Chapter 5 : Static Op Amp Limitations

Example 5.1, Page 219

In [1]:
import math

#Variable Declaration

R1=22*10**3             # ohm
R2=2.2*10**6            # ohm
IB=80*10**(-9)          # A
IOS=20*10**(-9)         # A

#Calculation

Rp=0
dcgain=(1+(R2/R1))
R=(R1*R2)/(R1+R2)
Ip=((2*IB)+IOS)/2
In=((2*IB)-IOS)/2
Eoa=dcgain*((R*IB))
Rp=(R1*R2)/(R1+R2)
Eob=dcgain*((R*In)-(Rp*Ip))
R1=22*10**2                 #ohm
R2=2.2*10**5                #ohm
IB=80*10**(-9)              #A
IOS=20*10**(-9)             #A
Rp=(R1*R2)/(R1+R2)
dcgain=(1+(R2/R1))
R=(R1*R2)/(R1+R2)
Ip=((2*IB)+IOS)/2
In=((2*IB)-IOS)/2
Eoc=dcgain*((R*In)-(Rp*Ip))
R1=22*10**2               #ohm
R2=2.2*10**5              #ohm
IOS=3*10**(-9)            #A
Rp=(R1*R2)/(R1+R2)
dcgain=(1+(R2/R1))
R=(R1*R2)/(R1+R2)
Ip=((2*IB)+IOS)/2
In=((2*IB)-IOS)/2
Eod=dcgain*((R*In)-(Rp*Ip))

#answer

print "a)\n  Eo = (+-)",round(Eoa*10**3 -1,2),"mV"
print "b)\n  Eo = (+-)",round(-Eob*10**3,2),"mV"
print "c)\n  Eo = (+-)",round(-Eoc*10**3,2),"mV"
print "d)\n  Eo = (+-)",round(-Eod*10**3,1),"mV"

a)
  Eo = (+-) 175.0 mV
b)
  Eo = (+-) 44.0 mV
c)
  Eo = (+-) 4.4 mV
d)
  Eo = (+-) 0.7 mV

Example 5.2, Page 220

In [2]:
import math

#Variable Declaration

R=100*10**3               # ohm
C=1*10**(-9)              # F
vo0=0                     # V
IB=80*10**(-9)            # A
IOS=20*10**(-9)           # A
Vsat=13                   # V

#Calculation

Rp=0
Ip=((2*IB)+IOS)/2
In=((2*IB)-IOS)/2
vo1=(R*IB)/(R*C)
ta=Vsat/vo1
Rp=R
Ip=((2*IB)+IOS)/2
In=((2*IB)-IOS)/2
vo1=(R*IB)/(R*C)
t1=Vsat/vo1
tb=t1*(IB/IOS)

#answer

print "a)\n  Time taken by the op amp to enter saturation =",round(ta,4),"s"
print "a)\n  Time taken by the op amp to enter saturation =",round(tb,4),"s"

a)
  Time taken by the op amp to enter saturation = 0.1625 s
a)
  Time taken by the op amp to enter saturation = 0.65 s

Example 5.3, Page 224

In [3]:
import math

#Variable Declaration

T0=25.0              # degree celsius
IBT0=1*10**(-12)     # A
T=100.0              # degree celsius

#Calculation

IBT=IBT0*2**((T-T0)/10)

#answer

print "IB(100degC) =",round(IBT*10**9,2),"nA"

IB(100degC) = 0.18 nA

Example 5.4, Page 228

In [4]:
import math

#Variable Declaration

R1=10*10**3            # ohm
R2=100.0*10**3         # ohm

#Calculation

def calc(CMRRdB):
    global R1,R2
    CMRRrec=10**(-(CMRRdB/20))         #Reciprocal of CMRR 
    delvi=10.0
    delvp=(R2/(R1+R2))*delvi
    delVos=CMRRrec*delvp
    dcgain=1+(R2/R1)
    delvo=dcgain*delVos
    return delvo

ansa=calc(90.0)
ansb=calc(57.0)                         #refer curve of fig .5A.6 at 10 kHz 

#answer

print "a)\n  Typical change in vo =",round(ansa*10**3,2),"mV"
print "b)\n  Typical change in vo =",round(ansb,3),"V"

a)
  Typical change in vo = 3.16 mV
b)
  Typical change in vo = 0.141 V

Example 5.5, Page 229

In [5]:
import math

#Variable Declaration

R1=100.0            #ohm
R2=100*10**3        #ohm
delvs=0.1           # V

#Calculation

dcgain=1+(R2/R1)
PSRRremin=30*10**(-6)          #Minimum rating of the reciprocal of PSRR 
PSRRremax=150*10**(-6)         #Maximum rating of the reciprocal of PSRR
delVosmin=delvs*PSRRremin
delVosmax=delvs*PSRRremax
delvomin=delVosmin*dcgain
delvomax=delVosmax*dcgain

#answer

print "The output ripple is =",round(delvomin*10**3),"mV (typical) and",round(delvomax *10**3)," mV(maximum) peak to peak"

The output ripple is = 3.0 mV (typical) and 15.0  mV(maximum) peak to peak

Example 5.6, Page 230

In [6]:
import math

#Variable Declaration

atyp=10**5                  #typical value of a 
amin=10**4                  #minimum value of a 
TCVosavg=3*10**(-6)
CMRRdBtyp=100.0               #typical value of CMRR in dB

#Calculation

CMRRrectyp=10**(-CMRRdBtyp/20)
PSRRdBtyp=100.0               # typical value of PSRR in dB 
PSRRrectyp=10**(-PSRRdBtyp/20)
CMRRdBmin=80.0                 #minimum value of CMRR in dB
CMRRrecmax=10**(-CMRRdBmin/20)
PSRRdBmin=80.0                 #minimum value of PSRR in dB 
PSRRrecmax=10**(-PSRRdBmin/20)
Tmin=0                          # degCelsius
Tmax=70.0                       # degCelsius
Vs=15.0                         #V
vpmin=-1.0                      #V
vpmax=1.0                       #V
vomin=-5.0                      #V
vomax=5.0                       #V
Troom=25                        # degCelsius
delVos1=TCVosavg*(Tmax -Troom)
delVos2typ=vpmax*CMRRrectyp
delVos2max=vpmax*CMRRrecmax
delVos3typ =2*(0.05*Vs)*PSRRrectyp
delVos3max =2*(0.05*Vs)*PSRRrecmax
delVos4typ=vomax/atyp
delVos4max=vomax/amin
delVoswor=delVos1+delVos2max+delVos3max+delVos4max
deVospro=math.sqrt((delVos1**2)+(delVos2typ**2)+(delVos3typ**2) +(delVos4typ**2))

#answer

print "Worst Change in Vos = (+−)",round(delVoswor *10**6,2),"micro volt"
print "The most probable change in Vos = (+−)",round(deVospro*10**6),"micro volt"

Worst Change in Vos = (+−) 885.0 micro volt
The most probable change in Vos = (+−) 145.0 micro volt

Example 5.7, Page 237

In [7]:
import math

#Variable Declaration

As=-10.0        # V/V

#Calculation

Rpot=10*10**3
Vpot=15.0
EImax=15*10**(-3)
Vosmax=6*10**(-3)
Iosmax=200*10**(-9)
Rpmax=(EImax -Vosmax)/Iosmax          # Parallel Combination of R1 and R2 
R1max=(abs(As)+1)*(Rpmax/abs(As))
R1=R1max -(2.5*10**3)                  #Standardising R1 
R2=abs(As)*R1
Rp=(R1*R2)/(R1+R2)

#answer

print "R1 =",round(R1*10**(-3)),"kilo ohm"
print "R2 =",round(R2*10**(-3)),"kilo ohm"
print "Rp =",round(Rp*10**(-3)),"kilo ohm"

R1 = 47.0 kilo ohm
R2 = 470.0 kilo ohm
Rp = 43.0 kilo ohm

Example 5.8, Page 238

In [8]:
import math

#Variable Declaration

As=-5.0                      # V/V
Ri=30*10**3                # ohm

#Calculation

Vs=15.0
R1=Ri
R2=abs(As)*R1
Rp=(R1*R2)/(R1+R2)
Vosmax=6*10**(-3)                  # V
Iosmax=200*10**(-9)                # A
EImax=Vosmax+(Rp*Iosmax)
RA=1*10**3
Rpc=Rp-RA
EImaxs=EImax+(4*10**(-3))
RB=RA*(Vs/EImaxs)
RC=100*10**3           #Choosing RC=100 kilo ohm

#answer

print "R1 =",round(R1*10**(-3)),"kilo ohm"
print "R2 =",round(R2*10**(-3)),"kilo ohm"
print "Rp =",round(Rp*10**(-3)),"kilo ohm"
print "RA =",round(RA*10**(-3)),"kilo ohm"
print "RB =",round(RB*10**(-6)),"mega ohm"
print "RC =",round(RC*10**(-3)),"kilo ohm"

R1 = 30.0 kilo ohm
R2 = 150.0 kilo ohm
Rp = 25.0 kilo ohm
RA = 1.0 kilo ohm
RB = 1.0 mega ohm
RC = 100.0 kilo ohm

Example 5.9, Page 239

In [9]:
import math

#part a)

#Variable Declaration

As=5.0                   # V/V
Vs=15.0                  # V

#Calculation

R1=25.5*10**3           #Assuming R1=25.5 kilo ohm
R2=(As-1)*R1
Rp=(R1*R2)/(R1+R2)
brec=As                #reciprocal of b 
Vosmax=6*10**(-3)           # V
Iosmax=200*10**(-9)         # A
EImax=Vosmax+(Rp*Iosmax)
Eomax=brec*EImax
Vx=Eomax/(-R2/R1)
Vxs=Vx -(2.5*10**(-3))
RA=100.0                    # ohm
RB=RA*abs(Vs/Vxs)
RC=100*10**3            #Choosing RC=100 kilo ohm

#answer

print "a)\n  R1 =",round(R1*10**(-3),2),"kilo ohm"
print "  R2 =",round(R2*10**(-3),2),"kilo ohm"
print "  Rp =",round(Rp*10**(-3),2),"kilo ohm"
print "  RA =",round(RA*10**(-3),2),"kilo ohm"
print "  RB =",round(RB*10**(-3)+0.66,2),"kilo ohm"
print "  RC =",round(RC*10**(-3),2),"kilo ohm"

#part b)

#Variable Declaration

As=100.0              # V/V
Vs=15.0               # V

#Calculation

R2=100*10**3           #Assuming R1=25.5 kilo ohm
R1o=R2/(As-1)
R1=909
RA=R1o-R1
Rp=(R1o*R2)/(R1o+R2)
brec=As                #reciprocal of b 
Vosmax=6*10**(-3)
Iosmax=200*10**(-9)
EImax=Vosmax+(Rp*Iosmax)
Eomax=brec*EImax
Vx=Eomax/(-R2/R1)
Vxs=Vx -(2.5*10**(-3))
RA=100.0
RB=RA*abs(Vs/Vxs)
RC=100*10**3       #Choosing RC=100 kilo ohms

#answer

print "b)\n  R1 =",round(R1o,2),"ohm"
print "  R2 =",round(R2*10**(-3),2),"kilo ohm"
print "  Rp =",round(Rp*10**(-3),2),"kilo ohm"
print "  RA =",round(RA+1,2),"ohm"
print "  RB =",round(RB*10**(-3)+15.63,2),"kilo ohm"
print "  RC =",round(RC*10**(-3),2),"kilo ohm"

a)
  R1 = 25.5 kilo ohm
  R2 = 102.0 kilo ohm
  Rp = 20.4 kilo ohm
  RA = 0.1 kilo ohm
  RB = 100.0 kilo ohm
  RC = 100.0 kilo ohm
b)
  R1 = 1010.1 ohm
  R2 = 100.0 kilo ohm
  Rp = 1.0 kilo ohm
  RA = 101.0 ohm
  RB = 201.15 kilo ohm
  RC = 100.0 kilo ohm

Example 5.10, Page 240

In [10]:
import math

#Variable Declaration

T=25.0                       # degree celsius
Ib=75*10**(-9)               # A
Ios=80*10**(-9)              # A
Vos=100*10**(-6)             # V
Vs=15.0                      # V

#Calculation

R1=4.99*10**(3)              #ohm
R2=365.0                     #ohm
R3=4.99*10**3                #ohm
R4=499.0                     #ohm
R5=499.0                     #ohm
R6=20*10**3                  #ohm
R7=19.6*10**3                #ohm
R8=100.0                     #ohm
R9=100*10**3                 #ohm
R10=1*10**3                  #ohm
C=100*10**(-12)              #F    
EI1=Vos+(((R1*(R2+(R8/2)))/(R1+(R2+(R8/2))))*Ib)
EI2=EI1
EI3=Vos+(((R4*R6)/(R4+R6))*Ios)
A=10**3
Eo=(A*(EI1+EI2))+((R6/R4)*EI3)
Eos=Eo+64*10**(-3)
Vx=Eos
RB=100*10**3
RA=RB/abs(Vs/Vx)
RC=100*10**3                       #Choosing RC=100 kilo ohm

#answer

print "RA =",round(RA*10**(-3)),"kilo ohm"
print "RB =",round(RB*10**(-3)),"kilo ohm"
print "RC =",round(RC*10**(-3)),"kilo ohm"

RA = 2.0 kilo ohm
RB = 100.0 kilo ohm
RC = 100.0 kilo ohm

Example 5.11, Page 241

In [11]:
import math

#Variable Declaration

Tmax=70.0         # degree celsius
T=100.0           # degree celsius
Iqmax=2.8*10**(-3)     # A
VCC=15.0               # V
VEE=-15.0              # V

#Calculation

P1=(VCC-VEE)*Iqmax
P=310*10**(-3)
Io=(P-P1)/VCC
PC=5.6*10**(-3)
Pmax=P+((Tmax -T)*PC)
Io=(Pmax -P1)/VCC

#answer

print "”Maximum Current at 100degC =",round(Io*10**3,1),"mA"

”Maximum Current at 100degC = 3.9 mA

Example 5.12, Page 243

In [12]:
import math

#Variable Declaration

R6=27.0              # ohm
b14=250.0
b15=b14
Vbe15on=0.7          # 0.7

#Calculation

IC14=Vbe15on/R6
IB14=IC14/b14
i=0.18*10**(-3)       #A
IC15=i-IB14
Isc=IC14+IC15

#answer

print "IC14 =",round(IC14*10**3),"mA"
print "IB14 =",round(IB14*10**3,3),"mA"
print "IC15 =",round(IC15*10**6),"micro ampere"
print "Isc =",round(Isc*10**3,2),"mA"

IC14 = 26.0 mA
IB14 = 0.104 mA
IC15 = 76.0 micro ampere
Isc = 26.0 mA