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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:57634c93bf4d4aea76e807a2cbb9e510f617e9cf546f62a2de10f5bf9157d3c1"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h1>Chapter 29: parallel resonance and Q-factor</h1>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 1, page no. 521</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "R = 10;# in ohms\n",
+ "L = 0.005;# IN Henry\n",
+ "C = 0.25e-6;# IN fARADS\n",
+ "V = 50;#in volts\n",
+ "\n",
+ "#calculation:\n",
+ " #Resonant frequency, for parallel\n",
+ "fr = ((1/(L*C) - ((R**2)/(L**2)))**0.5)/(2*math.pi)\n",
+ " #dynamic resistance\n",
+ "Rd = L/(C*R)\n",
+ " #Current at resonance\n",
+ "Ir = V/Rd\n",
+ "wr = 2*math.pi*fr\n",
+ " #Q-factor at resonance, Q = wr*L/R\n",
+ "Qr = wr*L/R\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Resonance frequency is \",round(fr,2),\" Hz\\n\"\n",
+ "print \"\\n (b)dynamic resistance \",round(Rd,2),\" ohm\\n\"\n",
+ "print \"\\n (c)Current at resonance, Ir is \",round(Ir,2),\" A\\n\"\n",
+ "print \"\\n (d)Q-factor at resonance is \",round(Qr,2),\"\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Resonance frequency is 4490.31 Hz\n",
+ "\n",
+ "\n",
+ " (b)dynamic resistance 2000.0 ohm\n",
+ "\n",
+ "\n",
+ " (c)Current at resonance, Ir is 0.02 A\n",
+ "\n",
+ "\n",
+ " (d)Q-factor at resonance is 14.11 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 2, page no. 521</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "RL1 = 0;# in ohms\n",
+ "RL2 = 30;# in ohms\n",
+ "L = 0.100;# IN Henry\n",
+ "C = 40e-6;# IN fARADS\n",
+ "V = 50;#in volts\n",
+ "\n",
+ "#calculation:\n",
+ " #for RL1\n",
+ " #Resonant frequency,\n",
+ "wr1 = (1/(L*C))**0.5\n",
+ "fr1 = wr1/(2*math.pi)\n",
+ " #for RL2\n",
+ " #Resonant frequency,\n",
+ "wr2 = (1/(L*C) - ((RL2**2)/(L**2)))**0.5\n",
+ "fr2 = wr2/(2*math.pi)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Resonance frequency at RL = 0 is \",round(fr1,2),\" Hz\"\n",
+ "print \"\\n (b)Resonance frequency at RL = 30 ohm is \",round(fr2,2),\" Hz\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Resonance frequency at RL = 0 is 79.58 Hz\n",
+ "\n",
+ " (b)Resonance frequency at RL = 30 ohm is 63.66 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 3, page no. 523</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "R = 150;# in ohms\n",
+ "L = 0.120;# IN Henry\n",
+ "V = 20;#in volts\n",
+ "fr = 4000;# in Hz\n",
+ "\n",
+ "#calculation:\n",
+ " #capacitance, C\n",
+ "C = 1/(L*((2*math.pi*fr)**2 + ((R**2)/(L**2))))\n",
+ "Rd = L/(C*R)\n",
+ " #Current at resonance\n",
+ "Ir = V/Rd\n",
+ "wr = 2*math.pi*fr\n",
+ " #Q-factor at resonance, Q = wr*L/R\n",
+ "Qr = wr*L/R\n",
+ " #bandwidth,.(f2 \u2212 f1)\n",
+ "bw = fr/Qr\n",
+ " #upper half-power frequency, f2\n",
+ "f2 = (bw + ((bw**2) + 4*(fr**2))**0.5)/2\n",
+ " #lower half-power frequency, f1\n",
+ "f1 = f2 - bw\n",
+ " #impedance at the \u22123 dB frequencies\n",
+ "Z = Rd/(2**0.5)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)the capacitance of the capacitor,C is \",round(C*1E6,2),\"uF\"\n",
+ "print \"\\n (b)dynamic resistance \",round(Rd,2),\"ohm\\n\"\n",
+ "print \"\\n (c)Current at resonance, Ir is \",round(Ir*1000,2),\"mA\\n\"\n",
+ "print \"\\n (d)Q-factor at resonance is \",round(Qr,2),\"\\n\"\n",
+ "print \"\\n (e)bandwidth is \",round(bw,2),\" Hz\\n\"\n",
+ "print \"\\n (f)the upper half-power frequency, f2 is \",round(f2,2),\" Hz and \"\n",
+ "print \" the lower half-power frequency, f1 is \",round(f1,2),\" Hz\\n\"\n",
+ "print \"\\n (g)impedance at the -3 dB frequencies is \",round(Z,2),\" ohm\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)the capacitance of the capacitor,C is 0.01 uF\n",
+ "\n",
+ " (b)dynamic resistance 60788.85 ohm\n",
+ "\n",
+ "\n",
+ " (c)Current at resonance, Ir is 0.33 mA\n",
+ "\n",
+ "\n",
+ " (d)Q-factor at resonance is 20.11 \n",
+ "\n",
+ "\n",
+ " (e)bandwidth is 198.94 Hz\n",
+ "\n",
+ "\n",
+ " (f)the upper half-power frequency, f2 is 4100.71 Hz and \n",
+ " the lower half-power frequency, f1 is 3901.76 Hz\n",
+ "\n",
+ "\n",
+ " (g)impedance at the -3 dB frequencies is 42984.21 ohm\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4, page no. 525</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "RL = 5;# in ohms\n",
+ "L = 0.002;# IN Henry\n",
+ "C = 25e-6;# IN fARADS\n",
+ "Rc = 3;# in ohms\n",
+ "\n",
+ "#calculation:\n",
+ " #Resonant frequency, for parallel\n",
+ "fr = (1/(2*math.pi*((L*C)**0.5)))*((RL**2 - (L/C))/(Rc**2 - (L/C)))**0.5\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n resonant frequency, fr is \",round(fr,2),\" Hz\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " resonant frequency, fr is 626.45 Hz"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 5, page no. 525</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "RL = 3;# in ohms\n",
+ "fr = 1000;# in Hz\n",
+ "Xc = 10;# IN ohms\n",
+ "Rc = 4;# in ohms\n",
+ "\n",
+ "#calculation:\n",
+ "XL1 = (((Rc**2 + Xc**2)/Xc) + ((((Rc**2 + Xc**2)/Xc)**2) - 4*(RL**2))**0.5)/2\n",
+ "XL2 = (((Rc**2 + Xc**2)/Xc) - ((((Rc**2 + Xc**2)/Xc)**2) - 4*(RL**2))**0.5)/2\n",
+ "wr = 2*math.pi*fr\n",
+ " #inductance\n",
+ "L1 = XL1/wr\n",
+ "L2 = XL2/wr\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n inductance is either \",round(L1*1000,2),\"mH or \",round(L2*1000,2),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " inductance is either 1.71 mH or 0.13 mH"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 6, page no. 526</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "QL = 60;# Q-factor\n",
+ "Qc = 300;# Q-factor\n",
+ "\n",
+ "#calculation:\n",
+ "QT = QL*Qc/(QL + Qc)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n the overall Q-factor is \",round(QT,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " the overall Q-factor is 50.0"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 7, page no. 527</h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "import cmath\n",
+ "#initializing the variables:\n",
+ "C = 10.61E-9;# in Farad\n",
+ "bw = 500;# in Hz\n",
+ "fr = 150000;# in Hz\n",
+ "x = 0.004\n",
+ "\n",
+ "#calculation:\n",
+ " #Q-factor\n",
+ "Q = fr/bw\n",
+ "wr = 2*math.pi*fr\n",
+ " #dynamic resistance, RD\n",
+ "Rd = Q/(C*wr)\n",
+ "de = x\n",
+ "Z = Rd/(1 + (2*de*Q*1j))\n",
+ "\n",
+ "#Results\n",
+ "print \"\\n\\n Result \\n\\n\"\n",
+ "print \"\\n (a)Q-factor \",round(Q,2),\"\"\n",
+ "print \"\\n (b)dynamic resistance \",round(Rd,2),\"ohm\"\n",
+ "print \"\\n (c)magnitude of the impedance \",round(abs(Z),2),\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\n",
+ " Result \n",
+ "\n",
+ "\n",
+ "\n",
+ " (a)Q-factor 300.0 \n",
+ "\n",
+ " (b)dynamic resistance 30000.93 ohm\n",
+ "\n",
+ " (c)magnitude of the impedance 11538.82 ohm"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 07:14:34 +0000