{
 "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": 18,
   "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": 19,
   "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",
    "#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": 20,
   "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": [
    "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": 21,
   "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": 22,
   "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": [
    "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": 23,
   "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": [
    "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": 24,
   "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": [
    "#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"
   ]
  }
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