{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  <center>  Moč pri izmeničnih signalih  </center>\n",
    "<br>\n",
    "<center>Dejan Križaj, 2019</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "**Namen:** Zvezek (Notebook) je namenjen seznanjanju študentov z uporabo Jupytra za razumevanje in analizo moči na elementih vezja ali celotnem vezju pri vzbujanju z izmeničnimi signali.\n",
    "\n",
    "Moč na elementih vezja ali celotnem vezju pri vzbujanju z izmeničnimi pojavi obravnavamo na dva načina. Najprej nas zanima, kako se moč spreminja s časom, kjer razpoznamo tri pojme: delovna moč, jalova moč in navidezna moč. Te pojme pa lahko obravnavamo tudi z analizo vezja s kompleksnim računom. Dobro je razumeti oba koncepta.\n",
    "\n",
    "**Prej bi lahko predelal tudi:**\n",
    "* O obravnavi vezij vzbujanih z izmeničnimi signali s kompleksnim računom\n",
    "* O obravnavi resonančnih vezij"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Namig:</b> Obstajata dve verziji tega dokumenta. Ena je v obliki html datoteke (končnica html), ki je ni mogoče izvajati, druga pa ima končnico ipny (Jupyter Notebook), ki jo lahko izvajamo z Jupyter aplikacijo. To aplikacijo imate lahko naloženo na vašem računalniku in se izvaja v brskalniku, lahko jo ogledujete s spletno aplikacijo nbViewer, s spletnimi aplikacijami Binder ali Google Colab pa jo lahko tudi zaganjate in spreminjate. Več o tem si preberite v \n",
    "<a href=\"http://lbm.fe.uni-lj.si/index.php?option=com_content&view=article&id=59&Itemid=135&lang=si\">tem članku</a>.\n",
    "<br>    \n",
    "Za izvajanje tega zvezka ne potrebujete posebnega znanja programiranja v Pythonu, lahko pa poljubno spreminjate kodo in se sproti učite tudi uporabe programskega jezika. Več podobnih primerov je na Githubu na https://github.com/osnove/Dodatno/\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teorija - supernakratko\n",
    "\n",
    "Vzemimo poljuben dvopol (vezje z dvema sponkama), ki vsebuje poljubno vezavo uporov, kondenzatorjev in tuljav. <img src=\"https://raw.githubusercontent.com/osnove/Slike/master/moc_1.png\" style=\"height:120px\">\n",
    "Ta dvopol vzbujamo s tokom in merimo napetost na zunanjih sponkah - ali pa obratno. (Trenutna) moč (ki se \"troši\") na dvopolu je definirana kot\n",
    "\n",
    "\n",
    "$$p(t)=u(t)i(t)$$.\n",
    "\n",
    "Ta definicija velja za popolnoma splošen vzbujalni signal, nas pa v tem zvezku zanima le moč na dvopolu pri vzbujanju z izmeničnim signalom. Če na primer vzbujamo dvopol z napetostjo \n",
    "$u(t)=U_m \\sin(\\omega t)$, bo tok v dvopol oblike $i(t)=I_m \\sin(\\omega t-\\varphi)$. Ohrani se torej frekvenca signala, ki ima določeno amplitudo in je fazno zamaknjen glede na vzbujalni signal. Če je $\\varphi=0$ deluje dvopol navzven kot ohmsko breme (morda tudi je, ni pa nujno, glej resonančni pojav), če je $\\varphi=\\pi/2$ tok zaostaja za napetostjo, dvopol je tuljava, če pa je $\\varphi=-\\pi/2$, je pa kondenzator. \n",
    "\n",
    "Trenutna moč (moč kot funkcija časa) za poljuben dvopol vzbujan z izmeničnim signalom je torej\n",
    "\n",
    "$$p(t)=u(t)\\cdot i(t)={{U}_{m}}\\sin (\\omega t)\\cdot {{I}_{m}}\\sin (\\omega t-\\varphi )$$.\n",
    "\n",
    "Ta oblika nam že zadošča, da grafično analiziramo moč pri izmeničnih pojavih. Preprosto zapišemo dva signala, ju zmnožimo in prikažemo na grafu.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Vnos potrebnih knjižnic (modulov)\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x97e6eb0>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Izracun in izris toka, napetosti in moči\n",
    "Im=0.8\n",
    "Um=1.2\n",
    "omega=1\n",
    "fi=0 #np.pi/4 #np.pi\n",
    "t=np.linspace(0,10*omega,1000)\n",
    "\n",
    "u=Um*np.sin(omega*t)\n",
    "i=Im*np.sin(omega*t-fi)\n",
    "p=u*i\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel('čas / s')\n",
    "plt.ylabel('Napetost, Tok, Moč')\n",
    "plt.plot(t,i,label='i(t)')\n",
    "plt.plot(t,u,label='u(t)')\n",
    "plt.plot(t,p,label='p(t)',linewidth=3,color='r')\n",
    "plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:** Ker je fazni kot 0, gre seveda za ohmsko breme. Tok in napetost sta v fazi, moč je vseskozi pozitivna in niha z dvojno frekvenco vzbujalnega signala. Zanima nas povprečna vrednost moči, ki je ravno na polovici zmnožka obeh amplitud, torej $P=\\frac{U_m I_m}{2} $. Toda ta enačba velja le za $\\varphi =0$. \n",
    "\n",
    "**Zdaj pa ti:** Ponovno zaženi zgornjo celico za $\\varphi =\\pi/2$ in $\\varphi =-\\pi/2$. \n",
    "Ugotovimo, da tok zaostaja ali prehiteva napetost za $\\varphi =\\pi/2$, trenutna moč še vedno niha z dvojno frkevenco signala, je pa v povprečju enaka 0 (niha okoli ničle). Kako je lahko moč negativna. Vzemimo primer kondenzatorja: ko sta napetost in tok pozitivna se kondenzator elektri in shranjuje energijo v električnem polju. Ko pa je napetost negativna in tok pozitiven ali obratno, pa se kondenzator prazni, moč je negativna, energija polja se manjša. To se zgodi 2x v periodi signala, v polovici periode se kondenzator polni in prazni na + napetost, v drugi polovici na na - napetost. Pri idealnem kondenzatorju ni izgube moči oz. energije, ta se le gradi in ruši. Enako je pri idealni tuljavi, le da se gradi in ruši magnetno polje. \n",
    "\n",
    "**Zdaj pa ti, 2 ič:** Spremeni fazni kot na $\\varphi =\\pi/4$ ali neko vrednost med 0 in $\\pi/2$.Tok še vedno zaostaja za napetostjo, kar pomeni, da ima dvopol induktivni značaj (dvopol lahko vsebuje tudi kondezatorje, vendar pri frekvenci signala prevladuje induktivnost tuljav).  Ugotovimo, da sedaj trenutna moč niha okoli neke povprečne moči, da pa je tudi delno negativna.\n",
    "Iz grafov težko razberemo zakonitost oz. formulo za izračun povprečne moči, je pa to popolnoma preprosto, če upoštevamo $\\sin (\\alpha )\\cdot \\sin (\\beta )=\\frac{1}{2}\\left( \\cos (\\alpha -\\beta )-\\cos (\\alpha +\\beta ) \\right)$ in dobimo izraz\n",
    "\n",
    "$$p(t)=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\left[ \\cos (\\varphi )-\\cos (2\\omega t-\\varphi ) \\right]$$.\n",
    "\n",
    "\n",
    "Prvi člen predstavlja enosmerno komponento, ki je hkrati povprečna moč, drugi člen pa nihanje okoli povprečne moči z dvojno frekvenco. Povprečno moč imenujemo tudi DELOVNA MOČ in je v bistvu moč, ki se troši na ohmskih komponentah. Ni ravno nujno, da je to tudi koristna moč, saj lahko  predstavlja tudi izgube. V angleščini jo imenujemo true power (resnična, prava ?).\n",
    "\n",
    "Delovna moč je torej določena kot $$P=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\cos (\\varphi )$$.\n",
    "\n",
    "Trenutna moč niha okoli delovne moči z amplitudo $$ S=\\frac{U_m I_m}{2} $$, ki jo imenujemo NAVIDEZNA MOČ (ang. apparent power). Ta \"navidezna\" moč je potrebna za delovanje naprave, ni pa to tista, ki dejansko opravi delo. Mimogrede - navidezno moč ločimo od delovne tudi po enoti. Za navidezno moč uporabimo enoto VA (volt*amper).\n",
    "\n",
    "(No, pri izjavah o moči naprav je potrebno biti previden. Še posebno pri audio ojačevalcih, kjer se je z leti spremenilo korektno označevanje z navidezno močjo v razne druge domišlijske moči, ki imajo komaj kaj povezave z navidezno kaj šele z delovno močjo. Dandanes brez težav kupine 500 ali 1000 W ojačevalec PMPO, kjer PMPO pomeni Peak Music Power Output. Ta arbitrarna enota, ki nima čisto jasne definicije, nima nobene zveze z navidezno močjo, ki bi bila npr. v konkretnem primeru lahko le 5 ali 10 VA. Več: https://www.audioholics.com/audio-amplifier/amplifier-power-ratings).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spreminjamo fazo z vtičnikom\n",
    "\n",
    "Za boljše spremljanje sprememb trenutne moči ob spremembi faze, uporabimo interaktivni gradnik (vtičnik) (ang. widget) z drsnikom, ki naj omogoča spreminjanje faze od $\\varphi =\\pi/2$ do $\\varphi =-\\pi/2$. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "06e0b09dd86d4f8cb26dc9c8f2f17b51",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='fi', max=1.5707963267948966, min=-1.5707963267948966…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "Im=0.8\n",
    "Um=1.2\n",
    "omega=1\n",
    "t=np.linspace(0,10*omega,1000)\n",
    "\n",
    "u=Um*np.sin(omega*t)\n",
    "\n",
    "def power(fi):\n",
    "\n",
    "    i=Im*np.sin(omega*t-fi)\n",
    "    p=u*i\n",
    "    P=Um*Im*np.cos(fi)/2\n",
    "    \n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.xlabel('čas / s')\n",
    "    plt.ylabel('Napetost, Tok, Moč')\n",
    "    plt.plot(t,i,label='i(t)')\n",
    "    plt.plot(t,u,label='u(t)')\n",
    "    plt.plot(t,p,label='p(t)',linewidth=3,color='r')\n",
    "    plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "    plt.plot([0, max(t)],[P, P], linestyle='-',color='b') # dodamo črto P\n",
    "    plt.text(10,P,' P') # dodamo tekst P na koncu črte P\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "interactive_plot = interactive(power, fi=(-np.pi/2, np.pi/2, np.pi/10))\n",
    "output = interactive_plot.children[-1]\n",
    "output.layout.height = '400px'\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jalova moč\n",
    "\n",
    "Poleg delovne in navidezne moči poznamo še eno moč, ki jo imenujemo jalova moč (simbol Q). Ime je morda izbrano nesrečno, ker brez te moči ne bi deloval praktično noben električni aparat. Gre namreč za moč, ki se oblikuje na kondenzatorjih v obliki električnega in v zuljavah v obliki magnetnega polja. Kot smo že ugotovili, je ta moč v povprečju enaka 0. Mora pa obstajati, saj npr. motorji ne bi delovali brez delovanja magnetnega polja (razen takih, ki ne temeljijo na magnetni sili). Pomembna je torej amplituda te moči, ki pa iz časovnega poteka trenutne moči ni direktno razvidna. \n",
    "\n",
    "Trenutno moč je potrebno razdeliti na dve moči, eno ki niha okoli ničle in eno, ki je vedno pozitivna. Amplituda prve je JALOVA MOČ, druga pa predstavlja moč, ki se troši na ohmskih komponentah dvopola. Zopet si pomagamo z matematiko, saj velja $\\cos (\\alpha -\\beta )=\\cos (\\alpha )\\cdot \\cos (\\beta )+\\sin (\\alpha )\\cdot \\sin (\\beta )$. Torej bo $\\cos (2\\omega t-\\varphi )=\\cos (2\\omega t)\\cdot \\cos (\\varphi )+\\sin (2\\omega t)\\cdot \\sin (\\varphi )$. Potem lahko trenutno moč zapišemo v obliki\n",
    "$$p(t)=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\left[ \\cos (\\varphi )\\left( 1-\\cos (2\\omega t) \\right)-\\sin (\\varphi )\\sin (2\\omega t) \\right]=r(t)+q(t)$$.\n",
    "\n",
    "Predvsem nas zanima drugi člen $q(t)$, ki predstavlja nihanje dela trenutne moči okoli ničle. Amplituda tega člena, ki jo tudi imenujemo JALOVA MOČ, je\n",
    "\n",
    "$$Q=\\frac{{{I}_{m}}{{U}_{m}}}{2}\\sin (\\varphi )$$.\n",
    "\n",
    "Prvi člen, $r(t)$ pa predstavlja nihanje okoli delovne moči.\n",
    "\n",
    "Izrišimo še ta dva signala na grafu. Z vtičnikom, tako kot v prejšnji celici."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2d64e873179741808c7b371180c7bf9f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='fi', max=1.5707963267948966, min=-1.5707963267948966…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Im=0.8\n",
    "Um=1.2\n",
    "omega=1\n",
    "t=np.linspace(0,10*omega,1000)\n",
    "\n",
    "u=Um*np.sin(omega*t)\n",
    "\n",
    "def power(fi):\n",
    "\n",
    "    i=Im*np.sin(omega*t-fi)\n",
    "    p=u*i\n",
    "    P=Um*Im*np.cos(fi)/2\n",
    "    Q=Um*Im*np.sin(fi)/2\n",
    "    q=-Q*np.sin(2*omega*t)\n",
    "    r=P*(1-np.cos(2*omega*t))\n",
    "    \n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.xlabel('čas / s')\n",
    "    plt.ylabel('Napetost, Tok, Moč')\n",
    "    plt.plot(t,i,label='i(t)')\n",
    "    #plt.plot(t,u,label='u(t)')\n",
    "    plt.plot(t,p,label='p(t)',linewidth=3,color='r')\n",
    "    plt.plot(t,q,label='q(t)',linestyle=':',linewidth=2,color='g')\n",
    "    plt.plot(t,r,label='r(t)',linestyle=':',linewidth=2,color='black')\n",
    "    #plt.plot(t,(r+q),label='r(t)',linewidth=2,color='black')\n",
    "    plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "    plt.plot([0, max(t)],[P, P], linestyle='-',color='b') # dodamo črto P\n",
    "    plt.text(10,P,' P') # dodamo tekst P na koncu črte P\n",
    "    plt.legend()\n",
    "    plt.show() # razširi po potrebi\n",
    "\n",
    "interactive_plot = interactive(power, fi=(-np.pi/2, np.pi/2, np.pi/10))\n",
    "output = interactive_plot.children[-1]\n",
    "output.layout.height = '450px'\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:** Sedaj, ko smo ločili trenutno moč na dve moči, je lepo razvidno, kako se moč dvopola lahko deli na moč, ki se troši na ohmskih elementih in moč, ki niha okoli ničle in je posledica grajenja in rušenja električnega in magnetnega polja v kondenzatorjih in tuljavah.\n",
    "Še enkrat ponovimo, da je JALOVA MOČ določena kot amplituda moči $q(t)$ in ne kot del signala trenutne moči. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Še čisto malo teorije\n",
    "\n",
    "Če kvadriramo in seštejemo delovno moč $P=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\cos (\\varphi )$ in jalovo moč $Q=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\sin (\\varphi )$ dobimo $(\\frac{{{U}_{m}}{{I}_{m}}}{2})^2$, kar je kvadrat navidezne moči. Torej velja\n",
    "\n",
    "$$S^2=P^2+Q^2 ,$$\n",
    "\n",
    "kar imenujemo trikotnik moči. Pomembna formula, ki pogosto pride prav. Velja tudi\n",
    "\n",
    "$P=S\\cos (\\varphi )$\n",
    "\n",
    "in\n",
    "\n",
    "$Q=S\\sin (\\varphi )$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zdaj pa ti\n",
    "\n",
    "Bi znal iz poljubnega signala moči razbrati S, P in Q? \n",
    "Na primer, v spodnji celici z generatorjem naključnih števil generiramo signal, ti pa dopiši kodo tako, da boš dobil iz analize signala S, P in Q. Pa brez goljufanja! Rešitev je na koncu zvezka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xd7a0950>]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Random moč\n",
    "Im=np.random.rand()+0.2 # rand() da v povprečju 0.5\n",
    "Um=np.random.rand()+0.1\n",
    "omega=1\n",
    "fi=np.random.rand()*np.pi/2 # \n",
    "\n",
    "t=np.linspace(0,10*omega,1000)\n",
    "#t=np.linspace(0,3*np.pi/omega,1000)\n",
    "u=Um*np.sin(omega*t)\n",
    "i=Im*np.sin(omega*t-fi)\n",
    "p=u*i\n",
    "\n",
    "plt.xlabel('čas / s')\n",
    "plt.ylabel(' Moč  / W')\n",
    "plt.plot(t,p,label='p(t)',linewidth=3,color='r')\n",
    "plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## S, P in Q s kompleksnim računom\n",
    "\n",
    "Navidezno, delovno in jalovo moč vezja vzbujanega z izmeničnim signalom najlažje izračunamo s pomočjo kompleksnega računa. Če skrajšamo teoretični del, izračunamo kompleksno navidezno moč kot\n",
    "\n",
    "$$\\underline S = \\frac{1}{2} \\underline U_m \\, \\underline I_m^* ,$$\n",
    "\n",
    "kjer sta $\\underline U_m $ in $\\underline I_m $ kompleksor napetosti in toka na zunanjih sponkah vezja. \n",
    "\n",
    "Če upoštevamo Ohmov zakon zapisan za izmenične signale $\\underline U = \\underline Z \\, \\underline I $, dobimo\n",
    "\n",
    "$$\\underline S =  \\frac{1}{2} I_m^2 \\underline Z $$\n",
    "\n",
    "ali tudi \n",
    "\n",
    "$$\\underline S =  \\frac{1}{2} U_m^2 \\underline Y^* .$$\n",
    "\n",
    "Pri uporabi kompleksnega računa je praktično vseeno katero formulo se uporabi, saj je preračunavanje iz impedance v admitanco itd. zelo hitro in enostavno. Če pa se to dela peš, pa je seveda potrebno vzeti izraz, ki omogoča najhitrejšo pot do rešitve.\n",
    "\n",
    "Včasih je videti formulo zapisano tudi v obliki $\\underline S =\\underline U \\, \\underline I^* $, torej brez polovičke. Tudi ta formula je OK, s tem, da sta sedaj kazalca toka in napetosti določena kot efektivni vrednosti.\n",
    "\n",
    "Če je $\\underline U = U_m e^{j\\varphi_u}$ in $\\underline I = I_m e^{j\\varphi_i}$, potem je \n",
    "$$\\underline S = \\frac{1}{2} U_m e^{j\\varphi_u}I_m e^{-j\\varphi_i}=\\frac{1}{2}U_m I_m e^{j(\\varphi_u - \\varphi_i)}= \\frac{1}{2}U_m I_m e^{j\\varphi} .$$\n",
    "\n",
    "Če uporabimo Eulerjev obrazec dobimo $$\\underline S = \\frac{1}{2} U_m I_m (\\cos\\varphi-j \\sin\\varphi) = P +j  Q .$$\n",
    "\n",
    "Očitno je torej realni del kompleksne moči kar delovna moč, imaginarni del pa jalova moč.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Primer izračuna navidezne, delovne in jalove moči vezja**\n",
    "\n",
    "Vzemimo vezje na sliki, ki ga vzbujamo z virom izmenične napetosti $u_g(t)=10 \\sin(2000 t)$ V,\n",
    "kjer je $C=50 \\, \\mathrm{ \\mu F}$, $L=\\mathrm{ 2  \\,mH}$ in $R = 20 \\, \\mathrm{\\Omega}$. Tuljavi dodajmo zaporedno še ohmsko komponento $ 1 \\, \\mathrm{\\Omega}$.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/osnove/Slike/master/impedanca_2.png\" style=\"height:150px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.804878048780488-7.2439024390243905j) 1.804878048780488 -7.2439024390243905\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1.804878048780488-7.24390243902439j)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Izračun S, P in Q\n",
    "C=50e-6\n",
    "L=2e-3\n",
    "R=20\n",
    "U= -1j*10  # množenje z -j ker gre za sinusni signal. Kar se izračuna moči tiče, je sicer vseeno.\n",
    "omega=2000\n",
    "\n",
    "Zc=1/(1j*omega*C)\n",
    "ZL=1j*omega*L+1 # dodamo še 1 ohm\n",
    "Z=Zc+1/(1/ZL+1/R)\n",
    "\n",
    "# Sedaj lahko izračunamo tok v vezje in nato S, P in Q\n",
    "I=U/Z\n",
    "S=0.5*U*np.conj(I)\n",
    "P=np.real(S)\n",
    "Q=np.imag(S)\n",
    "print(S,P,Q)\n",
    "# ali pa\n",
    "S=0.5*(abs(U))**2*np.conj(1/Z)\n",
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moč v odvisnosti od frekvence\n",
    "\n",
    "Lepota Jupytra je ravno v tem, da enostavno izrišemo grafe in s tem ugotavljamo spreminjanje določene veličine s časom, frekvenco ali kako drugače.\n",
    "\n",
    "Zgornji izračun lahko ponovimo in prikažemo, kako se S, P in Q spreminjajo s frekvenco vzbujalnega signala."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x9b611b0>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "eksponent=np.linspace(1,4,500) # izdelamo 500 točk od 1 do 4, linearno\n",
    "freq=10**(eksponent) # tvorimo niz frekvenc od 1e1 do 1e4\n",
    "omega=2*np.pi*freq\n",
    "\n",
    "Zc=1/(1j*omega*C)\n",
    "ZL=1j*omega*L+1\n",
    "Z=Zc+1/(1/ZL+1/R)\n",
    "\n",
    "# Izračun I, S, P, Q\n",
    "I=U/Z\n",
    "S=0.5*U*np.conj(I)\n",
    "P=np.real(S)\n",
    "Q=np.imag(S)\n",
    "\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Moč  / W, VA, VAr')\n",
    "plt.semilogx(freq,abs(S),label='S',linewidth=3,color='r')\n",
    "plt.semilogx(freq,P,label='P',linewidth=2,color='b')\n",
    "plt.semilogx(freq,Q,label='Q',linewidth=2,color='g')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:**\n",
    "* Očitno pri določeni frekvenci pride do izrazitega povečanja moči na bremenu. Značilno je, da je tedaj jalova moč majhna, kar lahko sklepamo tudi iz enačbe, saj mora biti za največji S največja tudi kompleksna prevodnost oz. najmanjša abs(Z). Ker se ohmske komponente ne spreminjajo s frekvenco, je edina možnost, da se izniči (kompenzira) vpliv induktivne in kapacitivne komponente.\n",
    "* Ko je abs(S) največji, je tudi največji tok v vezje. Ni pa nujno, da je takrat fazni kot enak nič, torej, da jalove komponente navzven (na zunanjih sponkah) ni zaznati. To bi veljalo za zaporedno RLC vezavo, ne pa tudi za splošno vezje. Je pa običajno blizu ničle.\n",
    "* Običajno nas bolj kot največja navidezna moč zanima največja delovna moč, še posebno, če ta opravlja koristno delo. Ko je največja max(S) ni nujno največja tudi delovna moč. Že v našem primeru je razvidno, da temu ni tako. Tudi pogoj je nekoliko drugačen, saj je za max delovno moč potrebno maksimirati realno komponento S, torej $Re[\\underline Y^*]$. Nastopata pa precej skupaj.\n",
    "\n",
    "Da bi bolj natančno pogledali vrednosti v okolici max(S) lahko izrišemo tabelo vrednosti frekvence, faznega kota in navidezne moči. To naredimo v spodnji celici, kjer si za lepši prikaz pomagamo z funkcijo DataFrame,ki je del modula Pandas. O njem smo na kratko pisali v drugem zvezku (BeautifulSoup & Pandas)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[516.92418739]\n",
      "[17.55272315-5.23648933j]\n",
      "[2.72967852]\n",
      "[-0.28992322]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>freq</th>\n",
       "      <th>fi</th>\n",
       "      <th>abs(S)</th>\n",
       "      <th>S</th>\n",
       "      <th>abs(I)</th>\n",
       "      <th>abs(Z)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>450.097513+0.000000j</td>\n",
       "      <td>-0.796012+0.000000j</td>\n",
       "      <td>15.610403+0.000000j</td>\n",
       "      <td>10.920442-11.154758j</td>\n",
       "      <td>3.122081+0.000000j</td>\n",
       "      <td>3.202992+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276</th>\n",
       "      <td>456.371628+0.000000j</td>\n",
       "      <td>-0.753586+0.000000j</td>\n",
       "      <td>16.031844+0.000000j</td>\n",
       "      <td>11.691060-10.969920j</td>\n",
       "      <td>3.206369+0.000000j</td>\n",
       "      <td>3.118793+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>277</th>\n",
       "      <td>462.733201+0.000000j</td>\n",
       "      <td>-0.708939+0.000000j</td>\n",
       "      <td>16.438139+0.000000j</td>\n",
       "      <td>12.477421-10.701700j</td>\n",
       "      <td>3.287628+0.000000j</td>\n",
       "      <td>3.041707+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>278</th>\n",
       "      <td>469.183451+0.000000j</td>\n",
       "      <td>-0.662130+0.000000j</td>\n",
       "      <td>16.822650+0.000000j</td>\n",
       "      <td>13.267760-10.342539j</td>\n",
       "      <td>3.364530+0.000000j</td>\n",
       "      <td>2.972183+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>279</th>\n",
       "      <td>475.723614+0.000000j</td>\n",
       "      <td>-0.613269+0.000000j</td>\n",
       "      <td>17.178217+0.000000j</td>\n",
       "      <td>14.047848-9.886815j</td>\n",
       "      <td>3.435643+0.000000j</td>\n",
       "      <td>2.910663+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>280</th>\n",
       "      <td>482.354943+0.000000j</td>\n",
       "      <td>-0.562517+0.000000j</td>\n",
       "      <td>17.497416+0.000000j</td>\n",
       "      <td>14.801334-9.331671j</td>\n",
       "      <td>3.499483+0.000000j</td>\n",
       "      <td>2.857565+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>281</th>\n",
       "      <td>489.078709+0.000000j</td>\n",
       "      <td>-0.510094+0.000000j</td>\n",
       "      <td>17.772902+0.000000j</td>\n",
       "      <td>15.510383-8.677792j</td>\n",
       "      <td>3.554580+0.000000j</td>\n",
       "      <td>2.813272+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>282</th>\n",
       "      <td>495.896201+0.000000j</td>\n",
       "      <td>-0.456277+0.000000j</td>\n",
       "      <td>17.997823+0.000000j</td>\n",
       "      <td>16.156632-7.930000j</td>\n",
       "      <td>3.599565+0.000000j</td>\n",
       "      <td>2.778114+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>283</th>\n",
       "      <td>502.808725+0.000000j</td>\n",
       "      <td>-0.401391+0.000000j</td>\n",
       "      <td>18.166260+0.000000j</td>\n",
       "      <td>16.722378-7.097542j</td>\n",
       "      <td>3.633252+0.000000j</td>\n",
       "      <td>2.752355+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>284</th>\n",
       "      <td>509.817606+0.000000j</td>\n",
       "      <td>-0.345807+0.000000j</td>\n",
       "      <td>18.273657+0.000000j</td>\n",
       "      <td>17.191899-6.193959j</td>\n",
       "      <td>3.654731+0.000000j</td>\n",
       "      <td>2.736179+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>285</th>\n",
       "      <td>516.924187+0.000000j</td>\n",
       "      <td>-0.289923+0.000000j</td>\n",
       "      <td>18.317175+0.000000j</td>\n",
       "      <td>17.552723-5.236489j</td>\n",
       "      <td>3.663435+0.000000j</td>\n",
       "      <td>2.729679+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>286</th>\n",
       "      <td>524.129830+0.000000j</td>\n",
       "      <td>-0.234154+0.000000j</td>\n",
       "      <td>18.295926+0.000000j</td>\n",
       "      <td>17.796646-4.245029j</td>\n",
       "      <td>3.659185+0.000000j</td>\n",
       "      <td>2.732849+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>287</th>\n",
       "      <td>531.435916+0.000000j</td>\n",
       "      <td>-0.178911+0.000000j</td>\n",
       "      <td>18.211035+0.000000j</td>\n",
       "      <td>17.920353-3.240793j</td>\n",
       "      <td>3.642207+0.000000j</td>\n",
       "      <td>2.745588+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>288</th>\n",
       "      <td>538.843844+0.000000j</td>\n",
       "      <td>-0.124583+0.000000j</td>\n",
       "      <td>18.065542+0.000000j</td>\n",
       "      <td>17.925527-2.244841j</td>\n",
       "      <td>3.613108+0.000000j</td>\n",
       "      <td>2.767700+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>289</th>\n",
       "      <td>546.355035+0.000000j</td>\n",
       "      <td>-0.071528+0.000000j</td>\n",
       "      <td>17.864144+0.000000j</td>\n",
       "      <td>17.818465-1.276697j</td>\n",
       "      <td>3.572829+0.000000j</td>\n",
       "      <td>2.798903+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>290</th>\n",
       "      <td>553.970928+0.000000j</td>\n",
       "      <td>-0.020056+0.000000j</td>\n",
       "      <td>17.612822+0.000000j</td>\n",
       "      <td>17.609279-0.353221j</td>\n",
       "      <td>3.522564+0.000000j</td>\n",
       "      <td>2.838841+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>291</th>\n",
       "      <td>561.692982+0.000000j</td>\n",
       "      <td>0.029576+0.000000j</td>\n",
       "      <td>17.318407+0.000000j</td>\n",
       "      <td>17.310833+0.512129j</td>\n",
       "      <td>3.463681+0.000000j</td>\n",
       "      <td>2.887102+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>292</th>\n",
       "      <td>569.522678+0.000000j</td>\n",
       "      <td>0.077167+0.000000j</td>\n",
       "      <td>16.988151+0.000000j</td>\n",
       "      <td>16.937595+1.309628j</td>\n",
       "      <td>3.397630+0.000000j</td>\n",
       "      <td>2.943228+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>293</th>\n",
       "      <td>577.461515+0.000000j</td>\n",
       "      <td>0.122575+0.000000j</td>\n",
       "      <td>16.629326+0.000000j</td>\n",
       "      <td>16.504558+2.033233j</td>\n",
       "      <td>3.325865+0.000000j</td>\n",
       "      <td>3.006736+0.000000j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294</th>\n",
       "      <td>585.511016+0.000000j</td>\n",
       "      <td>0.165707+0.000000j</td>\n",
       "      <td>16.248905+0.000000j</td>\n",
       "      <td>16.026328+2.680248j</td>\n",
       "      <td>3.249781+0.000000j</td>\n",
       "      <td>3.077130+0.000000j</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     freq                  fi               abs(S)  \\\n",
       "275  450.097513+0.000000j -0.796012+0.000000j  15.610403+0.000000j   \n",
       "276  456.371628+0.000000j -0.753586+0.000000j  16.031844+0.000000j   \n",
       "277  462.733201+0.000000j -0.708939+0.000000j  16.438139+0.000000j   \n",
       "278  469.183451+0.000000j -0.662130+0.000000j  16.822650+0.000000j   \n",
       "279  475.723614+0.000000j -0.613269+0.000000j  17.178217+0.000000j   \n",
       "280  482.354943+0.000000j -0.562517+0.000000j  17.497416+0.000000j   \n",
       "281  489.078709+0.000000j -0.510094+0.000000j  17.772902+0.000000j   \n",
       "282  495.896201+0.000000j -0.456277+0.000000j  17.997823+0.000000j   \n",
       "283  502.808725+0.000000j -0.401391+0.000000j  18.166260+0.000000j   \n",
       "284  509.817606+0.000000j -0.345807+0.000000j  18.273657+0.000000j   \n",
       "285  516.924187+0.000000j -0.289923+0.000000j  18.317175+0.000000j   \n",
       "286  524.129830+0.000000j -0.234154+0.000000j  18.295926+0.000000j   \n",
       "287  531.435916+0.000000j -0.178911+0.000000j  18.211035+0.000000j   \n",
       "288  538.843844+0.000000j -0.124583+0.000000j  18.065542+0.000000j   \n",
       "289  546.355035+0.000000j -0.071528+0.000000j  17.864144+0.000000j   \n",
       "290  553.970928+0.000000j -0.020056+0.000000j  17.612822+0.000000j   \n",
       "291  561.692982+0.000000j  0.029576+0.000000j  17.318407+0.000000j   \n",
       "292  569.522678+0.000000j  0.077167+0.000000j  16.988151+0.000000j   \n",
       "293  577.461515+0.000000j  0.122575+0.000000j  16.629326+0.000000j   \n",
       "294  585.511016+0.000000j  0.165707+0.000000j  16.248905+0.000000j   \n",
       "\n",
       "                        S              abs(I)              abs(Z)  \n",
       "275  10.920442-11.154758j  3.122081+0.000000j  3.202992+0.000000j  \n",
       "276  11.691060-10.969920j  3.206369+0.000000j  3.118793+0.000000j  \n",
       "277  12.477421-10.701700j  3.287628+0.000000j  3.041707+0.000000j  \n",
       "278  13.267760-10.342539j  3.364530+0.000000j  2.972183+0.000000j  \n",
       "279   14.047848-9.886815j  3.435643+0.000000j  2.910663+0.000000j  \n",
       "280   14.801334-9.331671j  3.499483+0.000000j  2.857565+0.000000j  \n",
       "281   15.510383-8.677792j  3.554580+0.000000j  2.813272+0.000000j  \n",
       "282   16.156632-7.930000j  3.599565+0.000000j  2.778114+0.000000j  \n",
       "283   16.722378-7.097542j  3.633252+0.000000j  2.752355+0.000000j  \n",
       "284   17.191899-6.193959j  3.654731+0.000000j  2.736179+0.000000j  \n",
       "285   17.552723-5.236489j  3.663435+0.000000j  2.729679+0.000000j  \n",
       "286   17.796646-4.245029j  3.659185+0.000000j  2.732849+0.000000j  \n",
       "287   17.920353-3.240793j  3.642207+0.000000j  2.745588+0.000000j  \n",
       "288   17.925527-2.244841j  3.613108+0.000000j  2.767700+0.000000j  \n",
       "289   17.818465-1.276697j  3.572829+0.000000j  2.798903+0.000000j  \n",
       "290   17.609279-0.353221j  3.522564+0.000000j  2.838841+0.000000j  \n",
       "291   17.310833+0.512129j  3.463681+0.000000j  2.887102+0.000000j  \n",
       "292   16.937595+1.309628j  3.397630+0.000000j  2.943228+0.000000j  \n",
       "293   16.504558+2.033233j  3.325865+0.000000j  3.006736+0.000000j  \n",
       "294   16.026328+2.680248j  3.249781+0.000000j  3.077130+0.000000j  "
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Izpis vrednosti S, P in Q okoli maximuma\n",
    "# Najprej poiščemo indeks niza, ko je moč največja\n",
    "index_S=np.where(abs(S)==max( abs(S))) # indeksi, kjer je izpolnjen pogoj\n",
    "res_freq=freq[index_S]\n",
    "print(res_freq)\n",
    "print(S[index_S])\n",
    "print(abs(Z[index_S]))\n",
    "fi=np.arctan(Q/P)\n",
    "print(fi[index_S])\n",
    "\n",
    "# Pripravimo skupne nize za izpis v tabeli\n",
    "tabela=np.array([freq,fi,abs(S),S,abs(I),abs(Z)])  # tvorim tabelo \n",
    "import pandas as pd  # vnos modula Pandas\n",
    "df = pd.DataFrame(data=tabela.T) # naredim DataFrame s Pandas, tabelo je potrebno tranponirati\n",
    "df.columns=['freq', 'fi','abs(S)','S','abs(I)','abs(Z)'] # označi stolpce\n",
    "s1=int(index_S[0]) # pretvorim index v integer\n",
    "df[s1-10:s1+10] # izrišem DataFrame za vrednosti okoli max(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zgoraj se je izpisala tabel vrednosti freq, fi, abs(S), S in abs(I). Preverite sami, pri katerih pogojih je max(S) ali max(P). \n",
    "\n",
    "V spodnji celici izrišemo še tok v vezje v odvisnosti od frekvence. Če želimo, da naš 10 V vir izmenične napetosti ustrezno deluje pri vseh frekvencah, mora hkrati zagotavljati tudi ustrezen tok. Tok bo največji, ko bo abs(Z) najmanjša, to je ko je navidezna moč največja. V konkretnem primeru je največja amplituda toka nekaj čez 3 A. To je tudi tok, ki ga mora zagotavljati vir za pričakovano delovanje. Običajno ponujajo proizvajalci modele, ki zagotavljajo npr. enako moč, vendar pri različnih pogojih. Npr., če pogledamo AC ojačevalnike Toellner https://www.toellner.de/datenblaetter/en_7621.pdf, ugotovimo, da ponujajo 300 W ojačevalnike, ki pa imajo lahko na izhodu max 10 V in 30 A ali max 60 V in 5 A ali max 100 V in 3 A. Torej, za naš konkreten primer ne bi bil primeren ojačevalec 100 V in 3 A, saj potrebujemo za max S ali max P cca. 5 A. Izbira je očitno odvisna od absolutne vrednosti impedance bremena pri želeni frekvenci delovanja, ki mora biti v prvem primeru najmanj $1/3 \\,\\Omega$, v drugem primeru $15 \\,\\Omega$ in v tretjem primeru $33 \\,\\Omega$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xe50ce70>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Tok / A')\n",
    "plt.semilogx(freq,abs(I),label='Z',linewidth=3,color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kompenzacija jalove komponente moči\n",
    "\n",
    "Jalova komponenta moči nam le  povečuje potrebo po večji izhodni moči. Zmanjšanje jalove moči z ustreznim dodajanjem elementov imenujemo kompenzacija. Ta je lahko popolna, kar pomeni, da bo Q=0 ali pa nepopolna, kjer jo zmanjšamo na nek določen nivo, običajno določen s $\\cos \\varphi$.\n",
    "Razlikujemo zaporedno ali vzporedno kompenzacijo, to pomeni, da lahko bremenu vežemo ustrezno impedanco zaporedno ali vzporedno. Morda izgleda na prvi pogled vseeno, ali se opravi vzporedno ali zaporedno komponzacijo vendar to ni res. Razlika je lahko precejšnja, kar lahko spoznamo kar z analizo konkretnega primera. \n",
    "\n",
    "### Zaporedna kompenzacijska vezava\n",
    "Če želimo, da bo breme navzven čisto ohmsko, moramo impedanci vezja zaporedno dodati impedanco, ki bo imela enako veliko a negativno vrednost imaginarnega dela impedance. To seveda pomeni, da bo ostal le še realni del impedance in Q=0.\n",
    "Naprej izrišimo impedanco ter njen realni in imaginarni del. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x99327b0>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Z / Ohm')\n",
    "plt.semilogx(freq,abs(Z),label='Z',linewidth=3,color='r')\n",
    "plt.semilogx(freq,Z.real,label='Z.real',linewidth=2,color='b')\n",
    "plt.semilogx(freq,Z.imag,label='Z.imag',linewidth=2,color='g')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pri nižjih frekvencah prevladuje negativen imaginaren del impedance, torej prevladuje $-j\\frac{1}{\\omega C}$. Dokler je imaginarni del negativen, ga je potrebno kompenzirati s pozitivnim členom, torej z $j\\omega L$. Ko pa postane imaginaren del pozitiven, ga pa je potrebno kompenzirati z negativno impedanco, torej z $-j\\frac{1}{\\omega C}$.\n",
    "\n",
    "To naredimo v spodnji celici, kjer določimo velikosti kompenzacijske tuljave ali kondenzatorja za popolno kompenzacijo.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe5fb350>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lzap=-Z.imag/omega\n",
    "Czap=1/(Z.imag*omega)\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' L in C')\n",
    "plt.loglog(freq,Lzap,label='Lzap / H',linewidth=3,color='r')\n",
    "plt.semilogx(freq,Czap,label='Czap / F',linewidth=2,color='b')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:** Pri nižjih frekvencah potrebujemo za popolno kompenzacijo precej veliko induktivnost, ki bi jo v praksi težko realizirali. Kar se tiče prakse je še bolj vprašljivo, če bi imeli na razpolago ustrezen vir, ki bi zagotavljal dovolj toka.  Pa ga izrišimo.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe9d0d30>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Izap=U/Z.real\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Izap / A')\n",
    "plt.loglog(freq,abs(Izap),label='Izap',linewidth=3,color='r')\n",
    "#plt.loglog(freq,abs(Ivzpo),label='Ivzpo',linewidth=2,color='b')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()\n",
    "#print(Izap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ugotovimo, da bi pri popolni zaporedni kompenzaciji potrebovali vir, ki bi omogočal najmanj 10 A. \n",
    "V vezje teče sedaj bistveno večji tok kot brez kompenzacije. To je sicer ugodno, kar se tiče maksimiranja delovne moči, čemur je običajno zaporedna kompenzacija tudi namenjena. Je pa potrebno ponovno preveriti, če imamo na razpolago ustrezne komponente, ki dovoljujejo tako velik tok in tudi napetost. \n",
    "\n",
    "Poleg tega moramo ugotoviti, da za vsako frekvenco potrebujemo za popolno kompenzacijo drugo vrednost kondenzatorja ali tuljave. Torej se komponzacije ne da preprosto opraviti kar z enim samim elementom.\n",
    "\n",
    "Preverimo napetost na kondenzatorju in tok skozi tuljavo pri popolni zaporedni kompenzaciji."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe860710>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Uc=Izap*Zc\n",
    "IL=Izap*R/(ZL+R) # tokovni delilnik\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel('Uc in IL')\n",
    "plt.loglog(freq,abs(Uc),label='Uc / V',linewidth=3,color='r')\n",
    "plt.loglog(freq,abs(IL),label='IL / A',linewidth=2,color='b')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()\n",
    "#print(Izap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ugotovimo, da je napetost na kondenzatorju bistveno povečana v primerjavi z napetostjo generatorja. Pri nizkih frekvencah tudi preko 1000 V, kar bi bilo v praksi potrebno upoštevati. Tuljava mora omogočati najmanj tok 10 A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vzporedna kompenzacijska vezava \n",
    "Druga varianta je, da kompenzacijo dosežemo z vzporedno vezavo. V tem primeru gledamo admitanco, katere imaginarni del mora biti enak nič. Ta kompenzacija se zelo pogosto uporablja za zmanjšanje jalove moči naprav, vsaj iz dveh razlogov: 1) zmanjša se tokovna obremenitev vira, saj si vzporedni impedanci izmenjujeta jalovo energijo, navzven deluje pa vezje čisto ohmsko. 2) Zmanjša se porabljena energija, kar se pozna na manjšem računu za elektriko, predvsem za tovarne, kjer je mnogo strojev. \n",
    "\n",
    "Najprej si poglejmo admitanco vezja v odvisnosti od frekvence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe830710>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y=1/Z\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Y / S')\n",
    "plt.semilogx(freq,abs(Y),label='Y',linewidth=3,color='r')\n",
    "plt.semilogx(freq,Y.real,label='Y.real',linewidth=2,color='b')\n",
    "plt.semilogx(freq,Y.imag,label='Y.imag',linewidth=2,color='g')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pri nizkih frekvencah prevladuje kapacitivni značaj, saj je imaginarni del pozitiven, torej $j\\omega C$, ki ga je potrebno kompenzirati z induktivnostjo $-j \\frac{1}{\\omega L}$. Pri višjih frekvencah se zadeva obrne. \n",
    "\n",
    "Izrišimo potrebne vrednosti L in C za popolno vzporedno kompenzacijo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xea3c110>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Cvzpo=-Y.imag/omega\n",
    "Lvzpo=1/(Y.imag*omega)\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' L in C')\n",
    "plt.loglog(freq,Lvzpo,label='Lvzpo / H',linewidth=3,color='r')\n",
    "plt.loglog(freq,Lzap,label='Lzap / H',linestyle=':',color='r')\n",
    "plt.semilogx(freq,Cvzpo,label='Cvzpo / F',linewidth=2,color='b')\n",
    "plt.semilogx(freq,Czap,label='Czap / F',linestyle=':',color='b')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:** Pri nizkih frekvencah, ko prevladuje kapacitivnost kondenzatorja, je v obeh primerih (tako za vporedno kot zaporedno kompenzacijo) potrebno zagotoviti enko veliko tuljavo. Okoli resonance in višje pa se vrednosti razlikujejo.\n",
    "\n",
    "Bi znal na enostaven način pokazati (brez grafov), zakaj je temu tako, torej, zakaj sta Lvzpo=Lzap pri nizkih frekvencah?\n",
    "\n",
    "Še enkat izrišimo moč S vezja po (skupaj z) kompenzaciji. Navzven je sedaj vezje čisto ohmsko, torej je S=P in Q=0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xee3fab0>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Zzap=Z\n",
    "Szap=0.5*100/Z.real\n",
    "Svzpo=0.5*100*Y.real\n",
    "plt.xlabel('Frekvenca / Hz')\n",
    "plt.ylabel(' Szap in Svzpo / VA')\n",
    "plt.loglog(freq,Szap,label='Szap',linewidth=3,color='r')\n",
    "plt.semilogx(freq,Svzpo,label='Svzpo',linewidth=2,color='b')\n",
    "plt.plot([0, max(freq)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ugotovitve:** Še enkrat lahko ugotovimo, da je zaporedna kompenzacija namenjena maksimiranju delovne moči, vzporedna pa zmanjšanju tokovnih potreb oz. zmanjšanju trošenja jalove moči iz omrežja.\n",
    "\n",
    "**Še to:** Morda velja omeniti, da kljub temu, da na prvi pogled opravlja kompenzacija jalove moči zelo koristno vlogo, je potrebno biti pri realizaciji previden. Pri popolni kompenzaciji smo namreč spravili vezje v stanje resonance, napetosti in tokovi znotraj vezja so lahko zelo veliki in povzročijo uničenje ali okvare vezja. Zato se pogosto namesto popolne kompenzacije opravi nepopolna, torej taka, kjer ostane tudi en del imaginarne komponente impedance oz. admitance)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maksimalna delovna moč na bremenu - prilagoditev bremena\n",
    "\n",
    "Tema je podobna, kot smo jo obravnavali v prejšnjem poglavju, kjer smo ugotovili, da z izničenjem oz. kompenzacijo imaginarne komponente impedance dosežemo popolno kompenzacijo jalove moči. Pri tem se poveča tok v vezje (pri napetostnem vzbujanju) in s tem tudi delovno moč na bremenu. Ali je to dejansko največja možna delovna moč, pa je potrebno bolj natančno pogledati.\n",
    "In sicer tako, da namesto idealnega napetostnega vira vzamemo bolj realističen model vira z notranjo impedanco $\\underline Z_g=R_g+jX_g$, ki ga priključimo na breme $\\underline Z_b=R_b+jX_b$.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/osnove/Slike/master/max_moc.png\" style=\"height:150px\">\n",
    "\n",
    "Delovna moč na bremenu je $P=\\frac{1}{2}{{I}^{2}}\\operatorname{Re}\\left\\{ {{\\underline{Z}}_{b}} \\right\\}=\\frac{1}{2}{{I}^{2}}{{R}_{b}}$\n",
    "\n",
    "Če želimo, da bo ta moč maksimalna, je potrebno razdelati enačbo in pogledati\n",
    "\n",
    "$${{P}_{b}}=\\frac{1}{2}{{R}_{b}}\\frac{U_{g}^{2}}{{{({{R}_{g}}+{{R}_{b}})}^{2}}+{{({{X}_{g}}+{{X}_{b}})}^{2}}}$$\n",
    "\n",
    "Očitno bo moč največja, če bo $${{X}_{g}}=-{{X}_{b}}$$ in hkrati $${{R}_{g}}={{R}_{b}} .$$ \n",
    "\n",
    "Prvi pogoj smo spoznali že pri zaporedni kompenzaciji jalove moči, drug pogoj pa smo tudi že poznali - iz OE1, saj velja tudi za enosmerna vezja. Naj pri tem opozorimo, da sedaj $R_g$ in $R_b$ nista nujno upora, pač pa predstavljata realni del impedance (X pa imaginarnega).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Primer analize vezja za prilagoditev bremena viru za prenos maksimalne delovne moči\n",
    "\n",
    "Vzemimo napetostni vir amplitude 10 V z notranjo impedanco iz vzporedne vezave upora $R=4  \\,\\Omega$ in kondenzatorja $C=10 \\, \\mu F$. \n",
    "\n",
    "Poiščimo ustrezno impedanco bremena za frekvenco 1 kHz, da bo na njej maksimalna delovna moč. Analizirajmo tudi vpliv posameznih elementov impedance bremena. \n",
    "\n",
    "Ker je $X_g$ negativen, bo $X_b$ pozitiven, to pomeni, da mora biti reaktivni element kompenzacije tuljava $X_b=\\omega L$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3.7623494364395524-0.9455815479804958j)\n",
      "(3.7623494364395524+0.9455815479804958j)\n",
      "max delovna moč =  3.3223920880217874  W\n",
      "L za P=Pmax je  0.00015049397745758213\n"
     ]
    }
   ],
   "source": [
    "## Max delovna moč\n",
    "U=10\n",
    "R=4\n",
    "C=10e-6\n",
    "freq=1000\n",
    "omega=2*np.pi*freq\n",
    "\n",
    "# Določitev impedance Zg\n",
    "Zc=1/(1j*omega*C)\n",
    "Zg=1/(1/Zc+1/R)\n",
    "print(Zg)\n",
    "\n",
    "# Določitev Zb za P=Pmax\n",
    "Zb_opt=np.conjugate(Zg)\n",
    "print(Zb_opt)\n",
    "Pb_max=U*U/(8*np.real(Zg))  # max delovna moč\n",
    "print('max delovna moč = ',Pb_max,' W')\n",
    "Xb_opt=Zb_opt.imag\n",
    "L_opt=Xb_opt/omega\n",
    "print('L za P=Pmax je ',L_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "V naslednji celici izrišimo spreminjanje velikosti delovne moči ob spreminjanju $R_b$. V določeni točki oz. za določen Rb moramo dobiti maksimalno delovno moč."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D3bu5+89SFTBqGk+oXXbdFX7zm6U88khYxGfSpDD2MGtW3MlE6oZkLYW2QCPg38AnwFpgfSpCpVJhUWjdOt4cUnlmcP754WK3rl3hww+hTx/4zW80d5LIjko2pjAIOBy4M/HUFcA7ZjbNzH6binCp8NVX4Xb33ePNIVV38MHwr3+FBXzc4fe/D1dGL60zI14iqZd0TMGDfGAq8DIwC9gPuLSiDzazfcwsz8yWmdkSM9vuPRb8ycxWmtliM+tazT9HtX39dbjVmUe1U8OGYanPvDxo1w7mzw+th7vvhm3b4k4nUvskG1P4hZnlmtka4HXgROB94FSgMqelbgGucPdDgB7AGDPrWGqf44EDEtsoYHzV/wg7RkWhbjj6aFi8OEyL8cMPcMUV4bmVK+NOJlK7JGsptAcmA93dvYO7n+Pu97v7Inev8N9g7v6Zu89P3P8OWAbsVWq3IcDjiRbJbKC5maX0PCAVhbqjWbMwid6UKWGM6M034bDDwjUOajWIVE6yMYXL3X2yu3+2o19iZu2BLmx/KutewJoSj9eyfeGIlIpC3XPSSbBkCZx1VphM77LLwkD0e+/FnUwk/Zm7R/sFZk2AmcAt7v5cqddeAm519zcTj6cDV7v7vFL7jSJ0L5GdnZ2Tm5tbrSwFBQU0adLkv54777zD+eijXZgw4R323XdDtT53R5WVKx3UhVxvvrk799xzIF991YgGDbZx7rkfMmzYGurXr/n/7+vC8Uq1dM1WF3P169dvnrt3q3BHd49sAxoArwKXl/P6A8DwEo/fB9ok+8ycnByvrry8vO2ea93aHdzXrq32x+6wsnKlg7qS66uv3M8/P/x3BvfDDnOfPTv+XKmSrrnc0zdbXcwFzPVK/G4nG2h+1cx+aWYHV6cqmZkBjwDL3P3ucnabApybOAupB/CN10B3VWW5q/soE+y2GzzyCLz2WpgmY/Fi6NkzTJ3x3XdxpxNJL8kGmkcAXwM3mdl8MxtvZkMS3UGV0Rs4BzjGzBYmtsFmNtrMRif2mQqsBlYCDwEXV/PPUS0bN4YzVRo1gp13TuU3Sxz694f8fLj6aqhXD/7853Ctw+TJ4R8IIgLlTovt7v8GHgMeM7N6wBGEU0ivNrONwDR3vyPJ+98Ekk4xl2jSjKlG7hpRspWgyfAyQ+PGcPvtMHw4XHhhWAv6jDNg0KAwA+t++8WdUCRelVpkx923ufu/3P0Gd+8NDCNMfVGrqesoc3XuDG+9BePHQ/Pm8MorcOihcMMNYTp1kUxVrZXX3P0Ld59U02FSTUUhs2VlwejR4VTVc88NXYm/+x107Ah/+5u6lCQzZfRynCoKApCdDRMnhovdOnWCjz6CU0+FAQPC9Q4imURFARUFCXr3Dst/jhsX/p+YPj0UibFj4csv404nkhoqCqgoSLH69WHMGFixIty6hyKx//5wzz2weXPcCUWipaKAioJsb/fdQzFYuDB0I61fD5dfHsYbnn1W4w1Sd6kooKIg5fuf/4FXX4UXXwzXNKxaBaefDkceGc5eEqlryiwKZrZniftjzKx5ice7mVlKLzKLioqCVIYZnHBCuBL6/vuhVatQEHr3hlNO0aI+UreU11LY18zuTdy/wN2LluF096+BCyJPlgIqClIVDRrARReFNRquvz5cCPf886E1MXIkfP55o7gjiuyw8orCamCfwn0S8xgBYGZZQMOog6VC4VKcKgpSFU2bhusZVq4M1zmYwYQJcM45R3DZZfD553EnFKm+8orC/sC5ifuvAn81s2PN7BjgaeCVVISLmloKsiPatAlXRC9bFqbN+PHHetx7L3ToENaN1mmsUhuVWRTc/Q13L0g8vAb4J3ARYZ6i6cDVqYkXLRUFqQkHHABPPQUPPfQOJ50Upsm4/fYwI+tvflPcIhWpDSo8+8jD0puPAL8FbgQmuPvWqINFreS02S0qs+K0SAX2338DU6bAnDlhgr3vvoPf/x7atw9jECoOUhtUWBTMrC+wAhgH3A8sN7M+EeeK3MaN4UIkTZstNa17d3j55TBtxoABoTjccgu0axe6ldatizuhSPkqc53CXcBx7n60u/cBBgL3RBsreuo6kqj17g3TpsGsWXDccVBQELqV2rcP60avXRt3QpHtVaYoNHD39wsfuPtywjKbtZqKgqRKr17hArjZs+Gkk0IrtXBAeuRIeP/9ij9DJFUqUxTmmtkjZtY3sT0EzIs6WNRUFCTVjjgCpkwJU2f89KewdWs4lfWQQ+C008JYhEjcKlMULgKWAL8ALgWWAqOTvqMWUFGQuHTqBLm5oYVwwQXhorjnnoMePaBv3zClxrZtcaeUTFWZs49+cPe73f1Udx/q7ve4+w+pCBclFQWJ2/77w4MPwgcfwDXXQLNmMHNm6GLq2BEeeCB0NYmkUrlFwcwWJ9tSGTIKKgqSLvbcE267DdasgTvvhH32Ca2I0aPD/euvh08/jTulZIpkLYVtwFbgCeB/gZNKbbWapriQdNOsGVxxRZiJ9emnoVu3cFV04emsZ52lcQeJXrlFwd07A8OBJsBTwC3AocAn7v5RauJFRy0FSVcNGsCwYfD22+Fah9NPD2MMTz0Vxh26d4cnnoBNm+JOKnVR0jEFd3/P3W90967AC8DjwC9TkixiKgqS7szCtQ7/93+wenUYd2jRAt55B849N3QtXXcdfPhh3EmlLklaFMxsLzO7wszeBM4mFITxKUkWMRUFqU3atQvjDmvXwsMPQ5cu8MUX4bkOHeDEE8NZS1tr/QQ0ErdkA80zCa2DBsB5wAjgJaChmVU4W5CZTTCzdWaWX87rfc3sGzNbmNhuqNafoJpUFKQ22nnncMHbvHlhoZ+zzgrdTS+9FM5a6tAhTOv9ySdxJ5XaKllLoR2wG3AhMA2Ym9jmJW4r8hgwqIJ93nD3zont5kp8Zo1RUZDazAx69oQnnwythzvuCAXh44/hhhugbVs4+eRwsdzWrVbxB4okJBtobu/u+ya2DiW2fd29Q0Uf7O6vA2k7L6RmSJW6Yo894KqrYMUKeO01OOMMyMqCF16AIUPgpz/twXXXwfLlcSeV2qAyVzRHqaeZLTKzl83s0FR9aclps9VSkLqiXj3o3x/++tfQevjjH+Ggg+DLLxtx223h/pFHwiOPwLffxp1W0pW5e3QfbtYeeNHdf1LGa82Abe5eYGaDgXvd/YByPmcUMAogOzs7Jzc3t1p5CgoKaNKkCZs21eP44/vQoME2pk17vVqfVZMKc6Ub5aqadMzlDm+/3YCZMzuQl9eKTZuyAGjUaCtHHfUFAwf+my5dviYrK5586XjMoG7m6tev3zx371bhju4e2Qa0B/Irue+HQMuK9svJyfHqysvLc3f3tWvdwb1162p/VI0qzJVulKtq0j3Xd9+5T5jgfvTR4f//wm3PPd2vusp98eL4sqWbupgLmOuV+C2OrfvIzFqbmSXudyd0ZaVkVVt1HUkmatIEfvYzmDEjXDV9001hcPrTT0NX02GHhe3228OUG5KZIisKZvY08C/gIDNba2YjzWy0mRXOsHo6kG9mi4A/AcMS1SxymuJCMl2HDnDjjbByZVgEaPTo8Pfh3XfD6nBt20KfPjB+PPznP3GnlVSqH9UHu/vwCl4fR1jiM+XUUhAJzMIiQL16hYV/XnkFJk0Kp7K+8UbYxo6FY48Na0AMHaq/N3Vd3GcfxUJFQWR7DRuGaxueeSasI/3EE3D88eG1adPCRXPZ2XDCCTBxIqxfH29eiYaKgohsp2lTOPtsmDoVPv88rPtwzDFhGo2pU+G886BVKxg8OKwe92VKRgMlFTKyKBT+C6d583hziNQGu+8eVoibPj0MSo8fX1wgXn65uAXRvz/cf7/WfqjtMrIofPdduG3WLN4cIrVNdnYYlJ4+HT77LLQgjjsuvDZ9OowZA3vtFabguP32sFiQ1C4ZWRQ2bAi3u+wSbw6R2qxVq9CCePXVMAYxcWKYVmOnnWD27HAW08EHh+3qq8NZTprFNf2pKIjIDmvRIqzx8Pe/hym9n3suPN5tt9Ba+OMfwxQbrVvDiBEwebKm2khXkZ2Sms4KCsJtGl7FLlLr7bJLOHV16FD48cfQQpgyBZ5/PiwW9PjjYWvQAH7yk06cc044o+mAA8IpshIvtRREJDINGkDfvnD33eFCuaVLw1jDkUeGrqQFC3bj8svDZH0HHBCuiZg6Fb7/Pu7kmUtFQURSwgwOOSSML7zxRhiH+PWvl3LmmeEMp1WrYNy40Gpo0QIGDoR77gmFJDVzHQio+0hEYrL77tC//zr69u3I1q1h7empU8NprnPnhgvmpk0L++69dzjL6bjjwtXVLVvGm70uU0tBRGKXlQU9esDNN4fi8Pnn4Yrqs88OZzmtXRsukhs2LDzOyQlnN/3jH7BxY9zp65aMbCkUFgW1FETSU6tWoSCcfTZs2waLFoVV5aZNC11P8+eH7fbboVEj6N07XFB37LHQrRvUz8hftpqRkYeusPtILQWR9FevHnTpErarrw6D0G+8ES6W+8c/YMEC+Oc/w3b99WGKjj59QpHo1y9MBx7XIkK1UcYVBffiMxtUFERqn8aNwyD0wIHh8RdfQF5eKBLTp4eznF56KWwQprPp0weOPjpsnTurSCSTcUVh48ZQGHbaSf9jiNQFLVvCGWeEDcL4Q15eaDnMmAEffhiuk5gyJbzerFk4JbZPn7Dl5IQZYiXIuKKgriORum3vveGcc8IGoSjMnFm8rV4dznKaOjW8vvPOcMQRoVAcdVQY8M5kGVcUdOaRSGZp3z5sI0aEx2vWFC8gNHMmLFsWWhQzZoTX69WDDh1yGDgwDGD36hVWosuUq60ztijozCORzLTPPnDmmWGDMCbx5puhSMyaBfPmwcqVTVm5Eu67L+xTOPNrr17htkuXcNZTXZRxRUHdRyJSUsuWcMopYYNwIsqDDy7g+++78NZb8NZb8MknYRK/yZPDPg0bQteuoaupR4/Q/dSuXd1oTWRcUVBLQUSSadwYOnf+hr59w+Nt22D58lAcZs0K04IvXRpuZ88ufl92NnTvHgpE9+7heonauLpjxhYFtRREpDLq1SteF+L888Nz69fDnDnF2+zZ4SrsF14IW6EDD4TDDy/eOncORSedZVxRUPeRiOyo5s3/+1oJ93BWU2GRePvtcFHd8uVhmzQp7JeVBYceGk6D7dYt3B52WDgDKl1kXFFQ95GI1DQz2G+/sBUOYG/eDPn5YS6nd94Jk/zl58PixWF79NGwX1YWdOwYCkTXrmHr1Cm+36iMLQpqKYhIlAoHo7t2hQsvDM99/32Yx2nu3LDNnx/GJ959N2yPPRb2MwtdT4XTe3TuHLZUiKwomNkE4ERgnbv/pIzXDbgXGAx8D5zn7vOjylNI3UciEpfGjcMprT17Fj9XWCgKJ/mbNw+WLAnLmL7/PuTmFu970EFdee+9aDNG2VJ4DBgHPF7O68cDByS2I4DxidtIqftIRNJJWYXihx9CYViwABYuLN5atNgceZ7IioK7v25m7ZPsMgR43N0dmG1mzc2sjbt/FlUmUEtBRNJfo0bFXU+Ftm2DqVPfA46M9LvjXGRnL2BNicdrE89FSmMKIlIb1asHTZpsifx74hxoLuvavzJXYjWzUcAogOzsbGYUTlJSRQUFBXzwwTqgFR9/vJQZM9ZV63NqWkFBQbX/TFFSrqpRrqpL12wZncvdI9uA9kB+Oa89AAwv8fh9oE1Fn5mTk+PVlZeX54MHu4P7lCnV/pgal5eXF3eEMilX1ShX1aVrtrqYC5jrlfjdjrP7aApwrgU9gG884vEE0ECziEgyUZ6S+jTQF2hpZmuBG4EGAO7+F2Aq4XTUlYRTUn8WVZaSNKYgIlK+KM8+Gl7B6w6Mier7y6Ozj0REyhdn91Es1H0kIlK+jC0KaimIiGwv44qCuo9ERMqXUUVh61Zj8+ZwEchOO8WdRkQk/WRUUdi4Mfxxd9mlbiybJyJS0zKsKGQB6joSESlPRhWFTZtCUdCZRyIiZcvIoqCWgohI2TKqKBR2H6mlICJStowqCmopiIgkl1FFoeTZRyIisr0MKwrqPhIRSSajioK6j0REksuooqDrFEREksuooqDrFEREksvIoqCWgohI2TKqKGg8GRwXAAAIb0lEQVSgWUQkuYwqCps26ZRUEZFkMqwoqPtIRCSZjCoK6j4SEUkuI4uCWgoiImXLqKKg7iMRkeQyqiio+0hEJLmMKgo6+0hEJLlIi4KZDTKz981spZldW8br55nZf8xsYWL7eZR51H0kIpJc/ag+2MyygPuAAcBa4B0zm+LuS0vt+oy7XxJVjkLuGmgWEalIlC2F7sBKd1/t7puBXGBIhN+X1KZN4G40agT1IyuFIiK1W5RFYS9gTYnHaxPPlXaamS02s8lmtk9UYTZsCLcaZBYRKZ+5ezQfbHYGMNDdf554fA7Q3d3Hlthnd6DA3X8ws9HA/7r7MWV81ihgFEB2dnZObm5ulfP8+987MXx4D7KzN5GbO7t6f6iIFBQU0CQNq5VyVY1yVV26ZquLufr16zfP3btVuKO7R7IBPYFXSzy+Drguyf5ZwDcVfW5OTo5XR36+O7gfcki13h6pvLy8uCOUSbmqRrmqLl2z1cVcwFyvxG93lN1H7wAHmNm+ZtYQGAZMKbmDmbUp8fBkYFlUYdR9JCJSsciGXN19i5ldArxKaAVMcPclZnYzoWJNAX5hZicDW4CvgPOiylNQEG515pGISPkiPQ/H3acCU0s9d0OJ+9cRupUiV9hSUFEQESlfxlzRXNhSUPeRiEj5MqYoqKUgIlIxFQURESmSMUVB3UciIhXLmKKgloKISMUyriiopSAiUr6MKQqNGkGzZj+y665xJxERSV8ZM1/oHXfA4MGz6Nu3b9xRRETSVsa0FEREpGIqCiIiUkRFQUREiqgoiIhIERUFEREpoqIgIiJFVBRERKSIioKIiBSxsHRn7WFm/wE+qubbWwJf1GCcmqJcVaNcVZOuuSB9s9XFXO3cfY+Kdqp1RWFHmNlcd+8Wd47SlKtqlKtq0jUXpG+2TM6l7iMRESmioiAiIkUyrSg8GHeAcihX1ShX1aRrLkjfbBmbK6PGFEREJLlMaymIiEgSGVEUzGyQmb1vZivN7Nq48xQysw/N7F0zW2hmc2POMsHM1plZfonnWpjZa2a2InG7W5rkusnMPkkct4VmNjiGXPuYWZ6ZLTOzJWZ2aeL5WI9ZklyxHjMz28nM3jazRYlcv008v6+ZzUkcr2fMrGGa5HrMzD4ocbw6pzJXiXxZZrbAzF5MPI7+eLl7nd6ALGAV0AFoCCwCOsadK5HtQ6Bl3DkSWfoAXYH8Es/dAVybuH8tcHua5LoJuDLm49UG6Jq43xRYDnSM+5glyRXrMQMMaJK43wCYA/QA/goMSzz/F+CiNMn1GHB6nP+PJTJdDjwFvJh4HPnxyoSWQndgpbuvdvfNQC4wJOZMacfdXwe+KvX0EGBi4v5E4JSUhqLcXLFz98/cfX7i/nfAMmAvYj5mSXLFyoOCxMMGic2BY4DJiefjOF7l5Yqdme0NnAA8nHhspOB4ZUJR2AtYU+LxWtLgL0mCA9PMbJ6ZjYo7TBmy3f0zCD82QKuY85R0iZktTnQvpbxbqyQzaw90IfwrM22OWalcEPMxS3SFLATWAa8RWvDr3X1LYpdY/m6WzuXuhcfrlsTxusfMGqU6F/D/gKuBbYnHu5OC45UJRcHKeC4t/iUA9Hb3rsDxwBgz6xN3oFpiPLAf0Bn4DLgrriBm1gR4FrjM3b+NK0dpZeSK/Zi5+1Z37wzsTWjBH1LWbqlNtX0uM/sJcB1wMHA40AK4JpWZzOxEYJ27zyv5dBm71vjxyoSisBbYp8TjvYFPY8ryX9z908TtOuBvhL8o6eRzM2sDkLhdF3MeANz988Rf5G3AQ8R03MysAeGHd5K7P5d4OvZjVlaudDlmiSzrgRmEvvvmZlY/8VKsfzdL5BqU6IZzd/8BeJTUH6/ewMlm9iGhy/sYQssh8uOVCUXhHeCAxKh9Q2AYMCXmTJjZLmbWtPA+cByQn/xdKTcFGJG4PwJ4PsYsRQp/dBOGEsNxS/TvPgIsc/e7S7wU6zErL1fcx8zM9jCz5on7OwP9CeMdecDpid3iOF5l5XqvRGE3Qr99So+Xu1/n7nu7e3vCb9Y/3f0sUnG84h5dT8UGDCachbEK+HXceRKZOhDOhFoELIk7F/A0oVvhR0LraiShD3M6sCJx2yJNcj0BvAssJvwIt4kh15GEpvtiYGFiGxz3MUuSK9ZjBhwGLEh8fz5wQ+L5DsDbwErg/4BGaZLrn4njlQ88SeIMpTg2oC/FZx9Ffrx0RbOIiBTJhO4jERGpJBUFEREpoqIgIiJFVBRERKSIioKIiBRRURARkSIqCiIiUkRFQaQMZrY1MY9+vpm9YGbNzax9yXUdKvEZD5hZ7zKeb29mUy2s8bHczK6r2fQi1aeiIFK2je7e2d1/Qpi6e0w1PuMIYHbJJ8ysHmFeor+4+0HA/wDd0nSWXMlAKgoiFfsXxVMU1zeziYkplSebWeOy3mBmhwDL3X1rqZcGAh+6+xQADxOuXQJcGVF2kSpRURBJwsyygGMpnkTxIOBBdz8M+Ba4uJy3Hg+8UsbzhxDmuyriYd2FZqleilKkLCoKImXbObHwypeE+fRfSzy/xt1nJe4/SZiAriwDKbsobAWalHwiMRNnY2BLGfuLpJSKgkjZNnpYeKUdYW3vwjGF0jNIbjejZKJLqbkn1ssoZQYwOFEICg0A5ntY60AkVioKIkm4+zfALwh9/g2AtmbWM/HycODNMt7WjzDvfVmft4gwVfPNAGaWDdwN/Kpmk4tUj4qCSAXcfQFhHGAYYWGYEWa2mNCtNL6Mt5Q3noCZXQt0A643s2MS728H3J9YU1kkVlpPQaSGmdl84Ah3/zHuLCJVpaIgIiJF1H0kIiJFVBRERKSIioKIiBRRURARkSIqCiIiUkRFQUREiqgoiIhIERUFEREp8v8B5ZeeaHZURSAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Rb=np.linspace(.1,40,100)  # Niz vrednosti Rb\n",
    "Zb=Rb+1j*Xb_opt\n",
    "\n",
    "# Sedaj lahko izračunamo tok v vezje in nato P\n",
    "I=U/(Zb+Zg)\n",
    "P=0.5*abs(I)**2*Zb.real\n",
    "\n",
    "plt.xlabel('Rb / $\\Omega$')\n",
    "plt.ylabel(' Moč  / W')\n",
    "plt.plot(Rb,P,label='P',linewidth=2,color='b')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zdaj pa ti\n",
    "\n",
    "1. Pokaži (izriši), da za Rb<<Rg P dobro aproksimira premica, za Rb>>Rg pa parabola 1/Rb. Rešitev je na koncu zvezka.\n",
    "\n",
    "2. Izriši P za različne vrednosti induktivnosti. Rešitev je na koncu zvezka.\n",
    "\n",
    "3. Poišči max(P) iz grafa (niza izračunanih vrednosti) in Rb(Pmax) ter primerjaj z eksaktno izračunanim. (Pomagaj si npr. s primerom iz Obravnava_resonancnega_pojava.ipynb, poglavje 2.4) Rešitev je na koncu zvezka.\n",
    "4. Izriši šop krivulj P za različne frekvence, kjer je na X osi induktivnost. Rešitev je na koncu zvezka."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dodatno: Lock-in princip ya detekcijo zašumljenega signala\n",
    "\n",
    "Recimo, da vemo, da je naš iskani signal sinusne oblike, vendar je določitev amplitude in faze otežena, ker je signal zelo zašumljen. Lock-in metoda temelji na množenju iskanega sinusnega signala z znanim sinusnim signalom in določanjem povprečja. \n",
    "\n",
    "Izhajamo iz analize, ki smo jo že opravili pri izračunu moči. Vzemimo, da iščemo amplitudo in fazo toka $i(t)=I_m \\sin(\\omega t+\\varphi)$, ki je \"skrit\" v šumu. Pomnožimo ta signal z znanim signalom (napetostjo $U=U_m\\sin (\\omega t )$. Če naredimo povprečje produkta teh dveh signalov dobimo  $X=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\cos (\\varphi )$. Iz znanega X in $U_m$ lahko določimo produkt $I_m \\cos \\varphi$. Potrebujemo še eno enačbo (meritev), ki jo dobimo z množenjem iskanega signala s kosinusnim signalom, torej z $U=U_m\\cos (\\omega t )$. Z malo matematike lahko pokažemo, da je tedaj povprečje signala določeno z $Y=\\frac{{{U}_{m}}{{I}_{m}}}{2}\\sin (\\varphi )$. Sedaj imamo vse, kar potrebujemo za določitev amplitude in faze iskanega signala. Če je $U_m=1$ je \n",
    "\n",
    "$$I_m^2 =4(X^2+Y^2)$$\n",
    "\n",
    "in\n",
    "\n",
    "$$\\varphi = \\arctan \\frac{Y}{X} .$$\n",
    "\n",
    "Za filtriranje signalov s pomočjo lock-in metode obstajajo posebne naprave - t.i. lock-in ojačevalniki. Včasih so bili ti analogni, dandanes pa se vedno bolj uporabljajo digitalni lock-in ojačevalniki, ki morajo vsebovati predvsem dovolj hitra in natančna analogno-digitalna pretovrnika. \n",
    "\n",
    "Morda še to: zakaj se metoda imenuje lock-in? Gre preprosto za to, da imajo analogni lock-in ojačevalniki poseben gumb, s katerim se lahko spreminja fazo znanega (vzbujalnega) signala. Na ta način se fazo \"zaklene\" v določeno pozicijo relativno glede na iskani signal. Običajno tako, da se jo zaklene kar v pozicijo, kjer je odziv največji, to pa je ravno pri $\\varphi=0$.Če nas zanima le amplituda iskanega signala, jo dobimo že z množenjem s sinusnim signalom in nastavitvijo faze na nič.\n",
    "\n",
    "V spodnji celici poiskusimo proceduro določanja amplitude in faze iskanega izmeničnega signala tako, da vzamemo znan tokovni signal, kateremu dodamo šum in ga poskušamo z lock-in metodo rekonstruirati. Ker temelji metoda na iskanju povprečja signala, je skoraj nujno, da poznamo frekvenco iskanega signala (lahko jo tudi iščemo tam, kjer je največji odziv) in tvorimo niz meritev z večkratnikom te periode. Napako zmanjšamo tudi s tem, da upoštevamo več period signala.\n",
    "\n",
    "Metodo s pridom uporabljamo pri impedančni spektrokopiji, kjer iščemo impedanco bremena tako, da na breme priključimo znan napetostni signal in merimo tok skozi breme ali obratno. V vsakem primeru moramo čim bolj natančno določiti amplitudo in fazo vzbujalnega signala in odziva, pri čemer si lahko pomagamo z lock-in principom.\n",
    "\n",
    "Malo več na https://en.wikipedia.org/wiki/Lock-in_amplifier. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe83af30>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Zašumljen signal, množenje s sin in cos signalom\n",
    "Im=2.5 # iskana vrednost\n",
    "Um=1.0 \n",
    "omega=1\n",
    "fi=0.62 # \n",
    "\n",
    "# Signal mora biti večkratnik periode\n",
    "t=np.linspace(0,4*np.pi/omega,1000)\n",
    "\n",
    "u1=Um*np.sin(omega*t)\n",
    "u2=Um*np.cos(omega*t)\n",
    "i=Im*np.sin(omega*t+fi)+0.2*np.random.randn(len(t)) # iskani signal kateremu je dodan šum\n",
    "p1=u1*i\n",
    "p2=u2*i\n",
    "\n",
    "plt.xlabel('čas / s')\n",
    "plt.ylabel(' Signali')\n",
    "plt.plot(t,i,label='i(t)')\n",
    "plt.plot(t,u1,label='u(t)')\n",
    "plt.plot(t,p1,label='p1(t)',linewidth=3,color='r')\n",
    "\n",
    "plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Im =  2.489897226152057\n",
      "fi =  0.6241290477964204\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xeccb610>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Določitev i(t) z lock-in metodo\n",
    "X=np.mean(p1) # povprečna vrednost p1\n",
    "Y=np.mean(p2)\n",
    "\n",
    "# Določitev amplitude in faze iskanega signala\n",
    "Im2=2*np.sqrt(X**2+Y**2) \n",
    "fi2=np.arctan(Y/X)\n",
    "\n",
    "print('Im = ',Im2)\n",
    "print('fi = ', fi2)\n",
    "\n",
    "# Izris zašumljenega signala i in določenega signala i2\n",
    "i2=Im2*np.sin(omega*t+fi2)\n",
    "plt.xlabel('čas / s')\n",
    "plt.ylabel(' Signali')\n",
    "plt.plot(t,i,'.',label='i(t)')\n",
    "plt.plot(t,i2,label='i2(t)',linewidth=3)\n",
    "\n",
    "plt.plot([0, max(t)],[0, 0], linestyle=':',color='k') # dodamo ničlo\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rešitve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rešitev določanja S, P in Q\n",
    "\n",
    "Imamo več možnosti. \n",
    "1. Iz razlike max in min vrednosti signala dobimo 2S. Nato moramo še poiskati, koliko je sredina krivulje, ki predstavlja povprečno vrednost in s tem delovno moč. To pa dobimo tako, da od S odštejemo abs vrednost od min, kar je enako, kot da min prištejemo k S. Q pa določimo s pomočjo trikotnika moči.\n",
    "2. S pomočjo funkcije np.mean() izračunamo povprečje signala, ki mora biti enako P. S je potem razlika med max(p)-P. Q dobimo iz trikotnika moči. Vendar pozor. Da bi metoda delovala, mora biti signal dolg točno n period. (Povprečna vrednosti sinusa je 0 samo, če je signal dolg točno eno ali več period). V našem primeru to ni, zato je potrebno zagotoviti, da bo dolžina signala T določena iz pogoja $n 2\\pi=\\omega T$. Če odkomentirate vrstico 8, bo to veljalo in izračun bo pravilen. \n",
    "\n",
    "Kateri način je torej bolj natančen? Hmm, to je težko reči. Za lep idealen signal se kaže bolj uporaben prvi način, če pa si zamislimo zašumljen signal, pa zna biti določitev max in min vrednosti precej nenatančna. Zato se slednji način tudi pogosto uporablja za analizo signalov. Z manjšim dodatkom. V izračunu 2 smo izračunali S iz razlike max(p) in P, kar je ok za lep signal, ne pa za zašumljenega, kjer bi zopet imeli problem določanja max(p). Torej potrebujemo drugačen način določanja. V praksi pogosto uporabljen je tako imenovan lock-in način, ki ga na kratko opisujem v naslednji celici\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "izračunane vrednosti S, P in Q so :  0.08734807843929322 0.08215973971494166 0.02965575790651725\n",
      "nastavljene S, P in Q so :  0.08734812209745894 0.08215978246909296 0.02965576804913205\n",
      "drugi način določitve S, P in Q so :  0.09204269232136093 0.07746512583287395 0.049709269653272124\n"
     ]
    }
   ],
   "source": [
    "## Rešitev določanja S, P in Q\n",
    "S=(np.max(p)-np.min(p))/2\n",
    "P=S+np.min(p)\n",
    "Q=np.sqrt(S**2-P**2)\n",
    "print('izračunane vrednosti S, P in Q so : ',S,P,Q)\n",
    "\n",
    "# preverim iz znanih vrednosti naključno generiranih amplitud in faze\n",
    "S=Im*Um/2\n",
    "P=S*np.cos(fi)\n",
    "Q=S*np.sin(fi)\n",
    "print('nastavljene S, P in Q so : ',S, P, Q)\n",
    "# Razlika v decimalkah je posledica \"digitaliziranja\" časa pri tvorjenju signala\n",
    "\n",
    "# Drugi način:\n",
    "P=np.mean(p)\n",
    "S=np.max(p)-P\n",
    "Q=np.sqrt(S**2-P**2)\n",
    "print('drugi način določitve S, P in Q so : ',S, P, Q)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e169770>]"
      ]
     },
     "execution_count": 455,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Rešitev 4.2 aproksimacije s premico in parabolo\n",
    "# dodamo naslednjo kodo\n",
    "# premica\n",
    "I2=U/Zg.real\n",
    "P2=0.5*abs(I2)**2*Zb.real\n",
    "plt.plot(Rb,P2,label='P2',linestyle=':',color='r')\n",
    "plt.ylim(0,5)\n",
    "\n",
    "## 1/Rb\n",
    "I3=U/Zb.real\n",
    "P3=0.5*abs(I3)**2*Zb.real\n",
    "plt.plot(Rb,P3,label='P3',linestyle=':',color='g')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xc399610>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##Rešitev 4.2: izris P za različne induktivnosti\n",
    "Xb=np.linspace(0,10,100)  # Niz vrednosti Xb\n",
    "L=Xb/omega\n",
    "Zb=Zb_opt.real+1j*Xb\n",
    "\n",
    "# Sedaj lahko izračunamo tok v vezje ali pa računamo s kompleksno admitanco.\n",
    "I=U/(Zb+Zg)\n",
    "P=0.5*abs(I)**2*Zb.real\n",
    "\n",
    "plt.xlabel('L / mH')\n",
    "plt.ylabel(' Delovna moč  / W')\n",
    "plt.plot(L*1e3,P,label='P',linewidth=2,color='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.7623494364395524\n",
      "3.1932000863735888\n",
      "1.5509065469566052\n",
      "0.5467059939904362\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xc6ce6f0>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Rešitev iz 4.2: Max delovna moč  pri različnih frekvencah\n",
    "U=10\n",
    "R=4\n",
    "C=10e-6\n",
    "\n",
    "\n",
    "\n",
    "def P(freq):\n",
    "    omega=2*np.pi*freq\n",
    "    Zc=1/(1j*omega*C)\n",
    "    Zg=1/(1/Zc+1/R)\n",
    "    Rb=Zg.real\n",
    "    Xb=np.linspace(1,10,100)\n",
    "    Zb=Rb+1j*Xb\n",
    "    L=Xb/omega\n",
    "    I=U/(Zb+Zg)\n",
    "    print(Zg.real)\n",
    "    return 0.5*abs(I)**2*Zb.real\n",
    "    \n",
    "    \n",
    "plt.xlabel('L / mH')\n",
    "plt.ylabel(' Delovna moč  / W')\n",
    "plt.plot(L*1e3,P(1000),label='1 kHz',linewidth=2,color='b')\n",
    "plt.plot(L*1e3,P(2000),label='2 kHz',linewidth=2,color='g')\n",
    "plt.plot(L*1e3,P(5000),label='5 kHz',linewidth=2,color='r')\n",
    "plt.plot(L*1e3,P(10000),label='10 kHz',linewidth=2,color='k')\n",
    "plt.legend()\n",
    "\n",
    "# Komentar: max delovna moč se spreminja s frekvenco, ker predstavlja Rg realni del impedance, ki pa je \n",
    "# ki je sestavljena iz vzporedne vezave R in C in je zato realni del odvisen tudi od omega*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([9], dtype=int32),)\n",
      "Max P na krivulji je  [3.32231921]\n",
      "Max P izračunan je  3.3223920880217874\n"
     ]
    }
   ],
   "source": [
    "## rešitev primera 4.2: iskanje Pmax\n",
    "indeks=np.where(P== max(P)) # indeksi, kjer je izpolnjen pogoj\n",
    "print(indeks)\n",
    "print('Max P na krivulji je ',P[indeks[0]])\n",
    "print('Max P izračunan je ',Pb_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zaključek\n",
    "\n",
    "Moč je pomembna v elektrotehniki. Vsaka električna naprava potrebuje za pravilno delovanje ustrezno napajanje, ki mora zagotavljati ustrezno moč. Pri vzbujanju z izmeničnimi signali nas običajno bolj kot trenutna moč zanima povprečna moč, saj je ta relevantna za dolgotrajno delovanje. Ločimo delovno, jalovo in navidezno moč, vse pa so med seboj povezane z znano enačbo za trikotnik moči.\n",
    "\n",
    "Pomembno je, da razumemo, kako se moč spreminja s časom, da dobimo občutek za to, kaj predstavlja P, Q in S. Za konkretne izračune pa je najprimernejša uporaba kompleksnega računa.\n",
    "\n",
    "Kompenzacija jalove moči omogoči bolj optimalno delovanje električnih sistemov. Zaporedno kompenzacijo običajno uporabimo za povečanje delovne moči na bremenu, vzporedna pa omogoča delovanje naprav z najmanjšimi izgubami pri enaki vzbujalni napetosti. \n",
    "\n",
    "Prilagajanje bremena za doseg maksilne (delovne) moči je mogoče doseči ob pogoju da je $\\underline Z_g =\\underline Z_b^*$. \n",
    "\n",
    "Kot dodatek smo pokazali še možnost uporabe množenja dveh sinusnih signalov za iskanje amplitude in faze enega signala relativno na drugega. To metodo poznamo kot lock-in in se pogosto uporablja tako v analognih specializiranih napravah kot v modernejših digitalnih za izluščenje amplitude (in faze) zašumljenega harmoničnega signala. \n",
    "\n",
    "\n",
    "**Naslednje branje:** "
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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