path: root/Electronics_Circuits_and_Systems_by_Y._N._Bapat/Ch7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7 - Feedback Amplifiers and Sinusoidal Oscillators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_1 Page No. 204"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A= 60000.00\n",
      "Af= 10000.00\n",
      "N_dB=20*log10(Af/A)= -15.56 dB\n",
      "B=(1/(Af))-(1/A)= 8.33e-05\n"
     ]
    }
   ],
   "source": [
    "from math import log10\n",
    "from __future__ import division  \n",
    "A=60000\n",
    "print \"A= %0.2f\"%(A) #Amplifier gain\n",
    "Af=10000\n",
    "print \"Af= %0.2f\"%(Af) #Feedback gain\n",
    "N_dB=20*log10(Af/A)\n",
    "print \"N_dB=20*log10(Af/A)= %0.2f\"%(N_dB),\"dB\" #Negative feedback gain\n",
    "B=(1/(Af))-(1/A)# formulae using (Af=A/(1+A*B))\n",
    "print \"B=(1/(Af))-(1/A)= %0.2e\"%(B) #Feedback factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_2 Page No. 205"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A= 10000.00\n",
      "B= 0.01\n",
      "Af= (A/(1+A*B))=99.01\n",
      "A1= 100000.00\n",
      "Af1= (A1/(1+A1*B))=99.90\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "A=10000\n",
    "print \"A= %0.2f\"%(A) #Amplifier gain\n",
    "B=0.01\n",
    "print \"B= %0.2f\"%(B) #Feedback factor\n",
    "Af=(A/(1+A*B))\n",
    "print \"Af= (A/(1+A*B))=%0.2f\"%(Af) #Feedback gain\n",
    "A1=100000\n",
    "print \"A1= %0.2f\"%(A1) #New amplifier gain value\n",
    "Af1=(A1/(1+A1*B))\n",
    "print \"Af1= (A1/(1+A1*B))=%0.2f\"%(Af1) #New feedback gain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_3 Page No. 208"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vo= 50.00  volts\n",
      "Vi= 0.50  volts\n",
      "part(i)\n",
      "A= Vo/Vi=100.00\n",
      "Harmonic_distortion=10.00 %\n",
      "D= (10*Vo)/100 = 5.00  volts\n",
      "Df= (1*Vo)/100 = 0.50  volts\n",
      "B=(D/(Df*A))-(1/A) = 0.09\n",
      "part(ii)\n",
      "Af= (A/(1+A*B)) = 10.00\n",
      "part(iii)\n",
      "Vif= Vo/Af = 5.00  volts\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "Vo=(50)\n",
    "print \"Vo= %0.2f\"%(Vo),\" volts\" # output voltage\n",
    "Vi=(0.5)\n",
    "print \"Vi= %0.2f\"%(Vi),\" volts\" # input voltage\n",
    "print \"part(i)\"  \n",
    "A=Vo/Vi\n",
    "print \"A= Vo/Vi=%0.2f\"%(A) #Amplifier gain\n",
    "HD=10\n",
    "print \"Harmonic_distortion=%0.2f\"%(HD),\"%\"# Percentage second harmonic distortion\n",
    "D=(10*Vo)/100\n",
    "print \"D= (10*Vo)/100 = %0.2f\"%(D),\" volts\" # Second Harmonic distortion \n",
    "Df=(1*Vo)/100\n",
    "print \"Df= (1*Vo)/100 = %0.2f\"%(Df),\" volts\" # Harmonic distortion with Feedback\n",
    "B=(D/(Df*A))-(1/A) #Using formulae Df=(D/(1+A*B))\n",
    "print \"B=(D/(Df*A))-(1/A) = %0.2f\"%(B) #Feedback factor\n",
    "print \"part(ii)\" \n",
    "Af=(A/(1+A*B))\n",
    "print \"Af= (A/(1+A*B)) = %0.2f\"%(Af) #Feedback gain\n",
    "print \"part(iii)\" \n",
    "Vif=Vo/Af\n",
    "print \"Vif= Vo/Af = %0.2f\"%(Vif),\" volts\" # New input voltage required"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_4 Page No. 210"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GBW= 1000000.00  Hz\n",
      "AMf=100.00\n",
      "fHF=GBW/AMf= 10000.00  Hz\n",
      "f_10per cent=(10*fHF)/100= 1000.00  Hz\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "GBW=10**(6)\n",
    "print \"GBW= %0.2f\"%(GBW),\" Hz\"# Gain-Bandwidth product\n",
    "AMf=100\n",
    "print \"AMf=%0.2f\"%(AMf) # Midband gain with feedback\n",
    "fHF=GBW/AMf\n",
    "print \"fHF=GBW/AMf= %0.2f\"%(fHF),\" Hz\"#Signal bandwidth\n",
    "f_10percent=(10*fHF)/100\n",
    "print \"f_10per cent=(10*fHF)/100= %0.2f\"%(f_10percent),\" Hz\"#Frequency below which AMf will not deviate by more than 10 percent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_5 Page No. 212"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AM=50000.00\n",
      "fH= 20000.00  Hz\n",
      "fL= 30.00  Hz\n",
      "B= 5.00e-05\n",
      "AMf=AM/(1+B*AM)=14285.71\n",
      "fHf=fH*(1+B*AM)= 70000.00  Hz\n",
      "fLf=fL/(1+B*AM)= 8.57  Hz\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "AM=50000\n",
    "print \"AM=%0.2f\"%(AM) # Midband gain \n",
    "fH=20*10**(3)\n",
    "print \"fH= %0.2f\"%(fH),\" Hz\"# Upper cut-off frequency\n",
    "fL=30\n",
    "print \"fL= %0.2f\"%(fL),\" Hz\"# Lower cut-off frequency\n",
    "B=5*10**(-5)\n",
    "print \"B= %0.2e\"%(B) #Feedback factor\n",
    "AMf=AM/(1+B*AM)\n",
    "print \"AMf=AM/(1+B*AM)=%0.2f\"%(AMf) # Midband gain with feedback\n",
    "fHf=fH*(1+B*AM)\n",
    "print \"fHf=fH*(1+B*AM)= %0.2f\"%(fHf),\" Hz\"#Upper cut-off frequency with feedback\n",
    "fLf=fL/(1+B*AM)\n",
    "print \"fLf=fL/(1+B*AM)= %0.2f\"%(fLf),\" Hz\"#Lower cut-off frequency with feedback\n",
    "#NOTE: calculated value of AMf is AMf=14285.714  and fLF=8.5714286 but in book given as AMf=14286  and fLF=8.58 Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_6 Page No. 214"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AM=100.00 dB\n",
      "fc1= 10000.00  Hz\n",
      "fc2= 100000.00  Hz\n",
      "fc3= 1000000.00  Hz\n",
      "part(i)\n",
      "Af1=85.00 dB\n",
      "f= 50000.00  Hz\n",
      "theta_A=-108.12  degree\n",
      "theta_pm=180-abs(theta_A)=71.88  degree\n",
      "Amplifier stable\n",
      "part(ii)\n",
      "Af2=50.00  dB\n",
      "f= 500000.00  Hz\n",
      "theta_A= -194.11  degree\n",
      "theta_pm=180-abs(theta_A)=-14.11  degree\n",
      "Amplifier  unstable\n",
      "part(iii)\n",
      "Af3=20.00 dB\n",
      "f= 1100000.00  Hz\n",
      "theta_A=-222.01  degree\n",
      "theta_pm=180-abs(theta_A)=-42.01  degree\n",
      "Amplifier unstable\n"
     ]
    }
   ],
   "source": [
    "from math import atan,pi\n",
    "from __future__ import division  \n",
    "AM=100\n",
    "print \"AM=%0.2f\"%(AM),\"dB\" # Midband gain \n",
    "fc1=1*10**(4)\n",
    "print \"fc1= %0.2f\"%(fc1),\" Hz\"# First Critical frequency\n",
    "fc2=10**5\n",
    "print \"fc2= %0.2f\"%(fc2),\" Hz\"# Second Critical frequency\n",
    "fc3=10**6\n",
    "print \"fc3= %0.2f\"%(fc3),\" Hz\"# Third Critical frequency\n",
    "print \"part(i)\"\n",
    "Af1=85\n",
    "print \"Af1=%0.2f\"%(Af1),\"dB\" #  gain at 50 kHz and -20dB/decade roll-off\n",
    "f=50*10**(3)\n",
    "print \"f= %0.2f\"%(f),\" Hz\"# operating frequency\n",
    "theta_A=- atan(f/fc1)*180/pi-  atan(f/fc2)*180/pi-  atan(f/fc3)*180/pi#phase shift in radians\n",
    "print \"theta_A=%0.2f\"%(theta_A),\" degree\"# Phase shift for feedback gain Af1\n",
    "theta_pm=180-abs(theta_A)# formulae phase margin\n",
    "print \"theta_pm=180-abs(theta_A)=%0.2f\"%(theta_pm),\" degree\"# Phase Margin for feedback gain Af1\n",
    "print \"Amplifier stable\"# Since phase margin is (+)ive\n",
    "print \"part(ii)\"\n",
    "Af2=50\n",
    "print \"Af2=%0.2f\"%(Af2),\" dB\" #  gain at 500 kHz and -40dB/decade roll-off\n",
    "f=500*10**(3)\n",
    "print \"f= %0.2f\"%(f),\" Hz\"#  frequency\n",
    "theta_A=- atan(f/fc1)-  atan(f/fc2)-  atan(f/fc3)#phase shift in radians\n",
    "theta_A=theta_A*180/pi # degree\n",
    "print \"theta_A= %0.2f\"%(theta_A),\" degree\"#  Phase shift for feedback gain Af2\n",
    "theta_pm=180-abs(theta_A)# formulae phase margin\n",
    "print \"theta_pm=180-abs(theta_A)=%0.2f\"%(theta_pm),\" degree\"# Phase Margin for feedback gain Af1\n",
    "print \"Amplifier  unstable\"# Since phase margin is (-)ive\n",
    "print \"part(iii)\"\n",
    "Af3=20\n",
    "print \"Af3=%0.2f\"%(Af3),\"dB\" #  gain at 1100 kHz and -60dB/decade roll-off\n",
    "f=1100*10**(3)\n",
    "print \"f= %0.2f\"%(f),\" Hz\"#  frequency\n",
    "theta_A=- atan(f/fc1)-  atan(f/fc2)-  atan(f/fc3)#phase shift in radians\n",
    "theta_A=theta_A*180/pi # degree\n",
    "print \"theta_A=%0.2f\"%(theta_A),\" degree\"# Phase shift for feedback gain Af3\n",
    "theta_pm=180-abs(theta_A)# formulae phase margin\n",
    "print \"theta_pm=180-abs(theta_A)=%0.2f\"%(theta_pm),\" degree\"# Phase Margin for feedback gain Af1\n",
    "print \"Amplifier unstable\"# Since phase margin is (-)ive\n",
    "#NOTE:Correct ans for part(i) phase margin ,theta_pm=71.882476 degree but in book given as 71.86 degree\n",
    "# correct ans for part(iii) phase shift, theta_A=-222.01103 degree but in book given as -220.02 degree    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_7 Page No. 216"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AV=50000.00\n",
      "Ri= 5.00e+07  ohm\n",
      "R0= 1000.00  ohm\n",
      "AVf=10.00\n",
      "RSf= 50000.00  ohm\n",
      "RF=AVf*(R1)= 5.00e+05  ohm\n",
      "VS= 30.00  volts\n",
      "Vomax=0.5*(VS)= -15.00 , +15.00  volts\n",
      "Vsmax=Vomax/AVf= -1.50 , +1.50  volts\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "AV=50000\n",
    "print \"AV=%0.2f\"%(AV) # Voltage gain \n",
    "Ri=50*10**(6)\n",
    "print \"Ri= %0.2e\"%(Ri),\" ohm\"  #Input resistance of OP-AMP\n",
    "R0=1*10**(3)\n",
    "print \"R0= %0.2f\"%(R0),\" ohm\"  #Output resistance\n",
    "AVf=10\n",
    "print \"AVf=%0.2f\"%(AVf) # Overall Voltage gain \n",
    "RSf=50*10**(3)\n",
    "print \"RSf= %0.2f\"%(RSf),\" ohm\"  #Source resistance\n",
    "R1=RSf\n",
    "RF=AVf*(R1)\n",
    "print \"RF=AVf*(R1)= %0.2e\"%(RF),\" ohm\"  #Feedback resistance\n",
    "VS=30\n",
    "print \"VS= %0.2f\"%(VS),\" volts\" # Peak-peak output swing voltage\n",
    "Vomax=0.5*(VS)\n",
    "print \"Vomax=0.5*(VS)= -%0.2f\"%(Vomax),\", +%0.2f\"%(Vomax),\" volts\" # Maximum output voltage swing at negative and positive polarities respectively\n",
    "Vsmax=Vomax/AVf\n",
    "print \"Vsmax=Vomax/AVf= -%0.2f\"%(Vsmax),\", +%0.2f\"%(Vsmax),\" volts\" # Maximum output voltage without overload clipping at both polarities\n",
    "\n",
    "\n",
    "#for overall voltage gain author has used two notations 'Avf' and 'Af' ... but I am working with 'Avf' only"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_8 Page No. 218"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R1= 50000.00  ohm\n",
      "RF= 500000.00  ohm\n",
      "VS= 1.00  volts\n",
      "part(i)\n",
      "A = infinite\n",
      "Vo1=-(RF/R1)= -10.00  volts\n",
      "part(ii)\n",
      "A=50000.00\n",
      "B=R1/(R1+RF)= 0.09\n",
      "Vo2=-((RF)*(B*A))/(R1*(1+A*B))= -10.00  volts\n",
      "%Error,e= ((Vo2-Vo1)*100)/Vo1=0.02 % \n",
      "part(iii)\n",
      "%Error,e=0.01 % \n",
      "Vo3=Vo1-(e*Vo1/100)= 10.00  volts\n",
      "A=(Vo*R1)/(B*RF*(1-(Vo*RF/R1)))=1.10e+05\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division  \n",
    "R1=50*10**(3)\n",
    "print \"R1= %0.2f\"%(R1),\" ohm\"  # resistance at input terminal of OP-AMP\n",
    "RF=500*10**(3)\n",
    "print \"RF= %0.2f\"%(RF),\" ohm\"  #Feedback resistance\n",
    "VS=1\n",
    "print \"VS= %0.2f\"%(VS),\" volts\" # Peak-peak output swing voltage\n",
    "print \"part(i)\"  \n",
    "print \"A = infinite\"# voltage gain\n",
    "Vo1=-(RF/R1) #Output voltage when gain, A=infinite\n",
    "print \"Vo1=-(RF/R1)= %0.2f\"%(Vo1),\" volts\"\n",
    "print \"part(ii)\"  \n",
    "A=50000\n",
    "print \"A=%0.2f\"%(A) #  gain of OP-AMP\n",
    "B=R1/(R1+RF)\n",
    "print \"B=R1/(R1+RF)= %0.2f\"%(B) #Feedback factor\n",
    "Vo2=-((RF)*(B*A))/(R1*(1+A*B))\n",
    "print \"Vo2=-((RF)*(B*A))/(R1*(1+A*B))= %0.2f\"%(Vo2),\" volts\"# output voltage for A=50000\n",
    "e=-((Vo2-Vo1)*100)/Vo1\n",
    "print \"%%Error,e= ((Vo2-Vo1)*100)/Vo1=%0.2f\"%(e),\"% \"#  calculation for percentage error in output voltage\n",
    "print \"part(iii)\"  \n",
    "e=0.01\n",
    "print \"%%Error,e=%0.2f\"%(e),\"% \"#Given percentage error in output voltage\n",
    "Vo3=-(Vo1-(e*Vo1/100))\n",
    "print \"Vo3=Vo1-(e*Vo1/100)= %0.2f\"%(Vo3),\" volts\"# output voltage for error 0.01%\n",
    "x=Vo3*(R1/RF)\n",
    "A=(x)/(B*(1-x)) #using formulae Vo=-(RF/R1)*((B*A)/1+A*B))\n",
    "print \"A=(Vo*R1)/(B*RF*(1-(Vo*RF/R1)))=%0.2e\"%(A) # New Required gain for error less than 0.01%\n",
    "\n",
    "# while solving the problem I have used 'e' for the error as no varriable is given for the same in textbook by author\n",
    "# in textbook author has used 'Vo' for output voltage in all parts.. but to remove any ambiguity in the programe I have used 'Vo1' 'Vo2' 'Vo3' for part i, ii, iii, respectively"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_9 Page No. 218"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AV=100000.00\n",
      "Ri= 10000.00  ohm\n",
      "Ro= 10.00  ohm\n",
      "Rs= 1.00e+07  ohm\n",
      "RL= 1000.00  ohm\n",
      "B=(Rs-Ri)/(AV*Ri)= 0.01\n",
      "AVf=AV/(1+B*AV)=100.00\n",
      "Rof=Ro/(1+B*AV) =0.01  ohm\n",
      "Rif=Ri/(1+B*AV) =1.00e+07  ohm\n",
      "Ap=(AVf**2)*(Rif/RL)=1.00e+08\n",
      "AP=10*log10(Ap)=80.00 dB\n"
     ]
    }
   ],
   "source": [
    "from math import log10\n",
    "from __future__ import division  \n",
    "AV=100000\n",
    "print \"AV=%0.2f\"%(AV) # Voltage gain \n",
    "Ri=10*10**(3)\n",
    "print \"Ri= %0.2f\"%(Ri),\" ohm\"  #Input resistance of OP-AMP\n",
    "Ro=10\n",
    "print \"Ro= %0.2f\"%(Ro),\" ohm\"  #Output resistance\n",
    "Rs=10*10**(6)\n",
    "print \"Rs= %0.2e\"%(Rs),\" ohm\"  #Source resistance\n",
    "RL=1*10**(3)\n",
    "print \"RL= %0.2f\"%(RL),\" ohm\"  #Load resistance\n",
    "B=(Rs-Ri)/(AV*Ri)\n",
    "print \"B=(Rs-Ri)/(AV*Ri)= %0.2f\"%(B) #Feedback factor\n",
    "AVf=AV/(1+B*AV)\n",
    "print \"AVf=AV/(1+B*AV)=%0.2f\"%(AVf) # Overall Voltage gain with feedback\n",
    "Rof=Ro/(1+B*AV)\n",
    "print \"Rof=Ro/(1+B*AV) =%0.2f\"%(Rof),\" ohm\"  #output resistance with feedback\n",
    "Rif=Ri*(1+B*AV)\n",
    "print \"Rif=Ri/(1+B*AV) =%0.2e\"%(Rif),\" ohm\"  #Input resistance with feedback\n",
    "Ap=(AVf**2)*(Rif/RL)\n",
    "print \"Ap=(AVf**2)*(Rif/RL)=%0.2e\"%(Ap) # Overall Power gain \n",
    "AP=10*log10(Ap)\n",
    "print \"AP=10*log10(Ap)=%0.2f\"%(AP),\"dB\" # Overall Power gain in dB "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 7_10 Page No. 220"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gm = 0.01  A/V\n",
      "Cgs= 5.00e-12  farad\n",
      "Cds= 1.00e-12  farad\n",
      "rd= 50000.00  ohm\n",
      "RG= 1.00e+07  ohm\n",
      "Rse= 1.00e+03  ohm\n",
      "L= 0.50  H\n",
      "C2= 5.00e-14  farad\n",
      "C1= 1.00e-12  farad\n",
      "part(i)\n",
      "CT= 0.00  farad\n",
      "part(ii)\n",
      "fo= sqrt(2)/(2*pi*sqrt(L*CT))=1.44e+06  Hz\n",
      "part(iii)\n",
      "fp= 1.03e+06  Hz\n",
      "fs= 1.01e+06  Hz\n",
      "Q=(sqrt(L/C2))/(Rse)= 3162.28\n",
      "part(iv)\n",
      "AB=gm*rd*(Cds/Cgs)= 100.00\n",
      "T_bias=RG*(Cgs+Cds)= 6.00e-05 s\n",
      "T_r =1/(2*pi*fo)= 1.10e-07 s\n",
      "for proper operation T_bias >> T_r\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,log10\n",
    "from __future__ import division  \n",
    "gm=10*10**(-3)\n",
    "print \"gm = %0.2f\"%(gm),\" A/V\"#  transconductance \n",
    "Cgs=5*10**(-12)\n",
    "print \"Cgs= %0.2e\"%(Cgs),\" farad\"  # capacitance between gate-source\n",
    "Cds=1*10**(-12)\n",
    "print \"Cds= %0.2e\"%(Cds),\" farad\"  # capacitance between drain-source\n",
    "rd=50*10**(3)\n",
    "print \"rd= %0.2f\"%(rd),\" ohm\"  #Drain resistance\n",
    "RG=10*10**(6)\n",
    "print \"RG= %0.2e\"%(RG),\" ohm\"  #Gate resistance\n",
    "Rse=1*10**(3)\n",
    "print \"Rse= %0.2e\"%(Rse),\" ohm\"  #Gate resistance\n",
    "L=0.5\n",
    "print \"L= %0.2f\"%(L),\" H\"  #Inductance\n",
    "C2=0.05*10**(-12)\n",
    "print \"C2= %0.2e\"%(C2),\" farad\"  # Crystal parameter \n",
    "C1=1*10**(-12)\n",
    "print \"C1= %0.2e\"%(C1),\" farad\"  # Crystal parameter\n",
    "print \"part(i)\" \n",
    "x=C1+((Cds*Cgs)/(Cds+Cgs))\n",
    "CT=1/((1/C2)+(1/x))\n",
    "print \"CT= %0.2f\"%(CT),\" farad\"  # Equivalent series-resonating capacitance\n",
    "print \"part(ii)\" \n",
    "fo=sqrt(2)/(2*pi*sqrt(L*CT))\n",
    "print \"fo= sqrt(2)/(2*pi*sqrt(L*CT))=%0.2e\"%(fo),\" Hz\"# frequency of oscillations\n",
    "print \"part(iii)\"\n",
    "z=sqrt((L*C1*C2)/(C1+C2))\n",
    "fp=1/(2*pi*z)\n",
    "print \"fp= %0.2e\"%(fp),\" Hz\"# parallel-resonant frequency\n",
    "p=sqrt(L*C2)\n",
    "fs=1/(2*pi*p)\n",
    "print \"fs= %0.2e\"%(fs),\" Hz\"# series-resonant frequency\n",
    "Q=(sqrt(L/C2))/(Rse)\n",
    "print \"Q=(sqrt(L/C2))/(Rse)= %0.2f\"%(Q) #Quality factor\n",
    "print \"part(iv)\"\n",
    "AB=gm*rd*(Cds/Cgs)\n",
    "print \"AB=gm*rd*(Cds/Cgs)= %0.2f\"%(AB) #Loop gain\n",
    "T_bias=RG*(Cgs+Cds)\n",
    "print \"T_bias=RG*(Cgs+Cds)= %0.2e\"%(T_bias),\"s\"#Bias Time-Constant\n",
    "T_r = 1/(2*pi*fo)\n",
    "print \"T_r =1/(2*pi*fo)= %0.2e\"%(T_r),\"s\"#resonant Time-Constant for 'fo'\n",
    "print \"for proper operation T_bias >> T_r\"\n",
    "\n",
    "\n",
    "# in part (ii)... value calculated for series resonant frequecy 'fo' is wrong in textbook.\n",
    "# NOTE: in part(iii)... there is a misprint in the calculated value of Quality factor 'Q' in the textbook.\n",
    "#I have used T_r instead of 1/wo (given in the book)"
   ]
  }
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