2016-05-23-array-resonance-spacing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Run this script to generate the data for the array\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "from scipy.constants import epsilon_0, hbar, k as k_B, pi\n",
    "from scipy.special import ellipk\n",
    "import scipy.optimize\n",
    "import pandas as pd\n",
    "import os\n",
    "import random\n",
    "\n",
    "\n",
    "def calc_caps(inductance = 16e-9, freqs=np.linspace(1e9,1.1e9,22)):\n",
    "    caps = (1/(2*np.pi*freqs)**2)/(inductance)\n",
    "    return caps\n",
    "\n",
    "def interdigitated_capacitance(epsilon_r, area, width, gap):\n",
    "    \"\"\"\n",
    "    Return the capacitance C of an interdigitated capacitor with the given surface area, tine width, and gap between\n",
    "    tines; epsilon_r is the dielectric constant of the substrate. The formula is given in Jonas's MKID design memo. Note\n",
    "    that all lengths and areas must use SI units (m and m^2) for the return value to be in farads.\n",
    "    \"\"\"\n",
    "    pitch = width + gap\n",
    "    k = np.tan(pi * width / (4 * pitch))**2\n",
    "    K = ellipk(k**2)\n",
    "    Kp = ellipk(1 - k**2)\n",
    "    C = epsilon_0 * (1 + epsilon_r) * (area / pitch) * (K / Kp)\n",
    "    return C\n",
    "\n",
    "\n",
    "def calc_idc_area(capacitance, epsilon_r, width, gap):\n",
    "    def objective(area):\n",
    "        return interdigitated_capacitance(epsilon_r,area,width,gap) - capacitance\n",
    "    return scipy.optimize.fsolve(objective,x0=100e-6*100e-6)\n",
    "\n",
    "def calc_cap_lengths_from_cap(caps,width=8e-6,gap=8e-6,cap_width=500e-6):\n",
    "    areas = []\n",
    "    for cap in caps:\n",
    "        areas.append(calc_idc_area(cap,epsilon_r=11.9,width=width,gap=gap))\n",
    "    areas = np.array(areas)\n",
    "    lengths = areas/cap_width\n",
    "    return lengths\n",
    "\n",
    "def calc_cap_lengths(inductance,freqs,width=8e-6,gap=8e-6,cap_width=500e-6):\n",
    "    caps = calc_caps(inductance,freqs)\n",
    "    if np.isscalar(gap):\n",
    "        gap = gap*np.ones(freqs.shape)\n",
    "    if np.isscalar(width):\n",
    "        width = width*np.ones(freqs.shape)\n",
    "    areas = []\n",
    "    for (cap,this_gap,this_width) in zip(caps,gap,width):\n",
    "        areas.append(calc_idc_area(cap,epsilon_r=11.9,width=this_width,gap=this_gap))\n",
    "    areas = np.array(areas).squeeze()\n",
    "    print areas.shape\n",
    "    lengths = areas/cap_width\n",
    "    return lengths\n",
    "\n",
    "def geometric_spacing(low,high,num):\n",
    "    return low*(high/low)**(np.arange(num,dtype='float')/(num-1))\n",
    "\n",
    "def uniform_length_spacing(low,high,num):\n",
    "    lengths = np.linspace(1/np.sqrt(high), 1/np.sqrt(low), num)\n",
    "    return lengths[::-1]**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f_low = 122.e6\n",
    "f_hi = 155e6\n",
    "freqs_b = uniform_length_spacing(f_low,f_hi,9)\n",
    "freqs_a = uniform_length_spacing(160e6,200e6,9)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.60000000e+08,   1.64308000e+08,   1.68792361e+08,\n",
       "         1.73462842e+08,   1.78329888e+08,   1.83404685e+08,\n",
       "         1.88699229e+08,   1.94226390e+08,   2.00000000e+08])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs_a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.22000000e+08,   1.25515042e+08,   1.29184215e+08,\n",
       "         1.33016662e+08,   1.37022216e+08,   1.41211463e+08,\n",
       "         1.45595808e+08,   1.50187556e+08,   1.55000000e+08])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 120.20862524,  113.57002914,  107.21027068,  101.12143042,\n",
       "         95.29570299,   89.72539712,   84.40293565,   79.32085548,\n",
       "         74.47180762])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_cap_lengths(33.5e-9,freqs_b,cap_width=7400.e-6)/16e-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9,)\n"
     ]
    }
   ],
   "source": [
    "turns_a = np.floor(calc_cap_lengths(19e-9,freqs_a,cap_width=7400.e-6)/16e-6).astype('int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9,)\n"
     ]
    }
   ],
   "source": [
    "turns_b = np.floor(calc_cap_lengths(33.5e-9,freqs_b,cap_width=7400.e-6)/16e-6).astype('int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([120, 113, 107, 101,  95,  89,  84,  79,  74])"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "turns_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([123, 116, 110, 104,  99,  93,  88,  83,  78])"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "turns_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lengths = 7400 - np.arange(np.ceil(256/8.))*11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "areas_a = np.outer(turns_a,lengths)*1e-6*16e-6\n",
    "areas_b = np.outer(turns_b,lengths)*1e-6*16e-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "caps_a = interdigitated_capacitance(11.9,area=areas_a,width=8e-6,gap=8e-6)\n",
    "caps_b = interdigitated_capacitance(11.9,area=areas_b,width=8e-6,gap=8e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_freq_a = 1/(2*np.pi*np.sqrt(caps_a*19e-9))\n",
    "actual_freq_b = 1/(2*np.pi*np.sqrt(caps_b*33.5e-9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1000000.0)"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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KZGLCBY46zhgz55KPLOcSw2+knXOZOhXGxmB8vNw6TSZMXDxQ54R++tY3MfSSyyTmnIsl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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ab2be0d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(actual_freq_a.flatten()[:-1]/1e6,np.diff(actual_freq_a.flatten()),'.-')\n",
    "ylim(0,1e6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2ab337ea90>]"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NHYvl2bNn1/R53VWDZX/pidkk4KvAFHd/s2y/BcB0MxtoZqOAMcAyd98EvGxm47OTzGcA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\nGVP3AAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ab2ba5e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(actual_freq_a.flatten()[:-1]/np.diff(actual_freq_a.flatten()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1000000.0)"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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88yksFp5LMFSsq8WsPBfrsFgVV+h7WeeS2eJRXKzDYr0SnkswdNrtLVbWCmgr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\nUhD0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ab2fb5550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(actual_freq_b.flatten()[:-1]/1e6,np.diff(actual_freq_b.flatten()),'.-')\n",
    "ylim(0,1e6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2ab2a29cd0>]"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A3iBSS3pKetRmwKp6FHylQBSEAtQCRenL7dQGtWrxVtKjEjtqkwk1X5VNFIQC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\nN7NSBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ab305b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(actual_freq_b.flatten()[:-1]/np.diff(actual_freq_b.flatten()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2ab28ad190>]"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Y2atmNiPTvmGZ9xPRPgAz28bMppvZE5nXSWrbO2b2eub791rmvSS1r5WZ/S0T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\nOCV6EZGEU6IXEUm4/w9/BZ81lAerrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ab299bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(np.hstack((actual_freq_b.flatten(),actual_freq_a.flatten())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 32)"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "actual_freq_a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7400.,  7389.,  7378.,  7367.,  7356.,  7345.,  7334.,  7323.,\n",
       "        7312.,  7301.,  7290.,  7279.,  7268.,  7257.,  7246.,  7235.,\n",
       "        7224.,  7213.,  7202.,  7191.,  7180.,  7169.,  7158.,  7147.,\n",
       "        7136.,  7125.,  7114.,  7103.,  7092.,  7081.,  7070.,  7059.])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([123, 116, 110, 104,  99,  93,  88,  83,  78])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "turns_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "288"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.product(actual_freq_a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.01024586,  0.00971563,  0.00920625,  0.00871717,  0.00824783,\n",
       "        0.00779772,  0.00736628,  0.00695299,  0.00655735])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_cap_lengths(19e-9,freqs_a,cap_width=89*16e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 55.875,  55.875,  55.875,  55.875,  55.875,  55.875,  55.875,\n",
       "        55.875])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diff(np.linspace(6953,7400,9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "turns = np.floor()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}