crystal-calc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crystal Calc\n",
    "A collection of tools to make an engineer's life easier\n",
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "parallel = lambda a,b : (a*b)/(a+b)\n",
    "Fs  = lambda cm,lm       : 1 / (2 * np.pi * np.sqrt(lm * cm))\n",
    "Fa  = lambda fs,c0,cm    : fs * np.sqrt(1 + cm / c0)\n",
    "Ts  = lambda cm,c0,cl    : -( cm / ( 2 * ( c0 + cl )**2 ) )*1e-6\n",
    "Q   = lambda rm,lm,cm    : (1 / rm) * np.sqrt(lm / cm)\n",
    "Esr = lambda rm,c0,cl    : rm * (1 + c0 / cl)**2\n",
    "\n",
    "def Fl(fs,c0,cm,cl):\n",
    "    \"\"\"\n",
    "    Calculates the crystal frequency given a load and\n",
    "    the its equivalent spice parameters.\n",
    "\n",
    "    Parameters:\n",
    "        fs : Series resonant frequency in Hz\n",
    "        c0 : Shunt capacitance usually in pF (ex. 1.2e-12)\n",
    "        cm : Motional capacitance also known as c1 \n",
    "             usually in fF (ex. 2.4e-15)\n",
    "        cl : Plating load usually specified in the datasheet\n",
    "             usually in pF (ex. AB07-120-32.768kHz is 6pF == 6e-12)\n",
    "\n",
    "    Returns:\n",
    "        fl : The calculated crystal frequency\n",
    "        \n",
    "    \"\"\"\n",
    "    return fs * (1 + cm / (2 * (c0 + cl)))\n",
    "\n",
    "def power_predict(rm, fl, cl, c0, vout_peak):\n",
    "    \"\"\"\n",
    "    Predicts the drive level of an oscillator configuration \n",
    "    based on the Intel App Note AP-155.\n",
    "    \n",
    "    Parameters:\n",
    "        rm : Motional resistance (approximately ESR)\n",
    "        fl : Crystal resonant frequency in Hz\n",
    "        cl : Approximate plating load the crystal sees\n",
    "        c0 : Shunt capacitance of the crystal usually\n",
    "             in pF (ex. 1.2e-12)\n",
    "        vout_peak : This is the peak voltage seen on the output\n",
    "                    of the oscillator usually marked as xtal_out\n",
    "                    in the IC datasheet\n",
    "                    \n",
    "    Returns:\n",
    "        A power prediction in watts.\n",
    "    \"\"\"\n",
    "    return 2 * rm * (np.pi * fl * (cl + c0) * vout_peak)**2\n",
    "\n",
    "def find_cl(fs,c1,c0,fl):\n",
    "    \"\"\"Determines the plating load apparent to the crystal\"\"\"\n",
    "    return -c0 + c1 / (2 * (-1 + fl/fs))\n",
    "\n",
    "def hz2ppm(f, fnom):\n",
    "    \"\"\"Convertst a frequency deviation to ppm\"\"\"\n",
    "    return (f - fnom) * 1e6 / fnom\n",
    "\n",
    "def ppm2hz(ppm, f_nominal_hz):\n",
    "    \"\"\"Converts ppm to Hz\"\"\"\n",
    "    return f_nominal_hz + ppm * f_nominal_hz / 1e6\n",
    "\n",
    "def rms(peak2peak):\n",
    "    \"\"\"Calculates the rms value of the peak-to-peak measurement.\"\"\"\n",
    "    return peak2peak / (2 * np.sqrt(2))\n",
    "\n",
    "def Z(f,rm,cm,lm,c0):\n",
    "    \"\"\"Determines the impedance of a crystal at a certain frequency.\"\"\" \n",
    "    w = 2 * np.pi * f\n",
    "    return  parallel((rm + 1/(cm*w) + lm*w) , (1/(c0*2)))\n",
    "\n",
    "def analyze(rm,cm,lm,c0,cl):\n",
    "    \"\"\"\"\n",
    "    Displays the magnitude and phase response of a crystal\n",
    "    ~~ Not working at the moment ~~\n",
    "    \"\"\"\n",
    "    fs = Fs(cm,lm)\n",
    "    fa = Fa(fs,c0,cm)\n",
    "    fl = Fl(fs,c0,cm,cl)\n",
    "    q  = Q (rm,lm,cm)\n",
    "    \n",
    "    print(f\"fs = {fs}\")\n",
    "    print(f\"fa = {fa}\")\n",
    "    print(f\"fl = {fl}\")\n",
    "    print(f\"q  = {q }\")\n",
    "    \n",
    "    # Frequency sweep range calc\n",
    "    sweepstart = fs - 0.5*(fa-fs)\n",
    "    sweepend   = fa + 0.5*(fa-fs)\n",
    "    sweeprange = np.linspace(sweepstart, sweepend, 100000)\n",
    "    print(f\"sweep range = [{sweepstart},{sweepend}]\")\n",
    "    z = Z(sweeprange,rm,cm,lm,c0)\n",
    "    mag = np.abs(z)\n",
    "    phase = np.angle(z)\n",
    "    \n",
    "#     plt.plot(sweeprange, mag, label='magnitude')\n",
    "#     plt.plot(sweeprange, phase, label='phase')\n",
    "#     plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scrapbook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current config\n",
      "F Current  = -53.71Hz\n",
      "Nominal DL = 33.46nW\n",
      "Max DL     = 34.06nW\n",
      "\n",
      "Worst Case\n",
      "F Current  = 1.04ppm\n",
      "Nominal DL = 24.73nW\n",
      "Max DL     = 25.17nW\n"
     ]
    }
   ],
   "source": [
    "fl = ppm2hz(2.41, 32768)\n",
    "fs = 32755.2452844868\n",
    "rm = 44213.21\n",
    "rm_max = 45e3\n",
    "cm = 6.67597348377331e-15\n",
    "c0 = 1.5194505369094e-12\n",
    "fmeas = 32766.24\n",
    "vout_peak = 0.4249 * np.sqrt(2)\n",
    "vin_peak  = 0.1852 * np.sqrt(2)\n",
    "cl_recommended = 7.03e-12\n",
    "fcur = hz2ppm(fmeas, 32768)\n",
    "measured_load = find_cl(fs, cm, c0, fmeas)\n",
    "\n",
    "pnw = power_predict(rm, fl, measured_load, c0, vout_peak) * 1e9\n",
    "pnw_max = power_predict(rm_max, fl, measured_load, c0, vout_peak) * 1e9\n",
    "\n",
    "fl_recommended = Fl(fs, c0, cm, cl_recommended)\n",
    "fl_ppm_recommended = hz2ppm(fl_recommended, 32768)\n",
    "cl_recommended = find_cl(fs, cm, c0, fl_recommended)\n",
    "pnw_recommended = power_predict(rm, fl_recommended, cl_recommended, c0, vout_peak) * 1e9\n",
    "pnw_max_recommended = power_predict(rm_max, fl_recommended, cl_recommended, c0, vout_peak) * 1e9\n",
    "\n",
    "print(\"Current config\")\n",
    "print(f\"F Current  = {fcur:.2f}Hz\")\n",
    "print(f\"Nominal DL = {pnw:.2f}nW\")\n",
    "print(f\"Max DL     = {pnw_max:.2f}nW\")\n",
    "print(f\"\\nWorst Case\")\n",
    "print(f\"F Current  = {fl_ppm_recommended:.2f}ppm\")\n",
    "print(f\"Nominal DL = {pnw_recommended:.2f}nW\")\n",
    "print(f\"Max DL     = {pnw_max_recommended:.2f}nW\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load to Freq Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FL:  32767.82\tppm:  -5.58\t@ 4.00pF\n",
      "FL:  32768.53\tppm:  16.15\t@ 3.75pF\n",
      "ΔFL: 0.71\tΔppm: 21.74\n",
      "Ts:  -82.73ppm/pF \n"
     ]
    }
   ],
   "source": [
    "fnom = 32768\n",
    "fs = None\n",
    "c0 = 1.11226379050365e-12\n",
    "cm = 4.3243121440552e-15\n",
    "cl = 4e-12\n",
    "cl_predict = 3.75e-12\n",
    "lm = 5460.03575083361\n",
    "rm = 0\n",
    "fs = Fs(cm, lm) \n",
    "\n",
    "fl = Fl(fs, c0, cm, cl)\n",
    "ppm = hz2ppm(fl, fnom)\n",
    "fl_predict = Fl(fs, c0, cm, cl_predict)\n",
    "ppm_predict = hz2ppm(fl_predict, fnom)\n",
    "\n",
    "print(f\"FL:  {fl:.2f}\\tppm:  {ppm:.2f}\\t@ {cl*1e12:.2f}pF\")\n",
    "print(f\"FL:  {fl_predict:.2f}\\tppm:  {ppm_predict:.2f}\\t@ {cl_predict*1e12:.2f}pF\")\n",
    "print(f\"ΔFL: {fl_predict - fl:.2f}\\tΔppm: {ppm_predict - ppm:.2f}\")\n",
    "print(f\"Ts:  {Ts(cm,c0,cl):.2f}ppm/pF \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Drive Level Estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rm   = 48214.91Ω\n",
      "C0   = 1.34pF\n",
      "CL   = 2.00pF\n",
      "ESR  = 134700.17Ω\n",
      "Ipp  = 36.01mA\n",
      "Irms = 12.73mA\n",
      "Prms = 21838402.85uW\n"
     ]
    }
   ],
   "source": [
    "# Crystal parameters\n",
    "rm = 48214.91\n",
    "c0 = 1.3429e-12\n",
    "cl = 2e-12 # Estimate\n",
    "\n",
    "# Current probe parameters\n",
    "Vcspp = 180.07e-3\n",
    "v2i = 1/5\n",
    "\n",
    "esr  = Esr(rm,c0,cl)\n",
    "i    = Vcspp * v2i\n",
    "irms = rms(i)\n",
    "p    = esr * irms**2\n",
    "\n",
    "print(f\"Rm   = {rm:.2f}Ω\")\n",
    "print(f\"C0   = {c0 * 1e12:.2f}pF\")\n",
    "print(f\"CL   = {cl * 1e12:.2f}pF\")\n",
    "print(f\"ESR  = {esr:.2f}Ω\")\n",
    "print(f\"Ipp  = {i*1e3:.2f}mA\")\n",
    "print(f\"Irms = {irms*1e3:.2f}mA\")\n",
    "print(f\"Prms = {p*1e6:.2f}uW\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fs = 32753.964260242337\n",
      "fa = 32806.65788045124\n",
      "fl = 32775.14921423685\n",
      "q  = 23305.469964983185\n",
      "sweep range = [32727.617450137885,32833.00469055569]\n",
      "FL ppm = 19.0625\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "analyze(rm,cm,lm,c0,cl)\n",
    "clsweep = np.linspace(12e-12,25e-12, 1000)\n",
    "fl = Fl(fs, c0, cm, clsweep)\n",
    "ppm = hz2ppm(fl, 32e6)\n",
    "plt.plot(ppm+110, clsweep*1e12)\n",
    "plt.xlabel('FL (ppm)')\n",
    "plt.ylabel('CL (pF)')\n",
    "plt.title('ABM3B 16MHz')\n",
    "plt.grid(alpha=0.5)\n",
    "\n",
    "print(f\"FL ppm = {hz2ppm(32000610, 32e6)}\")"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}