nmr-utils/Probe.ipynb

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   "cell_type": "code",
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   "source": [
    "from numpy import *"
   ]
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  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fb15ea05",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "e0 = 8.8541878188e-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "ec2633de",
   "metadata": {},
   "outputs": [],
   "source": [
    "def capacitor(ri, ra, l, er=9):\n",
    "    C = 2*pi*er*e0*l/log(ra/ri)*1e12\n",
    "    #print(f\"{C:.2f}pF\")\n",
    "    return C*1e-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "5193496d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def capacitor_query(ri, ra, l, er=9):\n",
    "    C_min = capacitor(ri,ra,l,er=1)\n",
    "    C_mid = capacitor(ri,ra,l/2,er=1) + capacitor(ri,ra,l/2,er=er)\n",
    "    C_max = capacitor(ri,ra,l,er=er)\n",
    "    print(\"----Params----\")\n",
    "    print(f\"ri = {ri*1e3:.2f}mm\\nra = {ra*1e3:.2f}mm\\nl = {l*1e3:.2f}mm\\ner = {er:.1f}\")\n",
    "    print(\"----Result----\")\n",
    "    print(f\"C_min = {C_min*1e12:.2f}pF\")\n",
    "    print(f\"C_max = {C_max*1e12:.2f}pF\")\n",
    "    print(f\"C_mid = {C_mid*1e12:.2f}pF\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1517377f",
   "metadata": {},
   "source": [
    "Capacitor\n",
    "========\n",
    "First we need to know the capacitor and the range we have available,\n",
    "we need the inner and outer diameter $r_i$, $r_a$, length $l$, and $\\epsilon_r$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e68edb6a",
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      "----Params----\n",
      "ri = 4.00mm\n",
      "ra = 8.00mm\n",
      "l = 100.00mm\n",
      "er = 2.0\n",
      "----Result----\n",
      "C_min = 8.03pF\n",
      "C_max = 16.05pF\n",
      "C_mid = 12.04pF\n"
     ]
    }
   ],
   "source": [
    "capacitor_query(4e-3,8e-3,10e-2,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1188809f",
   "metadata": {},
   "source": [
    "Resonance frequency of an LC circuit:\n",
    "$f_0 =  \\frac{1}{2\\pi\\sqrt{LC}}$\n",
    "\n",
    "Solve for L:\n",
    "\n",
    "$L_{RF}= \\frac{1}{(2\\pi f_0)^2C}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "5ceee5f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def probe_design(f0, C_mid=12e-12):\n",
    "    L_RF = 1e6/((2*pi*f0)**2*C_mid)\n",
    "    print(f\"L_RF={L_RF:.2f}µH\") \n",
    "    L_duplex = 50/(2*pi*f0)*1e6\n",
    "    print(f\"L_duplex={L_duplex:.2f}µH\") \n",
    "    C_duplex = 1/(2*pi*f0*50)*1e12\n",
    "    print(f\"C_duplex={C_duplex:.2f}pF\") \n",
    "    \n",
    "    return L_RF*1e6\n",
    "\n",
    "def probe_range(L_RF, C_min, C_max):\n",
    "    f_min = 1/(2*pi * sqrt(C_max*L_RF))\n",
    "    f_max = 1/(2*pi * sqrt(C_min*L_RF))\n",
    "    print(f\"f_min = {f_min:.1f}MHz\\nf_max = {f_max:.1f}MHz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92577356",
   "metadata": {},
   "source": [
    "Now we can calculate the needed coil inductance for the resonance circuit. Here, we also calculate the $\\Pi$-circuit C and L paramters for the duplexer (the \"$\\lambda/4$\" lumped circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "44c4a308",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L_RF=3.37µH\n",
      "L_duplex=0.32µH\n",
      "C_duplex=127.32pF\n"
     ]
    }
   ],
   "source": [
    "L_RF = probe_design(25e6, C_mid=12.04e-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "181a4255",
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f_min = 21.7MHz\n",
      "f_max = 30.6MHz\n"
     ]
    }
   ],
   "source": [
    "probe_range(L_RF, 8e-12, 16e-12)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdecc4f3",
   "metadata": {},
   "source": [
    "Coil64\n",
    "=====\n",
    "Calculate the coil windings:\n",
    "\n",
    "Give the wire diameter, incl. isolation thickness, former diameter (5mm)\n",
    "\n",
    "Coil64 v2.2.32 - One layer close-winding coil\n",
    "\n",
    "Input:\n",
    "=====\n",
    "    Inductance L: 3.38 microH\n",
    "    Frequency f: 25 MHz\n",
    "    Former diameter D: 5 mm\n",
    "    Wire diameter d: 0.3 mm\n",
    "    Wire diameter with insulation k: 0.436 mm\n",
    "    Wire material Mt: Copper\n",
    "\n",
    "Result:\n",
    "======\n",
    "\n",
    "    Number of turns of the coil N = 56.719 \n",
    "    Length of wire without leads lw = 96.894 cm\n",
    "    Length of winding l = 25.165 mm\n",
    "    Weight of wire m = 0.614 g\n",
    "    DC resistance of the coil Rdc = 0.236 Ohm\n",
    "    Reactance of the coil X = 530.929 Ohm\n",
    "\n",
    "    Self capacitance Cs = 0.356 pF\n",
    "    Coil self-resonance frequency Fsr = 218.021 MHz\n",
    "    Coil constructive Q-factor Q = 171 \n",
    "    Loss resistance ESR = 2.67 Ohm\n",
    "\n",
    "    Additional results for parallel LC circuit at the working frequency:\n",
    "    => Circuit capacitance: Ck = 11.635 pF\n",
    "    => Characteristic impedance: ρ = 531 Ohm\n",
    "    => Equivalent resistance: Re = 77.531 kOhm\n",
    "    => Bandwidth: 3dBΔf = 171.199 kHz\n",
    "\n",
    "    Input data for LTSpice:\n",
    "    Inductance: 3.380μ\n",
    "    Series resistance: 236.334m\n",
    "    Parallel resistance: 78.065k\n",
    "    Parallel capacitance: 0.356p\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff03bfb4",
   "metadata": {},
   "outputs": [],
   "source": []
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