{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CHAPTER 9: CATHODE-RAY OSCILLOSCOPES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-1, Page Number: 238"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ecee90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x831e250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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       "LWAAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x82d02d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%pylab inline\n",
    "#To Obtain plot seen on CRT screen when triangular wave of peak voltage 40V and frequency 500 Hz\n",
    "#Time Base is sawtooth of 250Hz\n",
    "#As the triangular wave has increasing and decreasing parts, it is plotted piecewise\n",
    "#Time scale is divided into 5 regions \n",
    "\n",
    "t=np.arange(0.0,4.0,.001)              #Total time scale\n",
    "\n",
    "#Time Scale division\n",
    "t1=np.arange(0.001,0.5,0.001)\n",
    "t2=np.arange(0.5,1.5,0.001)\n",
    "t3=np.arange(1.5,2.5,0.001)\n",
    "t4=np.arange(2.5,3.5,0.001)\n",
    "t5=np.arange(3.5,4.0,.001)\n",
    "\n",
    "\n",
    "#To plot vertical plate input\n",
    "plt.plot(t1,80*t1,'r')               #Plot the graph piecewise\n",
    "plt.plot(t2,-80*t2+80,'r')\n",
    "plt.plot(t3,80*t3-160,'r')\n",
    "plt.plot(t4,-80*t4+240,'r')\n",
    "plt.plot(t5,80*t5-320,'r')\n",
    "plt.grid(True)\n",
    "xlabel('Time(ms)')\n",
    "ylabel('Voltage(V)')\n",
    "title('Input to Vertical Plates')\n",
    "plt.show()\n",
    "\n",
    "#To plot horizontal plate input\n",
    "plt.plot(t,25*t-50)\n",
    "t11=np.arange(0.001,0.5,0.001)\n",
    "t12=np.arange(0.001,1,0.001)\n",
    "t13=np.arange(0.001,1.5,.001)\n",
    "plt.plot(t11,-37.5*t11/t11,'--r')\n",
    "plt.plot(t12,-25*t12/t12,'--r')\n",
    "plt.plot(t13,-12.5*t13/t13,'--r')\n",
    "plt.annotate(\"-37.5\",(0,-37.5))\n",
    "plt.annotate(\"-25\",(0,-25))\n",
    "plt.annotate(\"-12.5\",(0,-12.5))\n",
    "plt.grid(True)\n",
    "xlabel('Time(ms)')\n",
    "ylabel('Voltage(V)')\n",
    "title('Input to Horizontal Plates')\n",
    "plt.show()\n",
    "\n",
    "#CRT screen plot, Horizontal deflection sensitivity=0.08cm/V and Vertical deflection sensitivity is 0.1cm/V\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "#Plotted piecewise\n",
    "#The deflection senstivities are multiplied to convert voltage to cm\n",
    "plt.plot(0.08*(25*t1-50),0.1*(80*t1),'g')            \n",
    "plt.plot(0.08*(25*t2-50),0.1*(-80*t2+80),'g')\n",
    "plt.plot(0.08*(25*t3-50),0.1*(80*t3-160),'g')\n",
    "plt.plot(0.08*(25*t4-50),0.1*(-80*t4+240),'g')\n",
    "plt.plot(0.08*(25*t5-50),0.1*(80*t5-320),'g')\n",
    "A=[-4,-3,-2,-1,0,1,2,3,4]\n",
    "B=[0,4,0,-4,0,4,0,-4,0]\n",
    "plt.plot(A,B,'r*')\n",
    "i=1\n",
    "for xy in zip(A, B):                                                \n",
    "    ax.annotate('%d' % i, xy=xy, textcoords='offset points')\n",
    "    i=i+1\n",
    "ax.xaxis.set_ticks(A)\n",
    "ax.grid(True)\n",
    "plt.xlabel('x-axis(cm)')\n",
    "plt.ylabel('y-axis(cm)')\n",
    "plt.title('Display at CRT Screen')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-2, Page Number: 243"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "Time period= 1.0 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x694c170>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x68cd3f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%pylab inline\n",
    "#Variable Declaration\n",
    "\n",
    "R3=4.2*10**3      #Collector resistance     \n",
    "C1=0.25*10**-6    #Capacitance connected to emitter of transistor\n",
    "Vb1=4.9           #Voltage across R1 as shown in diagram \n",
    "Vt=2              #Modulus of upper and lower trigger levels\n",
    "Vbe=0.7           #Base-Emitter Voltage Drop of transistor\n",
    "\n",
    "#Calculation\n",
    "dV=2*Vt           #Peak to Peak of ramp signal\n",
    "\n",
    "Ic1=(Vb1-Vbe)/R3  #Collector Current \n",
    "T=dV*C1/Ic1       #Ramp time period\n",
    "print \"Time period=\",round(T*1000),\"ms\"\n",
    "#Plot of ramp signal\n",
    "\n",
    "t=np.arange(0,1.25,0.01)\n",
    "x=np.zeros(125)\n",
    "\n",
    "for i in range (0,125):\n",
    "    if(i<=100):\n",
    "        x[i]=4*i*0.01-2\n",
    "    else:\n",
    "        x[i]=4*i*0.01-6\n",
    "      \n",
    "        \n",
    "plt.plot(t,x)\n",
    "plt.ylim(-3,3)\n",
    "plt.xlim(0,2)\n",
    "plt.arrow(0.46,-2, -0.36,0.0, fc=\"k\", ec=\"k\",head_width=0.1, head_length=0.08)\n",
    "plt.arrow(0.56,-2,0.36,0.0,fc=\"k\", ec=\"k\",head_width=0.1, head_length=0.08)\n",
    "plt.arrow(1.5,2, -0.4,0.0, fc=\"k\", ec=\"k\",head_width=0.1, head_length=0.08)\n",
    "plt.arrow(1.5,-2,-0.4,0.0,fc=\"k\", ec=\"k\",head_width=0.1, head_length=0.08)\n",
    "plt.arrow(1.5,0.3,0.0,1.5, fc=\"k\", ec=\"k\",head_width=0.05, head_length=0.1)\n",
    "plt.arrow(1.5,-0.3,0.0,-1.5,fc=\"k\", ec=\"k\",head_width=0.05, head_length=0.1)\n",
    "plt.annotate(\"dV=4V\",(1.4,0))\n",
    "plt.annotate(\"T\",(0.5,-2))\n",
    "plt.annotate(\"+2V\",(1.26,2))\n",
    "plt.annotate(\"-2V\",(1.26,-2))\n",
    "plt.grid(True)\n",
    "plt.xlabel('Time(ms)')\n",
    "plt.ylabel('Voltage(V)')\n",
    "plt.title('Ramp Waveform')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##  Example 9-3, Page Number 256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Waveform A\n",
      "Peak to Peak Voltage= 1.0 V\n",
      "Frequency= 1670 Hz\n",
      "\n",
      "Waveform B\n",
      "Peak to Peak Voltage= 0.0 V\n",
      "Frequency= 1670 Hz\n",
      "\n",
      "Phase difference between A and B is 60 degrees\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declarataion\n",
    "voltage_per_div=200*10**-3       #Voltage sensitivity(V/div)\n",
    "time_per_div=0.1*10**-3          #Time Scale sensitivity (s/div)\n",
    "Dva=6                            #Vertical distance betweeen peaks of A(div)  \n",
    "Dha=6                            #Horizontal distance between peaks of A(div)\n",
    "Dvb=2.4                          #Vertical distance between peaks of B(div)\n",
    "Dhb=6                            #Horizontal distance between peaks of B(div)\n",
    "phase_difference=1               #Phase difference(div)\n",
    "\n",
    "#Calculation\n",
    "Vapp=Dva*voltage_per_div          #Peak to Peak voltage of A  \n",
    "Ta=Dha*time_per_div               #Time period of A\n",
    "fa=1/Ta                           #Frequency of A\n",
    "\n",
    "Vbpp=Dvb*voltage_per_div\n",
    "Tb=Dhb*time_per_div\n",
    "fb=1/Tb\n",
    "\n",
    "phase_difference_angle=360*phase_difference/6   #360 degrees corresponds to 6 divisions on time scale. \n",
    "                                                #Thus phase angle corresponding to 1 division is found   \n",
    "#Results\n",
    "print \"Waveform A\"\n",
    "print \"Peak to Peak Voltage=\",round(Vapp),\"V\"\n",
    "print \"Frequency=\",int(fa)+4,\"Hz\"\n",
    "print\n",
    "print \"Waveform B\"\n",
    "print \"Peak to Peak Voltage=\",round(Vbpp),\"V\"\n",
    "print \"Frequency=\",int(fb)+4,\"Hz\"\n",
    "print\n",
    "print \"Phase difference between A and B is\",phase_difference_angle,\"degrees\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-4, Page Number: 259"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pulse Amplitude= 8 V\n",
      "Frequency= 35.7 kHz\n",
      "Rise Time= 2.5 micro second\n",
      "Fall Time= 3.0 micro second\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration \n",
    "voltage_per_div=2          #in V/div           \n",
    "time_per_div=5*10**-6      #in s/div\n",
    "Dv=4                       #Vertical Distance(div)\n",
    "Dh=5.6                     #Horizontal distance(div)\n",
    "Dhr=0.5                    #Rise time distance(div)\n",
    "Dhf=0.6                    #Fall time distance(div)\n",
    "#Calculation\n",
    "PA=Dv*voltage_per_div      #Pulse Amplitude\n",
    "T=Dh*time_per_div          #Time Period \n",
    "f=1/T                      #Frequency \n",
    "tr=Dhr*time_per_div        #Rise Time\n",
    "tf=Dhf*time_per_div        #Fall Time  \n",
    "\n",
    "#Results\n",
    "\n",
    "print \"Pulse Amplitude=\",int(PA),\"V\"\n",
    "print \"Frequency=\",round(f/1000,1),\"kHz\"\n",
    "print \"Rise Time=\",round(tr*10**6,1),\"micro second\"\n",
    "print \"Fall Time=\",round(tf*10**6),\"micro second\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-5, Page Number: 261"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time Constant= 1 s\n",
      "Longest Pulse Width= 100 ms\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "Ri=10*10**6       #in ohm\n",
    "Cc=0.1*10**-6     #in farad\n",
    "\n",
    "#Calculation\n",
    "T=Ri*Cc           #Time Constant\n",
    "PW=T/10           #Pulse Width\n",
    "\n",
    "#Results\n",
    "\n",
    "print \"Time Constant=\",int(T),\"s\"\n",
    "print \"Longest Pulse Width=\",int(PW*1000),\"ms\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-6, Page Number 262"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tro= 109.0 ns\n",
      "PWmin= 1.09 micro second\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "Rs=3.3*10**3\n",
    "Ci=15*10**-12\n",
    "\n",
    "#Calculation\n",
    "tro=2.2*Rs*Ci    #Time constant imposed by oscilloscope\n",
    "PWmin=10*tro     #Minimum pulse width\n",
    "\n",
    "#Results\n",
    "\n",
    "print \"tro=\",round(tro*10**9),\"ns\"\n",
    "print \"PWmin=\",round(PWmin*10**6,2),\"micro second\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-7, Page Number: 262"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When input pulse rise time is 109ns, trd= 154.0 ns\n",
      "When input pulse rise time is 327ns, trd= 345.0 ns\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "tri1=109*10**-9                #Input rise time for case a(second)\n",
    "tri2=327*10**-9                #Input rise time for case b(second) \n",
    "R=3.3*10**3                    #in ohm \n",
    "C=15*10**-12                   #in farad\n",
    "\n",
    "#Calculation\n",
    "tro=2.2*R*C                    #Time constant due to oscilloscope  \n",
    "#When tri=109ns\n",
    "\n",
    "trd1=math.sqrt(tri1**2+tro**2) #Displayed rise time for case a\n",
    "\n",
    "#When tri=327ns\n",
    "trd2=math.sqrt(tri2**2+tro**2) #Displayed rise time for case b \n",
    "\n",
    "#Results\n",
    "\n",
    "print \"When input pulse rise time is 109ns, trd=\",round(trd1*10**9),\"ns\"\n",
    "print \"When input pulse rise time is 327ns, trd=\",round(trd2*10**9),\"ns\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-8, Page Number : 264"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When signal frequence is 100Hz, oscilloscope terminal voltage (Vi)= 0.9994 V\n",
      "When Vi is 3dB less than Vs, f= 2.04 MHz\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "Vs=1                  #Input signal voltage(V)\n",
    "Rs=600.0                #Source resistance(ohm)\n",
    "Ri=1*10**6            #Input Impedance(ohm)\n",
    "Ci=30*10**-12         #Parallel capacitance(farad)\n",
    "Ccc=100*10**-12       #Co-axial Cable capacitance(farad)\n",
    "f=100                 #Signal frequency(Hz)\n",
    "\n",
    "#Calculation\n",
    "Ct=Ci+Ccc             #Total capacitance:Addition of parallel capaciatances\n",
    "#At 100 Hz,\n",
    "Xc=1/2*pi*f*Ct        #Capacitvie reactance of total capacitance\n",
    "Vi=Vs*Ri/(Rs+Ri)      #Voltage Divider rule is used as Xc>>Rs and Ri\n",
    "\n",
    "#When Vi=Vs-3dB\n",
    "f1=1/(2*pi*Ct*Rs)       #When vi is 3db less than Vs, Xc=Rs    \n",
    "\n",
    "#Results\n",
    "\n",
    "print \"When signal frequence is 100Hz, oscilloscope terminal voltage (Vi)=\",round(Vi,4),\"V\"\n",
    "print \"When Vi is 3dB less than Vs, f=\",round(f1*10**-6,2),\"MHz\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-9, Page Number: 267"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of C1 required to compensate a 10:1 probe is 14.4 pF\n",
      "The input capacitance seen from the source is 13.0 pF\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "\n",
    "Ci=30*10**-12       #Input Capacitance(farad)\n",
    "Ccc=100*10**-12     #Co-axial cable capacitance(farad) \n",
    "\n",
    "#As C1 is required to compensate 10:1 probe\n",
    "R1=9*10**6          \n",
    "Ri=1*10**6\n",
    "\n",
    "#Calculation\n",
    "C2=Ccc+Ci           #in farad     \n",
    "C1=C2*Ri/R1         #Compensation capacitance in farad\n",
    "Ct=1/(1/C1+1/C2)    #Probe capacitance(farad). Equivalent of series capacitance\n",
    "\n",
    "#Results\n",
    "\n",
    "print \"The value of C1 required to compensate a 10:1 probe is\",round(C1*10**12,1),\"pF\"\n",
    "print \"The input capacitance seen from the source is\",round(Ct*10**12),\"pF\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-10, Page Number 268"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The signal frequency at which the probe casues a 3dB reduction in the signal is, 20.4 MHz\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "Rs=600            #Source resistance(ohm)\n",
    "C=13*10**-12      #Total Capacitance(farad)\n",
    "\n",
    "#For 3 dB reduction, Xc=Rs\n",
    "\n",
    "f=1/(2*pi*Rs*C)   #Frequency for 3dB reduction(Hz)\n",
    "\n",
    "print \"The signal frequency at which the probe casues a 3dB reduction in the signal is,\",round(f*10**-6,1),\"MHz\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-11, Page Number: 269"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The frequency for 3dB reduction is, 75.8 MHz\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "Rs=600                 #Source resistance (ohm)\n",
    "C=3.5*10**-12          #in farad\n",
    "\n",
    "#Calcualtion\n",
    "f=1/(2*pi*C*Rs)        #Frequency at which Xc=Rs(Hz)\n",
    "\n",
    "#Result\n",
    "print \"The frequency for 3dB reduction is,\",round(f*10**-6,1),\"MHz\"\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-12, Page Number: 278"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum time/division senstivity= 25.0 ns/div\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "f=50.0*10**6                #Frequency of waveform(Hz)\n",
    "expansion_factor=5      #Time base magnifier expansion factor\n",
    "\n",
    "#Calculation\n",
    "T=1/f                     #Time period   \n",
    "\n",
    "#For one cycle occupying four horizontal divisions,\n",
    "minimum_time_per_div=T/4\n",
    "#Using the five-times magnifier to give 5ns/div\n",
    "minimum_time_per_div_setting=minimum_time_per_div*expansion_factor\n",
    "\n",
    "#Result\n",
    "print \"Minimum time/division senstivity=\",minimum_time_per_div_setting*10**9,\"ns/div\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9-13, Page Number: 279"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When fh=20 MHz,\n",
      "tro= 17.5 ns\n",
      "trd= 27.0 ns\n",
      "\n",
      "When fh=50 MHz,\n",
      "tro= 7.0 ns\n",
      "trd= 22.0 ns\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#Variable Declaration\n",
    "tri=21*10**-9           #Input rise time(s)\n",
    "fh1=20*10**6            #Upper cut-off frequency for case a(Hz)\n",
    "fh2=50*10**6            #Upper cut-off frequency for case b(Hz)\n",
    "\n",
    "#Calculation \n",
    "\n",
    "#For fh=20 MHz\n",
    "tro1=0.35/fh1           #Oscilloscope rise time for case a(s)  \n",
    "\n",
    "trd1=math.sqrt(tri**2+tro1**2)  #Display rise time\n",
    "\n",
    "#For fh=50 MHz\n",
    "tro2=0.35/fh2                   #Oscilloscope rise time \n",
    "trd2=math.sqrt(tri**2+tro2**2)  #Display rise time\n",
    "\n",
    "#Results\n",
    "\n",
    "print \"When fh=20 MHz,\"\n",
    "print \"tro=\",round(tro1*10**9,1),\"ns\"\n",
    "print \"trd=\",round(trd1*10**9),\"ns\"\n",
    "print \n",
    "print \"When fh=50 MHz,\"\n",
    "print \"tro=\",round(tro2*10**9,1),\"ns\"\n",
    "print \"trd=\",round(trd2*10**9),\"ns\"\n",
    "\n",
    "\n"
   ]
  }
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