09_VoltageDividers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Universidade Federal do Rio Grande do Sul (UFRGS)   \n",
    "Programa de Pós-Graduação em Engenharia Civil (PPGEC)   \n",
    "\n",
    "# PEC00144: Experimental Methods in Civil Engineering\n",
    "\n",
    "\n",
    "### Part II: Instrumentation\n",
    "[9.   Review on electrical circuits](#section_8)  \n",
    "\n",
    "&nbsp;&nbsp;&nbsp;[9.1. Voltage dividers and impedance](#section_91)     \n",
    "&nbsp;&nbsp;&nbsp;[9.2. Power sources and batteries](#section_92)     \n",
    "&nbsp;&nbsp;&nbsp;[9.3. Passive circuit components](#section_93)   \n",
    "&nbsp;&nbsp;&nbsp;[9.4. How to light up a LED](#section_94)   \n",
    "&nbsp;&nbsp;&nbsp;[9.5. Low and high pass RC filters](#section_95)   \n",
    "&nbsp;&nbsp;&nbsp;[9.6. Regulated voltage and current sources](#section_96)   \n",
    "&nbsp;&nbsp;&nbsp;[9.7. Microprocessed power sources](#section_97)   \n",
    "\n",
    "---\n",
    "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020)  \n",
    "_Porto Alegre, RS, Brazil_ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Python modules required for this notebook\n",
    "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from   MRPy import MRPy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Review on electrical circuits  <a name=\"section_9\"></a> \n",
    "\n",
    "### 9.1. Voltage dividers and impedance  <a name=\"section_91\"></a> \n",
    "\n",
    "\n",
    "<img src=\"resources/VoltageDivider_2.png\" alt=\"Voltage divider\" width=\"240px\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logic level output:  3.33V\n"
     ]
    }
   ],
   "source": [
    "Vin  = 5.                # logic level 5V\n",
    "Z1   = 5000.             # top resistor (ohms)\n",
    "Z2   = 10000.            # bottom resistor (ohms)\n",
    "Vout = Vin*Z2/(Z1 + Z2)  # logic level ~3.3V\n",
    "\n",
    "print('Logic level output: {0:5.2f}V'.format(Vout))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.2. Power sources and batteries  <a name=\"section_92\"></a> \n",
    "\n",
    "<img src=\"resources/Batt_LeadAcid.jpg\" alt=\"Lead acid battery\" width=\"400px\"/>\n",
    "\n",
    "<img src=\"resources/Batt_18650.jpg\" alt=\"Lithium polimer battery\" width=\"240px\"/>\n",
    "\n",
    "<img src=\"resources/InternalResistance_1.png\" alt=\"Battery resistance\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.3. Passive circuit components  <a name=\"section_93\"></a> \n",
    "\n",
    "#### 9.3.1. Resistors\n",
    "\n",
    "$$ Z_R = R + 0i$$\n",
    "\n",
    "<img src=\"resources/Resistors_2.jpg\" alt=\"Types of resistors\" width=\"640px\"/>\n",
    "\n",
    "<img src=\"resources/Resistors_1.jpg\" alt=\"Resistors color code\" width=\"280px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 9.3.2. Capacitors\n",
    "\n",
    "$$ Z_C = 0 - i \\, \\frac{1}{2\\pi fC} $$\n",
    "\n",
    "<img src=\"resources/Capacitors_1.jpg\" alt=\"Types of capacitors\" width=\"360px\"/>\n",
    "\n",
    "#### 9.3.3. Inductors\n",
    "\n",
    "$$ Z_L = 0 + i \\, 2\\pi fL$$\n",
    "\n",
    "<img src=\"resources/Inductors_0.jpg\" alt=\"Types of inductors\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.4. How to light up a LED <a name=\"section_94\"></a> \n",
    "\n",
    "<tr>\n",
    "<td> <img src=\"resources/LED_example.gif\" alt=\"Light up a LED\" width=\"320px\">    \n",
    "<td> <img src=\"resources/LED_scheme.png\"  alt=\"LED symbol\"     width=\"240px\">    \n",
    "</tr>\n",
    "    \n",
    "<img src=\"resources/LEDVoltageByColor.png\" alt=\"LED voltage drop\" width=\"320px\"/>  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required resistor value: 480.0Ω\n"
     ]
    }
   ],
   "source": [
    "V_resist = 9000 - 1800      # voltage after a RED resistor (mV)\n",
    "I_light  = 15.              # light up current (mA)\n",
    "\n",
    "R = V_resist/I_light        # required resistor value (ohm)\n",
    "\n",
    "print('Required resistor value: {0:5.1f}Ω'.format(R))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.5. Low and high pass RC filters  <a name=\"section_95\"></a>\n",
    "\n",
    "For both low and high pass first order passive filters, with an association of a \n",
    "resistor and a capacitor, the cut off frequency is given by:\n",
    "\n",
    "$$ f_{\\rm 3dB} = \\frac{1}{2\\pi RC} $$\n",
    "\n",
    "The _decibel_ is a measure of logarithmic relation to a reference value:\n",
    "\n",
    "$$ {\\rm dB} = 20 \\log_{10} \\left( \\frac{V}{V_{\\rm ref}} \\right) $$\n",
    "\n",
    "Some important dB values:\n",
    "\n",
    " |     dB  |  ~fraction |\n",
    " |:-------:|:----------:|\n",
    " |   −20   |    0.100   |\n",
    " |   −10   |    0.316   |\n",
    " |   −6    |    0.501   |\n",
    " |   −3    |    0.708   |\n",
    " |   +3    |    1.41    |\n",
    " |   +6    |    2.00    |\n",
    " |   +10   |    3.16    |\n",
    " |   +20   |    10.     |\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cut off frequency (-3dB):  159.15Hz\n"
     ]
    }
   ],
   "source": [
    "e1 =  0.;  f1 = 10.**e1           #  frequency domain\n",
    "e2 =  4.;  f2 = 10.**e2\n",
    "\n",
    "N  =  1000\n",
    "f  =  np.logspace(e1, e2, N)\n",
    "w  =  2*np.pi*f\n",
    "\n",
    "C  =  0.1e-6                      #  100 nano Faraday\n",
    "R  =  10.e03                      #  10 kilo Ohm\n",
    "ZC = -1j/(w*C)\n",
    "\n",
    "f3dB =  1/(2*np.pi*R*C);          # -3dB frequency\n",
    "\n",
    "print('Cut off frequency (-3dB): {0:7.2f}Hz'.format(f3dB))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 9.5.1 Low pass\n",
    "\n",
    "<img src=\"resources/LowPass_1.png\" alt=\"Low pass filter\" width=\"360px\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HLP   =  ZC/(R + ZC);\n",
    "GLP   =  np.absolute(HLP);\n",
    "dLP   =  20*np.log10(GLP);\n",
    "pLP   =  180*np.angle(HLP)/np.pi;\n",
    "\n",
    "fig1  =  plt.figure(1, figsize=(12,4));\n",
    "\n",
    "sp11  =  plt.subplot(1,3,1)\n",
    "sp11  =  plt.loglog(f,GLP);\n",
    "sp11a =  plt.loglog([f3dB, f3dB], [0.1, 2], 'r', lw=2)\n",
    "plt.title('Filter gain')\n",
    "plt.axis([f1, f2, 0.1, 2]);\n",
    "plt.grid(True); \n",
    " \n",
    "sp12  =  plt.subplot(1,3,2)\n",
    "sp12  =  plt.semilogx(f,dLP);\n",
    "sp12a =  plt.semilogx([f3dB, f3dB], [-20, 5], 'r', lw=2)\n",
    "plt.title('Filter gain in dB')\n",
    "plt.axis([f1, f2, -20, 5]);\n",
    "plt.grid(True); \n",
    " \n",
    "sp13  =  plt.subplot(1,3,3)\n",
    "sp13  =  plt.semilogx(f,pLP);\n",
    "sp13a =  plt.semilogx([f3dB, f3dB], [-120, 30], 'r', lw=2)\n",
    "plt.title('Filter phase shift')\n",
    "plt.axis([f1, f2, -120, 30]);\n",
    "plt.grid(True); \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 9.5.2 High pass\n",
    "\n",
    "<img src=\"resources/HighPass_1.png\" alt=\"High pass filter\" width=\"360px\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HHP   =  R/(R + ZC);\n",
    "GHP   =  np.absolute(HHP);\n",
    "dHP   =  20*np.log10(GHP);\n",
    "pHP   =  180*np.angle(HHP)/np.pi;\n",
    "\n",
    "fig1  =  plt.figure(1, figsize=(12,4));\n",
    "\n",
    "sp11  =  plt.subplot(1,3,1)\n",
    "sp11  =  plt.loglog(f,GHP);\n",
    "sp11a =  plt.loglog([f3dB, f3dB], [0.1, 2], 'r', lw=2)\n",
    "plt.title('Filter gain')\n",
    "plt.axis([f1, f2, 0.1, 2]);\n",
    "plt.grid(True); \n",
    " \n",
    "sp12  =  plt.subplot(1,3,2)\n",
    "sp12  =  plt.semilogx(f,dHP);\n",
    "sp12a =  plt.semilogx([f3dB, f3dB], [-20, 5], 'r', lw=2)\n",
    "plt.title('Filter gain in dB')\n",
    "plt.axis([f1, f2, -20, 5]);\n",
    "plt.grid(True); \n",
    " \n",
    "sp13  =  plt.subplot(1,3,3)\n",
    "sp13  =  plt.semilogx(f,pHP);\n",
    "sp13a =  plt.semilogx([f3dB, f3dB], [-30, 120], 'r', lw=2)\n",
    "plt.title('Filter phase shift')\n",
    "plt.axis([f1, f2, -30, 120]);\n",
    "plt.grid(True); \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example of application: the low pass filtering capacitor for MEMS accelerometer ADXL203, \n",
    "with an output resistor of 32kΩ. \n",
    "\n",
    "<img src=\"resources/ADXL203_photo.jpg\" alt=\"ADXL203 photo\" width=\"360px\"/>\n",
    "\n",
    "<img src=\"resources/ADXL203_internals.png\" alt=\"ADXL203 internals\" width=\"480px\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum capacitor value:    0.10muF\n"
     ]
    }
   ],
   "source": [
    "f3dB = 50.         # set -3dB cut off frequency\n",
    "R    = 32000.      # internal output resistance\n",
    "\n",
    "C    = 1/(2*np.pi*R*f3dB)\n",
    "\n",
    "print('Minimum capacitor value: {0:7.2f}muF'.format(1e6*C))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.6. Regulated voltage and current sources  <a name=\"section_966\"></a> \n",
    "\n",
    "AC to DC conversion with diode bridges:\n",
    "\n",
    "<img src=\"resources/DiodeBridge_1.jpg\" alt=\"Rectifier\" width=\"480px\"/>\n",
    "\n",
    "<img src=\"resources/DiodeBridge_3.png\" alt=\"AC to DC conversion\" width=\"640px\"/>\n",
    "\n",
    "<img src=\"resources/DiodeBridge_0.jpg\" alt=\"LM7805 photo\" width=\"360px\"/>\n",
    "\n",
    "Fixed voltage regulator:\n",
    "\n",
    "<img src=\"resources/LM7805_foto.jpg\" alt=\"LM7805 photo\" width=\"160px\"/>\n",
    "\n",
    "<img src=\"resources/LM7805_scheme.gif\" alt=\"LM7805 schematics\" width=\"540px\"/>\n",
    "\n",
    "Variable voltage regulator:\n",
    "\n",
    "<img src=\"resources/LM317_scheme.jpg\" alt=\"LM317 schematics\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.7. Microprocessed power sources <a name=\"section_97\"></a> \n",
    "\n",
    "<img src=\"resources/StepDown_1.png\" alt=\"Step down microprocessor\" width=\"640px\"/>\n",
    "\n",
    "<img src=\"resources/StepUp_1.png\" alt=\"Step up microprocessor\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}