# Chapter 5 Characteristic of Operational Amplifier¶

## Example 5.1 Pg 110¶

In :
from __future__ import division
# find the total offset voltage of feedback op-amp

Vos = 4 # #mV  # input offset volt
Ios = 150*10**-3 # # input offset current
R1 = 5 # #kilo ohm  # input resistance
R2 = 500 # #kilo ohm  # feedback resistance

# the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is
Vo1 = ((R1+R2)/(R1)*Vos) #
print ' the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = %0.2f'%Vo1,' mV '#

# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is
Vo2 = R2*Ios #
print ' the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.2f'%Vo2,' mV '#

# the total offset voltage is
Vo = Vo1+Vo2 #
print ' the total offset voltage (Vo) of an op-amp circuit is = %0.2f'%Vo,' mV '#

 the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = 404.00  mV
the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 75.00  mV
the total offset voltage (Vo) of an op-amp circuit is = 479.00  mV


## Example 5.2 Pg 111¶

In :
# find the total offset voltage of feedback op-amp

Vos = 2 # #mV  # input offset volt
Ios = 20*10**-3 # # input offset current
R1 = 10 # #kilo ohm  # input resistance
R2 = 250 # #kilo ohm  # feedback resistance

# the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is
Vo1 = ((R1+R2)/(R1)*Vos) #
print ' the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = %0.2f'%Vo1,' mV '#

# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is
Vo2 = R2*Ios #
print ' the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.2f'%Vo2,' mV '#

# the total offset voltage is
Vo = Vo1+Vo2 #
print ' the total offset voltage (Vo) of an op-amp circuit is = %0.2f'%Vo,' mV '#

 the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = 52.00  mV
the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 5.00  mV
the total offset voltage (Vo) of an op-amp circuit is = 57.00  mV


## Example 5.3 Pg 111¶

In :
from __future__ import division
# find the input offset voltage of an op-amp circuit

Vo = 90.2 # #mV  # output voltage
R1 = 2 # #kilo ohm  # input resistence
R2 = 150 # #kilo ohm  # feedback resistence

# the input offset voltage (Vos) of an op-amp circuit is defined as
Vos = ((R1)/(R1+R2)*Vo) #
print 'the input offset voltage (Vos) of an op-amp circuit is = %0.3f'%Vos,' mV '#

the input offset voltage (Vos) of an op-amp circuit is = 1.187  mV


## Example 5.4 Pg 112¶

In :
from __future__ import division
# find the output voltage of an op-amp circuit

Vos = 1 # #mV  # input offset volt
R1 = 10 # #kilo ohm  # input resistance
R2 = 350 # #kilo ohm  # feedback resistance

# the output voltage due to the input offset voltage of the op-amp circuit is defined by
Vo1 = ((R1+R2)/(R1)*Vos) #
print 'the output voltage due to the input offset voltage  is = %0.2f'%Vo1,' mV '#

the output voltage due to the input offset voltage  is = 36.00  mV


## Example 5.5 Pg 113¶

In :
from __future__ import division
# Determine the bias current effect with and without current compensation method

R1 = 10 # #kilo ohm
R2 = 100 # #kilo ohm
Ib1 = 1.1*10**-3 #
Ib2 = 1*10**-3 #
# the output voltage of the circuit due to bias current is
Vo = Ib1*R2 #
print 'the output voltage of the circuit due to bias current is = %0.2f'%Vo,' V '#

#Bias compensated resistor is given by
R3 = (R1*R2)/(R1+R2) #
print 'Bias compensated resistor is = %0.2f'%R3,' kilo ohm '#

#Bias compensated output voltage is given by
Vo = R2*(Ib1-Ib2)#
print 'Bias compensated output voltage is = %0.2f'%Vo,' V '#

the output voltage of the circuit due to bias current is = 0.11  V
Bias compensated resistor is = 9.09  kilo ohm
Bias compensated output voltage is = 0.01  V


## Example 5.6 Pg 113¶

In :
from __future__ import division
# find the input offset current of an op-amp circuit

Vo = 12*10**-3# # V  # output voltage
R1 = 2*10**3 # # ohm  # input resistence
R2 = 150*10**3# # ohm  # feedback resistence

# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is
# Vo = R2*Ios #
Ios = Vo/R2 *1e9 # nA
print 'the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.f'%Ios,'nA '#

the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 80 nA


## Example 5.7 Pg 114¶

In :
from __future__ import division
# Determine the bias current of inverting and non-inverting
Ios = 5 # #nA # input offset current
Ib = 30 # #nA # input bias current

# the input bias current of an op-amp is

#Ib =(Ib1+Ib2)/(2)#

# the offset current Ios is define as

#Ios = abs(Ib1-Ib2) #

Ib1=Ib-(Ios/2)#
print 'The current in the inverting input terminal is = %0.2f'%Ib1,' nA '#

Ib2 =Ib+(Ios/2)#
print 'The current in the non-inverting input terminal is= %0.2f'%Ib2,' nA '#

The current in the inverting input terminal is = 27.50  nA
The current in the non-inverting input terminal is= 32.50  nA


## Example 5.8 Pg 115¶

In :
from __future__ import division
#determine the feedback transfer function of an op-amp for the following condition
# a) When open loop gain of 10**5 and the closed loop gain of 100
A = 10**5 # # open loop gain
Af = 100 # #closed loop gain
# Feedback transfer function is
beta =(1/Af)-(1/A)#
print 'Feedback transfer function is = %0.2f'%beta,''#
beta = 1/beta #
print 'OR 1/Beta  is = %0.2f'%beta,''#

# For an open loop gain of -10**5 and closed loop gain of -100
A = -10**5 # # open loop gain
Af = -100 # #closed loop gain
# Feedback transfer function is
beta =(1/Af)-(1/A)#
print 'Feedback transfer function is = %0.2f'%beta,''#
beta = 1/beta #
print 'OR 1/Beta  is = %0.2f'%beta,''#

Feedback transfer function is = 0.01
OR 1/Beta  is = 100.10
Feedback transfer function is = -0.01
OR 1/Beta  is = -100.10


## Example 5.9 Pg 115¶

In :
from __future__ import division
#to determine open loop gain
beta = 0.0120 # # Feedback transfer function
Af = 80 # #closed loop gain
A = (Af)/(1-beta*Af) #
print 'open loop gain is = %0.2f'%A

open loop gain is = 2000.00


## Example 5.10 Pg 116¶

In :
from __future__ import division
# To Determine the percent of change in the closed loop gain Af of feedback op-amp circuit
A = 10**5 #  # open loop gain
Af = 50 #  # close loop gain
beta = 0.01999 #  # feedback transfer function
dA = 10**4 #  # the change in the open llop gain

# close loop gain
dAf = ((dA)/(1+dA*beta))#
print 'close loop gain dAf is = %0.2f'%dAf

# the percent change of closed loop gain
dAf = (((Af-dAf)/(Af))*100)#
print 'the percent change of closed loop gain dAf is = %0.2f'%dAf,'%'#

close loop gain dAf is = 49.78
the percent change of closed loop gain dAf is = 0.45 %


## Example 5.11 Pg 116¶

In :
from __future__ import division
# To Determine the bandwidth of feedback amplifier
A = 10**4 #  # open loop gain
Af = 50 #  # close loop gain
wH = 628 # #(2*pi*100)  # rad/sec # open loop bandwidth

# close loop gain of an op-amp is defined as
# Af = ((A)/(1+A*beta))#

# the feedback transfer function is given as
beta = (1/Af)-(1/A) #
print 'the feedback transfer function beta is = %0.4f'%beta

# closed loop bandwidth
wfH = wH*(1+beta*A)#
print 'the closed loop bandwidth wfH is = %0.f'%wfH

the feedback transfer function beta is = 0.0199
the closed loop bandwidth wfH is = 125600


## Example 5.12 Pg 117¶

In :
from __future__ import division
# To calculate unity gain bandwidth and maximum close loop gain
A = 10**5 #  # open loop gain
fo = 10 # # Hz  # dominant pole frequency
fdb = 20*10**3 # #Hz  # 3-db frequency

# the unity gain bandwidth
f1 = fo*A #
print 'the unity gain bandwidth is = %0.e'%f1,'Hz'#

# the maximum close loop gain
ACL = (f1/fdb) #
print 'the maximum close loop gain ACL is = %0.2f'%ACL,''#

the unity gain bandwidth is = 1e+06 Hz
the maximum close loop gain ACL is = 50.00


## Example 5.13 Pg 117¶

In :
from __future__ import division
# To calculate unity gain bandwidth and maximum close loop gain
A = 10**3 #  # open loop gain
fo = 60 # # Hz  # dominant pole frequency
fdb = 12*10**3 # #Hz  # 3-db frequency

# the unity gain bandwidth
f1 = fo*A #
print 'the unity gain bandwidth is = %0.f'%(f1/1e3),'kHz'#

# the maximum close loop gain
ACL = (f1/fdb) #
print 'the maximum close loop gain ACL is = %0.2f'%ACL,''#

the unity gain bandwidth is = 60 kHz
the maximum close loop gain ACL is = 5.00


## Example 5.14 Pg 118¶

In :
from __future__ import division
# To determine the dominant pole frequency of an op-amp
Ao = 2*10**5 #  # low frequency open loop gain
f = 5*10**6 # # Hz  # pole frequency
ACL = 100 #  # low frequency closed lkoop gain
p_margin = 80 #

# the dominant pole frequency of an op-amp
fPD = (ACL)*(f/Ao)/1e3
print 'the dominant pole frequency (fPD) of an op-amp is = %0.1f'%fPD,'kHz'#

the dominant pole frequency (fPD) of an op-amp is = 2.5 kHz


## Example 5.15 Pg 118¶

In :
from __future__ import division
# Determine the loop gain of compensated network
C = 0.0025*10**-6 # # farad
R = 10*10**3 # #  ohm
F = 1*10**6 # # Hz
Ac1 = 100 #
angle1 = 90 #

# the close loop gain of a compensated network is defined as
# Ac = Acl*Acom #

#Acom = 1/(1+%(F/FL))#

FL = 1/(2*3.14*R*C)#
print 'FL = %0.2f'%(FL/1000),' KHz '#   # Round Off Error

#  Acom = 1/(1+%j(F/FL))#
# After putting value of F ,FL we get

#  Acom = 1/(1+%j(158.7))#  #  1+%j(158.7)  Rectangular Form   where real part is 1 and imaginary part is 158.7

# After converting  rectangular from into polar from we get

print 'Acom =  [ magnitude = 6.3*10**-3   angle = -89.6 degree ]'#

#   Ac = Ac1*Acom #         equation 1

# after putting Ac1 and Acom value in equation 1  we get   Ac1 = 100 angle 90  and Acom = 6.3*10**-3  angle = -89.6

print 'Ac =  [ magnitude = 0.68   angle = 0.4 degree ]'#

FL = 6.37  KHz
Acom =  [ magnitude = 6.3*10**-3   angle = -89.6 degree ]
Ac =  [ magnitude = 0.68   angle = 0.4 degree ]


## Example 5.16 Pg 119¶

In :
from __future__ import division
# Determine the loop gain of compensated network

C = 0.01*10**-6 # # farad
R = 15*10**3 # #  ohm
F = 1*10**6 # # Hz

# the close loop gain of a compensated network is defined as
# Ac = Acl*Acom #

#Acom = 1/(1+%(F/FL))#

FL = 1/(2*3.14*R*C)#
print 'FL = %0.1f'%(FL/1000),' KHz '#   # Round Off Error

#  Acom = 1/(1+%j(F/FL))#
# After putting value of F ,FL we get

#  Acom = 1/(1+%j(0.9))#  #  1+%j(0.9)  Rectangular Form   where real part is 1 and imaginary part is 0.9

# After converting  rectangular from into polar from we get

print 'Acom =  [ magnitude = 0.68   angle = -47.7 degree ]'#

FL = 1.1  KHz
Acom =  [ magnitude = 0.68   angle = -47.7 degree ]


## Example 5.18 Pg 123¶

In :
from __future__ import division
# to design compensating network
fp = 500*10**3 #  # pole frequency
C = 0.02*10**-6 # # F  # we choose
# loop gain of compensated network

# ACom =(1)/(1+j(f/fp))
# fp = (1/2*pie*R*C)
R = (1/(2*3.14*C*fp))#
print 'The compensating resistor value is = %0.2f'%R,' ohm '#

The compensating resistor value is = 15.92  ohm


## Example 5.19 Pg 123¶

In :
from __future__ import division
# Determine the loop gain of compensated network

C = 0.0025*10**-6 # # farad
R1 = 10*10**3 # #  ohm
R2 = 20*10**3 # #  ohm
F = 1*10**6 # # Hz
Ac1 = 100 #
angle1 = 90 #

# the close loop gain of a compensated network is defined as

# Ac = Acl*Acom #

#Acom = (1+%(F/FH))/(1+%(F/FL))#

FH = 1/(2*3.14*R1*C)#
print 'FH = %0.2f'%(FH/1000),' KHz '#   # Round Off Error

FL = 1/(2*3.14*(R1+R2)*C)#
print 'FL = %0.2f'%(FL/1000),' KHz '#   # Round Off Error

#Acom = (1+%(F/FH))/(1+%(F/FL))#

# After putting value of FH ,FL we get

#  Acom = (1+%j(158.7))/(1+%j(471.7)

# After converting  rectangular from into polar from we get

print 'Acom =  [ magnitude = 0.34   angle = -0.24 degree ]'#

#   Ac = Ac1*Acom #         equation 1

# after putting Ac1 and Acom value in equation 1  we get   Ac1 = 100 angle 90  and Acom = 0.34  angle = -0.24

print 'Ac = [ magnitude = 34   angle = 89.76 degree ]'#

FH = 6.37  KHz
FL = 2.12  KHz
Acom =  [ magnitude = 0.34   angle = -0.24 degree ]
Ac = [ magnitude = 34   angle = 89.76 degree ]


## Example 5.20 Pg 124¶

In :
from __future__ import division
# Determine the loop gain of compensated network
C = 0.01*10**-6 # # farad
R1 = 10*10**3 # #  ohm
R2 = 15*10**3 # #  ohm
F = 1*10**6 # # Hz

# the close loop gain of a compensated network is defined as

#Acom = (1+%(F/FH))/(1+%(F/FL))#

FH = 1/(2*3.14*R1*C)#
print 'FH = %0.2f'%(FH/1000),' KHz '#   # Round Off Error

FL = 1/(2*3.14*(R1+R2)*C)#
print 'FL = %0.2f'%(FL/1000),' KHz '#   # Round Off Error

#Acom = (1+%(F/FH))/(1+%(F/FL))#

# After putting value of FH ,FL we get

#  Acom = (1+%j(658.9))/(1+%j(1.56*10**3)

# After converting  rectangular from into polar from we get

print 'Acom =   [magnitude = 0.4]  '#

FH = 1.59  KHz
FL = 0.64  KHz
Acom =   [magnitude = 0.4]


## Example 5.21 Pg 125¶

In :
from __future__ import division
# to design compensating network
fH = 10 # #k ohm # break frequency initiated by a zero
fL = 1 #  #k ohm # break frequency initiated by a pole
C = 0.02# # uF  # we choose
# loop gain of compensated network

# ACom =(1+j(f/fH))/(1+j(f/fL))
# fH = (1/2*pie*R1*C)
# fL = (1/2*pie*(R1+R2)*C)
R1 = (1/(2*3.14*C*fH))#
print 'The compensating first resistor R1 value is = %0.2f'%R1,' K ohm '#
R2 = ((1)/(2*3.14*C*fL))-(R1)#
print 'The compensating second resistor R2 value is = %0.2f'%R2,' K ohm '#

The compensating first resistor R1 value is = 0.80  K ohm
The compensating second resistor R2 value is = 7.17  K ohm


## Example 5.22 Pg 126¶

In :
from __future__ import division
# To determine input output miller capacitances
A = 100 # #gain
Cm = 0.1 #  # uF # compensated capacitor

# the input output miller capacitance are defined as
Cin = Cm*(A+1)#
print 'The input miller capacitance Cin value is = %0.2f'%Cin,'uF '#
Cout = (Cm*((A+1)/A))#
print 'The output miller capacitance Cout value is = %0.2f'%Cout,'uF '#

The input miller capacitance Cin value is = 10.10 uF
The output miller capacitance Cout value is = 0.10 uF


## Example 5.23 Pg 127¶

In :
from __future__ import division
from math import pi
# To determine input output miller capacitances
A = 150 # #gain
Cm = 0.02 #  # uF # compensated capacitor

# the input output miller capacitance are defined as
Cin = Cm*(A+1)#
print 'The input miller capacitance Cin value is = %0.2f'%Cin,'uF '#
Cout = (Cm*((A+1)/A))#
print 'The output miller capacitance Cout value is = %0.2f'%Cout,'uF '#

# In the miller compensating network input capacitance introduce a pole . The initiated frequency of miller compensating network by pole is define as

# fp = 1/(2*pi*R*Cin)#
R = 1 # # K ohm
fp = 1/(2*pi*R*Cout)#
print 'The initiated frequency of miller compensating network by pole is = %0.2f'%fp,' KHz '#

The input miller capacitance Cin value is = 3.02 uF
The output miller capacitance Cout value is = 0.02 uF
The initiated frequency of miller compensating network by pole is = 7.91  KHz


## Example 5.24 Pg 128¶

In :
from __future__ import division
# To determine the slew rate of an op-amp
f = 1 # # MHz # unity frequency
Ic = 1*10**-6 #  # uA # capacitor current
Vt = 0.7 # # V  # threshold voltage

# the slew rate of an op-amp is defined as
# Slew rate = (dVo/dt)
Slewrate = 8*3.14*Vt*f #
print 'the slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec '#

# The compansated capacitance Cm is
gm = (Ic/Vt)#
Cm = (gm/4*3.14*f)*1e6 # pF
print 'The compansated capacitance value is = %0.2f'%Cm,'pF '#

the slew rate of an op-amp is = 17.58  V/u sec
The compansated capacitance value is = 1.12 pF


## Example 5.25 Pg 129¶

In :
from __future__ import division
# To determine the cut off frequency of an op-amp
f = 1*10**3 # # Hz # unity frequency
Av = 200 # # V/mV  # dc gain

# the unity gain frequency of an op-amp is defined as
# f = Av*fc #

# cut off frequency
fc = (f/Av)#
print 'Cut -off frequency of an op-amp is = %0.2f'%fc,' Hz '#

Cut -off frequency of an op-amp is = 5.00  Hz


## Example 5.26 Pg 129¶

In :
from __future__ import division
# To find the maximum frequency of input signal in op-amp circuit
Vin = 25*10**-3 # # V  # input voltage
Slewrate = 0.8/10**-6 #  # V/uV   # Slew rate of an op-amp
R2 = 350*10**3 #  #  ohm  # feedback resistance
R1 = 10*10**3 #  # ohm  # input resistance

# the closed loop gain
# ACL = (mod (Vo/Vin)) = (mod(R2/R1))#
ACL = abs(R2/R1)#
print 'the closed loop gain ACL is = %0.2f'%ACL,' '#

# the output gain factor K is given as
K = ACL*Vin #
print 'The output gain factor K is = %0.2f'%K,' V'#

# the maximum frequency of an op-amp is
wmax = (Slewrate/K)#
fmax = wmax/(2*3.14)#
print 'The maximum frequency of an op-amp fmax = %0.2f'%(fmax/1000),' KHz'#

the closed loop gain ACL is = 35.00
The output gain factor K is = 0.88  V
The maximum frequency of an op-amp fmax = 145.59  KHz


## Example 5.27 Pg 129¶

In :
from __future__ import division
# To find the maximum frequency of op-amp circuit
Vin = 0.015 # # V  # input voltage
Slewrate = 0.8 #  # V/uV   # Slew rate of an op-amp
R2 = 120*10**3 #  #  ohm  # feedback resistance
R1 = 5*10**3 #  # ohm  # input resistance

# the closed loop gain
# ACL = (mod (Vo/Vin)) = (mod(R2/R1))#
ACL = abs(R2/R1)#
print 'the closed loop gain ACL is = %0.2f'%ACL,' '#

# the output gain factor K is given as
K = ACL*Vin #
print 'The output gain factor K is = %0.2f'%K,' V'#

# the maximum frequency of an op-amp is
wmax = (Slewrate/K)#
print 'The wmax is = %0.2f'%wmax,'*10**6 rad/sec'# # *10**6 because Slewrate is V/uV

# the signal frequency may be w = 500*10**3 rad/sec  that is less than the maximum frequency value

the closed loop gain ACL is = 24.00
The output gain factor K is = 0.36  V
The wmax is = 2.22 *10**6 rad/sec


## Example 5.28 Pg 130¶

In :
from __future__ import division
# To determine the compensated capacitance of an op-amp
Slewrate = 10 # # V/u sec
Ic = 1*10**-3 #  # mA # capacitor current
Vt = 0.7 # # V  # threshold voltage

# the slew rate of an op-amp is defined as
# Slew rate = (dVo/dt)
# the unity frequency f is
f =(Slewrate/(8*3.14*Vt))#
f = f*10**6#  # *10**6 because Slew rate is V/uV
print 'the unity frequency f is = %0.2f'%(f/1e3),'kHz '#

# The compansated capacitance Cm is
gm = (Ic/Vt)#
Cm = (gm)/(4*3.14*f)*1e9 #
print 'The compansated capacitance Cm value is = %0.1f'%Cm,'nF '#

the unity frequency f is = 568.70 kHz
The compansated capacitance Cm value is = 0.2 nF


## Example 5.29 Pg 131¶

In :
from __future__ import division
# To find Slew rate of an op-amp
Iq = 15 # # uA  # bias current
Cm = 30  # # pF  # internal frequency compensated capacitor
Slewrate = (Iq/Cm)
print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec'#

the Slew rate of an op-amp is = 0.50  V/u sec


## Example 5.30 Pg 131¶

In :
from __future__ import division
# To find Slew rate of an op-amp
Iq = 21 # # uA  # bias current
Cm = 31  # # pF  # internal frequency compensated capacitor
Slewrate = (Iq/Cm)#
print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec'#

the Slew rate of an op-amp is = 0.68  V/u sec


## Example 5.31 Pg 131¶

In :
from __future__ import division
# To determine full power and small signal bandwidth of an op-amp with unity gain
f = 100*10**6 # # Hz  unity gain bandwidth
ACL = 10**4 # # maximum closed loop gain
Slewrate = 0.51 # # V/u sec
Vp = 10 # # V peak volt

# The full power bandwidth
FPBW = (Slewrate/(2*3.14*Vp))#
FPBW = FPBW*10**6 #  # *10**6 because Slew rate is V/uV
print 'The full power bandwidth FPBW is = %0.2f'%(FPBW/1e3),'kHz '#

# the 3-db frequency or small signal band width
f3db = (f/ACL)#
print 'The 3-db frequency or small signal band width f3db is = %0.f'%(f3db/1e3),'kHz '#

The full power bandwidth FPBW is = 8.12 kHz
The 3-db frequency or small signal band width f3db is = 10 kHz


## Example 5.32 Pg 132¶

In :
from __future__ import division
# To determine full power and small signal bandwidth of an op-amp with unity gain
f = 100*10**6 # # Hz  unity gain bandwidth
ACL = 10**4 # # maximum closed loop gain
Slewrate = 0.51 # # V/u sec
Vp = 10 # # V peak volt

# The full power bandwidth
FPBW = (Slewrate/(2*3.14*Vp))#
FPBW = FPBW*10**6 #  # *10**6 because Slew rate is V/uV
print 'The full power bandwidth FPBW is = %0.2f'%(FPBW/1e3),'kHz '#

# the 3-db frequency or small signal band width
f3db = (f/ACL)#
print 'The 3-db frequency or small signal band width f3db is = %0.f'%(f3db/1e3),'kHz '#

The full power bandwidth FPBW is = 8.12 kHz
The 3-db frequency or small signal band width f3db is = 10 kHz


## Example 5.33 Pg 132¶

In :
from __future__ import division
# To find Slew rate and closed loop gain of an op-amp
fu = 1*10**6 # # Hz  # unity gain bandwidth
fmax = 5*10**3 # # KHz  # full power bandwidth
F3db = 12*10**3 # # Hz  # small signal bandwidth
Vp = 10 # # V  # peak volt

# the full power bandwidth of an op-amp
# fmax=FPBW = (Slew rate/2*3.14*Vp)#
Slewrate = 2*3.14*Vp*fmax#
Slewrate = Slewrate*(10**-6)#  # *10**-6 because Slewrate is V/u
print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec '#

# # the 3-db frequency or small signal band width
#f3db = (f/ACL)#
#the closed loop gain ACL
ACL = fu/F3db #
print 'The closed loop gain ACL is = %0.2f'%ACL,' '#

the Slew rate of an op-amp is = 0.31  V/u sec
The closed loop gain ACL is = 83.33