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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "chapter 5: Feed Back"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.1, Page No.192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Percentage of output which is fed back\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=50.0 #gain(unitless)\n",
+ "Af=10.0 #gain(unitless)\n",
+ "\n",
+ "#calculation\n",
+ "\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Beta=(A/Af-1)/A #feedback ratio (unitless)\n",
+ "\n",
+ "#Result\n",
+ "print(\"Percentage of output feed back : %.0f%%\"%(Beta*100))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Percentage of output feed back : 8%\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.2, Page No.192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Voltage gain and reduction in voltage\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=1000.0 #gainWithoutFeedback(unitless)\n",
+ "Adash=800 #gainWithoutFeedback(unitless) \n",
+ "g_reduce=0.40 #factor by which gain reduced\n",
+ "#Calculations\n",
+ "\n",
+ "#Part (i) : \n",
+ "Af=A-A*g_reduce #gainWithFeedback(unitless)\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Beta=(A/Af-1)/A #feedback factor (unitless)\n",
+ "\n",
+ "Af_dash=Adash/(1+Adash*Beta)\n",
+ "\n",
+ "#Part (ii)\n",
+ "Reduction=((A-Adash)/A)*100 #% reduction without feedback\n",
+ "Reduction1=((Af-Af_dash)/Af)*100 #% reduction without feedback\n",
+ "\n",
+ "#Result\n",
+ "print(\"At normal collector supply :\")\n",
+ "print(\"with feedback gain reduces by a factor %.2f\"%g_reduce)\n",
+ "print(\"At normal collector supply, Gain with feedback :%.0f \"%Af)\n",
+ "print(\"\\nAt reduced power supply :\")\n",
+ "print(\"At Reduced collector supply, Gain with feedback : %.0f\"%(math.ceil(Af_dash)))\n",
+ "print(\"%% reduction in gain without feedback :%.0f%%\"%Reduction)\n",
+ "print(\"%% reduction in gain with feedback :%.0f%%\"%Reduction1)\n",
+ "#Note : answer of Af is wrong in the book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "At normal collector supply :\n",
+ "with feedback gain reduces by a factor 0.40\n",
+ "At normal collector supply, Gain with feedback :600 \n",
+ "\n",
+ "At reduced power supply :\n",
+ "At Reduced collector supply, Gain with feedback : 522\n",
+ "% reduction in gain without feedback :20%\n",
+ "% reduction in gain with feedback :13%\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.3, Page No.192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Gain with feedback factor and feedback voltage\n",
+ "import math\n",
+ "#Variable declaration\n",
+ "\n",
+ "A=100.0 #gain without feedback(unitless)\n",
+ "Beta=1.0/25.0 #feedback ratio (unitless)\n",
+ "Vi=50.0 #in mV\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part (i) :\n",
+ "Af=A/(1+A*Beta) #gain with feedback(unitless)\n",
+ "\n",
+ "\n",
+ "#Part (ii) :\n",
+ "FeedbackFactor=Beta*A #unitless\n",
+ "\n",
+ "\n",
+ "#Part (iii) :\n",
+ "Vo_dash=Af*Vi*10**-3 #in volt\n",
+ "\n",
+ "\n",
+ "#Part (iv) :\n",
+ "FeedbackVoltage=Beta*Vo_dash #in volt\n",
+ "\n",
+ "\n",
+ "#Part (v) :\n",
+ "Vi_dash=Vi*(1+Beta*A) #in mv\n",
+ "\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print(\"(i)\\n Gain with feedback :%.0f\"%Af)\n",
+ "print(\"(ii)\\n Feedback Factor :%.0f\"%FeedbackFactor)\n",
+ "print(\"(iii)\\n Output Voltage in volts :%.0f\"%Vo_dash)\n",
+ "print(\"(iv)\\n Feedback Voltage in volts :%.2f\"%FeedbackVoltage)\n",
+ "print(\"(v)\\n New Increased Input Voltage in milli volts :%.0f\"%Vi_dash)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)\n",
+ " Gain with feedback :20\n",
+ "(ii)\n",
+ " Feedback Factor :4\n",
+ "(iii)\n",
+ " Output Voltage in volts :1\n",
+ "(iv)\n",
+ " Feedback Voltage in volts :0.04\n",
+ "(v)\n",
+ " New Increased Input Voltage in milli volts :250\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.4, Page no.193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Bandwidth with negative feedback\n",
+ "import math\n",
+ "#variable declaration\n",
+ "BW=200.0 #in kHz\n",
+ "A=40.0 #gain without feedback(in dB)\n",
+ "Beta=5.0 #negative feedback in %\n",
+ "Beta=Beta/100.0 #feedback factor\n",
+ "\n",
+ "#calculation\n",
+ "\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Af=A/(1+A*Beta) #gain with feedback(in dB)\n",
+ "BW_dash=A*BW/Af #in kHz\n",
+ "\n",
+ "#Result\n",
+ "print(\"Since gain bandwidth product remains constant, A*BW=Af*BW_dash\")\n",
+ "print(\"New Bandwidth in kHz : %.0f\"%BW_dash)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Since gain bandwidth product remains constant, A*BW=Af*BW_dash\n",
+ "New Bandwidth in kHz : 600\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.5, Page No.193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Fraction of output fed back\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=140.0 #gain without feedback(unitless)\n",
+ "Af=17.5 #gain with feedback(unitless)\n",
+ "\n",
+ "#Calculations\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Beta=(A/Af-1)/A #feedback ratio (unitless)\n",
+ "\n",
+ "#Result\n",
+ "print(\"Fraction of output fed back to input : %.2f or 1/20\"%Beta)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Fraction of output fed back to input : 0.05 or 1/20\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.6, Page No.205"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Small Change in gain\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=200.0 #gain without feedback(unitless)\n",
+ "Beta=0.25 #fraction ratio(unitless)\n",
+ "\n",
+ "#CAlculations\n",
+ "#Given : Normal gain changes by 10 %, it means dA/A=10/100\n",
+ "dABYA=10.0/100.0 #change in gain\n",
+ "dAfBYAf=(1/(1+Beta*A))*(dABYA) #change in gain\n",
+ "\n",
+ "#Result\n",
+ "print(\"We have, Af=A/(1+Beta*A).................eqn(1)\")\n",
+ "print(\"\\nDifferentiating it with respect to A, we get\")\n",
+ "print(\"\\ndAf/dA=((1+Beta*A)-Beta*A)/(1+Beta*A)^2=1/(1+Beta*A)^2\")\n",
+ "print(\"\\ndAf=dA/(1+Beta*A)^2.......................eqn(2)\")\n",
+ "print(\"\\nDividing eqn(2) by eqn(1),\")\n",
+ "print(\"\\ndAf/Af=(dA/((1+Beta*A)^2))*((1+Beta*A)/A)=(1/(1+Beta*A))*(dA/A)\")\n",
+ "print(\"\\n\\nChange in gain : %.4f\"%((math.floor(dAfBYAf*10**4))/10**4))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "We have, Af=A/(1+Beta*A).................eqn(1)\n",
+ "\n",
+ "Differentiating it with respect to A, we get\n",
+ "\n",
+ "dAf/dA=((1+Beta*A)-Beta*A)/(1+Beta*A)^2=1/(1+Beta*A)^2\n",
+ "\n",
+ "dAf=dA/(1+Beta*A)^2.......................eqn(2)\n",
+ "\n",
+ "Dividing eqn(2) by eqn(1),\n",
+ "\n",
+ "dAf/Af=(dA/((1+Beta*A)^2))*((1+Beta*A)/A)=(1/(1+Beta*A))*(dA/A)\n",
+ "\n",
+ "\n",
+ "Change in gain : 0.0019\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.7, Page No.206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#New gain distortion and input voltage\n",
+ "import math\n",
+ "#Variable declaration\n",
+ "A=200.0 #gain without feedback(unitless)\n",
+ "Dn=10.0 #Distortion in %\n",
+ "Vi=0.5 #Initial input voltage in volt\n",
+ "Beta=0.05 #feedback ratio (unitless)\n",
+ "\n",
+ "#Calculations\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Af=A/(1+A*Beta) #gain with feedback(unitless)\n",
+ "Dn_dash=Dn/(1+A*Beta) #new distortion in %\n",
+ "InitialOutputVoltage=A*Vi #in Volt\n",
+ "NewInputVoltage=InitialOutputVoltage/Af\n",
+ "\n",
+ "print(\"New gain :%.3f\"%Af)\n",
+ "print(\"Distortion with negative feedback : %.3f%%\"%Dn_dash)\n",
+ "print(\"Initial Output Voltage in volt:%.0f\"%InitialOutputVoltage)\n",
+ "print(\"New Input Voltage in volts :%.2f\"%NewInputVoltage)\n",
+ "#Note :Ans of Af and NewInputVoltage is not acurate in the book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "New gain :18.182\n",
+ "Distortion with negative feedback : 0.909%\n",
+ "Initial Output Voltage in volt:100\n",
+ "New Input Voltage in volts :5.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.8, Page No. 206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Feedback rction voltage and impedence\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "A=10000.0 #gain without feedback(unitless)\n",
+ "Zi=10.0 #in kOhm\n",
+ "Zo=100.0 #in Ohm\n",
+ "R1=2.0 #in Ohm\n",
+ "R2=18.0 #in Ohm\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "#Part (i) :\n",
+ "Beta=R1/(R1+R2) #feedback fraction(unitless)\n",
+ "\n",
+ "#Part (ii) :\n",
+ "Af=A/(1+A*Beta) #Gain with negative feedback(unitless)\n",
+ "\n",
+ "#Part (iii) :\n",
+ "inputVoltge=0.5 #in mV\n",
+ "outputVoltge=Af*inputVoltge #in mV\n",
+ "\n",
+ "#Part (iv) :\n",
+ "Zif=Zi*(1+Beta*A) #in kOhm\n",
+ "\n",
+ "#Part (v) :\n",
+ "Zof=Zo/(1+Beta*A) #in kOhm\n",
+ "\n",
+ "print(\"(i)\\nFeedback Fraction :%.1f\"%Beta)\n",
+ "print(\"\\n(ii)\\nGain with negative feedback :%.0f\"%(math.ceil(Af)))\n",
+ "print(\"\\n(iii)\\nOutput Voltage in milli volts :%.0f\"%(math.ceil(outputVoltge)))\n",
+ "print(\"\\n(iv)\\nInput impedance of feedback amplifier in Mohm : %.2f\"%(Zif*10**-3))\n",
+ "print(\"\\n(v)\\nOutput impedance with feedback in Ohm : %.1f\"%Zof)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)\n",
+ "Feedback Fraction :0.1\n",
+ "\n",
+ "(ii)\n",
+ "Gain with negative feedback :10\n",
+ "\n",
+ "(iii)\n",
+ "Output Voltage in milli volts :5\n",
+ "\n",
+ "(iv)\n",
+ "Input impedance of feedback amplifier in Mohm : 10.01\n",
+ "\n",
+ "(v)\n",
+ "Output impedance with feedback in Ohm : 0.1\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.9, Page No.207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Voltage gain input and output resistance\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=200 #gain without feedback(unitless)\n",
+ "Ri=2 #in kOhm\n",
+ "Ro=12 #in kOhm\n",
+ "Beta=0.02 #feedbak ratio(unitless)\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Part (i) :\n",
+ "Af=A/(1+A*Beta) #gain with feedback(unitless)\n",
+ "\n",
+ "#Part (ii) :\n",
+ "Rif=Ri*(1+A*Beta) #in kOhm\n",
+ "\n",
+ "#Part (ii) :\n",
+ "Rof=Ro/(1+A*Beta) #in kOhm\n",
+ "\n",
+ "#Result\n",
+ "print(\"(i)\\nGain with Negative Feedback :%.0f\"%Af)\n",
+ "print(\"\\n(ii)\\nInput resistance with feedback in kOhm :%.0f\"%Rif)\n",
+ "print(\"\\n(iii)\\nOutput resistance with feedback in kOhm :%.1f\"%Rof)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)\n",
+ "Gain with Negative Feedback :40\n",
+ "\n",
+ "(ii)\n",
+ "Input resistance with feedback in kOhm :10\n",
+ "\n",
+ "(iii)\n",
+ "Output resistance with feedback in kOhm :2.4\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.10, Page No.207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Gain wih feedbck in dB\n",
+ "import math\n",
+ "#variable declaration\n",
+ "A=1000.0 #gain(unitless)\n",
+ "Beta=1.0/20.0 #feedback ratio (unitless)\n",
+ "\n",
+ "#Calculation\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Af=A/(1+A*Beta) #gain with feedback(unitless)\n",
+ "Af=20*math.log10(Af) #in dB\n",
+ "\n",
+ "#Result\n",
+ "print(\"Gain with feedback in dB : %.1f\"%Af)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gain with feedback in dB : 25.8\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ " example 5.11, page No.208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Bandwidth after feedback\n",
+ "import math\n",
+ "#Variable declarations\n",
+ "\n",
+ "A=800.0 #gain(unitless)\n",
+ "f1=40.0 #in Hz\n",
+ "f2=16.0 #in kHz\n",
+ "Beta=2.0/100.0 #feedback fator (unitless)\n",
+ "\n",
+ "#caalculations\n",
+ "\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Af=A/(1+A*Beta) #gain with feedback(unitless)\n",
+ "BW=f2*10**3-f1 #Bandwidth of amplifier in Hz\n",
+ "f1_f=f1/(1+A*Beta) #in Hz\n",
+ "f2_f=f2*(1+A*Beta) #in kHz\n",
+ "BW_f=f2_f*10**3-f1_f #Bandwith after feedback in Hz\n",
+ "\n",
+ "#result\n",
+ "print(\"Voltage gin with feedback : %.0f\"%Af)\n",
+ "print(\"Bandwidth of amplifier in kHz : %.2f\"%(BW*10**-3))\n",
+ "print(\"Bandwith after feedback in KHz : %.0f\"%(BW_f*10**-3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Voltage gin with feedback : 47\n",
+ "Bandwidth of amplifier in kHz : 15.96\n",
+ "Bandwith after feedback in KHz : 272\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ " example 5.12, Page No.208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Gain and new bandwidth\n",
+ "import math\n",
+ "#Variable declaration\n",
+ "A=100.0 #gain(unitless)\n",
+ "BW=10.0 #in Hz\n",
+ "Beta=5.0 #in %\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part (i) :\n",
+ "#Formula : Af=A/(1+A*Beta)\n",
+ "Af=A/(1+A*Beta/100.0) #gain with feedback(unitless)\n",
+ "\n",
+ "#Part (ii)\n",
+ "BW_f=BW*(1+A*Beta/100.0) #Bandwith after feedback in Hz\n",
+ "\n",
+ "#Result\n",
+ "print(\"Voltage gain with feedback :%.2f \"%Af)\n",
+ "print(\"Bandwith with negative feedback in KHz : %.0f\"%BW_f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Voltage gain with feedback :16.67 \n",
+ "Bandwith with negative feedback in KHz : 60\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "example 5.13, Page No.208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Input resistance and voltage gain\n",
+ "import math\n",
+ "#variable decclaration\n",
+ "hfe=50.0 #unitless\n",
+ "hie=1.1 #in kOhm\n",
+ "hoe=0.0 #unitless\n",
+ "hre=0.0 #unitless\n",
+ "RL=4.0 #in kOhm\n",
+ "Rs=10.0 #in kOhm\n",
+ "RB=40.0 #in kOhm\n",
+ "\n",
+ "#calculation\n",
+ "\n",
+ "RLdash=RB*RL/(RB+RL) #in Kohm\n",
+ "AV=-hfe*RLdash/hie #unitless\n",
+ "\n",
+ "#Part (i) ;\n",
+ "Rif=hie*(RB/(1-AV))/(hie+(RB/(1-AV))) #in kOhm\n",
+ "print(\"Input resistance with feedback in Ohm : %.0f\"%(Rif*1000))\n",
+ "#Part (ii) :\n",
+ "AVf=AV*(Rif/(Rs+Rif)) #unitless\n",
+ "print(\"Voltage gain with feedback : %.2f\"%((math.ceil(AVf*100))/100))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Input resistance with feedback in Ohm : 197\n",
+ "Voltage gain with feedback : -3.19\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file