{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 5 Characteristic of Operational Amplifier"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.1 Pg 110"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = 404.00 mV \n",
" the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 75.00 mV \n",
" the total offset voltage (Vo) of an op-amp circuit is = 479.00 mV \n"
]
}
],
"source": [
"from __future__ import division\n",
"# find the total offset voltage of feedback op-amp\n",
"\n",
"Vos = 4 # #mV # input offset volt\n",
"Ios = 150*10**-3 # # input offset current\n",
"R1 = 5 # #kilo ohm # input resistance\n",
"R2 = 500 # #kilo ohm # feedback resistance\n",
"\n",
"# the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is\n",
"Vo1 = ((R1+R2)/(R1)*Vos) #\n",
"print ' the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = %0.2f'%Vo1,' mV '#\n",
"\n",
"# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is\n",
"Vo2 = R2*Ios #\n",
"print ' the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.2f'%Vo2,' mV '#\n",
"\n",
"# the total offset voltage is\n",
"Vo = Vo1+Vo2 #\n",
"print ' the total offset voltage (Vo) of an op-amp circuit is = %0.2f'%Vo,' mV '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.2 Pg 111"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = 52.00 mV \n",
" the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 5.00 mV \n",
" the total offset voltage (Vo) of an op-amp circuit is = 57.00 mV \n"
]
}
],
"source": [
"# find the total offset voltage of feedback op-amp\n",
"\n",
"Vos = 2 # #mV # input offset volt\n",
"Ios = 20*10**-3 # # input offset current\n",
"R1 = 10 # #kilo ohm # input resistance\n",
"R2 = 250 # #kilo ohm # feedback resistance\n",
"\n",
"# the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is\n",
"Vo1 = ((R1+R2)/(R1)*Vos) #\n",
"print ' the output voltage (Vo) of an op-amp circuit due to input offset voltage (Vos) is = %0.2f'%Vo1,' mV '#\n",
"\n",
"# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is\n",
"Vo2 = R2*Ios #\n",
"print ' the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.2f'%Vo2,' mV '#\n",
"\n",
"# the total offset voltage is\n",
"Vo = Vo1+Vo2 #\n",
"print ' the total offset voltage (Vo) of an op-amp circuit is = %0.2f'%Vo,' mV '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.3 Pg 111"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the input offset voltage (Vos) of an op-amp circuit is = 1.187 mV \n"
]
}
],
"source": [
"# find the input offset voltage of an op-amp circuit\n",
"\n",
"Vo = 90.2 # #mV # output voltage\n",
"R1 = 2 # #kilo ohm # input resistence\n",
"R2 = 150 # #kilo ohm # feedback resistence\n",
"\n",
"# the input offset voltage (Vos) of an op-amp circuit is defined as\n",
"Vos = ((R1)/(R1+R2)*Vo) #\n",
"print 'the input offset voltage (Vos) of an op-amp circuit is = %0.3f'%Vos,' mV '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.4 Pg 112"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the output voltage due to the input offset voltage is = 36.00 mV \n"
]
}
],
"source": [
"# find the output voltage of an op-amp circuit\n",
"\n",
"Vos = 1 # #mV # input offset volt\n",
"R1 = 10 # #kilo ohm # input resistance\n",
"R2 = 350 # #kilo ohm # feedback resistance\n",
"\n",
"# the output voltage due to the input offset voltage of the op-amp circuit is defined by\n",
"Vo1 = ((R1+R2)/(R1)*Vos) #\n",
"print 'the output voltage due to the input offset voltage is = %0.2f'%Vo1,' mV '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.5 Pg 113"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the output voltage of the circuit due to bias current is = 0.11 V \n",
"Bias compensated resistor is = 9.09 kilo ohm \n",
"Bias compensated output voltage is = 0.01 V \n"
]
}
],
"source": [
"# Determine the bias current effect with and without current compensation method\n",
"\n",
"R1 = 10 # #kilo ohm\n",
"R2 = 100 # #kilo ohm\n",
"Ib1 = 1.1*10**-3 #\n",
"Ib2 = 1*10**-3 # \n",
"# the output voltage of the circuit due to bias current is\n",
"Vo = Ib1*R2 #\n",
"print 'the output voltage of the circuit due to bias current is = %0.2f'%Vo,' V '#\n",
"\n",
"#Bias compensated resistor is given by\n",
"R3 = (R1*R2)/(R1+R2) #\n",
"print 'Bias compensated resistor is = %0.2f'%R3,' kilo ohm '#\n",
"\n",
"#Bias compensated output voltage is given by\n",
"Vo = R2*(Ib1-Ib2)#\n",
"print 'Bias compensated output voltage is = %0.2f'%Vo,' V '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.6 Pg 113"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = 80 nA \n"
]
}
],
"source": [
"# find the input offset current of an op-amp circuit\n",
"\n",
"Vo = 12*10**-3# # V # output voltage\n",
"R1 = 2*10**3 # # ohm # input resistence\n",
"R2 = 150*10**3# # ohm # feedback resistence\n",
"\n",
"# the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is\n",
"# Vo = R2*Ios #\n",
"Ios = Vo/R2 *1e9 # nA\n",
"print 'the output voltage (Vo) of an op-amp circuit due to input offset current (Ios) is = %0.f'%Ios,'nA '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.7 Pg 114"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The current in the inverting input terminal is = 27.50 nA \n",
"The current in the non-inverting input terminal is= 32.50 nA \n"
]
}
],
"source": [
"# Determine the bias current of inverting and non-inverting\n",
"Ios = 5 # #nA # input offset current\n",
"Ib = 30 # #nA # input bias current\n",
"\n",
"# the input bias current of an op-amp is \n",
"\n",
"#Ib =(Ib1+Ib2)/(2)#\n",
"\n",
"# the offset current Ios is define as\n",
"\n",
"#Ios = abs(Ib1-Ib2) #\n",
"\n",
"Ib1=Ib-(Ios/2)#\n",
"print 'The current in the inverting input terminal is = %0.2f'%Ib1,' nA '#\n",
"\n",
"Ib2 =Ib+(Ios/2)#\n",
"print 'The current in the non-inverting input terminal is= %0.2f'%Ib2,' nA '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.8 Pg 115"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Feedback transfer function is = 0.01 \n",
"OR 1/Beta is = 100.10 \n",
"Feedback transfer function is = -0.01 \n",
"OR 1/Beta is = -100.10 \n"
]
}
],
"source": [
"#determine the feedback transfer function of an op-amp for the following condition\n",
"# a) When open loop gain of 10**5 and the closed loop gain of 100\n",
"A = 10**5 # # open loop gain\n",
"Af = 100 # #closed loop gain\n",
"# Feedback transfer function is\n",
"beta =(1/Af)-(1/A)#\n",
"print 'Feedback transfer function is = %0.2f'%beta,''#\n",
"beta = 1/beta #\n",
"print 'OR 1/Beta is = %0.2f'%beta,''#\n",
"\n",
"# For an open loop gain of -10**5 and closed loop gain of -100\n",
"A = -10**5 # # open loop gain\n",
"Af = -100 # #closed loop gain\n",
"# Feedback transfer function is\n",
"beta =(1/Af)-(1/A)#\n",
"print 'Feedback transfer function is = %0.2f'%beta,''#\n",
"beta = 1/beta #\n",
"print 'OR 1/Beta is = %0.2f'%beta,''#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.9 Pg 115"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"open loop gain is = 2000.00\n"
]
}
],
"source": [
"#to determine open loop gain\n",
"beta = 0.0120 # # Feedback transfer function\n",
"Af = 80 # #closed loop gain\n",
"A = (Af)/(1-beta*Af) #\n",
"print 'open loop gain is = %0.2f'%A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.10 Pg 116"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"close loop gain dAf is = 49.78\n",
"the percent change of closed loop gain dAf is = 0.45 %\n"
]
}
],
"source": [
" # To Determine the percent of change in the closed loop gain Af of feedback op-amp circuit\n",
"A = 10**5 # # open loop gain\n",
"Af = 50 # # close loop gain\n",
"beta = 0.01999 # # feedback transfer function\n",
"dA = 10**4 # # the change in the open llop gain \n",
"\n",
"# close loop gain\n",
"dAf = ((dA)/(1+dA*beta))#\n",
"print 'close loop gain dAf is = %0.2f'%dAf\n",
"\n",
"# the percent change of closed loop gain \n",
"dAf = (((Af-dAf)/(Af))*100)#\n",
"print 'the percent change of closed loop gain dAf is = %0.2f'%dAf,'%'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.11 Pg 116"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the feedback transfer function beta is = 0.0199\n",
"the closed loop bandwidth wfH is = 125600\n"
]
}
],
"source": [
"# To Determine the bandwidth of feedback amplifier\n",
"A = 10**4 # # open loop gain\n",
"Af = 50 # # close loop gain\n",
"wH = 628 # #(2*pi*100) # rad/sec # open loop bandwidth\n",
"\n",
"# close loop gain of an op-amp is defined as\n",
"# Af = ((A)/(1+A*beta))# \n",
"\n",
"# the feedback transfer function is given as\n",
"beta = (1/Af)-(1/A) #\n",
"print 'the feedback transfer function beta is = %0.4f'%beta\n",
"\n",
"# closed loop bandwidth\n",
"wfH = wH*(1+beta*A)#\n",
"print 'the closed loop bandwidth wfH is = %0.f'%wfH"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.12 Pg 117"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the unity gain bandwidth is = 1e+06 Hz\n",
"the maximum close loop gain ACL is = 50.00 \n"
]
}
],
"source": [
"from __future__ import division\n",
"# To calculate unity gain bandwidth and maximum close loop gain\n",
"A = 10**5 # # open loop gain\n",
"fo = 10 # # Hz # dominant pole frequency\n",
"fdb = 20*10**3 # #Hz # 3-db frequency\n",
"\n",
"# the unity gain bandwidth\n",
"f1 = fo*A #\n",
"print 'the unity gain bandwidth is = %0.e'%f1,'Hz'#\n",
"\n",
"# the maximum close loop gain\n",
"ACL = (f1/fdb) #\n",
"print 'the maximum close loop gain ACL is = %0.2f'%ACL,''#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.13 Pg 117"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the unity gain bandwidth is = 60 kHz\n",
"the maximum close loop gain ACL is = 5.00 \n"
]
}
],
"source": [
"# To calculate unity gain bandwidth and maximum close loop gain\n",
"A = 10**3 # # open loop gain\n",
"fo = 60 # # Hz # dominant pole frequency\n",
"fdb = 12*10**3 # #Hz # 3-db frequency\n",
"\n",
"# the unity gain bandwidth\n",
"f1 = fo*A #\n",
"print 'the unity gain bandwidth is = %0.f'%(f1/1e3),'kHz'#\n",
"\n",
"# the maximum close loop gain\n",
"ACL = (f1/fdb) #\n",
"print 'the maximum close loop gain ACL is = %0.2f'%ACL,''#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.14 Pg 118"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the dominant pole frequency (fPD) of an op-amp is = 2.5 kHz\n"
]
}
],
"source": [
"# To determine the dominant pole frequency of an op-amp\n",
"Ao = 2*10**5 # # low frequency open loop gain\n",
"f = 5*10**6 # # Hz # pole frequency\n",
"ACL = 100 # # low frequency closed lkoop gain\n",
"p_margin = 80 # \n",
"\n",
"# the dominant pole frequency of an op-amp\n",
"fPD = (ACL)*(f/Ao)/1e3\n",
"print 'the dominant pole frequency (fPD) of an op-amp is = %0.1f'%fPD,'kHz'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.15 Pg 118"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FL = 6.37 KHz \n",
"Acom = [ magnitude = 6.3*10**-3 angle = -89.6 degree ]\n",
"Ac = [ magnitude = 0.68 angle = 0.4 degree ]\n"
]
}
],
"source": [
" # Determine the loop gain of compensated network\n",
"C = 0.0025*10**-6 # # farad\n",
"R = 10*10**3 # # ohm\n",
"F = 1*10**6 # # Hz\n",
"Ac1 = 100 # \n",
"angle1 = 90 #\n",
"\n",
"# the close loop gain of a compensated network is defined as\n",
"# Ac = Acl*Acom #\n",
"\n",
"#Acom = 1/(1+%(F/FL))#\n",
"\n",
"FL = 1/(2*3.14*R*C)#\n",
"print 'FL = %0.2f'%(FL/1000),' KHz '# # Round Off Error\n",
"\n",
"# Acom = 1/(1+%j(F/FL))#\n",
"# After putting value of F ,FL we get\n",
"\n",
"# Acom = 1/(1+%j(158.7))# # 1+%j(158.7) Rectangular Form where real part is 1 and imaginary part is 158.7\n",
"\n",
"# After converting rectangular from into polar from we get\n",
" \n",
"print 'Acom = [ magnitude = 6.3*10**-3 angle = -89.6 degree ]'#\n",
"\n",
"# Ac = Ac1*Acom # equation 1\n",
"\n",
"# after putting Ac1 and Acom value in equation 1 we get Ac1 = 100 angle 90 and Acom = 6.3*10**-3 angle = -89.6 \n",
"\n",
"print 'Ac = [ magnitude = 0.68 angle = 0.4 degree ]'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.16 Pg 119"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FL = 1.1 KHz \n",
"Acom = [ magnitude = 0.68 angle = -47.7 degree ]\n"
]
}
],
"source": [
"# Determine the loop gain of compensated network\n",
"\n",
"C = 0.01*10**-6 # # farad\n",
"R = 15*10**3 # # ohm\n",
"F = 1*10**6 # # Hz\n",
"\n",
"# the close loop gain of a compensated network is defined as\n",
"# Ac = Acl*Acom #\n",
"\n",
"#Acom = 1/(1+%(F/FL))#\n",
"\n",
"FL = 1/(2*3.14*R*C)#\n",
"print 'FL = %0.1f'%(FL/1000),' KHz '# # Round Off Error\n",
"\n",
"# Acom = 1/(1+%j(F/FL))#\n",
"# After putting value of F ,FL we get\n",
"\n",
"# Acom = 1/(1+%j(0.9))# # 1+%j(0.9) Rectangular Form where real part is 1 and imaginary part is 0.9\n",
"\n",
"# After converting rectangular from into polar from we get\n",
" \n",
"print 'Acom = [ magnitude = 0.68 angle = -47.7 degree ]'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.17 Pg 120"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FL = 4.25 KHz \n",
"Acom for F = 0 KHz = [ magnitude = 150 angle = 85 degree ]\n",
"Acom for F = 2 KHz= [ magnitude = 136.4 angle = 64.5 degree ]\n",
"Acom for F = 4 KHz = [ magnitude = 107.14 angle = 41.7 degree ]\n",
"Acom for F = 6 KHz = [ magnitude = 88.24 angle = 30.25 degree ]\n",
"Acom for F = 8 KHz = [ magnitude = 71.4 angle = 23 degree ]\n",
"Acom for F = 10 KHz = [ magnitude = 58.59 angle = 18 degree ]\n",
"Acom for F = 20 KHz = [ magnitude = 31.12 angle = 7 degree ]\n",
"Acom for F = 40 KHz = [ magnitude = 15.9 angle = 1.1 degree ]\n",
"Acom for F = 80 KHz = [ magnitude = 7.9 angle = -2 degree ]\n",
"Acom for F = 100 KHz = [ magnitude = 6.4 angle = -2.6 degree ]\n",
"Acom for F = 200 KHz = [ magnitude = 3.18 angle = -3.8 degree ]\n",
"Acom for F = 400 KHz = [ magnitude = 1.59 angle = -4.4 degree ]\n",
"Acom for F = 800 KHz = [ magnitude = 0.79 angle = -4.7 degree ]\n",
"Acom for F = 1 MHz = [ magnitude = 0.64 angle = -4.7 degree ]\n",
"Acom for F = 1.2 MHz = [ magnitude = 0.52 angle = -4.7 degree ]\n",
"Acom for F = 1.4 MHz = [ magnitude = 0.45 angle = -4.7 degree ]\n",
"Acom for F = 1.6 MHz = [ magnitude = 0.4 angle = -4.7 degree ]\n"
]
}
],
"source": [
"# Determine the loop gain of compensated network\n",
"\n",
"C = 0.5*10**-6 # # farad\n",
"R = 75 # # ohm\n",
"F = 1*10**6 # # Hz\n",
"Ac1 = 150 # \n",
"angle1 = 85 #\n",
"\n",
"# the close loop gain of a compensated network is defined as\n",
"# Ac = Acl*Acom #\n",
"\n",
"#Acom = 1/(1+%(F/FL))#\n",
"\n",
"FL = 1/(2*3.14*R*C)#\n",
"print 'FL = %0.2f'%(FL/1000),' KHz '# # Round Off Error\n",
"\n",
"# Acom = 1/(1+%j(F/FL))#\n",
"\n",
"# After putting value of FL we get\n",
"\n",
"# Acom = 1/(1+%j(F/4.24*10**3))# equation 1\n",
"\n",
"# As F is unknown in above equation 1 \n",
"# by putting different value of F we get Acom for different frequency\n",
"\n",
"\n",
"# If F = 0 KHz\n",
"\n",
"# Acom = 1/(1+%j(0/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 0 KHz = [ magnitude = 150 angle = 85 degree ]'#\n",
"\n",
"\n",
"# If F = 2 KHz\n",
"\n",
"# Acom = 1/(1+%j(2*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 2 KHz= [ magnitude = 136.4 angle = 64.5 degree ]'#\n",
"\n",
"\n",
"# If F = 4 KHz\n",
"\n",
"# Acom = 1/(1+%j(4*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 4 KHz = [ magnitude = 107.14 angle = 41.7 degree ]'#\n",
"\n",
"\n",
"# If F = 6 KHz\n",
"\n",
"# Acom = 1/(1+%j(6*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 6 KHz = [ magnitude = 88.24 angle = 30.25 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 8 KHz\n",
"\n",
"# Acom = 1/(1+%j(8*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 8 KHz = [ magnitude = 71.4 angle = 23 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 10 KHz\n",
"\n",
"# Acom = 1/(1+%j(10*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 10 KHz = [ magnitude = 58.59 angle = 18 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 20 KHz\n",
"\n",
"# Acom = 1/(1+%j(20*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 20 KHz = [ magnitude = 31.12 angle = 7 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 40 KHz\n",
"\n",
"# Acom = 1/(1+%j(40*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 40 KHz = [ magnitude = 15.9 angle = 1.1 degree ]'#\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# If F = 80 KHz\n",
"\n",
"# Acom = 1/(1+%j(80*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 80 KHz = [ magnitude = 7.9 angle = -2 degree ]'#\n",
"\n",
"\n",
"\n",
"\n",
"# If F = 100 KHz\n",
"\n",
"# Acom = 1/(1+%j(100*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 100 KHz = [ magnitude = 6.4 angle = -2.6 degree ]'#\n",
"\n",
"\n",
"\n",
"\n",
"# If F = 200 KHz\n",
"\n",
"# Acom = 1/(1+%j(200*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 200 KHz = [ magnitude = 3.18 angle = -3.8 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 400 KHz\n",
"\n",
"# Acom = 1/(1+%j(400*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 400 KHz = [ magnitude = 1.59 angle = -4.4 degree ]'#\n",
"\n",
"\n",
"# If F = 800 KHz\n",
"\n",
"# Acom = 1/(1+%j(800*10**3/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 800 KHz = [ magnitude = 0.79 angle = -4.7 degree ]'#\n",
"\n",
"\n",
"# If F = 1 MHz\n",
"\n",
"# Acom = 1/(1+%j(1*10**6/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 1 MHz = [ magnitude = 0.64 angle = -4.7 degree ]'#\n",
"\n",
"\n",
"# If F = 1.2 MHz\n",
"\n",
"# Acom = 1/(1+%j(1.2*10**6/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 1.2 MHz = [ magnitude = 0.52 angle = -4.7 degree ]'#\n",
"\n",
"\n",
"\n",
"# If F = 1.4 MHz\n",
"\n",
"# Acom = 1/(1+%j(1.4*10**6/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 1.4 MHz = [ magnitude = 0.45 angle = -4.7 degree ]'#\n",
"\n",
"\n",
"# If F = 1.6 MHz\n",
"\n",
"# Acom = 1/(1+%j(1.6*10**6/4.24*10**3))# \n",
"\n",
"# After solving and converting rectangular from into polar from we get\n",
" \n",
"print 'Acom for F = 1.6 MHz = [ magnitude = 0.4 angle = -4.7 degree ]'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.18 Pg 123"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The compensating resistor value is = 15.92 ohm \n"
]
}
],
"source": [
"# to design compensating network\n",
"fp = 500*10**3 # # pole frequency\n",
"C = 0.02*10**-6 # # F # we choose\n",
"# loop gain of compensated network\n",
"\n",
"# ACom =(1)/(1+j(f/fp))\n",
"# fp = (1/2*pie*R*C)\n",
"R = (1/(2*3.14*C*fp))#\n",
"print 'The compensating resistor value is = %0.2f'%R,' ohm '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.19 Pg 123"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FH = 6.37 KHz \n",
"FL = 2.12 KHz \n",
"Acom = [ magnitude = 0.34 angle = -0.24 degree ]\n",
"Ac = [ magnitude = 34 angle = 89.76 degree ]\n"
]
}
],
"source": [
" # Determine the loop gain of compensated network\n",
"\n",
"C = 0.0025*10**-6 # # farad\n",
"R1 = 10*10**3 # # ohm\n",
"R2 = 20*10**3 # # ohm\n",
"F = 1*10**6 # # Hz\n",
"Ac1 = 100 # \n",
"angle1 = 90 #\n",
"\n",
"# the close loop gain of a compensated network is defined as\n",
"\n",
"# Ac = Acl*Acom #\n",
"\n",
"#Acom = (1+%(F/FH))/(1+%(F/FL))#\n",
"\n",
"FH = 1/(2*3.14*R1*C)#\n",
"print 'FH = %0.2f'%(FH/1000),' KHz '# # Round Off Error\n",
"\n",
"\n",
"FL = 1/(2*3.14*(R1+R2)*C)#\n",
"print 'FL = %0.2f'%(FL/1000),' KHz '# # Round Off Error\n",
"\n",
"\n",
"#Acom = (1+%(F/FH))/(1+%(F/FL))#\n",
"\n",
"# After putting value of FH ,FL we get\n",
"\n",
"# Acom = (1+%j(158.7))/(1+%j(471.7) \n",
"\n",
"# After converting rectangular from into polar from we get\n",
" \n",
"print 'Acom = [ magnitude = 0.34 angle = -0.24 degree ]'#\n",
"\n",
"# Ac = Ac1*Acom # equation 1\n",
"\n",
"# after putting Ac1 and Acom value in equation 1 we get Ac1 = 100 angle 90 and Acom = 0.34 angle = -0.24 \n",
"\n",
"print 'Ac = [ magnitude = 34 angle = 89.76 degree ]'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.20 Pg 124"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FH = 1.59 KHz \n",
"FL = 0.64 KHz \n",
"Acom = [magnitude = 0.4] \n"
]
}
],
"source": [
" # Determine the loop gain of compensated network\n",
"C = 0.01*10**-6 # # farad\n",
"R1 = 10*10**3 # # ohm\n",
"R2 = 15*10**3 # # ohm\n",
"F = 1*10**6 # # Hz\n",
"\n",
"\n",
"# the close loop gain of a compensated network is defined as\n",
"\n",
"#Acom = (1+%(F/FH))/(1+%(F/FL))#\n",
"\n",
"FH = 1/(2*3.14*R1*C)#\n",
"print 'FH = %0.2f'%(FH/1000),' KHz '# # Round Off Error\n",
"\n",
"\n",
"FL = 1/(2*3.14*(R1+R2)*C)#\n",
"print 'FL = %0.2f'%(FL/1000),' KHz '# # Round Off Error\n",
"\n",
"\n",
"#Acom = (1+%(F/FH))/(1+%(F/FL))#\n",
"\n",
"# After putting value of FH ,FL we get\n",
"\n",
"# Acom = (1+%j(658.9))/(1+%j(1.56*10**3) \n",
"\n",
"# After converting rectangular from into polar from we get\n",
" \n",
"print 'Acom = [magnitude = 0.4] '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.21 Pg 125"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The compensating first resistor R1 value is = 0.80 K ohm \n",
"The compensating second resistor R2 value is = 7.17 K ohm \n"
]
}
],
"source": [
"# to design compensating network\n",
"fH = 10 # #k ohm # break frequency initiated by a zero\n",
"fL = 1 # #k ohm # break frequency initiated by a pole\n",
"C = 0.02# # uF # we choose\n",
"# loop gain of compensated network\n",
"\n",
"# ACom =(1+j(f/fH))/(1+j(f/fL))\n",
"# fH = (1/2*pie*R1*C)\n",
"# fL = (1/2*pie*(R1+R2)*C)\n",
"R1 = (1/(2*3.14*C*fH))#\n",
"print 'The compensating first resistor R1 value is = %0.2f'%R1,' K ohm '#\n",
"R2 = ((1)/(2*3.14*C*fL))-(R1)#\n",
"print 'The compensating second resistor R2 value is = %0.2f'%R2,' K ohm '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.22 Pg 126"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The input miller capacitance Cin value is = 10.10 uF \n",
"The output miller capacitance Cout value is = 0.10 uF \n"
]
}
],
"source": [
"# To determine input output miller capacitances\n",
"A = 100 # #gain\n",
"Cm = 0.1 # # uF # compensated capacitor\n",
"\n",
"# the input output miller capacitance are defined as\n",
"Cin = Cm*(A+1)#\n",
"print 'The input miller capacitance Cin value is = %0.2f'%Cin,'uF '#\n",
"Cout = (Cm*((A+1)/A))# \n",
"print 'The output miller capacitance Cout value is = %0.2f'%Cout,'uF '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.23 Pg 127"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The input miller capacitance Cin value is = 3.02 uF \n",
"The output miller capacitance Cout value is = 0.02 uF \n",
"The initiated frequency of miller compensating network by pole is = 7.96 KHz \n"
]
}
],
"source": [
"from math import pi\n",
"# To determine input output miller capacitances\n",
"A = 150 # #gain\n",
"Cm = 0.02 # # uF # compensated capacitor\n",
"\n",
"# the input output miller capacitance are defined as\n",
"Cin = Cm*(A+1)#\n",
"print 'The input miller capacitance Cin value is = %0.2f'%Cin,'uF '#\n",
"Cout = (Cm*((A+1)/A))# \n",
"print 'The output miller capacitance Cout value is = %0.2f'%Cout,'uF '#\n",
"\n",
"# In the miller compensating network input capacitance introduce a pole . The initiated frequency of miller compensating network by pole is define as\n",
"\n",
"# fp = 1/(2*pi*R*Cin)#\n",
"R = 1 # # K ohm\n",
"fp = 1/(2*pi*R*Cout)#\n",
"print 'The initiated frequency of miller compensating network by pole is = %0.2f'%fp,' KHz '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.24 Pg 128"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the slew rate of an op-amp is = 17.58 V/u sec \n",
"The compansated capacitance value is = 1.12 pF \n"
]
}
],
"source": [
"# To determine the slew rate of an op-amp\n",
"f = 1 # # MHz # unity frequency\n",
"Ic = 1*10**-6 # # uA # capacitor current\n",
"Vt = 0.7 # # V # threshold voltage\n",
"\n",
"# the slew rate of an op-amp is defined as\n",
"# Slew rate = (dVo/dt)\n",
"Slewrate = 8*3.14*Vt*f #\n",
"print 'the slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec '#\n",
"\n",
"# The compansated capacitance Cm is\n",
"gm = (Ic/Vt)#\n",
"Cm = (gm/4*3.14*f)*1e6 # pF\n",
"print 'The compansated capacitance value is = %0.2f'%Cm,'pF '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.25 Pg 129"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cut -off frequency of an op-amp is = 5.00 Hz \n"
]
}
],
"source": [
" # To determine the cut off frequency of an op-amp\n",
"f = 1*10**3 # # Hz # unity frequency\n",
"Av = 200 # # V/mV # dc gain\n",
"\n",
"# the unity gain frequency of an op-amp is defined as\n",
"# f = Av*fc #\n",
"\n",
"# cut off frequency\n",
"fc = (f/Av)#\n",
"print 'Cut -off frequency of an op-amp is = %0.2f'%fc,' Hz '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.26 Pg 129"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the closed loop gain ACL is = 35.00 \n",
"The output gain factor K is = 0.88 V\n",
"The maximum frequency of an op-amp fmax = 145.59 KHz\n"
]
}
],
"source": [
"# To find the maximum frequency of input signal in op-amp circuit\n",
"Vin = 25*10**-3 # # V # input voltage\n",
"Slewrate = 0.8/10**-6 # # V/uV # Slew rate of an op-amp\n",
"R2 = 350*10**3 # # ohm # feedback resistance\n",
"R1 = 10*10**3 # # ohm # input resistance\n",
"\n",
"# the closed loop gain\n",
"# ACL = (mod (Vo/Vin)) = (mod(R2/R1))#\n",
"ACL = abs(R2/R1)#\n",
"print 'the closed loop gain ACL is = %0.2f'%ACL,' '#\n",
"\n",
"# the output gain factor K is given as\n",
"K = ACL*Vin #\n",
"print 'The output gain factor K is = %0.2f'%K,' V'#\n",
"\n",
"# the maximum frequency of an op-amp is\n",
"wmax = (Slewrate/K)#\n",
"fmax = wmax/(2*3.14)#\n",
"print 'The maximum frequency of an op-amp fmax = %0.2f'%(fmax/1000),' KHz'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.27 Pg 129"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the closed loop gain ACL is = 24.00 \n",
"The output gain factor K is = 0.36 V\n",
"The wmax is = 2.22 *10**6 rad/sec\n"
]
}
],
"source": [
"# To find the maximum frequency of op-amp circuit\n",
"Vin = 0.015 # # V # input voltage\n",
"Slewrate = 0.8 # # V/uV # Slew rate of an op-amp\n",
"R2 = 120*10**3 # # ohm # feedback resistance\n",
"R1 = 5*10**3 # # ohm # input resistance\n",
"\n",
"# the closed loop gain\n",
"# ACL = (mod (Vo/Vin)) = (mod(R2/R1))#\n",
"ACL = abs(R2/R1)#\n",
"print 'the closed loop gain ACL is = %0.2f'%ACL,' '#\n",
"\n",
"# the output gain factor K is given as\n",
"K = ACL*Vin #\n",
"print 'The output gain factor K is = %0.2f'%K,' V'#\n",
"\n",
"# the maximum frequency of an op-amp is\n",
"wmax = (Slewrate/K)#\n",
"print 'The wmax is = %0.2f'%wmax,'*10**6 rad/sec'# # *10**6 because Slewrate is V/uV \n",
"\n",
"# the signal frequency may be w = 500*10**3 rad/sec that is less than the maximum frequency value"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.28 Pg 130"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the unity frequency f is = 568.70 kHz \n",
"The compansated capacitance Cm value is = 0.2 nF \n"
]
}
],
"source": [
" # To determine the compensated capacitance of an op-amp\n",
"Slewrate = 10 # # V/u sec\n",
"Ic = 1*10**-3 # # mA # capacitor current\n",
"Vt = 0.7 # # V # threshold voltage\n",
"\n",
"# the slew rate of an op-amp is defined as\n",
"# Slew rate = (dVo/dt)\n",
"# the unity frequency f is\n",
"f =(Slewrate/(8*3.14*Vt))#\n",
"f = f*10**6# # *10**6 because Slew rate is V/uV \n",
"print 'the unity frequency f is = %0.2f'%(f/1e3),'kHz '#\n",
"\n",
"# The compansated capacitance Cm is\n",
"gm = (Ic/Vt)#\n",
"Cm = (gm)/(4*3.14*f)*1e9 #\n",
"print 'The compansated capacitance Cm value is = %0.1f'%Cm,'nF '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.29 Pg 131"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the Slew rate of an op-amp is = 0.50 V/u sec\n"
]
}
],
"source": [
" # To find Slew rate of an op-amp\n",
"Iq = 15 # # uA # bias current\n",
"Cm = 30 # # pF # internal frequency compensated capacitor\n",
"Slewrate = (Iq/Cm)\n",
"print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.30 Pg 131"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the Slew rate of an op-amp is = 0.68 V/u sec\n"
]
}
],
"source": [
"# To find Slew rate of an op-amp\n",
"Iq = 21 # # uA # bias current\n",
"Cm = 31 # # pF # internal frequency compensated capacitor\n",
"Slewrate = (Iq/Cm)#\n",
"print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec'#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.31 Pg 131"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The full power bandwidth FPBW is = 8.12 kHz \n",
"The 3-db frequency or small signal band width f3db is = 10 kHz \n"
]
}
],
"source": [
" # To determine full power and small signal bandwidth of an op-amp with unity gain\n",
"f = 100*10**6 # # Hz unity gain bandwidth\n",
"ACL = 10**4 # # maximum closed loop gain\n",
"Slewrate = 0.51 # # V/u sec\n",
"Vp = 10 # # V peak volt\n",
"\n",
"# The full power bandwidth\n",
"FPBW = (Slewrate/(2*3.14*Vp))#\n",
"FPBW = FPBW*10**6 # # *10**6 because Slew rate is V/uV \n",
"print 'The full power bandwidth FPBW is = %0.2f'%(FPBW/1e3),'kHz '#\n",
"\n",
"# the 3-db frequency or small signal band width \n",
"f3db = (f/ACL)#\n",
"print 'The 3-db frequency or small signal band width f3db is = %0.f'%(f3db/1e3),'kHz '#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5.32 Pg 132"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The full power bandwidth FPBW is = 8.12 kHz \n",
"The 3-db frequency or small signal band width f3db is = 10 kHz \n"
]
}
],
"source": [
"# To determine full power and small signal bandwidth of an op-amp with unity gain\n",
"f = 100*10**6 # # Hz unity gain bandwidth\n",
"ACL = 10**4 # # maximum closed loop gain\n",
"Slewrate = 0.51 # # V/u sec\n",
"Vp = 10 # # V peak volt\n",
"\n",
"# The full power bandwidth\n",
"FPBW = (Slewrate/(2*3.14*Vp))#\n",
"FPBW = FPBW*10**6 # # *10**6 because Slew rate is V/uV \n",
"print 'The full power bandwidth FPBW is = %0.2f'%(FPBW/1e3),'kHz '#\n",
"\n",
"# the 3-db frequency or small signal band width \n",
"f3db = (f/ACL)#\n",
"print 'The 3-db frequency or small signal band width f3db is = %0.f'%(f3db/1e3),'kHz '#"
]
},
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"source": [
"## Example 5.33 Pg 132"
]
},
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"name": "stdout",
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"text": [
"the Slew rate of an op-amp is = 0.31 V/u sec \n",
"The closed loop gain ACL is = 83.33 \n"
]
}
],
"source": [
"# To find Slew rate and closed loop gain of an op-amp\n",
"fu = 1*10**6 # # Hz # unity gain bandwidth\n",
"fmax = 5*10**3 # # KHz # full power bandwidth\n",
"F3db = 12*10**3 # # Hz # small signal bandwidth\n",
"Vp = 10 # # V # peak volt\n",
"\n",
"# the full power bandwidth of an op-amp\n",
"# fmax=FPBW = (Slew rate/2*3.14*Vp)#\n",
"Slewrate = 2*3.14*Vp*fmax#\n",
"Slewrate = Slewrate*(10**-6)# # *10**-6 because Slewrate is V/u \n",
"print 'the Slew rate of an op-amp is = %0.2f'%Slewrate,' V/u sec '#\n",
"\n",
"# # the 3-db frequency or small signal band width \n",
"#f3db = (f/ACL)#\n",
"#the closed loop gain ACL\n",
"ACL = fu/F3db #\n",
"print 'The closed loop gain ACL is = %0.2f'%ACL,' '#"
]
}
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