su_cauer_type_b.ipynb

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    "## Synthesis example for _EVEN_ order elliptic lowpass filters with _UNEQUAL_ 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 b\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 ${b}_{v,P}$, ${b}_{v,S}$, ${\\Delta}_{b}$, ${\\Omega}^{'}_{c}$, and ${\\Omega}_{s}$\n",
    "Once ${a}_{v}$ are found, calculate the following:\n",
    "\n",
    "${b}_{v,P} = \\displaystyle \\sqrt{\\frac{\\omega}{{a}_{v}^{-2} - {a}_{1}^{2}} }\\;\\;\\;\\;\\;\\;v=1,\\;2,\\;...,\\;n-1$  \n",
    "  \n",
    "${b}_{v,S} = \\displaystyle \\sqrt{\\frac{{a}_{v}^{2} - {a}_{1}^{2}}{\\omega} }\\;\\;\\;\\;\\;\\;v=1,\\;2,\\;...,\\;n-1$ \n",
    "  \n",
    "${\\omega} =\\displaystyle \\sqrt{(1 - {a}_{1}^{2}{a}_{n}^{2}) \\left(1 - \\displaystyle \\frac{{a}_{1}^{2}} {{a}_{n}^{2}}\\right)}$\n",
    "\n",
    "${\\Omega}^{'}_{c} = {b}_{n} = \\sqrt{{a}_{n} \\cdot {a}_{n-1}}$ \n",
    "  \n",
    "${\\Omega}_{s} = \\displaystyle \\frac{1}{({\\Omega}^{'}_{c})^{2}}$ \n",
    "\n",
    "See _equation (44)_ on pages 295-296.   \n"
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    "#EQN(44) for n even case b page 295-296\n",
    "w = np.sqrt((1-(a[1]**2)*(a[n]**2))*(1-(a[1]/a[n])**2))\n",
    "    \n",
    "bP = np.array([1])\n",
    "bS = np.array([1])\n",
    "for v in range(1, n):\n",
    "    bP = np.append(bP, np.sqrt(w/(a[v]**-2 - a[1]**2)))\n",
    "    bS = np.append(bS, np.sqrt((a[v]**2 - a[1]**2)/w))\n",
    "\n",
    "bn = np.sqrt(a[n]*a[n-1])\n",
    "\n",
    "wc_pb = bn\n",
    "ws = 1/wc_pb**2\n",
    "\n",
    "#print(bP[1:])\n",
    "#print(bS[1:])\n",
    "#print(bn)\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 ${\\Delta}_{b}$ using _equation (44)_ on page 296.\n",
    "\n",
    "${\\Delta}_{b} = \\displaystyle \\prod_{{\\mu} = 1}^{m} {b}^{2}_{2{\\mu} - 1,P}$"
   ]
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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_b = 1\n",
    "for u in range(1, m+1):\n",
    "    delta_b *= bP[2*u-1]**2    \n",
    "\n",
    "#print(delta_b)"
   ]
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    "___"
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    "### Calculate ${\\Delta}_{a}$ and ${A}_{s}$\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",
    "${A}_{s} = 10\\log_{10} \\displaystyle \\left[1+\\frac{1}{\\Delta^{4}_{a}({\\rho}^{-2}-1)}\\right]$  \n",
    "  \n",
    "${\\Delta}_{a} = \\displaystyle \\prod_{{\\mu} = 1}^{m} {a}^{2}_{2{\\mu} - 1}$"
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    "#See EQN(39) page 294 for delta_a even.\n",
    "delta_a = 1\n",
    "for u in range(1, m+1):\n",
    "    delta_a *= a[2*u-1]**2\n",
    "\n",
    "#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 (43)_ on page 295.  \n",
    "\n",
    "$K({\\lambda}) = \\displaystyle \\frac{{\\lambda} + {b}^{2}_{1,P}}{{c}^{-1}} \\cdot \\prod_{{\\mu} = 2}^{m} \\displaystyle \\frac{{\\lambda}^{2}+{{b}^{2}_{2{\\mu}-1,P}}} {{b}^{2}_{2{\\mu}-1,S} \\cdot {\\lambda}^{2}+1}$\n",
    "\n",
    "\n",
    "${c}^{-1} = {\\Delta}_{b}\\sqrt{{\\rho}^{-1} - 1}$\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 304\n",
    "const_c = 1/(delta_b*np.sqrt(1/(p**2)-1))\n",
    "\n",
    "#EQN(43) expand for n even\n",
    "F = np.array([1, 0, (bP[1]**2)])\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, bP[2*u-1]**2]))\n",
    "        \n",
    "    #form denominator of K(lambda) or P(lambda)\n",
    "    P = np.polymul(P, np.array([bS[2*u-1]**2, 0, 1]))\n",
    "        \n",
    "    #collect the constants bS used in P(lambda)\n",
    "    co_tz = np.append(co_tz, bS[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_pb \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": 11,
   "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": 12,
   "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",
    "${\\Omega}_{2(\\mu -1)} = \\displaystyle \\frac{1} {{b}_{2{\\mu}-1,S}}\\;\\;\\;\\;\\;\\;{\\mu}=2,\\;3,\\;...,\\;m$\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": 13,
   "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",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 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",
    "${l}_{n} = \\displaystyle \\bigg(\\bigg[\\frac{{X}_{2O}({\\lambda})}{\\lambda}\\bigg]_{{\\lambda} = {\\infty}}\\bigg) \\cdot {R}_{2}$  \n",
    "  \n",
    "${R}_{2}$ is related to the reflection coefficient by the following:  \n",
    "\n",
    "${R}_{2} = \\displaystyle \\frac{1 - {\\rho}}{1 + {\\rho}}$\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": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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",
    "R2 = (1-p)/(1+p)\n",
    "l_srs = (X2On[0])/(X2Od[0])*R2\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_pb\n",
    "ind_array = ind_array*wc_pb\n",
    "omega_array = omega_array/wc_pb\n",
    "\n",
    "#Create termination array\n",
    "terms = np.array([1, R2])\n",
    "\n",
    "#print(cap_array)\n",
    "#print(ind_array) \n",
    "#print(omega_array)\n",
    "#print(terms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": 15,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "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])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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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": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style  type=\"text/css\" >\n",
       "</style>  \n",
       "<table id=\"T_41d60c50_af7a_11e9_b21f_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_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row0\" class=\"row_heading level0 row0\" >0</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row0_col0\" class=\"data row0 col0\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row0_col1\" class=\"data row0 col1\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row0_col2\" class=\"data row0 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row0_col3\" class=\"data row0 col3\" >1</td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row1\" class=\"row_heading level0 row1\" >1</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row1_col0\" class=\"data row1 col0\" >1.16582</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row1_col1\" class=\"data row1 col1\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row1_col2\" class=\"data row1 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row1_col3\" class=\"data row1 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row2\" class=\"row_heading level0 row2\" >2</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row2_col0\" class=\"data row2 col0\" >0.183019</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row2_col1\" class=\"data row2 col1\" >1.18137</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row2_col2\" class=\"data row2 col2\" >2.15059</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row2_col3\" class=\"data row2 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row3\" class=\"row_heading level0 row3\" >3</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row3_col0\" class=\"data row3 col0\" >1.80969</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row3_col1\" class=\"data row3 col1\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row3_col2\" class=\"data row3 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row3_col3\" class=\"data row3 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row4\" class=\"row_heading level0 row4\" >4</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row4_col0\" class=\"data row4 col0\" >0.349779</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row4_col1\" class=\"data row4 col1\" >1.10264</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row4_col2\" class=\"data row4 col2\" >1.61023</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row4_col3\" class=\"data row4 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row5\" class=\"row_heading level0 row5\" >5</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row5_col0\" class=\"data row5 col0\" >1.78467</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row5_col1\" class=\"data row5 col1\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row5_col2\" class=\"data row5 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row5_col3\" class=\"data row5 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row6\" class=\"row_heading level0 row6\" >6</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row6_col0\" class=\"data row6 col0\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row6_col1\" class=\"data row6 col1\" >0.889456</td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row6_col2\" class=\"data row6 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row6_col3\" class=\"data row6 col3\" ></td> \n",
       "    </tr>    <tr> \n",
       "        <th id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8level0_row7\" class=\"row_heading level0 row7\" >7</th> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row7_col0\" class=\"data row7 col0\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row7_col1\" class=\"data row7 col1\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row7_col2\" class=\"data row7 col2\" ></td> \n",
       "        <td id=\"T_41d60c50_af7a_11e9_b21f_b4b52fd97ec8row7_col3\" class=\"data row7 col3\" >0.666667</td> \n",
       "    </tr></tbody> \n",
       "</table> "
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x1727ec56f98>"
      ]
     },
     "execution_count": 17,
     "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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