #coupling capacitors(uF)
Ce=150*10**-6.        #emitter capacitor(uF)  
Cpi=100       
Cu=5.

#Calculations
#Part a
Rb=(R1*R2)/(R1+R2)                 #R1||R2(k ohms)
Vbb=Vcc*(R1/(R1+R2))               #suply voltage to base(V)
Ib=(Vbb-Vbe)/(Rb+(Rs*(1+beta)))   #base current(mA)
Ic=beta*Ib                        #collector current(mA)  
Vce=Vcc-(Ic*Rc)-(Ic+Ib)*Re         #collector to emitter voltage(V) 
rpi=(25*beta)*10**-3/Ic                  #dynamic junction resistance(K ohms) 
    
#Part b
rpi=1                              #dynamic junction resistance(K ohms)  
R=(rpi*Rb)/(rpi+Rb)                #equivalent resistance(rpi||Rb) 
Vbe=(R*Rs)/(R+Rs)                  #base to emitter voltage(V)
Ib1=Vbe/rpi                        #base current(mA)
Ro=(Rc*Rl)/(Rc+Rl)                 #Rc||Rl(k ohms)   
Vo=-(beta*Ib1*Ro)                 #output voltage(V)
Avo=Vo                             #voltage gain

#Part c
r1=(Rs*Rb)/(Rs+Rb)                #Rs||Rb(k ohms) 
w11=1/(Cc1*(Rs+R))                #low freq cutoff(rad/s)
w12=1/(Cc2*(Rc+Rl))               #high freq cutoff(rad/s) 
w1p=1/((Ce/(beta+1))*(r1+rpi))   #low cutoff freq(rad/s)

#Part d
Co1=5                          #as Co1=Cw+Cl
gm=beta/rpi                    #transconductance(mS)    
Ceq=Cpi+(Cu*(1+(gm*Ro)))   #equivalent capacitance(pF)
Rs1=(Rb*Rs)/(Rb+Rs)            #Rb||Rs(k ohms)
r2=(Rs1*rpi)/(Rs1+rpi)         #Rs1||rpi(k ohms)
w21=10**12/(Ceq*r2*10**3)                 #low freq cutoff(MHz) 

#Results
print"a)dc bias values are Vbb:",round(Vbb,2),"V, Ib:",round(Ib,4),"mA, Ic:",round(Ic,2),"mA, Vce:",round(Vce,3),"V, rpi:",rpi,"k ohms"
print"mid freq gain is",round(Avo,2)
print"low freq cut-off is",round(w1p/1E+3),"rad/s"
print"high cut-off freq is",round((w21/1E+6),2),"*10**6 rad/s"

a)dc bias values are Vbb: 2.17 V, Ib: 0.0246 mA, Ic: 1.23 mA, Vce: 2.606 V, rpi: 1 k ohms
mid freq gain is -78.95
low freq cut-off is 179.0 rad/s
high cut-off freq is 2.25 *10**6 rad/s

Example 4.10,Page number 243

In [9]:
import math

#Variable declaration
Qcoil=75.               #coil inductance
f=200.                  #frequency(Hz) 
BW=4.                   #bandwidth(kHz)
C=470*10**-9.           #capacitance(pF) 

#Calculations
#Part a
Qcircuit=f/BW                     #circuit inductance
L=1/(((2*(math.pi)*f)**2)*C)      #inductance(mH)  

#Part b
R=Qcircuit*2*(math.pi)*f*L        #resistance(k ohms)

#Part c
r=(2*(math.pi)*f*L)/Qcoil         #internal resistance(ohms)
req=(Qcoil**2)*r                  #equivalent resistance(k ohms)
ro=(R*req)/(req-R)                #output resistance(k ohms)

#Part d
BW=5                               #bandwidth(kHz)
Qcircuit=f/BW                      #circuit inductance 
Req=Qcircuit*2*(math.pi)*f*L       #equivalent resistance(k ohms) 
Rl=(Req*R)/(R-Req)                 #load resistance(k ohms)

#Results
print"a)coil inductance is",round(L,2),"mH"
print"b)circuit output impedance atresonant freq is",round((R/1E+3),2),"K ohms"
print"c)internal resistance ro is",round((ro/1E+3),2),"k ohms"
print"d)value of load resistance is",round((Rl/1E+3),2),"k ohms"

a)coil inductance is 1.35 mH
b)circuit output impedance atresonant freq is 84.66 K ohms
c)internal resistance ro is 253.97 k ohms
d)value of load resistance is 338.63 k ohms

Example 4.11,Page number 246

In [1]:
import math

#Variable declaration
fo=50                           #output frequency(KHz)
L=10**-3                        #inductance(H)  
ro=100                          #output resistance(k ohms)
Q=80                            #coil inductance
Ri=10                           #input resistance(k ohms)
beta=125                        #common emitter current gain 

#Calculations
#Part a
C =1/(((2*(math.pi)*fo)**2)*L)   #tunning capacitance(nF)
r=(2*(math.pi)*fo*L)/Q           #internal resistance(k ohms)
req=(Q**2)*r                     #equivalent resistance(k ohms) 
R=(ro*req)/(ro+req)              #ro||req(k ohms)
Avo=-(beta*R)/Ri                 #voltage gain

#Part b
Qcircuit=R/(2*(math.pi)*fo*L)    #circuit inductance
BW=fo/Qcircuit                   #bandwidth

#Results
print"a)value of capacitance is",round(C/1E-3),"nF"
print"  gain is",round(Avo,1)
print"b)bandwidth is",round(BW/1E-3),"Hz","(value used for beta in texbook is wrong in the solution)"

a)value of capacitance is 10.0 nF
  gain is -251.1
b)bandwidth is 782.0 Hz (value used for beta in texbook is wrong in the solution)

Example 4.12,Page number 248

In [15]:
#Variable declaration

f=1*10**6                  #radio frequency(Hz)
beta=50                    #common emitter current gain 
fT=5*10**6                 #short circuit current gain bandwidth product(Hz)

#Calculations
betaf=fT/f                 #measurement of short circuit current gain
fbeta=fT/beta              #frequency at beta(Hz)

#Results
print"frequency is",fbeta,"Hz"
if fbeta<1*10**6:
    print"transistor is not suitable for 1Mhz amplifier as fbeta is less than 1Mhz"
else:
    print"transistor is suitable for 1Mhz amplifier"
    

frequency is 100000 Hz
transistor is not suitable for 1Mhz amplifier as fbeta is less than 1Mhz

Example 4.13,Page number 249

In [2]:
import math

#Variable declaration
rpi=2                     #dynamic junction resistance(K ohms)  
beta=50.                   #common emitter current gain 
f=1                        #frequency(MHz)
beta1=2.5                  #common emitter current gain 
f1=20*10**6                #frequency(Hz)

#Calculations
fT=beta1*f1                  #short circuit current gain bandwidth product(Hz)
fbeta=fT/beta                #frequency at beta(Hz)
Cpi=1/(2*(math.pi)*fbeta*rpi)   #dynamic capacitance(pF)

#Results
print"fT is",round(fT/1e+6),"MHz"
print"fB is",round(fbeta/1e+6),"MHz"
print"Cpi is",round(Cpi/1e-9),"pF"   

fT is 50.0 MHz
fB is 1.0 MHz
Cpi is 80.0 pF

Example 4.14,Page number 256

In [11]:
import math

#Variable declaration
R1=60                 #resistance(k ohms)
R2=140                #resistance(k ohms)
Rs=4                  #source resistance(k ohms)
Re=3                  #emitter resistance(k ohms)
Rc=4                  #collector resistance(k ohms)
Vcc=10                #supply voltage to collector(V)
Vbe=0.7               #base to emitter voltage(V)
beta=100              #common emitter current gain 
Avo=-30               #voltage gain 

#Calculations
#Part a
Rb=(R1*R2)/(R1+R2)                  #R1||R2(k ohms)
Vth=(Vcc*R1)/(R1+R2)                #thevinine's voltage(V)
Ib=(Vth-Vbe)/(Rb+(beta+1)*Re)       #base current(uA)
Ic=Ib*beta                          #collector current(mA) 
Vce=Vcc-(Rc*Ic)-((beta+1)*Ib*Re)    #collector to emitter voltage(V)

#Part b
rpi=((25*beta)/Ic)*10**-3         #dynamic junction resistance(k ohms)
r=(Rb*rpi)/(Rb+rpi)               #resistance across Vs
Ib1=r/((Rs+r)*rpi)                #base current(mA)
Rl=(-Rc*Avo)/(Avo+(beta*Ib1*Rc))  #load resistance(k ohms)

#Results
print"value of Ic and Vce are",round(Ic,3),"mA and",round(Vce,2),"V"
print"Rl is",round(Rl,2),"k ohms"    

value of Ic and Vce are 0.667 mA and 5.31 V
Rl is 6.21 k ohms

Example 4.15,Page number 257

In [3]:
import math

#Variable declaration
R1=25.                      #resistances(k ohms)
R2=100.                     #resistances(k ohms)
Re=2.                       #emitter resistance(k ohms) 
Vcc=10.                     #supply voltage to collector
Vbe=0.7                    #base to emitter voltage(V)
beta=100.                   #common emitter current gain
Avo=160                    #voltage gain
Rs=1                       #source resistance(k ohms)
Vs=1                       #source voltage(V) 
Rl=12.5                    #load resistance(k ohms)
Rc1=20.                     #collector resistance(k ohms)

#Calculations
#Part a
Rb=(R1*R2)/(R1+R2)              #R1||R2
Vth=(Vcc*R1)/(R1+R2)            #thevinines voltage(V)
Ib=(Vth-Vbe)/(Rb+(beta+1)*Re)   #base current(uA)
Ic=Ib*beta                      #collector current(mA)
rpi=(25*beta)*10**-3/Ic                #dynamic junction resistance(k ohms)

#Part b
Ib1=1/rpi                       #small signal analysis 
Rc=-Avo/(-beta*Ib1)             #collector resistance() 

#Part c
r=(Rc1*rpi)/(Rc1+rpi)              #Rc1||rpi1(k ohms) 
Ib2=(Vs*r)/((1+r)*rpi)               #base curret(mA)
Rc2=6.84                             #collector resistance(k ohms)                                      
Avo=-(beta*Ib2)*((Rl*Rc2)/(Rl+Rc2))  #voltage gain

#Results
print"value of Ic",round(Ic,3),"mA and rpi is",round(rpi,2),"k ohms"  
print"Rc is",round(Rc,2),"k ohms"
print"Avo is",round(Avo,1)

value of Ic 0.586 mA and rpi is 4.27 k ohms
Rc is 6.83 k ohms
Avo is -80.6

Example 4.16,Page number 258

In [5]:
#Variable declaration
R1=12.                 #resistance(k ohms)
R2=100.                #resistance(k ohms)
Rc=2                   #collector resistance(k ohms)
Ic=1.2                 #collector current(mA)
beta=60                #common emitter current gain
Ib1=1                  #(say)
Rs=1                   #source resistance(k ohms)
Vs=1                   #source vcoltage(say)

#Calculations
#Part a
rpi=((25*beta)/Ic)*10**-3     #dynamic junction resistance(k ohms)
Rb=(R1*R2)/(R1+R2)            #R1||R2(k ohms)
r=(Rb*rpi)/(Rb+rpi)           #Rb||rpi(k ohms)
Ro1=(Rc*rpi)/(Rc+rpi)         #Rc||rpi(k ohms)
Vo1=Vbe2=-(beta*Ib1*Ro1)      #base to emitter voltage(V)
Ib2=Vo1/rpi                   #base current(mA)
Ai=Ib2/Ib1                    #current gain 

#Part b
Ib11=(Rs*r)/((Rs+r)*rpi)          #base currents(mA)
Ib21=Ib11*Ai                #base current(mA)
Avo1=Vo1=Ib21*rpi           #voltage gain

#Results
print"current gain is",round(Ai,2)
print"overall voltage gain is",round(Avo1,2),"(solution in the textbook is incorrect)"

current gain is -36.92
overall voltage gain is -19.5 (solution in the textbook is incorrect)

Example 4.17,Page number 259

In [2]:
#Variable declaration
beeta=50.                 #common emitter current gain
R1=25.                   #resistance(k ohms)
R2=75.                   #resistance(k ohms)
Ic=1.25                  #collector current(mA)
Vcc=10                   #supply voltage to collector(V)
s=10*10**-3              #signal strength(V)
Rs=0.5                  #output impedance(k ohms)
Vo=1                    #output voltage(V)
Vs=1.                    #source voltage(V) 
Vl=12                   #load at output terminal(Vl)
Vbe=0.7                 #base to emitter voltage(V)
Rl=12

#Calculations
rpi=((25*beeta)/Ic)              #dynamic junction resistance(k ohms)
Rb=(R1*R2)/(R1+R2)               #R1||R2(k ohms)
r=(Rb*rpi*10**-3)/(Rb+rpi*10**-3)              #Rb||rpi(k ohms)
Avo=((Vo*rpi)/Vcc)                     #voltage gain
Ib=(r*Vs)/(Rs+r)*Vs                    #base current(mA)
Rc=(Rl*Avo)/(beeta*Ib*Rl-Avo)          #collector resistance(k ohms)
Vth=(Vcc*R1)/(R1+R2)                   #thevinine's voltage(V)
Ib1=Ic/beeta                           #base current(mA)
Re=(Vth-Vbe-(Rb*Ib1))/((beeta+1)*Ib1)    #emitter resistance(k ohms) 

#Results
print"value of Rc is",round(Rc,2),"and Re is",round(Re,2),"k ohms (Vth value is wrong substituted in the book)"

value of Rc is 4.1 and Re is 1.04 k ohms (Vth value is wrong substituted in the book)

Example 4.18,Page number 260

In [36]:
import math

#Variable declaration
Cpi=20*10**-9           #opening capacitor(F)
Cu=5*10**-9  
C=50*10**-9             #here C=Cl+Cw
rpi=3.75*10**3          #dynamic drain resistance(ohms)
r1=4*10**3              #resistance(ohms)
r2=42*10**3             #resistance(ohms)
r3=303*10**3            #resistance(ohms)
f=20                    #frequency(Hz)
beeta=100               #common emitter current gain
Rl=10*10**3             #load resistance(ohms)

#Calculations
#Part a
Req=(((r1*r2)/(r1+r2)+rpi)*r3)/(((r1*r2)/(r1+r2)+rpi)+r3)    #equivalent resistance(ohms)
Ce=(beeta+1)/(2*(math.pi)*f*Req)                             #emitter capacitance(uF)

#Part b
gm=beeta/rpi                   #transconductance
Ro=(Rl*r1)/(r1+Rl)             #output resistance(k ohms)
Ceq=Cpi+(Cu*(1+gm*Ro))         #equivalent capacitance(pF)
Co=C+(Cu*(1+(1/(gm*Ro))))      #output capacitance(pF)
r=(rpi*r1)/(rpi+r1)            #rpi||r1
w21=1/(Ceq*r)                  #lower cutoff frequency(MHz)
w22=1/(Co*Ro)                  #higher cutoff frequenct(MHz)

#Part c
Ceqnew=Cpi+(Cu*(1+(0.75*(gm*Ro))))           #as gain is reduced to 75% of original value
wHnew=(10**12)/(Ceqnew*r)                    #corner value of high frequency(Mrad/s)  
fHnew=wHnew/(2*(math.pi))                    #new value of higher frequency cutoff(KHz)

#Results
print"a)value of bypass capacitor Ce is",round(Ce/1E-6),"uF"
if w21>w22:
       print"higher frequency is w21"
else:
    print"higher frequency is w22"

print"b)high frequency cut-off is",round((w22/1E+3),2),"Mrad/s"
print"c)high frequency cut-off is",fHnew,"Hz"

a)value of bypass capacitor Ce is 111.0 uF
higher frequency is w22
b)high frequency cut-off is 6.36 Mrad/s
c)high frequency cut-off is 2.64660617737e+14 Hz

Example 4.19,Page number 262

In [33]:
import math

#Variable declaration
Vcc=3.                     #supply voltage to collector(V)
Vee=-3.                    #supply voltage to emitter(V)
r1=40.                     #resistance(ohms) 
r2=25.                     #resistance(ohms)
r3=1.56                    #resistance(ohms)
Vs=3.                      #source voltage(V)
beeta=200                  #common emitter current gain
r4=0.6                     #resistance(ohms)
r5=0.15                    #resistance(ohms)
Vbe=0.7                    #base to emitter voltage
r=0.5                      #resistance(k ohms)
fL=20                      #frequency(Hz)
Req1=24.24                 #solving r||(Rth+rpi+R)||Re
f=2                        #non dominant cutoff freq is fL/10 i.e 20/10

#Calculations
#Part a
Vth=Vs-(((Vcc-Vee)/(r1+r2))*r1)             #thevinine's voltage(V)
Rth=(r1*r2)/(r1+r2)                         #thevinine's voltage(V)
Ib=(Vth-Vbe+Vcc)/(Rth+((r4+r5)*(beeta+1)))  #base current(mA)
Ic=Ib*beeta                                 #Collector current(mA)  
Vo=Vcc-(r3*Ic)                              #output voltage(V)

#Part b
rpi=(25*beeta)/Ic                          #dynamic drain resistance(ohms)
R=r4*(beeta+1)                             #resistance(k ohms)
ro=(rpi*R)/(rpi+R)                         #rpi||R(k ohms)
Req=r+((Rth*ro)/(Rth+ro))                  #equivalent resistance(k ohms) 
Cc1=1/(Req*2*(math.pi)*fL)                 #coupling capacitor(uF)

#Part c
Ce=1/(2*(math.pi)*fL*Req1)                #emitter capacitance(uF)
CE=beeta*Ce                               #emitter capacitance(uF) after current gain

#Part d
Ce1=1/(2*(math.pi)*f*Req1)              #emitter capacitance(uF)
CE1=beeta*Ce1                           #emitter capacitance(uF) after current gain
Csum=Cc1+CE1                            #total capacitance(uF)

#Results
print"a)Ic and Vo are",round(Ic,2),"mA and",round(Vo),"V"
print"b)Cc1 is",round((Cc1/1E-3),3),"uF"
print"c)Ce is",round((CE/1E-3),1),"uF"
print"d)Csum is",round((Csum/1E-2),3),"uF"

a)Ic and Vo are 1.94 mA and -0.0 V
b)Cc1 is 0.565 uF
c)Ce is 65.7 uF
d)Csum is 65.715 uF

Example 4.21,Page number 265

In [9]:
import math

#Variable declaration
gm=2                   #transconductance
rd=200*10**3           #dynamic drain resistance(ohms)
Cgs=10                 #gate to source capacitance(pF)
Cgd=0                  #gate to drain capacitance(pF)
Rs=1*10**3             #source resistance(ohms)
Rg=1*10**6             #Rg=R1||R2
Rd=5*10**3             #drain resistance(ohms) 
Rs1=2                  #resistance(k ohms) 
Cc1=Cc2=0.1*10**-6     #coupling capacitors(F)
Co=10*10**-12          #output capacitance(F)
Vgs=1                  #gate to source voltage(V)

#Calculations
#Part a
R=(Rd*rd)/(Rd+rd)     #Rd||rd(k ohms)
Avo=Vo=-Vgs*gm*R      #voltage gain

#Part b
w11=1/(Cc1*(Rs*Rg))           #corner freq(rad/s)
wL=w11                        #input circuit corner freq(rad/s)

#Part c
w22=10**12/((Cgs*R)*10**3)     #output circuit corner frequency(rad/s)
wH=w22/(2*math.pi)                          

#Part d
G=-Avo*wH                         #gain bandwidth product

#Part e
Rd=4*10**3                      #drain resistance reduced(ohms) 
Rnew=(Rd*rd)/(Rd+rd)            #new resistance(ohms)
Avo1=-Vgs*gm*Rnew               #new voltage gain
BWnew=(10**8/Rnew)/(2*math.pi)                #new bandwidth(Mrad/s)
Gnew=-Avo1*BWnew                 #gain bandwidth product new

#Results
print"a)Avo is",round((Avo/1E+3),2)
print"b)wL is",round((wL/1E-3),2),"rad/s"
print"c)wH is",round((wH/1E+3),1),"MHz"
print"d)G is",round((G/1E+6),2),"MHz"
print"e)Gnew is",round((Gnew/1E+6),1),"MHz"

a)Avo is -9.76
b)wL is 10.0 rad/s
c)wH is 3.3 MHz
d)G is 31.83 MHz
e)Gnew is 31.8 MHz

Example 4.23,Page number 268

In [21]:
import math

#Variable declaration
gm=1                    #transconductance
rd=40                   #dynamic drain resistance(k ohms) 
Cgs=5                   #gate to source capacitance(pF)
Cgd=1                   #gate to drain capacitance(pF)
Cds=1                   #drain to source capacitance(pF)
Avo1=20.                #voltage gain of JFET 1
Avo2=8.                 #voltage gain of JFET 2 
R1=5                    #resistance(k ohms)
R2=20                   #resistance(k ohms)
R3=8                    #resistance(k ohms)

#Calculations
#Part a
Avo=Avo1*Avo2               #voltage gain
Ceq1=Cgs+Cgd*(1+Avo1)       #input crcuit for first JFET
Co1=Cds+(Cgd*(1+(1/Avo1)))  #output crcuit for first JFET
Ceq2=Cgs+Cgd*(1+Avo2)       #input crcuit for second JFET
Co2=Cds+(Cgd*(1+(1/Avo2)))  #output crcuit for second JFET

#Part b
w21=1/(R1*Ceq1)             #input circuit frequency
w2=10**12/(R2*10**3*(Co1+Ceq2))        #common circuit frequency
w22=1/(R3*Co2)              #output circuit frequency


#Results
print"a)Avo is",Avo
print"b)w21,w2,w22 are",round((w21/1E-3),2),"Mrad/sec,",round((w2/1E+6),2),"Mrad/sec and",round((w22/1E-3),2),"Mrad/sec"
print"nondominant corner freq is",round((w2/1E+6),2),"Mrad/sec"

a)Avo is 160.0
b)w21,w2,w22 are 7.69 Mrad/sec, 3.12 Mrad/sec and 58.82 Mrad/sec
nondominant corner freq is 3.12 Mrad/sec
In [ ]: