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diff --git a/sample_notebooks/Hrituraj/Ch-6_1.ipynb b/sample_notebooks/Hrituraj/Ch-6_1.ipynb new file mode 100644 index 00000000..4aa9a7a3 --- /dev/null +++ b/sample_notebooks/Hrituraj/Ch-6_1.ipynb @@ -0,0 +1,547 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ch-6 : Frequency response, bode plots and resonance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.1 Page No: 476" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "peak value of Vout = 6.00 volts\n", + "phase angle of Vout = 70.00 degrees\n", + "with frequency equal to = 1000.00\n" + ] + } + ], + "source": [ + "from math import pi, cos, sin, atan, sqrt\n", + "# given V_in(t)=2*cos(2000*pi*t+A), A=40*pi/180\n", + "w=2000*pi# #omega\n", + "f=w/(2*pi)# #frequency\n", + "A=40*pi/180# #40 degrees = %0.2f radians\n", + "#equation of straight line of H_magnitude vs f is x+1000*y-4000=0\n", + "H_max=(4000-f)/1000# #magnitude of H(traansfer function)\n", + "#equation of straight line of H_phase angle vs f is 6000*y=pi*x (phase angle = %0.2f radians)\n", + "H_phi=pi*f/6000# #phase angle of H\n", + "H=H_max*complex(cos(H_phi),sin(H_phi))\n", + "V_in=2*complex(cos(A),sin(A))# #input voltage phasor\n", + "V_out=H*V_in# #output voltage phasor\n", + "V_out_R=(V_out.real)# #real part\n", + "V_out_I=(V_out.imag)# #imaginary part\n", + "V_out_max=sqrt((V_out_R**2)+(V_out_I**2))# #peak value\n", + "V_out_phi=atan(V_out_I/V_out_R)\n", + "print 'peak value of Vout = %0.2f volts'%V_out_max\n", + "print 'phase angle of Vout = %0.2f degrees'%(V_out_phi*180/pi)\n", + "print 'with frequency equal to = %0.2f'%f" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.2 Page No: 477" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Output voltage is Vout1+Vout2+Vout3 where\n", + "\n", + "FOR Vout1:\n", + "peak value = 12.00 volts\n", + "phase angle = 0.00 degrees\n", + "with frequency = 0.00 hertz\n", + "\n", + "FOR Vout2:\n", + "peak value = 6.00 volts\n", + "phase angle = 30.00 degrees\n", + "with frequency = 1000.00 hertz\n", + "\n", + "FOR Vout3:\n", + "peak value = 2.00 volts\n", + "phase angle = -10.00 degrees\n", + "with frequency = 2000.00 hertz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import pi, cos, sin, atan, sqrt\n", + "\n", + "#given V_in(t)=3+2*cos(2000*pi*t)+cos(4000*pi*t-A), A=70*pi/180\n", + "#the three parts of V_in(t) are V_in_1=3, V_in_2=2*cos(2000*pi*t),V_in_3=cos(4000*pi*t-A)\n", + "\n", + "#first component V_1\n", + "V_in_1=3\n", + "f_1=0# #as omega is zero\n", + "#equation of straight line of H_magnitude vs f is x+1000*y-4000=0\n", + "H_1_max=(4000-f_1)/1000# #magnitude of H(traansfer function)\n", + "#equation of straight line of H_phase angle vs f is 6000*y=pi*x (phase angle = %0.2f radians)\n", + "H_1_phi=pi*f_1/6000# #phase angle of H\n", + "H_1=H_1_max*complex(cos(H_1_phi),sin(H_1_phi))\n", + "V_out_1=H_1*V_in_1\n", + "V_out_1_R=(V_out_1).real# #real part\n", + "V_out_1_I=(V_out_1).imag# #imaginary part\n", + "V_out_1_max=sqrt((V_out_1_R**2)+(V_out_1_I**2))# #peak value\n", + "V_out_1_phi=atan(V_out_1_I/V_out_1_R)# #phase angle\n", + "\n", + "#second component V_in_2\n", + "V_in_2=2*complex(cos(0),sin(0))# #V_in_2 phasor\n", + "w=2000*pi# #omega\n", + "f_2=w/(2*pi)# #frequency\n", + "#equation of straight line of H_magnitude vs f is x+1000*y-4000=0\n", + "H_2_max=(4000-f_2)/1000# #magnitude of H(traansfer function)\n", + "#equation of straight line of H_phase angle vs f is 6000*y=pi*x (phase angle = %0.2f radians)\n", + "H_2_phi=pi*f_2/6000# #phase angle of H\n", + "H_2=H_2_max*complex(cos(H_2_phi),sin(H_2_phi))\n", + "V_out_2=H_2*V_in_2\n", + "V_out_2_R=(V_out_2).real# #real part\n", + "V_out_2_I=(V_out_2).imag# #imaginary part\n", + "V_out_2_max=sqrt((V_out_2_R**2)+(V_out_2_I**2))# #peak value\n", + "V_out_2_phi=atan(V_out_2_I/V_out_2_R)# #phase angle\n", + "\n", + "#third component\n", + "A=-70*pi/180# #-70 degrees = %0.2f radians\n", + "V_in_3=complex(cos(A),sin(A))# #V_in_3 phasor\n", + "w=4000*pi# #omega\n", + "f_3=w/(2*pi)# #frequency\n", + "#equation of straight line of H_magnitude vs f is x+1000*y-4000=0\n", + "H_3_max=(4000-f_3)/1000# #magnitude of H(traansfer function)\n", + "#equation of straight line of H_phase angle vs f is 6000*y=pi*x (phase angle = %0.2f radians)\n", + "H_3_phi=pi*f_3/6000# #phase angle of H\n", + "H_3=H_3_max*complex(cos(H_3_phi),sin(H_3_phi))\n", + "V_out_3=H_3*V_in_3\n", + "V_out_3_R=(V_out_3).real# #real part\n", + "V_out_3_I=(V_out_3).imag# #imaginary part\n", + "V_out_3_max=sqrt((V_out_3_R**2)+(V_out_3_I**2))# #peak value\n", + "V_out_3_phi=atan(V_out_3_I/V_out_3_R)# #phase angle\n", + "\n", + "print 'Output voltage is Vout1+Vout2+Vout3 where'\n", + "print ''\n", + "print 'FOR Vout1:'\n", + "print 'peak value = %0.2f volts'%V_out_1_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_1_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_1\n", + "print ''\n", + "print 'FOR Vout2:'\n", + "print 'peak value = %0.2f volts'%V_out_2_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_2_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_2\n", + "print ''\n", + "print 'FOR Vout3:'\n", + "print 'peak value = %0.2f volts'%V_out_3_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_3_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.3 Page No: 477" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\n", + "Output voltage is Vout1+Vout2+Vout3 where\n", + "\n", + "FOR Vout1:\n", + "peak value = 4.98 volts\n", + "phase angle = -5.71 degrees\n", + "with frequency = 10.00 hertz\n", + "\n", + "FOR Vout2:\n", + "peak value = 3.54 volts\n", + "phase angle = -45.00 degrees\n", + "with frequency = 100.00 hertz\n", + "\n", + "FOR Vout3:\n", + "peak value = 0.50 volts\n", + "phase angle = -84.29 degrees\n", + "with frequency = 1000.00 hertz\n" + ] + } + ], + "source": [ + "from math import pi, cos, sin, atan, sqrt\n", + "\n", + "R=1000/(2*pi)# #resistance\n", + "C=10*10**-6# #capacitance\n", + "f_B=1/(2*pi*R*C)# #half-power frequency\n", + "#the three parts of V_in are V_1=5*cos(20*pi*t)+5*cos(200*pi*t)+5*cos(2000*pi*t)\n", + "\n", + "#first component V_in_1\n", + "V_in_1=5*complex(cos(0),sin(0))# #V_in_1 phasor\n", + "w_1=20*pi# #omega\n", + "f_1=w_1/(2*pi)# #frequency\n", + "H_1=1/(1+1J*(f_1/f_B))# #transfer function\n", + "V_out_1=H_1*V_in_1\n", + "V_out_1_R=(V_out_1).real# #real part\n", + "V_out_1_I=(V_out_1).imag# #imaginary part\n", + "V_out_1_max=sqrt((V_out_1_R**2)+(V_out_1_I**2))# #peak value\n", + "V_out_1_phi=atan(V_out_1_I/V_out_1_R)# #phase angle\n", + "\n", + "#second component V_in_2\n", + "V_in_2=5*complex(cos(0),sin(0))# #V_in_2 phasor\n", + "w_2=200*pi# #omega\n", + "f_2=w_2/(2*pi)# #frequency\n", + "H_2=1/(1+1J*(f_2/f_B))# #transfer function\n", + "V_out_2=H_2*V_in_2\n", + "V_out_2_R=(V_out_2).real #real part\n", + "V_out_2_I=(V_out_2).imag #imaginary part\n", + "V_out_2_max=sqrt((V_out_2_R**2)+(V_out_2_I**2))# #peak value\n", + "V_out_2_phi=atan(V_out_2_I/V_out_2_R)# #phase angle\n", + "\n", + "#third component V_in_3\n", + "V_in_3=5*complex(cos(0),sin(0))# #V_in_3 phasor\n", + "w_3=2000*pi# #omega\n", + "f_3=w_3/(2*pi)# #frequency\n", + "H_3=1/(1+1J*(f_3/f_B))# #transfer function\n", + "V_out_3=H_3*V_in_3\n", + "V_out_3_R=(V_out_3).real #real part\n", + "V_out_3_I=(V_out_3).imag #imaginary part\n", + "V_out_3_max=sqrt((V_out_3_R**2)+(V_out_3_I**2))# #peak value\n", + "V_out_3_phi=atan(V_out_3_I/V_out_3_R)# #phase angle\n", + "\n", + "print \" All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\"\n", + "print 'Output voltage is Vout1+Vout2+Vout3 where'\n", + "print ''\n", + "print 'FOR Vout1:'\n", + "print 'peak value = %0.2f volts'%V_out_1_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_1_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_1\n", + "print ''\n", + "print 'FOR Vout2:'\n", + "print 'peak value = %0.2f volts'%V_out_2_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_2_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_2\n", + "print ''\n", + "print 'FOR Vout3:'\n", + "print 'peak value = %0.2f volts'%V_out_3_max\n", + "print 'phase angle = %0.2f degrees'%(V_out_3_phi*180/pi)\n", + "print 'with frequency = %0.2f hertz'%f_3\n", + "#we can observe that there is a clear discrimination = %0.2f output signals based on frequencies i.e, lesser the frequency lesser the effect." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.4 Page No: 478" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\n", + "Break frequency = 1897.37 Hz\n" + ] + } + ], + "source": [ + "H_max=-30# #transfer function magnitude\n", + "f=60\n", + "m=20# #low-frequency asymptote slope rate = %0.2f db/decade\n", + "#f_B must be K higher than f where K is\n", + "K=abs(H_max)/m\n", + "#(base 10)log(f_B/60)=1.5 ==>\n", + "f_B=60*10**1.5\n", + "print \" All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\"\n", + "print 'Break frequency = %0.2f Hz'%f_B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.5 Page No: 479" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Phasor voltage across Resistance\n", + "peak value = 1.00 volts\n", + "phase angle = 0.00 degrees\n", + "\n", + "Phasor voltage across Inductance\n", + "peak value = 10.00 volts\n", + "phase angle = 90.00 degrees\n", + "\n", + "Phasor voltage across Capacitance\n", + "peak value = 10.00 volts\n", + "phase angle = -90.00 degrees\n" + ] + } + ], + "source": [ + "from math import pi, cos, sin, atan, sqrt\n", + "V_s=1*complex(cos(0),sin(0))\n", + "L=159.2*10**-3\n", + "R=100\n", + "C=0.1592*10**-6\n", + "f_o=1/(2*pi*sqrt(L*C))# #resonant frequency\n", + "Q_s=2*pi*f_o*L/R# #quality factor\n", + "B=f_o/Q_s# #Bandwidth\n", + "#Approximate half-power frequencies are\n", + "f_H=f_o+(B/2)\n", + "f_L=f_o-(B/2)\n", + "#At resonance\n", + "Z_L=1J*2*pi*f_o*L# #impedance of inductance\n", + "Z_C=-1J/(2*pi*f_o*C)# #impedance of capacitance\n", + "Z_s=R+Z_L+Z_C\n", + "I=V_s/Z_s# #phasor current\n", + "#voltages across diffrent elements are\n", + "#for resistance\n", + "V_R=R*I\n", + "V_R_R=(V_R).real #real part\n", + "V_R_I=(V_R).imag #imaginary part\n", + "V_R_max=sqrt((V_R_R**2)+(V_R_I**2))# #peak value\n", + "V_R_phi=atan(V_R_I/V_R_R)# #phase angle\n", + "#for inductance\n", + "V_L=Z_L*I\n", + "V_L_R=(V_L).real #real part\n", + "V_L_I=(V_L).imag #imaginary part\n", + "V_L_max=sqrt((V_L_R**2)+(V_L_I**2))# #peak value\n", + "#Z_L is pure imaginary ==> V_L is pure imaginary which means V_L_phi can be +or- pi/2\n", + "if ((V_L/1J)==abs(V_L)):\n", + " V_L_phi=pi/2\n", + "elif ((V_L/1J)==-abs(V_L)):\n", + " V_L_phi=-pi/2\n", + "\n", + "\n", + "#for capacitance\n", + "V_C=Z_C*I\n", + "V_C_R=(V_C).real #real part\n", + "V_C_I=(V_C).imag #imaginary part\n", + "V_C_max=sqrt((V_C_R**2)+(V_C_I**2))# #peak value\n", + "#Z_C is pure imaginary ==> V_C is pure imaginary which means V_C_phi can be +or- pi/2\n", + "if ((V_C/1J)==abs(V_C)) :\n", + " V_C_phi=pi/2\n", + "elif ((V_C/1J)==-abs(V_C)) :\n", + " V_C_phi=-pi/2\n", + "\n", + " \n", + "print 'Phasor voltage across Resistance'\n", + "print 'peak value = %0.2f volts'%V_R_max\n", + "print 'phase angle = %0.2f degrees'%(V_R_phi*180/pi)\n", + "print ''\n", + "print 'Phasor voltage across Inductance'\n", + "print 'peak value = %0.2f volts'%V_L_max\n", + "print 'phase angle = %0.2f degrees'%(V_L_phi*180/pi)\n", + "print ''\n", + "print 'Phasor voltage across Capacitance'\n", + "print 'peak value = %0.2f volts'%V_C_max\n", + "print 'phase angle = %0.2f degrees'%(V_C_phi*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.6 Page No: 480" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Current phasor across Resistance\n", + "peak value = 0.001 amperes\n", + "phase angle = 0 degrees\n", + "\n", + "Current phasor across Inductance\n", + "peak value = 0.010 amperes\n", + "phase angle = -90.00 degrees\n", + "\n", + "current phasor across capacitance\n", + "peak value = 0.010 amperes\n", + "phase angle = 90.00 degrees\n" + ] + } + ], + "source": [ + "from math import pi, cos, sin, atan, sqrt\n", + "R=10*10**3\n", + "f_o=1*10**6\n", + "B=100*10**3\n", + "I=10**-3*complex(cos(0),sin(0))\n", + "Q_p=f_o/B# #quality factor\n", + "L=R/(2*pi*f_o*Q_p)\n", + "C=Q_p/(2*pi*f_o*R)\n", + "#At resonance\n", + "V_out=I*R\n", + "Z_L=1J*2*pi*f_o*L\n", + "Z_C=-1J/(2*pi*f_o*C)\n", + "\n", + "#across resistance\n", + "I_R=V_out/R\n", + "I_R_R=(I_R).real# #real part\n", + "I_R_I=(I_R).imag# #imaginary part\n", + "I_R_max=sqrt((I_R_R**2)+(I_R_I**2))# #peak value\n", + "I_R_phi=atan(I_R_I/I_R_R)# #phase angle\n", + "\n", + "#across inductance\n", + "I_L=V_out/Z_L\n", + "I_L_R=(I_L).real #real part\n", + "I_L_I=(I_L).imag# #imaginary part\n", + "I_L_max=sqrt((I_L_R**2)+(I_L_I**2))# #peak value\n", + "#Z_L is pure imaginary ==> V_L is pure imaginary which means V_L_phi can be +or- pi/2\n", + "if ((I_L/1J)==abs(I_L)):\n", + " I_L_phi=pi/2\n", + "elif ((I_L/1J)==-abs(I_L)) :\n", + " I_L_phi=-pi/2\n", + "\n", + "\n", + "#across capacitor\n", + "I_C=V_out/Z_C\n", + "I_C_R=(I_C).real# #real part\n", + "I_C_I=(I_C).imag# #imaginary part\n", + "I_C_max=sqrt((I_C_R**2)+(I_C_I**2))# #peak value\n", + "#Z_C is pure imaginary ==> V_C is pure imaginary which means V_C_phi can be +or- pi/2\n", + "if ((I_C/1J)==abs(I_C)):\n", + " I_C_phi=pi/2\n", + "elif ((I_C/1J)==-abs(I_C)) :\n", + " I_C_phi=-pi/2\n", + "\n", + "\n", + "print 'Current phasor across Resistance'\n", + "print 'peak value = %0.3f amperes'%I_R_max\n", + "print 'phase angle = %0.f degrees'%(I_R_phi*180/pi)\n", + "print ''\n", + "print 'Current phasor across Inductance'\n", + "print 'peak value = %0.3f amperes'%I_L_max\n", + "print 'phase angle = %0.2f degrees'%(I_L_phi*180/pi)\n", + "print ''\n", + "print 'current phasor across capacitance'\n", + "print 'peak value = %0.3f amperes'%I_C_max\n", + "print 'phase angle = %0.2f degrees'%(I_C_phi*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: 6.7 Page No: 481" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\n", + "\n", + "The required second order circuit configuration is\n", + "Inductance = 50.00 KH\n", + "Capacitance = 0.51 mF(micro Farads)\n", + "Resistance = 314.16 ohms\n" + ] + } + ], + "source": [ + "from math import pi\n", + "#We need a high-pass filter\n", + "L=50*10**-3\n", + "#for the transfer function to be approximately constant = %0.2f passband area(from graph given = %0.2f the text), we choose\n", + "Q_s=1\n", + "f_o=1*10**3\n", + "C=1/(((2*pi)**2)*f_o**2*L)\n", + "R=2*pi*f_o*L/Q_s\n", + "print \" All the values in the textbook are approximated, hence the values in this code differ from those of Textbook\"\n", + "print ''\n", + "print 'The required second order circuit configuration is'\n", + "print 'Inductance = %0.2f KH'%(L*10**3)\n", + "print 'Capacitance = %0.2f mF(micro Farads)'%(C*10**6)\n", + "print 'Resistance = %0.2f ohms'%R\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |