Chapter-8 FET Amplifiers

Example-8.2 Page Number-475

In [5]:
from math import *
#Studying the transfer characterstics given:
Idss=8                     #drain source saturation current in mA
Vp=-4                      #pinch voltage in volts

#calculation:

gmo=2*Idss/abs(Vp)

print "a.)"
Vgs=-0.5                 #gate source voltage in volts
gm=gmo*(1-(Vgs/Vp))      #in mS
print "gm=",gm,"mS"

print "\nb.)"
Vgs=-1.5                 #gate source voltage in volts
gm=gmo*(1-(Vgs/Vp))      #in mS
print "gm=",gm,"mS"

print "\nc.)"
Vgs=-2.5                 #gate source voltage in volts
gm=gmo*(1-(Vgs/Vp))      #in mS
print "gm=",gm,"mS"

a.)
gm= 3.5 mS

b.)
gm= 2.5 mS

c.)
gm= 1.5 mS

Example-8.3 Page Number-476

In [11]:
import matplotlib.pyplot as plt
%matplotlib inline

print "The plot is :"

y=[0,2,4]
x=[-4,-2,0]
plt.plot(x,y,'r')
plt.xlabel('Vgs(V)---->')
plt.ylabel('gm(S)---->')
plt.xlim(0,-4)
plt.ylim(0,4)
plt.show()

The plot is :

Example-8.7 Page Number-482

In [17]:
from math import *
#from the given figure:
Idss=10.0                     #drain source saturation current in mA
Vp=-8.0                       #pinch voltage in volts
Vdd=20.0                      #supply voltage in volts
Rd=2.0                        #drain resistance in kohm
Rg=1.0                        #gate resistance in Mohm
Vgs=-2.0                      #gate source voltage in volts 
Id=5.625                      #drain current in mA
yos=40.0                      #in microS

#calculations:
gmo=2*Idss/abs(Vp)            #in mS
gm=gmo*(1-(Vgs/Vp))           #in mS
rd=1/yos                      #in kohm
Zi=Rg                         #input impedance in Mohm
rd=rd*1000
Zo=(Rd*rd)/(Rd+rd)            #output impedence in kohm
Av=-gm*Zo                     #Voltage gain
Avw=-gm*Rd                    #gain ignoring rd

print "gm=",gm,"mS"
print "rd=",rd,"kohm"
print "Zi=",round(Zi,2),"Mohm"
print "Zo=",round(Zo,2),"kohm"
print "Voltage gain=",round(Av,2)
print "Voltage gain without rd=",Avw

gm= 1.875 mS
rd= 25.0 kohm
Zi= 1.0 Mohm
Zo= 1.85 kohm
Voltage gain= -3.47
Voltage gain without rd= -3.75

Example-8.8 Page Number-487

In [3]:
from math import *
#from the given figure:
Idss=8.0                      #drain source saturation current in mA
Vp=-6.0                       #pinch voltage in volts
Vdd=20.0                      #supply voltage in volts
Rd=3.3                        #drain resistance in kohm
Rg=1.0                        #gate resistance in Mohm
Rs=1                          #source reisitance in kohm
Vgs=-2.6                      #gate source voltage in volts 
Id=2.6                        #drain current in mA
yos=20.0                      #in microS

#calculations:
gmo=2*Idss/abs(Vp)            #in mS
gm=gmo*(1-(Vgs/Vp))           #in mS
rd=1/yos                      #in kohm
Zi=Rg                         #input impedance in Mohm
rd=rd*1000
#rd>10Rd
Zo=Rd                         #output impedence in kohm
X=-gm*Rd                      #temporary variable 
Y=1+gm*Rs                     #temporary variable
Av=X/Y+((Rd+Rs)/rd)           #Voltage gain
Avw=-gm*Rd/Y                  #gain ignoring rd

print "gm=",round(gm,2),"mS"
print "rd=",rd,"kohm"
print "Zi=",round(Zi,2),"Mohm"
print "Zo=",round(Zo,2),"kohm"
print "Voltage gain=",round(Av,3)
print "Voltage gain without rd=",round(Avw,2)

gm= 1.51 mS
rd= 50.0 kohm
Zi= 1.0 Mohm
Zo= 3.3 kohm
Voltage gain= -1.9
Voltage gain without rd= -1.99

Example-8.9 Page Number-492

In [11]:
from math import *
#from the given figure:
Idss=10.0                      #drain source saturation current in mA
Vp=-4.0                       #pinch voltage in volts
Vdd=12.0                      #supply voltage in volts
Rd=3.6                        #drain resistance in kohm
Rs=1.1                        #source reisitance in kohm
Vgs=-2.2                      #gate source voltage in volts 
Id=2.03                       #drain current in mA
yos=50.0                      #in microS
Vi=40                         #inputvoltage in mV

#calculations:
gmo=2*Idss/abs(Vp)            #in mS
gm=gmo*(1-(Vgs/Vp))           #in mS
rd=1/yos                      #in kohm
rd=rd*1000

#CASE-I (with rd)
Y=(rd+Rd)/(1+gm*rd)           #temporary variable
Zi=(Rs*Y)/(Rs+Y)              #input impedance in kohm
Zo=(Rd*rd)/(Rd+rd)            #output impedence in kohm
X= gm*Rd                      #temporary variable 
Av=(X+(Rd/rd))/(1+(Rd/rd))    #Voltage gain
Vo=Av*Vi                      #output voltage in mV

#CASE-II (without rd)
p=1/gm                         #temporary variable
Zir=(Rs*p)/(Rs+p)              #input impedance in kohm
Zor=Rd                         #output impedence in kohm
Avr=gm*Rd                      #Voltage gain
Vor=Avr*Vi                      #output voltage in mV

print "gm=",round(gm,2),"mS"
print "rd=",rd,"kohm"
print "Zi (with rd) =",round(Zi,2),"kohm"
print "Zi (without rd) =",round(Zir,2),"kohm"
print "Zo (with rd) =",round(Zo,2),"kohm"
print "Zo (without rd) =",round(Zor,2),"kohm"
print "Voltage gain (with rd) =",round(Av,2)
print "Output voltage (with rd) =",round(Vo,2),"mV"
print "Voltage gain (without rd) =",round(Avr,2)
print "Output voltage (without rd) =",round(Vor,2),"mV"

gm= 2.25 mS
rd= 20.0 kohm
Zi (with rd) = 0.35 kohm
Zi (without rd) = 0.32 kohm
Zo (with rd) = 3.05 kohm
Zo (without rd) = 3.6 kohm
Voltage gain (with rd) = 7.02
Output voltage (with rd) = 280.68 mV
Voltage gain (without rd) = 8.1
Output voltage (without rd) = 324.0 mV

Example-8.10 Page Number-496

In [14]:
from math import *
#from the given figure:
Idss=16.0                      #drain source saturation current in mA
Vp=-4.0                       #pinch voltage in volts
Vdd=9.0                      #supply voltage in volts
Rs=2.2                        #source reisitance in kohm
Vgs=-2.86                      #gate source voltage in volts 
Id=4.56                       #drain current in mA
yos=25.0                      #in microS

#calculations:
gmo=2*Idss/abs(Vp)            #in mS
gm=gmo*(1-(Vgs/Vp))           #in mS
rd=1/yos                      #in kohm
rd=rd*1000
Zi=Rg                         #input impedance in Mohm

#CASE-I (with rd)
X= (rd*Rs)/(rd+Rs)                      #temporary variable 
y=1/gm                                  #temporary variable
Zo=(X*y)/(X+y)                          #output impedence in kohm
Av=(gm*X)/(1+gm*X)                      #Voltage gain

#CASE-II (without rd)
p=1/gm                         #temporary variable
Zor=(Rs*p)/(Rs+p)              #output impedence in kohm
Avr=(gm*Rs)/(1+gm*Rs)          #Voltage gain

print "gm=",round(gm,2),"mS"
print "rd=",rd,"kohm"
print "Zi =",round(Zi,2),"Mohm"
print "Zo (with rd) =",round(Zo*1000,2),"kohm"
print "Zo (without rd) =",round(Zor*1000,2),"kohm"
print "Voltage gain (with rd) =",round(Av,2)
print "Voltage gain (without rd) =",round(Avr,2)

gm= 2.28 mS
rd= 40.0 kohm
Zi = 1.0 Mohm
Zo (with rd) = 362.38 kohm
Zo (without rd) = 365.69 kohm
Voltage gain (with rd) = 0.83
Voltage gain (without rd) = 0.83

Example-8.11 Page Number-497

In [3]:
from math import *
#from the given figure:
Idss=6.0                      #drain source saturation current in mA
Vp=-3.0                       #pinch voltage in volts
Vdd=18.0                      #supply voltage in volts
Rs=150                        #source reisitance in ohm
Vgs=0.35                      #gate source voltage in volts 
Id=7.6                        #drain current in mA
yos=10.0                      #in microS
Rd=1.8                        #drain resistance in kohm
R1=110.0                      #resistance in Mohm
R2=10.0                       #resistance in Mohm

#calculations:
gmo=2*Idss/abs(Vp)            #in mS
gm=gmo*(1-(Vgs/Vp))           #in mS
rd=1/yos                      #in kohm
rd=rd*1000
Zi=(R1*R2)/(R1+R2)            #input impedance in Mohm
Zo= (rd*Rd)/(rd+Rd)           #output impedence in kohm
Av=-gm*Rd                      #Voltage gain

print "gm=",round(gm,2),"mS"
print "rd=",rd,"kohm"
print "Zi =",round(Zi,2),"Mohm"
print "Zo=",round(Zo,2),"kohm"
print "Voltage gain=",round(Av,2)

gm= 4.47 mS
rd= 100.0 kohm
Zi = 9.17 Mohm
Zo= 1.77 kohm
Voltage gain= -8.04

Example-8.12 Page Number-501

In [27]:
#from the given figure:
k=0.24*10**-3                   #constant in A/V2
Vgsq=6.4                        #gate source voltage in volts at Q-point
Idq=2.75                        #drain current in mA at Q-point
Idon=6.0                         #drain current in mA
Vgson=8.0                        #gate source voltage in volts
Vgsth=3.0                        #gate source threshold voltage in voltage
yos=20.0                         #in microS
Rd=2.0                           #drain resistance in kohm
Rf=10.0                          #gate resistance in Mohm

#Calculation:
gm=2*k*(Vgsq-Vgsth)            #in mS
rd=1/yos                       #in kohm
rd=rd*1000

#CASE-I (with rd)
Y=(rd*Rd)/(Rd+rd)            #temporary variable
Y=Y/1000
W=gm*Y*10**6                #converting values to ohm
Zi=(Rf+Y)/(1+W)             #input impedance in Mohm
Zo=(Rf*Y)/(Rf+Y)            #output impedence in kohm
Av=-gm*1000*Zo               #Voltage gain

#CASE-II (without rd)
Zir=Rf/(1+gm*Rd*1000)          #input impedance in Mohm
Zor=Rd                         #output impedence in kohm
Avr=-gm*Rd                      #Voltage gain

print "gm=",round(gm*1000,2),"mS"
print "rd=",rd,"kohm"
print "Zi (with rd) =",round(Zi,2),"Mohm"
print "Zi (without rd) =",round(Zir,2),"Mohm"
print "Zo (with rd) =",round(Zo*1000,2),"kohm"
print "Zo (without rd) =",round(Zor,2),"kohm"
print "Voltage gain (with rd) =",round(Av*1000,2)
print "Voltage gain (without rd) =",round(Avr*1000,2)

gm= 1.63 mS
rd= 50.0 kohm
Zi (with rd) = 2.42 Mohm
Zi (without rd) = 2.35 Mohm
Zo (with rd) = 1.92 kohm
Zo (without rd) = 2.0 kohm
Voltage gain (with rd) = -3.14
Voltage gain (without rd) = -3.26

Variation in results obtained may be due to different precision of answers taken at each step

Example-8.13 Page Number-503

In [6]:
from math import *
#from the given figure:
Idss=10.0                      #drain source saturation current in mA
Vp=-4.0                       #pinch voltage in volts
Vdd=30.0                      #supply voltage in volts
Rg=10.0                       #source reisitance in Mohm
yos=20.0                      #in microS
Av=-10                        #voltage gain

#calculations:
#At Vgs=0V,  gm=gmo
gmo=2*Idss/abs(Vp)            #in mS
Y=-Av/gmo                     #temprary variable
rd=1/yos                      #in kohm
Rd=(50*Y)/(50-Y)              #drain resistance in kohm
Vds=Vdd-Idss*Rd               #drain source voltage in volts
Zi=Rg                         #input impedance in Mohm
rd=round(rd*1000,2)           #converting rd to kohm
Zo=(Rd*rd)/(Rd+rd)            #output impedence in kohm

print "Rd=",round(Rd,2),"kohm"
print "Vds=",round(Vds,2),"V"
print "Zi =",round(Zi,2),"Mohm"
print "Zo =",round(Zo,2),"kohm"

Rd= 2.08 kohm
Vds= 9.17 V
Zi = 10.0 Mohm
Zo = 2.0 kohm

Example-8.15 Page Number-505

In [35]:
#from the given figure:
Vgsq=-1                            #gate source voltage in volts at Qpoint
Idq=5.625                          #drain current in mA
gm=3.75*10**-3                     #in S
Av=8                               #voltage gain
#since the equation, Vgs=-Id*Rs has not changed,
Rs=180.0                             #source resistance in ohm

Rd=(Av*(1+gm*Rs))/gm               #drain resistance in kohm

print "Rs=",Rs,"ohm"
print "Rd=",round(Rd/1000,1),"kohm"

Rs= 180.0 ohm
Rd= 3.6 kohm