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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Chapter 5: Frequency response of an Op-Amp"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 5.1"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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2jHQUh/KfBIzF/iDtV9/FUUkFtwew1NmvZ9qNBNjvgL/4XYgSqQYm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\ntwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff51168c210>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum gain is 40 dB\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff4f28db750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Example 5.1\n",
"#The 741C is connected as a noniverting amplifier.What maximum gain can be used\n",
"#that will still keep the amplifier's response flat to 10kHz.\n",
"\n",
"%matplotlib inline\n",
"\n",
"from scipy import pi\n",
"import numpy as np\n",
"from matplotlib.pyplot import ylabel, xlabel, title, plot, show, clf, subplot, semilogx, savefig\n",
"import matplotlib.pyplot as plt\n",
"#Variable declaration\n",
"f=np.arange(0,1000000) #frequency range\n",
"s=2.0j*pi*f\n",
"A=200000 #Gain of opamp at 0 Hz\n",
"f0=5 #first break frequency in Hz\n",
"p=2.0*pi*f0\n",
"\n",
"#Calculation\n",
"\n",
"tf=A*p/(s+p) #open loop gain\n",
"\n",
"#Magnitude plot\n",
"clf() #clear the figure\n",
"subplot(211)\n",
"title('tf=p/(s+p)')\n",
"semilogx(f,20*log10(abs(tf)))\n",
"ylabel('Mag. Ratio (dB)')\n",
"\n",
"#Phase plot\n",
"subplot(212)\n",
"semilogx(f,arctan2(imag(tf),real(tf))*180.0/pi)\n",
"plt.ylabel('Phase (deg.)')\n",
"plt.xlabel('Freq (Hz)')\n",
"plt.show()\n",
"savefig('fig1.png') #savefig('fig1.eps')\n",
"\n",
"Amax=40 #from the graph\n",
"\n",
"#Result\n",
"print \"Maximum gain is\",Amax,\"dB\""
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 5.2"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gain equation is Aol(f)=A((1+(f/fo1)*j)*(1+(f/fo2)*j)\n",
"A,the gain of the opamp at 0 Hz is 140000\n",
"First break frequency fo1 is 6 Hz\n",
"Second break frequency fo2 is 1.24 MHz\n"
]
}
],
"source": [
"#Example 5.2\n",
"#Using the frequency response and phase response curves obtained in figure 5-5\n",
"#Obtain the equation for the MC1556 opamp. Also determine the approximate values\n",
"#of the break frequencies.\n",
"\n",
"from __future__ import division #to perform decimal division\n",
"import math\n",
"\n",
"\n",
"#Variable declaration\n",
"phase=-157.5 #Phase shift at about 3 MHz\n",
"f=3*10**6\n",
"fo1=6 #first break frequency,from the graph\n",
"A=140000 #Gain of the opamp at 0Hz\n",
"\n",
"\n",
"#calculation\n",
"k=-math.atan(f/fo1)*180/math.pi-phase\n",
"fo2=f/math.tan(k*math.pi/180) #second break frequency\n",
"\n",
"\n",
"#result\n",
"print \"Gain equation is Aol(f)=A((1+(f/fo1)*j)*(1+(f/fo2)*j)\"\n",
"print \"A,the gain of the opamp at 0 Hz is\",A\n",
"print \"First break frequency fo1 is\",fo1,\"Hz\" \n",
"print \"Second break frequency fo2 is\",round(fo2/10**6,2),\"MHz\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 5.3"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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wSzwFDLAnjV69YPToho8VESkmuQwYyUZHpXtMIskWUAph04UsdT6bhWV7x/Mc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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff51a48b7d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"From the plot it is seen that phase angle is -90 degree\n",
"when the magnitude is o dB.Since the phase angle reaches >-180\n",
"when the magnitude is 0dB, voltage follower is stable at 0dB\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff4f2c08510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"#Example 5.3\n",
"#Determine the stability of the voltage follower shown in figure 3-7.\n",
"#Assume that the opamp is a 741 IC\n",
"\n",
"\n",
"%matplotlib inline\n",
"\n",
"from scipy import pi\n",
"import numpy as np\n",
"from matplotlib.pyplot import ylabel, xlabel, title, plot, show, clf, subplot, semilogx, savefig\n",
"import matplotlib.pyplot as plt\n",
"#Variable declaration\n",
"f=arange(10,1000000)\n",
"s=2.0j*pi*f\n",
"A=200000\n",
"f0=5\n",
"p=2.0*pi*f0\n",
"B=1 #For voltage follower B=1\n",
"\n",
"#Calculation\n",
"tf=A*p*B/(s+p) #open loop gain\n",
"\n",
"#Magnitude plot\n",
"clf() #clear the figure\n",
"subplot(211)\n",
"title('tf=p/(s+p)')\n",
"semilogx(f,20*log10(abs(tf)))\n",
"ylabel('Mag. Ratio (dB)')\n",
"\n",
"#Phase plot\n",
"subplot(212)\n",
"semilogx(f,arctan2(imag(tf),real(tf))*180.0/pi)\n",
"ylabel('Phase (deg.)')\n",
"xlabel('Freq (Hz)')\n",
"\n",
"show()\n",
"savefig('fig1.png') #savefig('fig1.eps')\n",
"\n",
"#Result\n",
"print \"From the plot it is seen that phase angle is -90 degree\"\n",
"print \"when the magnitude is o dB.Since the phase angle reaches >-180\"\n",
"print \"when the magnitude is 0dB, voltage follower is stable at 0dB\""
]
}
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