su_cauer_type_c.ipynb

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    "## Synthesis example for _EVEN_ order elliptic lowpass filters with _EQUAL_ terminations\n",
    "Based on the paper ***_On the Design of Filters by Synthesis_*** by Saal and Ulbrich   \n",
    "https://ieeexplore.ieee.org/document/1086481   \n",
    "**_Warning, the notations used in this paper is dated!_**  \n",
    "  \n",
    "### _Low-Pass_ C 06 20 41 c\n",
    "*This filter is tabulated on page 318*\n",
    "\n",
    "\n",
    "$n = 6$  \n",
    "${\\rho} = 20\\ \\%$  \n",
    "${\\theta} = 41$ &deg;\n",
    "\n",
    "For even order lowpass filters, note that ${\\Omega}_{s}\\ {\\neq}\\ \\displaystyle \\frac{1}{sin{\\theta}}$.\n",
    "\n",
    "The cutoff frequency (equi-ripple) ${\\Omega}_{c}$ is set to 1 as usual."
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    "import numpy as np\n",
    "#np.seterr(divide='ignore', invalid='ignore')\n",
    "\n",
    "import scipy.special as ss\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
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    "# number of section\n",
    "n = 6  \n",
    "\n",
    "# reflection coefficient of filter\n",
    "p = 0.2   \n",
    "\n",
    "# ws=2.790428, normalized stopband frequency\n",
    "theta_deg = 41  \n",
    "\n",
    "# convert theta to radians for later calculations\n",
    "theta = theta_deg*np.pi/180  \n",
    "\n",
    "#print(\"n = \", n)\n",
    "#print(\"p = \", p)\n",
    "#print(\"theta = \", theta_deg, \"deg\")"
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    "___"
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    "### Calculate ${a}_{v}$\n",
    "Calculate ${a}_{v}$ and ${a}_{n}$ using _equation (38)_ on page 294.  \n",
    "\n",
    "${a}_{v} = \\sqrt{sin{\\theta}}  \\cdot sn\\bigg(\\displaystyle\\frac{v}{n}K;{\\theta}\\bigg)\\;\\;\\;\\;\\;\\;v=1,\\;2,\\;...,\\;n-1$ \n",
    "\n",
    "${a}_{n} = \\sqrt{sin{\\theta}}$  \n",
    "\n",
    "The variable $K$ is the complete elliptic integral of the first kind with the modulus $k=sin{\\theta}$.  \n",
    "The function $sn(u,m)$ is the Jacobian elliptic function.  \n",
    "\n"
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    "#In scipy library: ellipk(u,m) is the complete elliptic integral of the first kind where m = k^2 or sin^2(theta)\n",
    "K = ss.ellipk(np.sin(theta)**2)\n",
    "\n",
    "#a[0] is filled with a dummy 1 so indices of a[] complies with Saal & Ulbrich(SU)\n",
    "a = np.array([1])   \n",
    "for v in range(1, n):    \n",
    "    u = K*v/n\n",
    "    #In scipy library: ellipj(u,m) is the Jacobian elliptic function where m = sin^2(theta)\n",
    "    jac_ell = ss.ellipj(u, np.sin(theta)**2)\n",
    "    sn = jac_ell[0]\n",
    "    a = np.append(a, np.sqrt(np.sin(theta))*sn)\n",
    "    \n",
    "#Append a[n] into the array a.\n",
    "a = np.append(a, np.sqrt(np.sin(theta)))\n",
    "\n",
    "#print(a[1:])"
   ]
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    "___"
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    "### Calculate ${c}_{v}$,  ${\\Delta}_{c}$, ${\\Omega}^{'}_{c}$, and ${\\Omega}_{s}$\n",
    "Once ${a}_{v}$ are found, calculate the following:\n",
    "\n",
    "${c}_{v} = \\displaystyle \\sqrt{\\frac{{a}_{v}^{2} - {a}_{1}^{2}}{1 - {a}_{v}^{2}\\cdot{a}_{1}^{2}} }\\;\\;\\;\\;\\;\\;v=1,\\;2,\\;...,\\;n-1$  \n",
    "  \n",
    "${\\Omega}^{'}_{c} = {a}_{n-1}$ \n",
    "  \n",
    "${\\Omega}_{s} = \\displaystyle \\frac{1}{({\\Omega}^{'}_{c})^{2}}$ \n",
    "\n",
    "See _equation (47)_ on pages 296.   \n"
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    "#EQN(47) for n even case c page 296\n",
    "c = np.array([1])\n",
    "for v in range(1, n):\n",
    "    c = np.append(c, np.sqrt((a[v]**2-a[1]**2)/(1-(a[v]**2)*(a[1]**2))))\n",
    "\n",
    "wc_pc = a[n-1]\n",
    "ws = 1/wc_pc**2\n",
    "\n",
    "#print(c[1:])\n",
    "#print(wc_pc)\n",
    "#print(ws)"
   ]
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    "Calculate  $m$ using _equations (37)_ page 294 for even $n$. \n",
    "  \n",
    "$m = \\displaystyle\\frac{n}{2}$  \n",
    "  \n",
    "Calculate $m$ and ${\\Delta}_{c}$ using _equation (44)_ on page 296.\n",
    "\n",
    "${\\Delta}_{c} = {\\Delta}_{a} = \\displaystyle \\prod_{{\\mu} = 1}^{m} {a}^{2}_{2{\\mu} - 1}$"
   ]
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    "#m calculation, see EQN(37) p294\n",
    "#n is even\n",
    "m = n//2 \n",
    "       \n",
    "#EQN(44) for n even\n",
    "delta_a = 1\n",
    "for u in range(1, m+1):\n",
    "    delta_a *= a[2*u-1]**2    \n",
    "\n",
    "delta_c = delta_a\n",
    "#print(delta_c)"
   ]
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    "___"
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    "### Calculate ${A}_{s}$\n",
    "The rejection ${A}_{s}$ in $dB$ can be calculated according to _equation (40)_ on page 294.  ${\\Delta}$ should be replaced with ${\\Delta}_{a}$ to clarify that the ${\\Delta}$ used is from _equation (39)_ on page 294 for the even $n$ case.\n",
    "\n",
    "${A}_{s} = 10\\log_{10} \\displaystyle \\left[1+\\frac{1}{\\Delta^{4}_{a}({\\rho}^{-2}-1)}\\right]$   "
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    "#See EQN(40) page 294 for rejection calculation.\n",
    "As = 10*np.log10(1+1/((delta_a**4)*(1/p**2-1))) #dB\n",
    "\n",
    "#print(As)"
   ]
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    "___"
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    "### The characteristic function $K({\\lambda})$\n",
    "Construct the characteristic polynomial $K({\\lambda})$.  See _equation (46)_ on page 296.  \n",
    "\n",
    "$K({\\lambda}) = \\displaystyle \\frac{{\\lambda}^{2}}{{c}^{-1}} \\prod_{{\\mu} = 2}^{m} \\displaystyle \\frac{{\\lambda}^{2}+{{c}^{2}_{2{\\mu}-1}}} {{c}^{2}_{2{\\mu}-1} \\cdot {\\lambda}^{2}+1}$\n",
    "\n",
    "\n",
    "${c}^{-1} = {\\Delta}_{c}\\sqrt{{\\rho}^{-1} - 1}$\n",
    "\n",
    "\n",
    "The polynomial $K({\\lambda})$ has the numnerator and denominator $F({\\lambda})$ and $P({\\lambda})$ respectively.  See _equation (12)_ on page 286. \n",
    "\n",
    "$K({\\lambda}) = \\displaystyle \\frac{F({\\lambda})} {P({\\lambda})}$"
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    "#c calculation from page 296\n",
    "const_c = 1/(delta_c*np.sqrt(1/(p**2)-1))\n",
    "\n",
    "#EQN(43) expand for n even\n",
    "F = np.array([1, 0, 0])\n",
    "P = np.array([1/const_c])\n",
    "\n",
    "#These are the inverse of the transmission zero frequencies\n",
    "co_tz = np.array([])\n",
    "\n",
    "for u in range(2, m+1):\n",
    "    #form numerator of K(lambda) or F(lambda)\n",
    "    F = np.polymul(F, np.array([1, 0, c[2*u-1]**2]))\n",
    "        \n",
    "    #form denominator of K(lambda) or P(lambda)\n",
    "    P = np.polymul(P, np.array([c[2*u-1]**2, 0, 1]))\n",
    "        \n",
    "    #collect the constants bS used in P(lambda)\n",
    "    co_tz = np.append(co_tz, c[2*u-1])\n",
    "\n",
    "#print(F)\n",
    "#print(P)"
   ]
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    "### Lowpass filter response using $K({\\lambda})$\n",
    "Once the characteristic polynomial $K({\\lambda})$ has been found,  a plot of the filter response can be generated to check the validity of the calculations.\n",
    "\n",
    "Form polynomial $\\lvert K({\\lambda}) \\rvert ^{2}$, where ${\\lambda} = j{\\Omega}$.        \n",
    "  \n",
    "$\\lvert K({\\lambda}) \\rvert ^{2}=\\displaystyle \\frac{F({\\lambda})F({-\\lambda})} {P({\\lambda})P({-\\lambda})}$   "
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    "#Generate F(jw)*F(-jw) and P(jw)*p(-jw) for n even\n",
    "\n",
    "#nX = X(-jw).  Changes sign of coefficients of odd order only.\n",
    "nF = np.copy(F)\n",
    "nP = np.copy(P)\n",
    "\n",
    "#Odd order indexing from penultimate element while stepping by 2 in reverse. \n",
    "nF[-2::-2] = -1*nF[-2::-2]\n",
    "nP[-2::-2] = -1*nP[-2::-2]\n",
    "    \n",
    "FnF = np.polymul(F, nF)\n",
    "PnP = np.polymul(P, nP)\n",
    "\n",
    "#print(FnF)\n",
    "#print(PnP)"
   ]
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    "The $\\lvert S_{21} \\rvert^2$ is related to $\\lvert K({\\lambda}) \\rvert ^{2}$ by the following:\n",
    "\n",
    "$\\lvert S_{21} \\rvert ^2 = \\displaystyle \\frac{1} {1 + \\lvert K({\\lambda}) \\rvert ^{2}}$     \n",
    "  \n",
    "Applying conservation of energy,  \n",
    "  \n",
    "$\\lvert S_{11} \\rvert^2 = 1-\\lvert S_{21} \\rvert ^2$\n",
    "  \n",
    "When evaluating $\\lvert K({\\lambda}) \\rvert ^{2}$, ${\\lambda} = j{\\Omega}$ and ${\\Omega}$ is normalized to ${\\Omega}^{'}_{c}$.  For example, when plotting the value at ${\\Omega} = 1$, $\\lvert K({\\lambda}) \\rvert ^{2}$ should be evaluated for ${\\lambda} = j1 \\cdot {\\Omega}^{'}_{c}$.  "
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    "def Plot_S(S11_dB, S21_dB, w, ws, rej_dB, title = '???', fig = 1):\n",
    "    #test plot of transfer function \n",
    "    \n",
    "    #plt.clf()\n",
    "    plt.figure(fig, (10, 6))\n",
    "    plt.plot(w, S21_dB, label = '$|S_{21}|^2$')\n",
    "    plt.plot(w, S11_dB, label = '$|S_{11}|^2$')\n",
    "    plt.legend(loc = 'lower right', shadow=False, fontsize = 'large')\n",
    "    \n",
    "    #Plot stop band limits\n",
    "    As = -1*rej_dB\n",
    "    plt.plot([ws, w[-1]], [As, As], 'g', linestyle=':')\n",
    "    plt.plot([ws, ws], [As, 0], 'g', linestyle=':')\n",
    "    txt = '('+ str(round(ws, 2)) + ', ' + str(np.ceil(As)) + ')' \n",
    "    plt.text(ws + .01*w[-1], round(As,0)+1, txt, fontsize = 12)\n",
    "    \n",
    "    #Limit the lower y-axis to 20dB below the rejection rounded to x10. E.g. 43->50  \n",
    "    plt.axis([0, w[-1], np.floor(As/10)*10-20, 0])\n",
    "    plt.xticks(np.arange(0, w[-1]+1, 1))\n",
    "    \n",
    "    plt.xlabel('${\\Omega}$(rad)', fontsize = 'large')\n",
    "    plt.ylabel('(dB)', fontsize = 'large')\n",
    "    plt.title(title, fontsize = 'large')\n",
    "\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Generate the lambdas to be evaluated\n",
    "wstep = .001\n",
    "w = np.arange(wstep, 10, wstep)\n",
    "lamb = 1j*w*wc_pc \n",
    "        \n",
    "Kn2 = np.polyval(FnF,lamb)\n",
    "Kd2 = np.polyval(PnP,lamb) \n",
    "K2 = np.real(Kn2)/np.real(Kd2)\n",
    "\n",
    "S21_2 = 1/(1+K2)\n",
    "S21_dB = 10*np.log10(S21_2)\n",
    "\n",
    "S11_2 =  1-S21_2 \n",
    "S11_dB = 10*np.log10(S11_2)\n",
    "\n",
    "title = 'Filter response from polynomial $K({\\lambda})$'\n",
    "\n",
    "Plot_S(S11_dB, S21_dB, w, ws, As, title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### The Hurwitz polynomial $E({\\lambda})$\n",
    "  \n",
    "Form the polynomial $E({\\lambda})E({-\\lambda})$,    \n",
    "\n",
    "$E({\\lambda})E({-\\lambda}) = F({\\lambda})F({-\\lambda}) + P({\\lambda})P({-\\lambda})$ \n",
    "  \n",
    "Build polynomial $E({\\lambda})$ using the negative roots of $E({\\lambda})E({-\\lambda})$.  \n",
    "   \n",
    "Read the top left half of page 287."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "#Form (E)(nE)=(F)(nF)+(P)(nP). Page 287. EQN(14), EQN(15)\n",
    "EnE = np.polyadd(FnF,PnP)\n",
    "\n",
    "E = np.array([1])\n",
    "for root in np.roots(EnE):\n",
    "    if np.real(root) < 0:\n",
    "        E = np.polymul(E, np.array([1, -1*root]))\n",
    "    \n",
    "E = np.real(E) #E has imaginary parts that are zero.  They are not dropped by numpy.\n",
    "\n",
    "#print(E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Capacitor and inductor extraction\n",
    "#### a) Construct ${X}_{1O}$ and ${X}_{2O}$ polynomials\n",
    "From _equation (16)_ on page 4, form the following reactance polynomials:\n",
    "\n",
    "${X}_{1O} = \\displaystyle\\frac{{E}_{e} - {F}_{e}}{{E}_{o} + {F}_{o}}$  \n",
    "  \n",
    "${X}_{2O} = \\displaystyle\\frac{{E}_{e} + {F}_{e}}{{E}_{o} + {F}_{o}}$ \n",
    "\n",
    "The subscript $e$ and $o$ represent the even order and odd order portions of the polynomial.  \n",
    "The subscripts $_{1}$ and $_{2}$ of $X$ stands for the left or input side and right or output side of the ladder network respectively.  The $_{O}$ subscript indicates open-circuit.  ${X}_{1O}$ is used if the start the extraction process is from the input side.  ${X}_{2O}$ is used if the start the extraction process is from the output side.  Both polynomials are used in the presented extraction method of even order elliptic lowpass filters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "#See EQN(16) on page 4 for P even\n",
    "Ee = np.copy(E)\n",
    "Eo = np.copy(E)\n",
    "Fe = np.copy(F)\n",
    "Fo = np.copy(F)\n",
    "\n",
    "#Form X1o for n=odd (length of E or F is even)\n",
    "Ee[-2::-2] = 0\n",
    "Eo[-1::-2] = 0\n",
    "\n",
    "Fe[-2::-2] = 0\n",
    "Fo[-1::-2] = 0     \n",
    "\n",
    "#X1O numerator            \n",
    "X1On = np.polysub(Ee,Fe)\n",
    "X1On = np.trim_zeros(X1On, 'f')\n",
    "\n",
    "#X1O denominator\n",
    "X1Od = np.polyadd(Eo,Fo)  \n",
    "X1Od = np.trim_zeros(X1Od, 'f')\n",
    "\n",
    "#X2O numerator            \n",
    "X2On = np.polyadd(Ee,Fe)\n",
    "X2On = np.trim_zeros(X2On, 'f')\n",
    "\n",
    "#X2O denominator\n",
    "X2Od = np.polyadd(Eo,Fo)  \n",
    "X2Od = np.trim_zeros(X2Od, 'f')\n",
    "\n",
    "#print(X1On)\n",
    "#print(X1Od)\n",
    "\n",
    "#print(X2On)\n",
    "#print(X2Od)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### b) Transmission zero frequencies and their sequence\n",
    "Prior to element extraction, the frequencies for the evaluation of the polynomials need to be known.  The formula is the  following:\n",
    "\n",
    "${\\Omega}_{2(\\mu -1)} = \\displaystyle \\frac{1} {{c}_{2{\\mu}-1}}\\;\\;\\;\\;\\;\\;{\\mu}=2,\\;3,\\;...,\\;m$\n",
    "\n",
    "For filter order $n>4$, the shunt capacitors and transmission zero elements need to be extracted in a sequence such that the highest to lowest zero frequencies are aligned in a spiral fashion (see figure).  This is necessary to avoid negative circuit elements.  For example, if the zero frequencies are ${\\Omega}_{2} > {\\Omega}_{4} > {\\Omega}_{6} > {\\Omega}_{8}$, the extraction sequence should be ${\\Omega}_{2}$, ${\\Omega}_{6}$, ${\\Omega}_{8}$, then ${\\Omega}_{4}$.\n",
    "\n",
    "$~$\n",
    "![TransZeroOrder](tz2.svg)\n",
    "$~$\n",
    "\n",
    "If the number of transmission zeros is odd, the lowest frequency is in the middle of the sequence.  \n",
    "Read the section **_4) Computation of the Circuit-Element Values_** on page 296.  \n",
    "In the python script, the frequencies are appended to an array in extraction sequence.  Therefore, they now have updated indices.    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "#Sort and organize transmission zeros for synthesis.\n",
    "#According SU p296, finite pole frequencies(of K(lambda)) closest to the bandedge should\n",
    "#be placed in the middle of the filter to avoid negative components.\n",
    "tz = 1/(np.sort(co_tz)) #co_tz was conveniently collected when P(lambda) was formed.\n",
    "\n",
    "#tzo stands for Transmission Zero Ordered or rearranged for order of extraction.\n",
    "tzo = tz[::2]\n",
    "tzo = np.append(tzo,np.sort(tz[1::2]))\n",
    "\n",
    "#pad zeroes into tzo so the indices match with SU comvention. \n",
    "#tzop -> Transmission Zero Ordered Padded.\n",
    "tzop = np.array([0])\n",
    "for z in tzo:\n",
    "    tzop = np.append(tzop, [0,z])\n",
    "    \n",
    "#print(tzop)"
   ]
  },
  {
   "cell_type": "markdown",
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    "#### c) Extraction procedure\n",
    "The element extraction procedure for even $n$ is outlined below:\n",
    "\n",
    "**_Step 1_**  \n",
    "Since the 1st element to extract is a shunt capacitance, start with the susceptance polynomial ${B}_{1}({\\lambda})$ below:\n",
    "\n",
    "${B}_{1}({\\lambda}) = \\displaystyle\\frac{1}{{X}_{1O}}$  \n",
    "  \n",
    "Set index ${\\mu}$ = 2  \n",
    "\n",
    "**_Step 2_**   \n",
    "Extract shunt ${c}_{{\\mu}-1}$ by evaluating the equation below:\n",
    "\n",
    "${c}_{{\\mu}-1} = \\displaystyle\\bigg[\\frac{{B}_{1}({\\lambda})}{\\lambda}\\bigg]_{{\\lambda}^{2} = -{\\Omega}^{2}_{\\mu}}$\n",
    "\n",
    "**_Step 3_**   \n",
    "Form the remaining susceptance polynomial ${B}_{2}({\\lambda})$:\n",
    "\n",
    "${B}_{2}({\\lambda}) = {B}_{1}({\\lambda}) - {\\lambda}{c}_{{\\mu}-1}$\n",
    "\n",
    "**_Step 4_**   \n",
    "Extract series ${c}_{{\\mu}}$ of the series parallel resonator by evaluating the equation below:\n",
    "\n",
    "${c}_{{\\mu}} = \\displaystyle\\bigg[\\frac{\\lambda \\cdot {B}_{2}({\\lambda})}{{\\lambda}^2 + {\\Omega}^{2}_{\\mu}}\\bigg]_{{\\lambda}^{2} = -{\\Omega}^{2}_{\\mu}}$\n",
    "\n",
    "In the implemention, the polynomial division by ${\\lambda}^2 + {\\Omega}^{2}_{\\mu}$ needs to be performed first since the evaluation will use ${\\lambda}^{2} = -{\\Omega}^{2}_{\\mu}$. Else, a division by 0 is implied.\n",
    "\n",
    "**_Step 5_**   \n",
    "Since series ${l}_{\\mu}$ resonates with ${c}_{\\mu}$ at ${\\Omega}_{\\mu}$:\n",
    "\n",
    "${l}_{\\mu} = \\displaystyle \\frac{1}{{c}_{\\mu}{\\Omega}^{2}_{\\mu}}$\n",
    "\n",
    "**_Step 6_**   \n",
    "Form the remaining susceptance polynomial ${B}_{3}({\\lambda})$:\n",
    "\n",
    "$\\displaystyle\\frac{1}{{B}_{3}({\\lambda})} = \\displaystyle\\frac{1}{{B}_{2}({\\lambda})} -  \\displaystyle\\frac{\\lambda}{{c}_{\\mu}({\\lambda}^2 + {\\Omega}^{2}_{\\mu})}$\n",
    "\n",
    "Increment ${\\mu}$ by 2.  \n",
    "If ${\\mu}$ < $n$, the process repeats by setting ${B}_{1}({\\lambda}) = {B}_{3}({\\lambda})$ and go back to **_Step 2_**.\n",
    "\n",
    "**_Step 7_**   \n",
    "Once ${\\mu}$ = $n$, evaluate the last shunt capacitor ${c}_{n-1}$:\n",
    "\n",
    "${c}_{n-1} = \\displaystyle \\bigg[\\frac{{B}_{3}({\\lambda})}{\\lambda}\\bigg]_{{\\lambda} = {\\infty}}$\n",
    "\n",
    "**_Step 8_**  \n",
    "Extract the final series ${l}_{n}$ by evaluating the equation below:  \n",
    "\n",
    "${l}_{n} = \\displaystyle \\bigg[\\frac{{X}_{2O}({\\lambda})}{\\lambda}\\bigg]_{{\\lambda} = {\\infty}}$  \n",
    "  \n",
    "**_Step 9_**   \n",
    "Denormalize capacitor and inductor values by ${\\Omega}^{'}_{c}$:  \n",
    "${c}^{d} = c \\cdot {\\Omega}^{'}_{c}$    \n",
    "${l}^{d} = l \\cdot {\\Omega}^{'}_{c}$\n",
    "\n",
    "The superscript $d$ is only added here for clarity.  It will not appear any further."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
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   "source": [
    "cap_array = np.array([])\n",
    "ind_array = np.array([])\n",
    "omega_array = np.array([])\n",
    "\n",
    "#Step 1:\n",
    "B_num = np.copy(X1Od)\n",
    "B_den = np.copy(X1On)\n",
    "\n",
    "#element extraction SU p306\n",
    "#transmission zeros are padded with zeros in the array omega.  The useful indices are 2,4,... therefore index increments by 2 \n",
    "index = 2\n",
    "\n",
    "while index < n:\n",
    "    #Step 2:\n",
    "    #shunt removal\n",
    "    BdivL_num = B_num[:-1] #B divided by lambda. Since constant or last term of B is 0, just remove the last term \n",
    "    BdivL_num_eval = np.polyval(BdivL_num, 1j*tzop[index])\n",
    "    BdivL_den_eval = np.polyval(B_den, 1j*tzop[index])\n",
    "    c_shnt = BdivL_num_eval/BdivL_den_eval\n",
    "    \n",
    "    #update component and frequency arrays\n",
    "    cap_array = np.append(cap_array, np.real(c_shnt))\n",
    "    ind_array = np.append(ind_array, [0])\n",
    "    omega_array = np.append(omega_array, [0])\n",
    "    \n",
    "    #Step 3:\n",
    "    #update polynomial B\n",
    "    lambda_cap = np.array([np.real(c_shnt), 0])  #lambda*c(extracted)\n",
    "    B_num = np.polysub(B_num, np.polymul(lambda_cap, B_den))\n",
    "    \n",
    "    #Step 4:\n",
    "    #series removal\n",
    "    temp_num = np.polymul(np.array([1,0]), B_num)\n",
    "    temp_num = np.polydiv(temp_num, np.array([1, 0, tzop[index]**2]))[0]\n",
    "    temp_num_eval = np.polyval(temp_num, 1j*tzop[index])\n",
    "    temp_den_eval = np.polyval(B_den, 1j*tzop[index])\n",
    "    c_srs = temp_num_eval/temp_den_eval\n",
    "    \n",
    "    #Step 5:\n",
    "    #calculate series inductor\n",
    "    w = tzop[index]\n",
    "    l_srs = 1/(w)**2/(np.real(c_srs))\n",
    "    \n",
    "    #update component and frequency array\n",
    "    cap_array = np.append(cap_array, np.real(c_srs))\n",
    "    ind_array = np.append(ind_array, [l_srs])\n",
    "    omega_array = np.append(omega_array, [w])   \n",
    "    \n",
    "    #Step 6:\n",
    "    #update polynomial B\n",
    "    temp1 = np.polymul(B_den, [1, 0, tzop[index]**2])\n",
    "    temp2 = np.polymul(B_num, [1/np.real(c_srs), 0])\n",
    "    B_den = np.polysub(temp1, temp2)\n",
    "    B_num = np.polymul(B_num, [1, 0, tzop[index]**2])\n",
    "    \n",
    "    index += 2\n",
    "\n",
    "#Step 7:\n",
    "#shunt removal\n",
    "BdivL_num = B_num[:-1] #B divided by lambda when constant term of B is 0\n",
    "BdivL_num_eval = BdivL_num[0]\n",
    "BdivL_den_eval = B_den[0]\n",
    "c_shnt = BdivL_num_eval/BdivL_den_eval\n",
    "#c_shnt = np.polyval(B_num[:-1], 1)/np.polyval(B_den, 1)\n",
    "\n",
    "#update component and frequency array\n",
    "cap_array = np.append(cap_array, np.real(c_shnt))\n",
    "ind_array = np.append(ind_array, [0])\n",
    "omega_array = np.append(omega_array, [0])\n",
    "\n",
    "#Step 8:\n",
    "#Final series inductor\n",
    "l_srs = (X2On[0])/(X2Od[0])\n",
    "\n",
    "#update component and frequency array        \n",
    "cap_array = np.append(cap_array, 0)\n",
    "ind_array = np.append(ind_array, l_srs)\n",
    "omega_array = np.append(omega_array, [0])\n",
    "        \n",
    "#Step 9:\n",
    "#Denormalize component values and frequencies\n",
    "cap_array = cap_array*wc_pc\n",
    "ind_array = ind_array*wc_pc\n",
    "omega_array = omega_array/wc_pc\n",
    "\n",
    "#Create termination array\n",
    "terms = np.array([1, 1])\n",
    "\n",
    "#print(cap_array)\n",
    "#print(ind_array) \n",
    "#print(omega_array)\n",
    "#print(terms)"
   ]
  },
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   "source": [
    "___"
   ]
  },
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   "source": [
    "### Lowpass Filter Simulation\n",
    "The frequency response of the resulting lowpass filter from the extracted capacitors and inductors can be analyzed and plotted.  The function below utilizes the cascadability of the ABCD parameters.  The resulting ABCD parameters of the whole network is then converted to S parameters for analysis.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
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   "source": [
    "def SPARCLad(E, First_Element = 'shnt'):\n",
    "    \n",
    "    \"\"\"\n",
    "    S-PARameter Cauer Ladder(SPARCLad)\n",
    "    Function for computing the S-Parameters of an cauer \n",
    "    doubly terminated ladder network\n",
    "    \n",
    "    E = an array of network elements including the terminations\n",
    "    First_Element = 'shnt'(shunt) or 'srs'(series)\n",
    "    \"\"\"\n",
    "    \n",
    "    w = sp.symbols('w')\n",
    "    Rs = E[0][0]\n",
    "    Rl = E[0][1]\n",
    "    orientation = First_Element\n",
    "    abcd = np.matrix([[1, 0], [0, 1]])\n",
    "        \n",
    "    for k in range(1, len(E)):\n",
    "        if orientation == 'shnt':\n",
    "            abcd = np.dot(abcd, np.matrix([[1, 0], [((1j*w*E[k][0])**-1+(1j*w*E[k][1]))**-1, 1]]))\n",
    "            #abcd = np.dot(abcd, np.matrix([[1, 0], [(1j*w*E[k][1])**-1, 1]]))\n",
    "            orientation = 'srs'\n",
    "        else:\n",
    "            abcd = np.dot(abcd, np.matrix([[1, ((1j*w*E[k][0])+(1j*w*E[k][1])**-1)**-1], [0, 1]]))\n",
    "            #abcd = np.dot(abcd, np.matrix([[1, (1j*w*E[k][1])**-1], [0, 1]]))\n",
    "            orientation = 'shnt'\n",
    "\n",
    "    abcd = np.dot(abcd, np.matrix([[np.sqrt(Rl/Rs), 0], [0, 1/np.sqrt(Rl/Rs)]]))\n",
    "    \n",
    "    A = abcd[0, 0]\n",
    "    B = abcd[0, 1]\n",
    "    C = abcd[1, 0]\n",
    "    D = abcd[1, 1]\n",
    "    \n",
    "    denom = A+B/Rs+C*Rs+D\n",
    "    \n",
    "    S11_sym = (A+B/Rs-C*Rs-D)/denom\n",
    "    S21_sym = 2/denom\n",
    "    S12_sym = 2*(A*D-B*C)/denom\n",
    "    S22_sym = (-A+B/Rs-C*Rs+D)/denom\n",
    "    \n",
    "    S11 = sp.lambdify(w, S11_sym, 'numpy')\n",
    "    S21 = sp.lambdify(w, S21_sym, 'numpy')\n",
    "    S12 = sp.lambdify(w, S12_sym, 'numpy')\n",
    "    S22 = sp.lambdify(w, S22_sym, 'numpy')\n",
    "    \n",
    "    return np.array([S11, S21, S12, S22])"
   ]
  },
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   "execution_count": 33,
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "EE = np.array([[terms[0], terms[1]]])\n",
    "for i in range(len(cap_array)):\n",
    "        EE = np.append(EE, [[cap_array[i], ind_array[i]]], axis = 0)\n",
    "#print(EE)  \n",
    "\n",
    "Sparm = SPARCLad(EE)\n",
    "S11 = Sparm[0]\n",
    "S21 = Sparm[1]\n",
    "\n",
    "wstep = .001\n",
    "w = np.arange(wstep, 10, wstep)\n",
    "S11_dB = 20*np.log10(abs(S11(w)) + 1e-8) #1e-8 is added to prevent log(0) condition\n",
    "S21_dB = 20*np.log10(abs(S21(w)) + 1e-8) #1e-8 is added to prevent log(0) condition\n",
    "\n",
    "title = 'Filter response from extracted capacitors and inductors'\n",
    "\n",
    "Plot_S(S11_dB, S21_dB, w, ws, As, title, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### List component values\n",
    "The components and their indicies can be clearly displayed.  \n",
    "Using dataframes just to display a table is probably an overkill. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style  type=\"text/css\" >\n",
       "</style>  \n",
       "<table id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8\" > \n",
       "<thead>    <tr> \n",
       "        <th class=\"blank level0\" ></th> \n",
       "        <th class=\"col_heading level0 col0\" >$C$</th> \n",
       "        <th class=\"col_heading level0 col1\" >$L$</th> \n",
       "        <th class=\"col_heading level0 col2\" >${\\Omega}$</th> \n",
       "        <th class=\"col_heading level0 col3\" >${R}$</th> \n",
       "    </tr></thead> \n",
       "<tbody>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row0\" class=\"row_heading level0 row0\" >0</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row0_col0\" class=\"data row0 col0\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row0_col1\" class=\"data row0 col1\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row0_col2\" class=\"data row0 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row0_col3\" class=\"data row0 col3\" >1</td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row1\" class=\"row_heading level0 row1\" >1</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row1_col0\" class=\"data row1 col0\" >1.01183</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row1_col1\" class=\"data row1 col1\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row1_col2\" class=\"data row1 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row1_col3\" class=\"data row1 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row2\" class=\"row_heading level0 row2\" >2</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row2_col0\" class=\"data row2 col0\" >0.151579</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row2_col1\" class=\"data row2 col1\" >1.33161</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row2_col2\" class=\"data row2 col2\" >2.22582</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row2_col3\" class=\"data row2 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row3\" class=\"row_heading level0 row3\" >3</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row3_col0\" class=\"data row3 col0\" >1.52845</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row3_col1\" class=\"data row3 col1\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row3_col2\" class=\"data row3 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row3_col3\" class=\"data row3 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row4\" class=\"row_heading level0 row4\" >4</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row4_col0\" class=\"data row4 col0\" >0.261728</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row4_col1\" class=\"data row4 col1\" >1.39571</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row4_col2\" class=\"data row4 col2\" >1.65454</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row4_col3\" class=\"data row4 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row5\" class=\"row_heading level0 row5\" >5</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row5_col0\" class=\"data row5 col0\" >1.33835</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row5_col1\" class=\"data row5 col1\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row5_col2\" class=\"data row5 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row5_col3\" class=\"data row5 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row6\" class=\"row_heading level0 row6\" >6</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row6_col0\" class=\"data row6 col0\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row6_col1\" class=\"data row6 col1\" >1.15131</td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row6_col2\" class=\"data row6 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row6_col3\" class=\"data row6 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8level0_row7\" class=\"row_heading level0 row7\" >7</th> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row7_col0\" class=\"data row7 col0\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row7_col1\" class=\"data row7 col1\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row7_col2\" class=\"data row7 col2\" ></td> \n",
       "        <td id=\"T_324c455a_af7a_11e9_8b97_b4b52fd97ec8row7_col3\" class=\"data row7 col3\" >1</td> \n",
       "    </tr></tbody> \n",
       "</table> "
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x21829e27358>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Component table\n",
    "#Pad zeros so indices match those of SU\n",
    "cap_table = np.array([0])\n",
    "cap_table = np.append(cap_table, cap_array)\n",
    "cap_table = np.append(cap_table, 0)\n",
    "\n",
    "ind_table = np.array([0])\n",
    "ind_table = np.append(ind_table, ind_array)\n",
    "ind_table = np.append(ind_table, 0)\n",
    "\n",
    "omega_table = np.array([0])\n",
    "omega_table = np.append(omega_table, omega_array)\n",
    "omega_table = np.append(omega_table, 0)\n",
    "\n",
    "terms_table = np.array(terms[0])\n",
    "terms_table = np.append(terms_table, np.zeros(n))\n",
    "terms_table = np.append(terms_table, terms[1])\n",
    "\n",
    "data = [cap_table, ind_table, omega_table, terms_table] \n",
    "df = pd.DataFrame(data, columns = np.arange(0, n+2), index = ['$C$','$L$','${\\Omega}$','${R}$'])\n",
    "df.replace(0, '', inplace = True)\n",
    "df = df.T\n",
    "df.style\n",
    "#print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
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