{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "**Overview**:
\n", "A Real-Time sampling oscilloscope is designed to capture time-domain phenomena but the combination of an extremely accurate timebase and Fast Fourier Transforms can make them very useful at measuring frequency domain phenomena.
\n", "Phase Noise is traditionally measured using a frequency domain instrument such as a Spectrum Analyzer or specialised Signal Source Analyzer. While these frequency domain instruments typically have high dynamic range there are limitations to their measurement capability in terms of the offset frequency they are capable of measuring to or the fact they are unable to measure the phase noise of a non-clock signal.
\n", "
\n", "This note will explain how to measure the phase noise of a clock or data signal using an Agilent Infiniium real-time sampling oscilloscope using a tool called Infiniium Phase Noise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First a bit of background on Phase Modulation PM.
\n", "Although phase noise refers to the uncorrelated portion of the phase modulation it is informative to take the simple example of sinusoidal phase modulation to build our intuition first.
\n", "
\n", "$$y(t) = sin(\\omega_c t + \\phi(t))$$\n", "\n", "\n", "
\n", "We can simulate the spectra of some simple signals and then confirm with some measurements." ] }, { "cell_type": "code", "collapsed": false, "input": [ "f_c = 1e9 # The carrier frequency 1GHz\n", "sa_rate = 80e9 # Sample rate 80GSa/s\n", "mem_depth = 2**21 # Number of samples to take ~ 2 million (a power of 2 makes fft's simpler)\n", "t = linspace(0,mem_depth/sa_rate,mem_depth) # Create the time sample array\n", "\n", "def plot_wfm_spectrum(t,dt,f_c,beta,f_m):\n", " \"\"\"Since we'll create a few plots of similar waveforms let's not duplicate our work\"\"\"\n", " v = sin(2*pi*f_c*t + beta*cos(2*pi*f_m*t))\n", " window = hanning(mem_depth)\n", " v_windowed=v*window # Apply a Hanning window to improve the spectrum\n", " v_spec = fft.fft(v_windowed)\n", " freqs = fft.fftfreq(mem_depth, 1/sa_rate)\n", " dfreqs = freqs[1]\n", " f_freq_idx = round(f/dfreqs)\n", " span = 10*f_mod\n", " f_min_idx = int(f_freq_idx - span/(2*dfreqs))\n", " f_max_idx = int(f_freq_idx + span/(2*dfreqs))\n", " psd_v_spec = 20*log10(2*sqrt(2)*abs(v_spec)/(len(v)*0.2236))\n", " plot(freqs[f_min_idx:f_max_idx],psd_v_spec[f_min_idx:f_max_idx])\n", " f_c_idx = round(f_c/dfreqs)\n", " annotate(\"{:.2f}\".format(psd_v_spec[f_c_idx]),(freqs[f_c_idx],psd_v_spec[f_c_idx]))\n", " f_m_idx = round((f_c+f_m)/dfreqs)\n", " annotate(\"{:.2f}\".format(psd_v_spec[f_m_idx]),(freqs[f_m_idx],psd_v_spec[f_m_idx])) \n", " grid(1)\n", "\n", "# First let's look at the spectrum of the carrier with no modulation\n", "beta = 0 # Phase Modulation, PM\n", "f_m = 1e6\n", "plot_wfm_spectrum(t,dt,f_c,beta,f_m)\n", "grid(1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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5BF2ukVcIC+zYoSfBXc7NN+t5ECdOQL165sclhDsZ3gcRGRnJgQMHyM3NJTc3l+DgYDZt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\n+FNPPUXPnj1L7Rs2bBgzZ84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"text": [ "" ] } ], "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's add some sinusoidal Phase Modulation @ 1MHz\n", "f_m = 1e6\n", "figure(figsize = (16,5))\n", "subplot(1,3,1)\n", "beta = 0.0001\n", "title(r\"$\\beta$ = %.4f\" %beta)\n", "plot_wfm_spectrum(t,dt,f_c,beta,f_m)\n", "subplot(1,3,2)\n", "beta = 0.001\n", "title(r\"$\\beta$ = %.4f\" %beta)\n", "plot_wfm_spectrum(t,dt,f_c,beta,f_m)\n", "subplot(1,3,3)\n", "beta = 0.01\n", "title(r\"$\\beta$ = %.4f\" %beta)\n", "plot_wfm_spectrum(t,dt,f_c,beta,f_m)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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VagNrHenx88/A8OHA/Pni759/lp2IrED5NbZdu3ZFWloaMjIyUFBQgIULF2Lw4MH+jkEW\nx7UYpDrWOtKDtY5Ux1pHerDWkT/4vWMbHByMt956C/3790dUVBQeeOCBUjvnqcg5xK4CVbI6C+CB\nA1yLYSbV8qqEtU4uVbI6a11qKmudmVTLqxLWOvlUyOusdSkprHVmUi2v0fy+xhYABg4ciIEDB8p4\na1IEr+1IdsBaR1VhrSM7YK2jqrDWkT/4fY2tHlyLQc88AzRuDHTpAsyYAaxeLTsRyWbHumDHz0Se\nmTVLXMv20UeBe+8F9u6VnYiswG61wW6fhzz35ZfAggXAhx8CERHAmTOyE5EVKL/GlkiPS5fEOgyu\nxSAiO2OtI6JAwFpH/sCOrQFUms+uStaCAlH89uxJUmrKiirfr5NqeUkuldqLKlmdtS45mbXOTKrl\nJblUay8q5HV2bDdsSEJhIVBUJDuRPip8t65Uy2s0dmzJki5dEuswqlfnL3tEZF+sdUQUCAoKRJ1z\nOEQHV6Uf8kgdXGNLljR8OHD77UC3bsCgQUBamuxEJJsd64IdPxN5xrmfwJ//DISHiw1WiOxWG+z2\nechzs2cDBw+Kvxs0EP9u0EB2KpKNa2wpIDin53EtBhHZWdlax3N/IrIj51RkgOd2ZB52bA2g0nx2\nVbI6p+dt3851Z2ZSLS/JpVJ7USWrs9atX5+EatWAwkLZifRR5ft1Ui0vyaVae1Ehr3MqclJSEmrW\nVGcqsgrfrSvV8hqNHVuyJOcve1x3RkR25jqKUbMm6x0R2RNrHfkD19iSJcXHAy+8ANx0E1C3rvil\njwKbHeuCHT8TeWbECLGPwIgRYo3t3r1izS0FNrvVBrt9HvLclCmixk2ZAsTEAB9/DHTuLDsVycY1\nthQQXHcKvXxZnW3hiYg84ax1AEcxiMi+nFORAdY6Mg87tgZQaT67KlmdU1Z++IFrMcykWl6SS6X2\nokpWZ63jujNzqZaX5FKtvaiQl7XOP1TLazR2bMmSnDuFAvxlj4jsi7WOiAIB19iSP3CNLVlS27bA\nt98C7doBzZoBKSnAVVfJTkUy2bEu2PEzkWfi44Hp04FevYAbbgDmzgW6dpWdimSzW22w2+chz/3x\nj8CAAeLvwYOBRx4B7rpLdiqSjWtsKSDwlz0iCgSsdUQUCFjryB/YsTWASvPZVcnK6535h2p5SS6V\n2osqWVnr/EO1vCSXau1FhbzOjfJY68ylWl6jsWNLlsRf9ogoELDWEVEgYK0jf+AaW7Kk2rWB48eB\n0FCge3dg9mygRw/ZqUgmO9YFO34m8ozrfgL33iuuZztkiOxUJJvdaoPdPg95rlcv4P/+T/w9aZKo\nfY8/LjsVycY1thQQyl7vTJUpK0REnmCtI6JAUPaa3ax1ZAZ2bA2g0nx2FbJeuQIUFQHBwSVrMVSZ\nsqLC9+tKtbwkl0rtRZWsZa/tyFpnDtXyklyqtRcV8rLW+YdqeY3Gji1ZjrP4ORzido0a6hRAIiJP\nuK47Y60jIrtyvWY3ax2ZhWtsyXJyc4GWLYG8PHF76FCx5uyBB+TmIrnsWBfs+JnIM6GhQE4OUKcO\nMHky0KIF8NRTslORbHarDXb7POS5du2AZcuA664DZs4EjhwB/vUv2alINq6xJdtzHcEAuBaDiOyr\n7E6hrHVEZEesdeQP7NgaQKX57CpkdS1+XIthLtXyklwqtRcVsnI/Af9RLS/JpVp7USGvcyoya525\nVMtrNHZsyXJcdwkFuBaDiOzJWeu4nwAR2Z3rrsisdWQWrrEly9mzB7j/fiA1Vdx+5hmgcWNgyhS5\nuUguO9YFO34m0q/sfgKzZgHp6eK63RTY7FYb7PZ5yHOu+wl88QWwcCHw5ZeyU5FsXGNLtsc1tkQU\nCFjriChQuO6KzFpHZjGlY/vMM8+gQ4cOiImJwb333os858/RABISEtC2bVu0b98eq1atMuPt/U6l\n+ewqZHWdisy1GOZSLa/VsNZZlwpZWev8R7W8VsNaZ21Wz1tUJPYU4H4C5lMtr9FM6dj269cPe/bs\nwc6dO9GuXTskJCQAAFJTU7Fw4UKkpqYiMTEREyZMQFFRkRkRSGFlRzG4FoOsirWOfMFaR6pgrSNf\nONfXcj8BMpspHdu+ffsiKEgcunv37sjMzAQALFmyBMOGDUNISAgiIyPRpk0bbNmyxYwIfhUfHy87\ngm4qZHU92YuPj1fqlz0Vvl9XquW1GtY661IhK2ud/6iW12pY66zN6nldpyGz1plLtbxGM32N7Ycf\nfohBgwYBALKzsxEREVH8WEREBLKyssyOQIopuysy12KQCljryFOsdaQi1jrylOuOyABrHZkn2NsX\n9u3bF0ePHi13/8svv4w777wTAPDSSy+hevXqGD58eIXHcTjnJZQxatQoREZGAgDCwsLQuXPn4l8h\nnPPHrXJ71qxZls7nett17r0V8ri7nZychDNnAEDkPXgQ+O03cdsK+VT/flXJ6/x3RkYGZGKtY60z\n6/bGjUm/n9yJvHv3AqKpWSOf6t+vSnmTkpIwb948ACiuB/7GWqdmrVMpr7PWHT4MnDolblspn4q1\nQ7W8ptc6zSQfffSRdvPNN2sXLlwovi8hIUFLSEgovt2/f39t06ZN5V5rYixTrF27VnYE3VTI+t//\natqDD4p/r127Vlu0SNOGDJGbSS8Vvl9XKuW1al1grbMmFbImJWnaLbeIf69du1b76SdN69FDbia9\nVPh+XamW14q1gbXOuqyeNy1N01q3Fv9eu3atlpGhaS1ayM2kl9W/27JUy2t0bTDlOraJiYn4y1/+\ngh9++AHh4eHF96empmL48OHYsmULsrKy0KdPH+zfv7/cr3u83llg+/BDYN064PcfdLBsGfDuu+Jv\nClxWrAusdeSLlSuBmTOB774Tt5OTgbFjxd8U2KxWG1jryBe7dwNDhwKpqeJ2Tg5w/fXibwpsRtcG\nr6ciV2bSpEkoKChA3759AQA33XQT5syZg6ioKAwdOhRRUVEIDg7GnDlzKpyyQoHr3Dmgbt2S2ypt\nMkCBhbWOfMFaR6pgrSNfsNaRv5gyYusr1X7ZS0pKKp5HbnUqZH35ZeDsWSAhQeQNCorH3/4GrF8v\nO1nVVPh+XamUV7W6oIdqn0ml9qJC1o8/Br7/HvjkE5G3RYt49O0LHDwoO1nVVPh+XamWV7XaUBXV\nPo9q7cXqeVevFud0338vsvboEY/69dXYQMrq321ZquU1ujYEGXYkIoPwlz0iCgSsdUQUCMrWuho1\nxK7wvOQxGY0jtmQ5kyYBbdsCjz8ubu/ZA9x/f8naDApMdqwLdvxMpN+MGcDp08Arr4jbublAy5ZA\nXp7cXCSf3WqD3T4PeebTT8WeAp99VnJfaKhYY1unjrxcJB9HbMn2zp0rXejq1hVTk4mI7KRsratT\nR9zH838ispOytQ7guR2Zgx1bA7heM8rqVMh69mzJlJWkpCTUrYvfr2trfSp8v65Uy0tyqdReVMha\nttYFB4speufPy82lhwrfryvV8pJcqrUXq+ctW+sAKHNuZ/XvtizV8hqNHVuyHHcjthzFICK7cTeK\nUa8eRzGIyF5Y68hfuMaWLOcPfxBrznr2LLmvdm3g+HGxJoMCkx3rgh0/E+k3dCgwZAjwwAMl97Vt\nC3z7LdCunbxcJJ/daoPdPg95ZvJkoEUL4KmnSu6LjwemTwd69ZIWiyyAa2zJ9ipai6HClBUiIr1Y\n64goELDWkb+wY2sAleazq5DVtQA686oyZUWF79eVanlJLpXaiwpZWev8R7W8JJdq7cXqeVnr/Ee1\nvEZjx5Ysx3WTASfunkdEdsNaR0SBgLWO/IVrbMly3K2njYsDXniBazECmR3rgh0/E+nnbj3t8OHA\noEHAH/8oLxfJZ7faYLfPQ55xt572mWeA8HBg6lRpscgCuMaWbK2wELh0SXRuXakyZYWISC93oxis\ndURkN6x15C/s2BpApfnsVs96/rwYqXU4xG3X652pUACt/v2WpVpekkul9qJCVnfrzljrzKFaXpJL\ntfZi9bysdf6jWl6jsWNLluJu5zyAu+cRkb0UFQH5+eUvYcZaR0R2w12RyV+4xpYs5ZdfgLvuAn79\ntfT9zzwDNG4MTJkiJxfJZ8e6YMfPRPqcPQtcdZU44XM1axaQng7Mni0nF1mD3WqD3T4PeaZePeDw\nYaB+/ZL7vvgCWLgQ+PJLeblIPq6xJVs7e7biEVsVpqwQEenBWkdEgaCoqGSZmSvWOjIDO7YGUGk+\nu9Wznj4NNGhQctt1LYYKU1as/v2WpVpekkul9mL1rKx1/qVaXpJLtfZi5bxnzohObXCwuM1aZy7V\n8hqNHVuylLIne078ZY+I7IS1jogCgaxat2TJEsTExCA2NhY33HAD1qxZU/xYbm4u7rvvPnTo0AFR\nUVHYtGlTudfPnDkTsbGxGDduHKKjoxEcHIzc3FwAwOzZsxEdHY1OnTphNteNWArX2JKlvPMOkJIC\nzJ1b+v4vvwTmzwe+/lpOLpLPjnXBjp+J9Fm2TNS55ctL379xI/Dkk8DmzXJykTXYrTbY7fOQfsnJ\nwCOPiHM7V4cOATffDGRmmvO+58+fR+jv859//vln3HPPPdi/fz8AYOTIkYiLi8OYMWNQWFiI8+fP\no77rAuAyli9fjlmzZmH16tXYvXs3hg0bhq1btyIkJAQDBgzAO++8g2uvvdacD2JzXGNLtnbqlPtf\n9ho1Eo8REdkBax0RBQJZtS7UZVHvuXPnEB4eDgDIy8vD+vXrMWbMGABAcHBwpZ1aAJg/fz6GDRsG\nANi7dy+6d++OmjVrolq1aoiLi8PXHHWxDHZsDaDSfHarZz19GmjYsOS2M2/Dhmqc7Fn9+y1Ltbwk\nl0rtxepZWev8S7W8JJdq7cXKeSuqdbVrA1euABcumPfeixcvRocOHTBw4EC88cYbAID09HQ0btwY\no0ePRpcuXTBu3Djk5+dXeIzExESsXLkSQ4YMAQBER0dj/fr1OHXqFPLz8/Htt98i06xhZy9YuS34\nAzu2ZCkV/bLXsCFw8qT/8xARmaGiWhcWBuTliRM+IiLVVVTrHA7zf8i7++67sXfvXixbtgwPPfQQ\nAKCwsBDJycmYMGECkpOTERoaihkzZlR4jI0bN6Jnz54ICwsDALRv3x5Tp05Fv379MHDgQMTGxiIo\niN0pq+AaW7KUe+8FRowAfv9hrFh+vpi2YuYve2RtdqwLdvxMpM+kSUDbtsDjj5d/rEED4MCB0qMc\nFFjsVhvs9nlIvxkzxKjtK6+Uf6xTJ+Dzz4HoaGPea86cOXjvvffgcDjw7bff4qqrrip+7Nprr8WW\nLVtw+fJl3HTTTUhPTwcA/Pjjj5gxYwaWl93w4Hf33HMPHnjgATz44INuH582bRquueYaPProo8Z8\niADDNbZkaxXtnlerFqBp7NgSkT1UVOsAdaYjE5E95eUBH35ozLH8WesmTJiAlJQUJCcnIz8/v7jD\nlJycDABo1KgRmjVrhhYtWmDfvn0AgNWrV6Njx45uj5eXl4d169bhrrvuKnX/sWPHAACHDh3CN998\ng+HDhxv3Icgn7NgaQKX57FbPeuqU+7UYzikrVp+ObPXvtyzV8pJcKrUXq2etqNYBrHVmUC0vyaVa\nezE67549wPPPG3Msf9Q6TQPGjgUKC0vu++qrrxAdHY3Y2Fg88cQTWLBgQfFjb775JkaMGIGYmBjs\n2rUL06ZNAwDMnTsXc10uy7F48WLExsaiVq1apd7vvvvuQ8eOHTF48GDMmTMH9erV8/1DGES1tmu0\nYNkBiFxV9suecwe9iAj/ZiIiMpqeWkdEJMOZM0B2tpglV6ZP5zF/1LodO4APPgASEoDGjcV9U6ZM\nwZQpU9w+PyYmBlu3bi13//jx40vdHjlyJFq2bFnueevWrfM9NJmCI7YGiI+Plx1BN6tnLfvLnmte\nFabnWf37LUu1vCSXSu3F6llZ6/xLtbwkl2rtxei8Z86Ivw8e9P1Y/qh133wj/q5kc2OvBXpbUI2p\nHdt//etfCAoKwimXVpuQkIC2bduiffv2WLVqlZlvT4opKAAuXQLq1HH/uAonexSYWOvIU1xjSypi\nrQsMzo7t/v2+H8sftW7NGvG3GR1bUotpHdvDhw/ju+++KzWEn5qaioULFyI1NRWJiYmYMGECioqK\nzIrgNyrBL0dwAAAgAElEQVTNZ7dy1hMngPBwsZ7WyTVvo0Zcd2Y01fJaEWudNVk565Ur4mSvUaOS\n+1jrzKVaXitirbMuo/M6O7YHDvh+rOPHS6YHA+bUurNngaAg4Px5349VVqC3BdWY1rF96qmn8Oqr\nr5a6b8mSJRg2bBhCQkIQGRmJNm3aYMuWLWZFIMXk5ABNmlT8uAobqlDgYa0jT508CdSvDwRXsMsF\nax1ZEWtd4MjLK7nsmC80DTh2rHTH1pVRte7iRXEsjtiSKZtHLVmyBBEREbj++utL3Z+dnY0ePXoU\n346IiEBWVpbbY4waNQqRkZEAgLCwMHTu3Ll43rjz1wir3HbeZ5U8ld2Oj4+3VB7X25cuxaNp04rz\nNmkSj+xs6+RV7ftVLa/z3xkZGbAq1jpr5VOlbYeHV13rNmywTl7Vvl8V8yYlJWHevHkAUFwPrIS1\nzlr5zM6bmpqEJk2Akyd9O15MTDxq1wY2bSp5vGytO3bM97x5eUmoWRM4f96Yz69S7VAtr9m1zqF5\neVXcvn374ujRo+Xuf+mll/Dyyy9j1apVqFevHlq1aoVt27ahUaNGmDRpEnr06IERI0YAAMaOHYtB\ngwbh3nvvLR2KF/IOSJ9+CqxcCXz2WcWPJyYC//2vf3ORNciqC6x1ZLQ1a4B//ANYu7bix//+d8Dl\nNx4KMDJqA2sdOT3yCJCVBYSGAl995f1xfv0VuPNO4PdLxrp9/I47gLQ0798DAK66CoiMBJ5+Ghgy\nxLdjkX8ZXRuCvH3hd999h59//rncn9atWyM9PR0xMTFo1aoVMjMzccMNNyAnJwfNmzfH4cOHi4+R\nmZmJ5s2bG/JBZEpS6OzDylndTUV2zdusGeDm/3Mtxcrfrzuq5ZWBta6ESu3FyllZ6/xPtbwysNaV\nUK29GJ33zBmx/vXyZd+O469ad/GimDrNNbbq5TWa1x3binTq1Ak5OTlIT09Heno6IiIikJycjKZN\nm2Lw4MFYsGABCgoKkJ6ejrS0NHTr1s3oCKSoY8eApk0rfrxpU1EkiayAtY68xVpHKmGtCzxGdWyr\nqnX16on38HVt7KVLXGNLgilrbF05XLa4jYqKwtChQxEVFYXg4GDMmTOn1OOqcl3jYHVWzpqTA3To\nUPo+17wqnOxZ+ft1R7W8VsZaZy1WzupuFMM1r3Pk4dIloEYN/2bTy8rfrzuq5bUy1jrrMTrvmTPi\nKhWpqb4dp6pa53CUnNu1auXde2iaqJWNGpkzYhvobUE1pndsD5a5uvO0adMwbdo0s9+WFFTVL3vh\n4UBurvh1LyTEf7mI9GCtI72OHQO6d6/48aAgsYvosWNAixb+y0WkB2ud/Tk7tgUFvh2nqvM6wPeO\nbWGh+LtePY7YkomX+wkkKs1nt3LWY8cqX4tRrZr4Re74cf/m8oSVv193VMtLcqnUXqyctapaB1h/\nna2Vv193VMtLcqnWXqy6xtYfte7SJaBmTaB2ba6xBdTLazR2bMkyjh7V/8seEZGqWOuIyMqM6tj6\no9Y5l2yEhprTsSW1eH25HzNxW/jAU1hY8mtbZdOM+/UDJk8GBg70XzayBjvWBTt+Jqpa8+bApk2V\nTzMePRr4wx+AsWP9l4usw261wW6fx86KisR52Natog7t3On9sbp1A954A3C51HE5zz0n3m/6dO/e\nIysL6NpVXEJt40bggw+8Ow7JYZnL/RAZKSdH/DpY1drZ5s2BI0f8k4mIyGiFhWI5RbNmlT+PtY6I\nZLh0CaheXUzv9XWNbVaWqGWV8bXWOacic8SWAHZsDaHSfHarZq2o+JXNGxEBZGb6J5M3rPr9VkS1\nvCSXSu3Fqlkr+hGPtc5cquUluVRrL0bmdW7QGRLi21Tkin7EM7rWOaci165tzuZRgdwWVMSOLVlC\nZmbVv+oB1j/ZIyKqDGsdEVlZQYEYsfW1Y3v0qL6ZeEZ1bDliSwA7toZQ6ZpRVs2alSWKW1ll81r9\nZM+q329FVMtLcqnUXqyalbVODtXyklyqtRcj8xo1YuuvWnfxYsmuyGaM2AZyW1ARO7ZkCXrWYQDW\nP9kjIqoMax0RWZmRHVs9tS48HDh3Drhwwbv34YgtuWLH1gAqzWe3alausZVDtbwkl0rtxapZ9da6\nRo3E6IMZIxBGsOr3WxHV8pJcqrUXM9bYVq/u2+ZRemudwyGel5Xl3ftwjW1pquU1Gju2ZAmHD7uf\nslJWw4biVz3+KkdEKtJb63w92SMi8kZBgTEjtnprHeDboIVzKnKtWtb9IZD8hx1bA6g0n92qWTMy\ngFatyt9fNq/DIQrg4cN+ieUxq36/FVEtL8mlUnuxala9tQ4Qte7QIdMjecWq329FVMtLcqnWXoxe\nY2vE5lG//eafWuccsa1Rw7e8FQnktqAidmxJusJCcQ0zvb/stW4NHDhgbiYiIjNkZACRkfqey1pH\nRP7musa2sBDQNO+O469a5+zY+jp1muyBHVsDqDSf3YpZMzOBpk1FUSrLXd5rr7XuyZ4Vv9/KqJaX\n5FKpvVgx66VLwIkTwNVXl3+Mtc5cquUluVRrL2assXU4gGrVROfWGxV1bI2udc6pyNWrixprtEBu\nCypix5ak8+RXPcDaJ3tERBU5dEjMTKlWTd/zWeuIyN+cHVvA+1HQ/HzgzBkxaKFHmzbGjdh6O8JM\n9uDQNOs1AYfDAQvGIpPMmwesWQN88om+5y9ZArz3HrB8uamxyGLsWBfs+JmoYt99B8yYAXz/vb7n\nb9sGjBsHpKSYm4usx261wW6fx86+/x546SVxXla/vlgrGxbm2TH27gXuuQf45Rd9zz9yBIiJAY4d\n8zzvv/8t9l15/XUgOFiM4AYHe34cksPo2sARW5IuIwNo2VL/8zmKQUQq8rbWsT9ARP7i3DwK8H4D\nKU9rXbNm4moXZ896/l7OEVuA62yJHVtDqDSf3YpZ09LENBR33OVt3VoUzaIiU2N5xYrfb2VUy0ty\nqdRerJj1wAHRWXXHXd4GDcTIw4kTxrx/UlIS6tevj9jYWMTGxuKf//xn8WO5ubm477770KFDB0RF\nRWHTpk0VHiM2NhatWrUqtfvmmDFj0LRpU0RHRxsT1mBWbA9kXaq1FzPW2ALed2w9Pa9zOLzfQMq5\nxhYwZ51tILcFFbFjS9L9+itw3XX6n1+7tjjh4/UdiUglaWlA27aevcboGSpxcXFISUlBSkoKnnvu\nueL7n3jiCQwaNAh79+7Frl270KFDh3Kvzc3NxcSJE7Fs2TJ89NFH+PLLL4sfGz16NBITE40LSkRS\nGLHG1tPzOsD7WscRW3LFjq0BVLpmlNWyahqwb1/FBbCivFadjmy177cqquUluVRqL1bMWtkohr9q\nnbu1THl5eVi/fj3GjBkDAAgODkb9+vXLPW/+/PkYMmQIIiIiEB8fj/Dw8OLHbrnlFjRo0MC4oAaz\nYnsg61KtvRh9HVtfR2wr69gaXetcO7Y1ahjfsQ3ktqAidmxJqiNHxBQST8+HrNqxJSJyp6hI1CyZ\nI7YOhwMbNmxATEwMBg0ahNTUVABAeno6GjdujNGjR6NLly4YN24c8vPzy70+LS0Np06dQq9evdC1\na1d8+umnxgQjIssoKDC3Y1sRb2td2anIHLENbOzYGkCl+exWy1pV8asor1U7tlb7fquiWl6SS6X2\nYrWsR44AdeuKP+74o9Z16dIFhw8fxs6dOzFp0iTcfffdAIDCwkIkJydjwoQJSE5ORmhoKGbMmFHu\n9ZcvX0ZycjJWrFiB559/Hv/4xz+QlpZmTDiTWa09kLWp1l6stMb2/Hng5EngmmvcP250rSs7FZlr\nbJNkR5CKHVuSyptf9QDrdmyJiNzxZn0t4HutmzNnDmJjY9GlSxecP38etWvXBgAMHDgQly9fxqlT\npxAREYGIiAjceOONAID77rsPycnJ5Y7VokUL9OvXD7Vq1UL9+vVx6623YufOnd6HIyLL8XVX5H37\nxJKLIA97GN7WugsXgFq1xL85Ykvs2BpApfnsVstaVce2orxt2gD795uTyRdW+36rolpekkul9mJG\n1txcYPNm7167Zw/gZj+mYmbVukcemYCUlBQkJyeXul7gli1boGkaGjZsiGbNmqFFixbYt28fAGD1\n6tXo2LFjuWPddddd+PHHH3HlyhV069YNmzdvRlRUlPfh/EiltkvyqdZezFpj601H0dvzupYtxcwW\nT0dcXacic42tenmNxo4tSeXtiG379uLC31euGJ+JiMid1auBJ5/07rV79gCdOnn+uquvFiMSJ096\n/tqMjJITPgD48ssvER0djc6dO+PJJ5/EggULih978803MWLECMTExGDXrl2YNm0aAGDu3LmYO3cu\nAKB9+/YYMGAArr/+enTv3h3jxo0r7tgOGzYMN998M/bt24cWLVrgo48+8jwwEUnn6xpbb8/rQkLE\nJX9+/dWz13HEllyxY2sAleazWy1rZTsiAxXnrVcPaNwYSE83J5e3rPb9VkW1vCSXSu3FjKx5eeIH\nNTcbC1dp9+7KO7YV5XU4xOt27/b8PdetE387806cOBG7d+/Gjh07sGHDBvTo0aP4uTExMdi6dSt2\n7tyJr7/+unhX5PHjx2P8+PHFz3v66aexZ88evPnmm3j88ceL7//888+RnZ2NS5cu4fDhwxg9erTn\ngU2kUtsl+VRrL1ZaY+vt3imAqHU//+zZ+5Xt2HKNbZLsCFKxY0vSXLoEZGaKX+i8ER3teQEkIvJW\nXp6YjnzsmGev07SqO7aV8bbW/fST+JsjGESkl9kd28p4U+u4KzK5Mq1j++abb6JDhw7o1KkTpk6d\nWnx/QkIC2rZti/bt22PVqlVmvb1fqTSf3UpZDxwQayqcBdSdyvJ6O4phJit9v3qolteKWOusyYys\neXni719+8ex1R44AwcFAkyYVP8eMWrd+vfj7wgXPX1sVldoCoF5eK2Ktsy6j19g6N4+qXt2zjq2m\niZl47dpV/JzKskZHe17rXEdsucZWvbxGCzbjoGvXrsXSpUuxa9cuhISE4Pjx4wCA1NRULFy4EKmp\nqcjKykKfPn2wb98+BHm6dRrZwq5d3o9gAKIALl5sXB4iT7HWBZa8PDE1eO9eIC5O/+t27wbc7MWk\nW3Q08Pnnnr/u+HGgWjUgPx8IC/P+/YlY6wLH5ctAnTri3yEhnnUU09NFrfG23hgxFZkjtoHNlMrz\n9ttv469//StCfh+Ka9y4MQBgyZIlGDZsGEJCQhAZGYk2bdpgy5YtZkTwK5Xms1spa0oKEBtb+XOq\nWothtRFbK32/eqiW12pY66zLjKy5ueKSFJ6u7dezcZSeWufp2t6LF4GGDUXH1mgqtQVAvbxWw1pn\nbUbm9WXzqB07fDuva90aOHGiZHaMHlxjW5pqeY1myohtWloa1q1bh2nTpqFmzZqYOXMmunbtiuzs\n7FKbVURERCArK8vtMUaNGoXIyEgAQFhYGDp37lw8vO78j2aV2zt27LBUHlVu79gRj0mTvH/9zTfH\nIz0d+O67JISEyP88vG3sbee/MzIyYFWsddbKZ/btAweSULMmcOmSZ6/fvTse3br59v6hocCiRUlo\n2lT/6/Pzk37v2Prn++Ft728nJSVh3rx5AFBcD6yEtc5a+czMe/ky8NtvSUhKAkJCxG29r09JiUfn\nzr69f1QU8OmnSejUSd/zL14Etm9PwoEDQPXq8SgokP/fg7crvm12rXNomjf7OwJ9+/bF0aNHy93/\n0ksv4W9/+xt69+6N2bNnY+vWrXjggQdw8OBBTJo0CT169MCIESMAAGPHjsWgQYNw7733lg7lcq09\nsidNA5o2FaO2zZt7f5xOnYDPPgM6dzYuG1mTrLrAWkdOvXuLHdkjIoC33tL/uu7dgX//G/jDH7x/\n7/79gccfB26/Xd/zCwvFerOuXYHZswGXvgcpQEZtYK0jAJgwQSydmDgRGDNG1K1HHtH32jvvBEaP\nBsr85/fImDGiZrpsxl6p0FAgJ0dMn370UXE++Oij3r8/+ZfRtcHrEdvvvvuuwsfefvvt4qJ24403\nIigoCCdOnEDz5s1x+PDh4udlZmaiuS+9GlLWkSOic3v11b4dxzlFjx1bMgtrHTnl5Ympcp5Mzbty\nBUhN9W2NLVBS6/R2bJ3T80JDzZmKTPbDWkdA+c2jPFmzmpICvPGGb+/vyc7ImiZqHXdFJqcgMw56\n9913Y82aNQCAffv2oaCgAOHh4Rg8eDAWLFiAgoICpKenIy0tDd26dTMjgl85h9hVYJWszvW1Dkfl\nz6sqb0yMOJZVWOX71Uu1vFbDWmddZmTNywPCwz3r2P7yC9CsWdWbqRhd65yXwKhVi2tsAfXyWg1r\nnbUZmdfby/0cPw6cOwdUNbu0qqzXX6+/1l2+LDbIC/59mK56da6xVS2v0UxZYztmzBiMGTMG0dHR\nqF69Oj755BMAQFRUFIYOHYqoqCgEBwdjzpw5cFTVsyFb2rHDmFHWbt2AF1/0/ThE3mCtCyzOjm0F\nSwjd2roVuPFG39/b01rn7NjWrs0RW/Ida13g8HbzKOd5na//+bt2BXbuLN3BrojrxlEAR2zJhzW2\nZuJaDPu77z5gyBBg2DDfjpOXJ9a7nT5d8osd2ZMd64IdP5NdaZpYs/ruu0BiIrBggb7XTZgAtG0L\nTJ7s2/sXFYkdjvfvF53rquzbJ6Yt33wz0KsXMGqUb+9P/mW32mC3z2Nn998v/gwdCkydCjRoADz7\nbNWve+018aPfrFm+Z4iKAubPr3oA5OhRMZslJ0fcfvFFUSs54KEOo2uDKVORiaqSkmLMiG39+qJj\nm5rq+7GIiCpy8SIQFCQ2KPFkKrJRI7ZBQWIkQ++VVDhiS0TecB0prVFD/9Te5GTj9jvp1k1frXNd\nXwtwxJbYsTWESvPZrZA1Jwc4dQq47rqqn6snb7duwObNvucyghW+X0+olpfkUqm9GJ01L0/8kObJ\n1LxLl8Q1bKu6riOgv9Z50rGtVcu8jq1KbQFQLy/JpVp7MXqNrXPzqJo1RS3RY9MmfbuvG1nrnHXO\nyYyObSC3BRWxY0t+t3GjKH5BBrU+T072iIi8cfasGK31pGO7a5eYhhwaakwGT2qdcySjdm3xbyIi\nPVzX2Ort2GZnA2fOAO3aGZOhe3d9Axbu1tgavXkUqYUdWwM4L0CsAitk3bBBrPvSQ09eK3VsrfD9\nekK1vCSXSu3F6KwFBeIkz5OOrSfTkD2pdXqWI5k9YqtSWwDUy0tyqdZejMzrOhVZb8d240bgppv0\nDVjoyRodDRw8KH5QrIw/No8K5LagInZsye82btTfsdXj+uuBtDTg/HnjjklE5OrSJXHSFBysv2O7\nebPojBrl6qvFiWZ6etXP5RpbIvKGa8e2Vi39HVsjz+uqVxfndtu3V/48Z51zqlGDa2wDHTu2BlBp\nPrvsrAUFYuMovSd7evLWqCF2xbPCOlvZ36+nVMtLcqnUXozOWlAgao0nI7br1gG33KLvuXrz9ugB\n/Phj1c9znYrMNbbq5SW5VGsvZl3HVu+I7YYNYsRWD71Zb75ZHLcy/hixDeS2oCJ2bMmvUlLEmrO6\ndY09bnw88MMPxh6TiMjJOWIbEgIUFlb9/EOHxCyS9u2NzaG31pk9FZmI7MnTju3Fi+K6s0bs/u4q\nPh6oqo/GNbZUFju2BlBpPrvsrJ6srwX0542Lq7oA+oPs79dTquUluVRqL0ZnvXTJsxHbdeuAW28F\nHA59x9eb15OObc2a4qSPa2zVy0tyqdZejMxbUODZrsjJyeIHvDp19B1fb9ZbbhE7LVc2AuuPy/0E\ncltQETu25FdJSfqn5nniD38QazH0bktPROQJ58me3o7tDz+IH9yMFhUF5OYCmZmVP885ksERWyLy\nhKcjtt9/b06tCwsTM/y2bav4OWUv9+PJ5YnIntixNYBK89llZi0sFCd7vXvrf43evHXrAp06iV/3\nZFKpLQDq5SW5VGovRmf1dMTW046t3rxBQeK4VY3aum4eZcbGeiq1BUC9vCSXau3FyLyuGzLVrFn1\n5cL+9z9g4ED9x/cka1XTkctORQ4NNb7eBXJbUBE7tuQ327YBLVsCTZqYc3w9J3tERN7wZMT2yBHg\n5EnxY5sZ9K49q1lT/OGaMyLS6+zZkn1QqhoBPXkS2L1bLLswQ1W1znl9cSczOrakFnZsDaDSfHaZ\nWVevBvr08ew1nuSNjwfWrvXs+EZTqS0A6uUluVRqLzLX2K5dK5Zc6Lmmo5Onta6qjq1zip5Zl79Q\nqS0A6uUluVRrL0bl1TTPOrarVol6VKOG/vfwJOstt4hLCVX049zJk0CjRiW3zejYBmpbUBU7tuQ3\n338P3Habece/5RaxzraqC3oTEXnKk8v9JCYCAwaYl6VjR1HnDh6s+DnO6YRmbKZCRPZ08aK4Vrfe\nNbYrVgCDBpmXJyxMzHxZv9794ydOAOHhJbdDQ4Fz58zLQ9bHjq0BVJrPLitrfj6wdavn01U8yVun\nDtC9O7BmjWfvMXPmTMTGxiI2NhbR0dEIDg5Gbm5u8eNXrlxBbGws7rzzTrevP3HiBAYMGIDOnTuj\nVatWmDdvXqnHq3q9TCq1XZJPpfZixhpbPVORi4qAlSuB/v09O74neYOCRMf5f/+r+DnOtWdmdWxV\naguAenlJLtXai1F5XUdrAVFDKurYOmudJ+trAc+zDhoEfPut+8dOnizdsa1Th2tsVctrNHZsyS9+\n+AGIjdW/Hby3Bg6s/GTPnaeffhopKSlISUlBQkIC4uPjERYWVvz47NmzERUVBUcF1+146623EBsb\nix07dmDWrFn4y1/+gkKXC11W9Xoisj69U5F37AAaNABatTI3T1W1jiO2ROSpsh3bykZst20DGjcW\ne6eY6fbbK+7Yuhuxzc8XU6opMLFjawCV5rPLyrpsGXDHHZ6/ztO8zpM9b4va/PnzMWzYsOLbmZmZ\nWLFiBcaOHQutgoNeddVVOHPmDAAgOjoajRo1QnBwsO7Xy6RS2yX5VGovRmfVu3lUYqLnIxiA53n7\n9hXXyq3opNO1Y2vG5lEqtQVAvbwkl2rtxai8nnRsPd0N2cnTrLGxYnpxWlr5x06cKL3Gtlo1UaON\nvORPoLYFVbFjS6bTNGD5csAfM3E7dBB/793r+Wvz8/OxcuVKDBkypPi+yZMn47XXXkNQJbvAjBs3\nDnv27MHVV1+NmJgYzJ4926PXE5H1OUdsg4Or7tiaub7WqWFDIDpadG7dMXsqMhHZT9mOrXPzOXe/\ny5u9vtbJ4ah4OnLZqcgA19kGOp5tG0Cl+ewysu7cKX5Bc3Y6PeFpXodD/IK4YoXn77Vs2TL07Nmz\neBry8uXL0aRJE8TGxlY62vryyy+jc+fOyM7OxjvvvIOJEyfi7Nmzul8vk0ptl+RTqb0YndV1xPbK\nFfcnesePA7t2eXfpC2/yVrb27Px5cQ1bs3ZFVqktAOrlJblUay9mrbF1OETdKzsCevw48MsvQM+e\nnr+HN1nvuANYurT0fQUFYtpx/fql7zd6nW2gtgVVsWNLpnOO1vprielddwGLF1f+nDlz5hRvGHX0\n6FEAwIIFC0pNQ96wYQOWLl2KVq1aYdiwYVizZg0efvjhcsfasGED7r//fgBA8+bN0apVK/zyyy+6\nX09E1uccsXU4xHQ3l2X0xb7+WvywVquWfzI5a527Tvbp02KtL0dsiUivsh1bwP105JUrgd69RX3x\nh/79gZQUIDu75L6TJ8XMlbLnlryWbWBzaBYcSnI4HJYd4SLPde8OvPyyuZf6cXXpEtCsGZCaClx1\nVfnHi4rEVOWOHUvuy8vLQ+vWrZGZmYlabs5Kf/jhB8ycORPLli0r99hTTz2F+vXrY/r06cjJycEN\nN9yAXbt2oWHDhrpeT/rYsS7Y8TPZ1Z//DLRvL/6uVUucVNWuXfo5vXsDkyYB99zjn0yaJjJ99hlw\n442lH2vZUmza17Kl6Ihfviz+JjXYrTbY7fPY1fvvi+vGfvBByX3NmolOpev51IgR4vq148b5L9vo\n0cD11wOTJ4vbu3cDDzwA7NlT+nk33gj85z9At27+y0beM7o2cMSWTHXoEHDggHdT87xVo4bYRa+i\nUdudOwGXZbQAgMWLF6N///5uO7VOrrsaz507F3PnzgUATJs2Ddu2bUNMTAz69OmDV199tVSn1t3r\niUgtzsv9AO43kDp6VJz8ebOZirccDlHLvvqq/GPOEVvnVEKO2hJRVfSM2F654t1lfnw1YgQwf37J\n7bI7IjtxxDawsWNrAJXms/s76xdfiNEL58W+PeVt3opO9gBxAlq26I0cORLzXStmGXFxcVjqssBj\n/PjxGD9+PAAgPDwcy5Ytw86dO/Hmm29i+PDhVb7eKlRquySfSu3FjOvY1qgh/u2uY/vVV2IdWM2a\n3h3f11rn+oN3YaFYe+Y8QTWjY6tSWwDUy0tyqdZezFpjC5Tv2G7dClx9NRAR4d17eJu1Vy8gMxPY\nt0/c/vVX95dVM3rzqEBtC6pix5YMcfGi+51CFy0Chg71f57+/UXxPXGi/GPHjokdQ4mI9HJuHgW4\n79guXCin1nXpIjqyO3eW3JeXB9SrBzg3Y+eILRHp4a5jW6tW6Y7tihX+H60FxFKKESOA994Ttzdv\nBnr0KP88ozePIrWwY2sAla4ZZVbWsDDg6adL35eRAaSni1/ZvOVt3tq1ReH98svyj+XkmNexVakt\nAOrlJblUai9GZ61sxDYrS6z36tfP++N7m9fhAIYNE+tsnZzTkJ3M2BlZpbYAqJeX5FKtvRh5Hds6\ndUrfV3bE9n//8+0yP75knTQJ+PBD8ePdpk3uO7ZGT0UO1LagKnZsyWdHj4qTvrKXal20CLj3XnHd\nRxn++Efg00/L3+/s2HIfCyLSq7IR2y++EDsUOzu+/jZyJPDf/5bs1Fy2Y8sRWyLSo6qpyDk5QFoa\ncPPN/s8GiM3whg4FHnwQOHwY6NSp/HO4xjawsWNrAJXms5uR1bmW9cqVkvs0Dfj4Y8DNclOP+JK3\nfzq8Yo0AACAASURBVH9RgA8eLH3/sWMin7up075SqS0A6uUluVRqL/5cY7tokdid0xe+5L3uOnHC\nt2qVuO2uY3vpkm/5ylKpLQDq5SW5VGsvRuU9c0YsY3Dl2rFduRLo08f7fVMA37POnCl2av7sM/cD\nJ1xjmyQ7glSmdGy3bNmCbt26ITY2FjfeeCO2bt1a/FhCQgLatm2L9u3bY5Xz/4VJabt2iW3Vc3NL\n7tuyRYwQ3HKLvFwhIeJk87//LX1/To74m+tsyVesdYGjohHbQ4fEZib+upxZRUaNEj8mAhyxJeOx\n1gWGY8eAxo1L31enjujwAvLW17oKDQU++kjMknGHa2wDnGaCuLg4LTExUdM0TVuxYoUWHx+vaZqm\n7dmzR4uJidEKCgq09PR07dprr9WuXLlS7vUmxSKT3HSTpv3lL5p2xx0l9/3pT5r28svyMjlt2qRp\nbdpommszi4nRNEDTjhyRl4s8Z8W6wFoXOLp107SNG8W/Y2I0bft28e/XXtO0sWPl5XI6dUrTwsI0\n7ehRTXv7bVGDnbp00bStW+VlI89ZrTaw1gWGli017cCB0vdNnKhps2dr2uXLmtawoaZlZUmJptvr\nr2va44/LTkF6GV0bTBmxveqqq5CXlwcAyM3NRfPmzQEAS5YswbBhwxASEoLIyEi0adMGW7ZsMSMC\n+YmmiU1TevYsGbE9f16sORs5Um42QIwk16oFrF1bcl9OjhjB4Igt+Yq1LnCUnYrsXM9qxDRkIzRo\nINaevf22GLENCyt5jCO25CvWOvvTNHF+1LRp6fubNRN7qWzbJi7xc/XVcvLpVb++2FyKApMp2/rM\nmDEDPXv2xNNPP42ioiJs3LgRAJCdnY0eLluYRUREICsry+0xRo0ahcjISABAWFgYOnfuXLzTl3P+\nuFVuz5o1y9L5XG+7zr034niHDgEhIUk4dQo4fVo8/s9/JuG664Crr5af1+EAevdOwj/+Adx2WzwK\nCoATJ5LQuDFw4YLv+YzO6+/bVs7r/HdGRgasirXOWvnMbNsFBcDOnUnIywNCQuJx+TIwf34S9u2z\nTt6ePZMwaRLQu3c8unUrebxGDZHfyt+v2betnjcpKQnz5s0DgOJ6YCWsddbKZ0be8+eBatXiERpa\n+vGrrgK+/DIJJ04AvXr5ntfs/y2GhQH79ychKSkwaodqeU2vdd4O9fbp00fr1KlTuT9LlizRbrvt\nNu3rr7/WNE3TFi1apPXp00fTNE3785//rH322WfFx3jkkUe0r776qtyxfYglxdq1a2VH0M3orN9/\nr2lxcZp2+LCmNW8u7ouL0zQ3/1m9YkTe3FwxRe/IEU3bsEHTOnfWtNhYTdu2zfd8ZanUFjRNrbyy\n6gJrXQmV2ovRWVu31rS0NPHvW2/VtLVrNS0hQdMefdSY4xuVd9o0TevQQdMOHSq5r29fTVu50pDD\nF1OpLWiaenll1AbWuhKqtRcj8v76q6hzZS1frmkDB2pa//6a9s03Pr+N6d/tmjXiPNQogdgW/Mno\n2uD4/aCGqlevHs78vtJc0zSEhYUhLy8PM2bMAAA8++yzAIABAwbgxRdfRPfu3Uu93uFwwIRYZIJF\ni8S0448+EtNXdu4U28BnZpZstGIF48YBLVqIqYTZ2WJKzSuviCnUpAYr1gXWusDRogXw00/ANdeI\nXUGnThV//v1v4PcfpS1B04CiIqBatZL77rgDGD8euPNOebnIM1arDax19rd+vahpGzaUvn/7drE5\n3W+/AenpQKNGUuLplpwMPPIIkJIiOwnpYXRtCDLsSC7atGmDH374AQCwZs0atGvXDgAwePBgLFiw\nAAUFBUhPT0daWhq6detmRgTyk5MnRZELDRVruN59V1w/1kqdWgD4y1+At94Cli4Fbr1VrLvlGlvy\nFWtd4Ci7xva338QfmTu/u+NwlO7UAlxjS75jrbO/nByxnrasZs3EXiqtWlm/UwuI/QVcr9JBgcWU\nju27776LKVOmoHPnznjuuefw7rvvAgCioqIwdOhQREVFYeDAgZgzZw4cDocZEfzKdT671Rmd1dmx\ndThEMXn3XWD0aOOOb1Te9u2BESPEaEu/fuZ1bFVqC4B6ea2Gtc66jM5a9nI/iYlAr17lO5HeMvO7\nNaNjq1JbANTLazWsddZmRF53G0cBQJMm4hwvLs7ntwBg/ncbFmbs5lGB2BZUZsrmUV27dsXmzZvd\nPjZt2jRMmzbNjLclCU6eFFP0ALErZ1AQEB0tN1NFXn+95N8csSUjsNYFBk0DLl4EatYUt50d29de\nk5tLrxo1OGJLvmGts7+jR913bENCgPBway25qEy9eqJjW1QkzkkpsJiyxtZXXIuhjocfBm67TVza\np1s3UfhefVV2qqqNHAn07m2NSxKRPnasC3b8THZ04gTQtq24jA4g1th+/72YinzNNXKz6TFunKjP\n48bJTkJ62a022O3z2NGIEWJGm7vzolmzgDFjRKdRBXXrAllZ6uQNZEqssaXAceJEyZqLAQOAhx6S\nm0evmjU5YktE+mRkiPVlTr/8IpY3qNCpBcRU5EuXZKcgIiv79VfguuvcP/bkk2p1Enkt28DFjq0B\nVJrPbtYaWwD4+9+Nn4Zs1nfLNbaCanlJLpXai5FZ09MB18vtbdkidgo1EtfYmku1vCSXau3F17ya\nJjq2v+8JZip/fLdGbiAVaG1BdaassaXAcfKkWHuhGq6xJSK9MjJKd2yvvlpWEu9wV2QiqszRo2Im\nW8OGspMYw+gNpEgdXGNLPmnQADhwQL1i+Pe/A5cvA//4h+wkpJcd64IdP5MdTZgAdOgATJokO4l3\nnn9ebADzf/8nOwnpZbfaYLfPYzdJScBzzwE//ig7iTFuvx147DFxDW+yNq6xJcsoLATOnhW/jKmG\nI7ZEpFfZEVvVcFdkIqrM7t3ixzu74LVsAxc7tgZQaT67kVnT0sSFu83cTp1rbM2lWl6SS6X2YlRW\nTQN27jT/pI9rbM2lWl6SS7X24mven34Cbr7ZmCxV8cd327gxcPy4MccKtLagOnZsyWsffQQMHy47\nhXdq1QLy84ErV2QnISIr27VL1Itrr5WdxHvcFZnIvv7wB+DMGd+O8dNP4jh2cfXVQHa278dJSwPe\nfdf345D/cI0teeX8eaB1a2D9ev/some0Tz8V1+AdMABYulSsPyNrs2NdsONnspuXXxYbq7zxhuwk\n3pszB/j5Z+Dtt2UnIb3sVhvs9nmsQtPEUoPt272/KsXhw0CXLsCxY4DDYWw+WT77DFixApg/37fj\nfPEFMGOG8bvgUwmusSVLmDMHuPVWNTu1gMj+1lvi/xS4gRQRuaNp4gRpyBDZSXxTt6645jgR2cu5\nc2IjzJMnvT9GYiJw22326dQCxo3YZmf7PhpO/sWOrQFUms9uRNaTJ4HXXgNeeMHnQ1XJrO+2ZUtg\n4kTggw/EKEZqqjHHVaktAOrlJblUai9GZF27VuwhcOutvuepipnfbb9+wHffieUXRlGpLQDq5SW5\nVGkvzg7tunVJXh/jm2+Ae+4xJo8e/vhumzcHsrJ8P052NnDiRJLvB/IjVdquWdixJY+98AJw//1A\nx46yk/iueXPgxReBP/0JKCqSnYaIrELTgH/+E5g8Wf2RjKZNgRtvBJ59Fjh9WnYaIjKKs2N79qx3\nr8/NFetrBw40LpMVOEdsfZ3heuSIWHpH6uAaW/LInj1Ar15ihDM8XHYaYxQVAT17AiNHAuPHy05D\nFbFjXbDjZ7KL1avF9WtTU4HgYNlpfLdnj+io//or8MMPYnoyWZfdaoPdPo9VrFwp9gqZMQOYOtXz\n17/1lujYfv658dlkq1sXyMwE6tf3/hh9+gDffw9cvCjWMpPxuMaWpNE04KmngL/9zT6dWkBMNXz3\nXXFx8iNHZKchItk0DZg2Tay/t0OnFhAzbObPB2JjxTIMIlKfc8T21CnPX6tp4txn7FhjM1mFEdOR\nnet0vR0RJ/9jx9YAKs1n9yXr0qXAoUNiFMNf/PXdduokpiM/8YRvx1GpLQDq5SW5VGovvmT9/HNx\nKbD77zcuT1X88d06HMCbbwLbtomd4X2hUlsA1MtLcqnSXk6eFCOJe/Ykefza774TndvevY3PVRl/\nfbft2wM7dvh2jCNHgNDQJOTlGZPJH1Rpu2Zhx5Z0ycsD/vxn4J137HtpnOeeA1JSgGXLZCchIlnO\nnAGeeUZM0Quy4f9D1q4NLFggZt+kp8tOQ0S+OHkSaNMGHne8NA146SVR61TfQ6AiffsCq1Z5//oL\nF8SfZs24M7JKuMaWdJkwQWwp/957spOYa80aYNQosR6Na9CsxY51wY6fSXWTJ4tpZ++/LzuJuf71\nL7Eb6g8/ANWqyU5DZdmtNtjt81jFpEliHenp04AnA3UrVgBPPw3s2mWf5RZl7d8vdrTPzPTuR8rM\nTKB7d/HDwd//DsTFGZ+RuMaWJPjpJ2DxYuDVV2UnMV/v3uJ6bs8/LzsJEfnbpk1iGvKMGbKTmG/y\nZKB69cCo60R2deIE0K6dZ2tsr1wRO6QnJNi3UwsA114LtGoFvPKKd68/d04McNSr5/mIOMnDjq0B\nVJrP7mnW/HzgkUeAN94AGjQwJ1NlZHy3M2eKqXpbt3r+WpXaAqBeXpJLpfbiadaLF4HRo8UaVBmb\n4/n7uw0KAj7+GHj9dWD7ds9fr1JbANTLS3Kp0l5OnQLatgWys5N0v+bjj0WHbfBg02JVyl/frcMB\nLFwoltC9+qrnl/45exaoUwe4cCFJqanIqrRds7BjS5WaOhXo0gW47z7ZSfynUSPRuR03DigokJ2G\niPzhhRfEJnL+3DBKthYtgFmzgD/+UfyISURqOXsWaNlS/669J04Af/2r+AHPrmtrXUVEiFmHn34q\nRqk96dyePSt+AAgN5RpblXCNLVVo5UrRudu5U85orUyaBtx1l9hVj1P1rMGOdcGOn0lFmzeL/73v\n2gU0aSI7jf8NGyZGqd98U3YScrJbbbDb57GK668XnbYbbhA/TlWvXvnzR40S53Ovv+6XeJZx6hQQ\nHw8MHSo2CtVj6VKx10JUFBAWJjrGZDyja4ONZ9eTL06eFFOQP/448Dq1gPgl88MPgc6dxQW6+/WT\nnYiIzJCXBwwfDsyZE5idWkB89pgY4I47gP79ZachIr2c60Dr1xe1rHHjip/7v/8Ba9cCu3f7L59V\nNGwodki+5RbxHY0fX/VrnFORucZWLZyKbACV5rPryVpUJH7Ve+ABsZGSTDK/2/Bw4JNPxHeRk6Pv\nNSq1BUC9vCSXSu1FT1ZNAx57TFwW4t57zc9UGZnfbYMGwLx5wJgx4rqNeqjUFgD18pJcqrSXc+dE\n56tGjcqvtXriBDB2rPjfuewrPsj6bps1AxITxbKTFSuqfr5zKnJODtfYqoQdWyrntdfEiG0g7Axa\nld69xYYyI0eKDj8R2ccnn4ilFv/+t+wk8vXuDfzpT+IHzcuXZachIj2cHdvQUCA31/1zNE2MUA4b\nBvTq5d98VnPtteIqH6NGVb1pnut3q1LHNtBxjS2Vsm6dWIOwdavYWITESV5cHHDnnWLTBZLDjnXB\njp9JFdu3AwMGiGtXR0fLTmMNRUXA7beLTbRee012msBmt9pgt89jBVeuiDW1hYVidt3f/uZ+lt28\neeLHuy1bgJo1/R7TkhYvBiZOFBtLRUa6f8706WJZWmws8MEHYs0tGc8y17H94osv0LFjR1SrVg3J\nycmlHktISEDbtm3Rvn17rFq1qvj+7du3Izo6Gm3btsUTTzzhfWoyxbFjYq3ZvHns1LoKCQEWLRIb\nqyQmyk5D/sZaZz9ZWcDddwNz57JT6yooCPjsM+CLL4BvvpGdhvyNtU4t588DtWuLzpdzjW1ZP/8M\nPPMMMH8+O7Wu7r5bXPVj0CDg9Gn3z3G9ji1HbNXhdcc2Ojoa33zzDW699dZS96empmLhwoVITU1F\nYmIiJkyYUNwTf+yxx/DBBx8gLS0NaWlpSLRJL0Gl+ewVZS0oEFPQRo0SoxhWYZXvNiJCXA9t5Ehg\n//6Kn2eVvHqpllcG1roSKrWXirLm54sdkB97TP66WldW+W4bNRI/5I0fD/zyS8XPs0pevVTLKwNr\nXQkV2otzqiwAXLyYVG4qcl4eMGSI2AG5Uyf/56uIVb7bxx8X57v33ANculT+cefmUWlpXGOrEq87\ntu3bt0e7du3K3b9kyRIMGzYMISEhiIyMRJs2bbB582YcOXIEZ8+eRbdu3QAADz/8MBYvXux9cjKM\npgGTJolfpl58UXYa67rlFjE15e67xf+hUGBgrbOPoiLx41RUFJcVVKZbN+CVV8Tyi5MnZachf2Gt\nU8v58yUd29DQ0iO2miY2g+vTR1ynmtybOVNsFDp6dPl9VFyvY8tdkdVh+OZR2dnZiIiIKL4dERGB\nrKyscvc3b94cWVlZRr+9FPHx8bIj6OYu65tvAhs3Av/9L1Ctmv8zVcZq3+1jjwHduwMPP+x+Mymr\n5a2KanmthLXO2txlnT4dyM4G3ntPTN+zEqt9t6NHixHtIUPEjJ6yrJa3KqrltRLWOmtyHbHt2DG+\nVOfrxRfFkgsrXq/WSt9tUJC4DnBGRvnr2zq/375945UasbXS9ytDpdex7du3L44ePVru/pdffhl3\n3nmnaaGA/2/vzuN8qvc/gL9mJiXh0mL4mREGMzFjxk6hEWKSSBsq+02yFNfS6lJZIhI3bWi6LnUr\n62Uo4ovCMKRSuJN9FxpLljG8f3+8rzEyNMs533M+5/t6Ph498v3OzPf7Ot855z3nc85nATp16oSy\n/xvRXaxYMcTFxWX+si7eZufj/D9euBAYOtSHd94BihRxPo/bHwcFAW3b+jBgADBgQDzGjHFXPi89\nvvjvHTt2wG6sdd5/PG0aMGmSDxMnAjfc4HweEx43a+bDt98CPXrEY9IkYNkyd+Xz0mOfz4fExEQA\nyKwHdmCt887jH34AChfWx4cP+/63LKHWuvffZ63L6eMbbwQGDfKhZ0+gbNl4PPWUfn33bj0v/stf\ngLQ0H3w+d+Q1/bHttU7yKT4+XtatW5f5eMSIETJixIjMx82aNZPVq1fL/v37JSoqKvP56dOnS/fu\n3bN9TQti+dXSpUudjpBjWbNu2CBy220iK1Y4l+fPuPWzPXpU5I47RMaPv/x5t+a9GpPyOl0XWOvM\n2l+yZl25UuTWW0V++MG5PH/GrZ/tiRMicXEib7xx+fNuzXs1puV1sjaw1pmxvyQliTRvrv8eMGCp\ndOqk53O33Sby44/OZrsWt362qakiJUuKzJ+vj6tXF1m7VvNef73ImTPO5sspt36+V2N1bQi2qHGc\n+e8HHngAn376KdLT07F9+3akpqaidu3aKFmyJIoWLYrk5GSICKZOnYrWrVtb8faUB9u367IO77wD\n1K/vdBrzFC+uC3yPHAnMmeN0GvIX1jrz7Nyp3WkTEzkDcl4ULgzMm6d/K6ZPdzoN+Qtrnftl7Ypc\nuLDOgPzII7o+t5smizJFhQrAzJk6D8PatZd/vkWLcpytMfLaIp45c6aEhYVJwYIFJTQ0VJpfvGwk\nIsOGDZOIiAiJjIyUhQsXZj6fkpIi0dHREhERIb17977qa+cjFuXAwYMiFSuKvPOO00nMl5KiV0eX\nL3c6ifc5VRdY68x1/LhITIzI2LFOJzHfxo0iJUqIfP2100kCgxO1gbXOLFOmiHTqpP9evFgE4Hmd\nFebO1fO6ggVF9uzR58qX1zu6ZD2ra0PQ/17UVbiQt31OnADuuQdISABefdXpNN6weLGu/5uUBNSs\n6XQa7/JiXfDiNrlFRoYu41CqlK5X67bJoky0bJneEVq8GKha1ek03ua12uC17XGDCROA//5X/3/8\nuN5t7NTJ6VTe8NNPwM8/Aw8/rH87qlcHJk3S/5O1rK4NlnRFDnQXB0W73cmTwF13+VCjhjnL+pjw\n2TZporOs3n8/kJjoczpOrpjw+ZJ7mLK/nDwJxMb6EBQE/OMfZjRqTfhs775bT6KbNgWGDfM5HSdX\nTPh8yT1M2F9OntSlaABg/XqfMY1aEz7bKlX0Il5QkOY1qSuyCZ+vna45KzJ5x++/65ja8HBg4kQz\nTvRM0qqVfsZ9+gB33QVUrOh0IqLAJAL06gWEhen4d9Y6az32GHD77UDz5rqmd5UqTiciCkxZx4CS\nvYoWhVFL/gQydkUOAKdOaaO2XDntShHM+/S2mTxZ18pcvBiIinI6jbd4sS54cZucdOGCrjX9/ffA\nokVAkSJOJ/KuadOAAQOA+fOBatWcTuM9XqsNXtsep505AzRurOtNd+vmdBrve/JJ4N579f9kLXZF\nplw5dQpo2RIoU0a7y7JRa6+uXYFhw3Qc88aNTqchChwZGTqb5ZYtbNT6w+OPazfvZs2AJUucTkMU\nOE6f1vkDwsK0YUv2K1kS+Pe/edfWBGzmWMCt/dmPHdNJokqXBqZMAUJC3Jv1akzM27EjMHasjr39\n7junE12baZ8vOcut+8uZMzrJx+HDOolbkSLuzXo1JuZt0wb47DOgbVvg88+dTnRtpn2+5Cy37i8n\nT2oPvJtv1l4TISH6vFvzZsekrIDmHTIE+L//0+Uxd+1yOtG1mfb5Wo0NW486dAho1EjXbUxMvFT8\nyD/attWxzM2bA8nJTqch8q7jx/UCXsGCOqa2UCGnEwWW+Hi9Q/7cc1rziMgex45pD4ny5XWt2us4\nS47f3HSTzq7fuTNw551ASorTiehqOMbWg3bu1Fkr27UDhgzh5ClOmj9fp9//+GPgvvucTmM2L9YF\nL26TP/36qzZqa9XSbrG8gOecbdv0pLtdO511n3938sdrtcFr2+NvBw7ondp69YDx4zmszElz5ui4\n5g8/1An0KH84xpau6eefgQYNdFZQnlw4r0ULYO5coEsX7Q5ORNbYtUtrXUKC3ilko9ZZ5csD336r\nXcGffho4f97pRETesGWL3iVs1UqX22Kj1lmtWgELF+p59tixOhM/uQcPDwu4pT/7kiXa/XjYMF12\nJjtuyZpTXshbrx6wbBnw+uvAa6+5qwia9vmSs9yyv6Sk6Ile9+56TGV3Ac8tWXPKC3lLlACWLgW2\nbtU1IM+c8X+uqzHt8yVnuWV/WbVK149++WVg8OCr36xwS96cMCkrkH3eGjWAlSt1qF/Pnjp5oVuY\n9vlajQ1bj5g8WbuAffoppyN3o8hIvZsxc6aejJ8753QiIjPNnq13aSdMAPr2dToN/VGRIjoE4/rr\ntWtyWprTiYjMNHs28MADwEcfaa8vcpcyZYBvvgG2b9fVRzhjsjtwjK3hLlwAXnwR+OILPZmIjHQ6\nEV3LiRNA+/b6/y++AG691elE5vBiXfDiNtlFBBgzBhg3Tk/4atZ0OhFdy4ULOqHUsmXAggU6oyjl\nnNdqg9e2x04iwKhROpZ2zhzWOrfLyNBekt98A8ybpw1eyjmOsaVMJ05od6+VK4HVq9moNUGRInpS\nXrcuULs217olyomzZ4G//hWYOlW75vFEz/2Cg4G339YZ4uvU4ezwRDlx+jTwxBO6fFZyMmudCa67\nDnjnnUszJq9b53SiwMaGrQWc6M++ebM2jG65RZdayOmdP9P63nsxb0gIMHIk8OqrOiZ67lz7c12N\naZ8vOcuJ/WX3bp0kKi1Nr4iHh+fs50zbt72YNygIeOEFPelr2VKHzDjFtM+XnOXE/rJnD9Cwod6x\nXbECCAvL+c+atH+blBXIea3r21dn509I0DvtTjHt87UaG7YGmjFDi1///sAHHwA33OB0IsqLJ57Q\n7uM9ewIvveSuyQeI3GDJEr2A98gjegejSBGnE1FePPAAsHw5MHo00KMHkJ7udCIid1m2THs2PPww\nMG0acOONTieivGjdWode9OwJ/P3vnB3eCRxja5CMDG0A/fvfOj6TXVS84dAh4PHH9fc7fTpQqpTT\nidzJi3XBi9tkBRFtBL31lp7k3XOP04nICseP6+SGhw7pRIe33+50IvfyWm3w2vZY5cIF4I03tNt+\nYiLQvLnTicgKBw7ofCrBwfo3LDTU6UTuxTG2AWrfPp1hcv16XeqCjVrvKFFC10SLj9ff69KlTici\ncs7Ro8BDD2nPlDVr2Kj1kqJFgVmzgDZt9E787NlOJyJyzuHDwP3364RDa9eyUeslJUvqMMG77gKq\nVwcCvHewX7FhawG7+7P/5z96YNx9tzaA8jOTrml97wMlb0iIdltJTNSrfK+/7p8uLKZ9vuQsu/eX\n5cuBatX0Tt7y5TkfT5sd0/btQMkbHAwMGKBj0Pr21dlEz561Nlt2TPt8yVl27y8rV+p5XZUq2ujJ\nT60DzNq/TcoK5O+8buhQPa9r147ndf7Chq2LnT4N9O6t/82YoYtzh4Q4nYrs1LSp3pFfvFgnltqx\nw+lERPbLyND69thjwLvvahdkzh3gbXXrag+kvXuBevWA1FSnExHZT0QnGGrdWv8/ejRQoIDTqchO\nTZvqTMmLFgFNmugkYWQfjrF1qZ9+0mUSKlcG3n8fKFbM6UTkT+fP65qdF8cZPv64zroXyLxYF7y4\nTbm1Y4fu3zfdBPzzn9qFiwKHiF7M+Pvfdab4p59mrQO8Vxu8tj158cknwIcfahfkWbOAiAinE5E/\nnT+v46nffFPv5Pbu7XQid7C6NrBh6zLnzwNjx+rOP2qUrovFP/KBa8MGPemPidGTv+LFnU7kHC/W\nBS9uU06JAJMmAS++CAwaBPTrp91UKTBt3gx06KA1bvLk3C114kVeqw1e257cENGlyh58EBg/HmjV\nSi/kUWDavl17rLRvD3Trpt3RAxknj3Ihq/qzb94M1K+vU4WvXQt06WJ9o9a0vveBnjcuTrsmlywJ\nVK2qk0xYybTPl5xl1f6ye7eu9ff++zpZWv/+1jdqTdu3Az1vVJSOO6xfX8ceTpumDQKrmPb5krOs\nrnWdOmmjtn17exq1Ju3fJmUFrM9brpyubBIcrF2T//MfS1/euM/XamzYusD589o1oX59Xdt0zD8L\nSQAAGotJREFU8WLd8YkAXc9u3Djtpvnss7qPHD7sdCqi3BPRu3HVqwMNGgCrVgHR0U6nIre47jrg\nlVd0ksThw3V27H37nE5FlHsXe6RcrHWbN2ujlgjQfWLMGO2e3revTi516JDTqbyBXZEd9uOPwFNP\nAddfD0yZwjEXdG2nTumJ3/Tp2th99NHA6aruxbrgxW26mm3bgGee0T/eiYnaA4Hoas6c0cbtu+/q\n2Nvu3QOrq7rXaoPXtudadu7U87rDh7XWxcQ4nYjc7NQpYMgQ4OOPdV6VJ58MnPM6gF2RPeP334GB\nA3WNxo4dtTseG7X0ZwoV0qt8s2fryV7r1vpHlMit0tO1gVK7tta75GQ2aunPFSyoNc7nA/71L73D\n8dNPTqciurpz53RulBo1dHnG1avZqKU/V6iQ7jdJSTrHTkICV8TIDzZsLZDb/uzz5ulg8X37gI0b\ndRZIf12JNq3vPfNmr04dXSqjZk39IzpihDYgcsu0z5ecldv9ZdkyHSe+cqWOFR840H9LW5i2bzNv\n9qpUAVas0LsY8fHaY+XMmdy/jmmfLzkrt/vLihW6BvfSpXrx7sUX/buMj0n7t0lZAf/lrVFD59eJ\nj9dzuxEj8rbGt2mfr9XYsPWjPXuANm109s9Jk/QqdGio06nIVDfcoCd5a9Zow6FqVeDrr51ORaRd\n8Dp31vHgr7+uk2OULet0KjJVcLBeAP7+e2DTJh2XPXeutZNLEeXF4cM60Wf79tqdNCmJve8o7woU\nAJ5/Xi+OrFqld/wXLnQ6lWEkjz777DOpXLmyBAcHS0pKSubzX331ldSoUUNiYmKkRo0asmTJksyv\npaSkSHR0tFSoUEH69Olz1dfORyxX+v13kaFDRW6+WWTwYJHTp51ORF40Z45I2bIijz4qsmeP02ms\n51RdYK3LufR0kbfeErn1VpHnnhM5ftzpRORFX30lcscdIs2aiWza5HQaezhRG1jrcu7cOZGJE0VK\nlBDp25e1juwxb55IRIRI69Yi27c7ncYeVteGPL/apk2bZMuWLRIfHy/r1q3LfP67776T/fv3i4jI\nxo0bpXTp0plfq1WrliQnJ4uISEJCgixYsCD7UB4pgBcuiHzyiUiZMiKPPCKybZvTicjrfv9d5OWX\n9SLK0KEiJ086ncg6TtUF1rqcSUoSiYwUufdekZ9+cjoNeV3Wiyj9+om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"text": [ "" ] } ], "prompt_number": 85 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that at first the modulation sideband at +/- 1MHz increases linearly (+20dB for a 10x step) with increase in the modulation amplitude. Eventually other sidebands appear at +/- N MHz." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's compare a measurement at large modulation amplitude with a measurement from a scope \n", "f_m = 1e6\n", "beta = 0.1\n", "figure(figsize = (16,5))\n", "subplot(1,2,1)\n", "title(r\"$\\beta$ = %.4f\" %beta)\n", "plot_wfm_spectrum(t,dt,f_c,beta,f_m)\n", "#from visa import *\n", "#scope = instrument(\"TCPIP0::130.30.240.189::inst0::INSTR\")\n", "#scope.write(\":wav:sour func2\")\n", "#wfm_ascii = scope.ask(\":wav:data?\")\n", "#wfm = wfm_ascii[:-1].split(',')\n", "#wfm_xor = float(scope.ask(\":wav:xor?\"))\n", "#wfm_dx = float(scope.ask(\":wav:xinc?\"))\n", "#wfm_freqs = linspace(wfm_xor, len(wfm)*wfm_dx, len(wfm))\n", "#subplot(1,2,2)\n", "#title(\"PSD from Scope FFT - PM Amplitude = %.4f\" %pm_amp)\n", "#plot(wfm_freqs, wfm)\n", "#grid(1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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eo32p6WHwNDjmLaRr1+T9MzMyTJovkmDOd9paCN3dwfPHH4FBg+q/h6cle64P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\n6mLwJJvy8hwPnjt3AnfeCSxYAHz2GfD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"text": [ "" ] } ], "prompt_number": 86 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the first modulation sideband is down ~26dB from the carrier.\n", "\n", "
\n", "The amplitudes of these sidebands can be predicted using Bessel Functions.\n", "\n", "$$y(t) = sin(\\omega_c t + \\beta cos(\\omega_\\phi t))$$\n", "\n", "It can be shown that our signal:\n", "\n", "$$sin(\\omega_c t + \\beta cos(\\omega_\\phi t))$$\n", "
\n", "$$ = J_0 (\\beta) cos(\\omega_c t)$$\n", "$$ - J_1 (\\beta) (cos(\\omega_c - \\omega_m)t - cos(\\omega_c + \\omega_m)t)$$\n", "$$ + J_2 (\\beta) (cos(\\omega_c - 2\\omega_m)t - cos(\\omega_c + 2\\omega_m)t)$$\n", "$$ - ...$$\n", "
\n", "Where $J_0$, $J_1$, $J_2$ are Bessel Functions.\n", "

\n", "$J_0$ sets the amplitude of the carrier $f_c$\n", "
\n", "$J_1$ sets the amplitude of the 1st sidebands at $\\pm f_m$\n", "
\n", "$J_2$ sets the amplitude of the 2nd sidebands at $\\pm 2f_m$\n", "
\n", "
\n", "So what do the Bessel functions look like?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta_marker = 0.1\n", "from scipy.special import j0,j1\n", "beta=linspace(0,10,10000)\n", "dbeta = beta[1]\n", "y0=j0(beta)\n", "y1=j1(beta)\n", "figure(figsize=(14,6))\n", "subplot(1,2,1)\n", "plot(beta,y0,label=\"$J_0$\")\n", "plot(beta,y1,label=\"$J_1$\")\n", "legend()\n", "xlabel(r\"$\\beta$\")\n", "grid(1)\n", "subplot(1,2,2)\n", "loglog(beta,y0,label=\"$J_0$\")\n", "loglog(beta,y1,label=\"$J_1$\")\n", "beta_marker_idx = beta_marker/dbeta\n", "annotate(\"{:.2f}\".format(y0[beta_marker_idx]),(beta_marker,y0[beta_marker_idx]))\n", "annotate(\"{:.2f}\".format(y1[beta_marker_idx]),(beta_marker,y1[beta_marker_idx]))\n", "print y1[beta_marker]\n", "legend()\n", "ylim(ymin=1e-3)\n", "xlabel(r\"$\\beta$\")\n", "grid(which='both')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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s+VGmLWt+5PXPbHv27lkM3DwQP/X+CZUDK+fZbs3raLnmBzBcQvb777a/VvY4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\nDKhUfwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 87 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "What does this tell us?\n", "
\n", "$J_0$ tells us the carrier amplitude and $J_1$ tells us the first sideband amplitude\n", "
\n", "If $\\beta = 0$ (no modulation) $J_1$ (first sideband) is at zero amplitude relative to the carrier.\n", "
\n", "If $\\beta \\approx 2$ (peak phase deviation ~ 2 rads) the first sideband is actually larger than the carrier.\n", "
\n", "
\n", "In our example where $\\beta = 0.1$ rad, the carrier peak was at +9.01dBm & the first sideband at -16.8dBm for a delta of -26dB\n", "
\n", "This matches well with the Bessel function values of:\n", "
\n", "$J_0 = 1.0$, $J_1 = 0.05$\n", "
\n", "
\n", "$20log10(0.05/1.0) = -26 dB$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What we are looking at in both of these plots is the power spectral density PSD of the signal, $S(f)$.
\n", "When a Spectrum Analyzer makes a Phase Noise measurement it starts with this $S(f)$ data.\n", "If there is **no Amplitude Modulation** of the signal we can call say $S(f) = S_\\phi(f)$, the Frequency Spectral Density.\n", "\n", "\n", "To get to from $S_\\phi(f)$ to $L(f_\\phi)$ we need to:\n", "
    \n", "
  1. Normalize to a 1Hz resolution bandwidth\n", "
  2. Normalize to the total power of the signal\n", "
  3. Plot the data versus offset frequency from the carrier\n", "
\n", "\n", "This is the NIST definition of Phase Noise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another approach is to first de-modulate the phase from the signal and then calculate the Power Spectral Density of the phase, $S_\\phi(f_\\phi)$
\n", "An advantage of this approach is that it is more immune to amplitude modulation on the signal.\n", "The Signal Source Analyzer and dedicated Phase Noise test systems use this approach with a hardware phase demodulater.\n", "However a real-time oscilloscope can also demodulate phase using a software clock recovery algorithm to find the phase deviation, ph(t).\n", "If we then take the Fourier Transform of this we get the PSD of the phase modulation, $S_\\phi(f_\\phi)$
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Translation of Bessel Functions\n", "\n", "$$y(t) = sin(\\omega_c t + \\beta cos(\\omega_\\phi t))$$\n", "From:\n", "$$sin(A + B) = sin(A)cos(B) + cos(a)sin(B)$$\n", "

\n", "$A = \\omega_c t$; $B = \\beta cos(\\omega_\\phi t)$\n", "

\n", "$y(t) = sin(\\omega_c t)cos(\\beta cos(\\omega_\\phi t)) + cos(\\omega_c t)sin(\\beta cos(\\omega_\\phi t))$\n", "

\n", "From:\n", "$sin(A)cos(B) = 1/2(sin(A-B)+sin(A+B))$\n", "

\n", "$y(t) = 1/2(sin(\\omega_c t - \\beta cos(\\omega_\\phi t)) + sin(\\omega_c t + \\beta cos(\\omega_\\phi t))) + 1/2(sin(\\beta cos(\\omega_\\phi t)-\\omega_c t) + sin(\\beta cos(\\omega_\\phi t)+\\omega_c t))$" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }