Exp2_Filters.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Exp2_Filters (1) (1).ipynb","provenance":[],"collapsed_sections":[]},"kernelspec":{"display_name":"Octave","language":"octave","name":"octave"},"language_info":{"file_extension":".m","help_links":[{"text":"GNU Octave","url":"https://www.gnu.org/software/octave/support.html"},{"text":"Octave Kernel","url":"https://github.com/Calysto/octave_kernel"},{"text":"MetaKernel Magics","url":"https://metakernel.readthedocs.io/en/latest/source/README.html"}],"mimetype":"text/x-octave","name":"octave","version":"5.2.0"}},"cells":[{"cell_type":"markdown","metadata":{"collapsed":false,"id":"EjD9BMCE7PfL"},"source":["# Analog Passive Filters\n","\n","## Objective\n","\n","This experiment aims:\n","\n","1-To investigate passive filters and determine their characteristics.\n","\n","## Introduction\n","\n","In electronics, filters are circuits that allow certain frequencies to pass and block others. \n","Filters can be classified according to the element they are made of: \n","Active filters, which are made of active component like transistors and Op. amplifiers, \n","and Passive filters: which are made of passive component like resistors, capacitors and inductors. \n","Filters also can be classified by their frequency response as low-pass, high-pass, band-pass, band-reject and all-pass. \n","Filters are used in many applications:\n","High-pass filters are used to block DC in certain circuits like audio speakers and RF devices. They can also be used in conjunction with a low-pass filter to make a band-pass filter. \n","Low-pass filters are used as integrators and in radio transmitters to block unwanted harmonics which cause interference. \n","Band-pass filters are widely used in tuning circuit to select certain channel. Band-reject filters are used to block certain bands like the noise generated from power lines in 50 Hz and non-linearity of power amplifiers. All-pass filters are generally used to compensate for other undesired phase shifts that arise in the system.\n","\n","## Data Plot\n","\n","It is usually preferred to plot a data on a graph than a table, 2-Dimensions graphs illustrate clearly more information and hence Data could be investigated easily.\n","The input data will be on a horizontal “x” scale and the output will be on a vertical “y” scale. When the range of both variables is not large, both scales would be linear. However, If one of the variables has a wide range then its scale will be logarithmic, semi-log plot. When both variables cover large range then both scales will be logarithmic, log-log plot. \n","\n","![semilog.png](data:image/png;base64,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)\n","\n","\n","## Procedure\n","\n","### First Order Filters\n","\n","The experimental work proposed consists in determine magnitude and phase characteristics of filters.\n","\n","First of all, consider the circuits shown below.\n","\n","Determine the transfer function, $\\frac{Vin(\\omega)}{Vout(\\omega)}$ and plot its frequency response.\n","\n","The attenuation, defined as ratio of Vout/Vin shall be plotted on semi-log graph as a function of the frequency.\n","\n","### Low Pass Filter\n","\n","![Webp.net-resizeimage.png](data:image/png;base64,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)\n","\n","$\\frac{Vin(\\omega)}{Vout(\\omega)} = \\frac{X_c}{R+X_c}$\n"]},{"cell_type":"code","metadata":{"id":"WjBVPI-D7PfO","outputId":"882432af-ed73-4c32-b307-57c55191c1dc"},"source":["clear all;\n","warning (\"off\")\n","f   = 0:1e2:1e7;  % frequency vector\n","\n","c   = 1e-7;       % capacitor Farad\n","l   = 1e-3;       % inductor Henry\n","r   = 100;        % resistor Ohm\n","xc  = 1./(1i*2*pi*f*c);\n","xl  = 1i*2*pi*f*l;\n","\n","lp  = xc./(r+xc);       % low-pass filter transfer function\n","MgL = abs(lp);          % Magnitude response\n","PhL = angle(lp)*180/pi; % Phase response in degree\n","\n","\n","figure();\n","subplot(211);semilogx(f,MgL);grid on; title('Low-pass filter: Magnitude response')\n","subplot(212);semilogx(f,PhL);grid on; title('Low-pass filter: Phase response')"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":1}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"G0V6NILO7Pfc"},"source":["---\n","\n","### High Pass Filter\n","\n","![hp_rc.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAY8AAAD8CAAAAACqMHfgAAAABGdBTUEAALGPC/xhBQAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAAAAmJLR0QA/4ePzL8AAAAJcEhZcwAADsMAAA7DAcdvqGQAAAAHdElNRQfkCxUJOw0cxM2CAAATS0lEQVR42u2dB1QU1xqAL21pglRFQ7FgfRpBjaBo7CT6Yk8ixoYRSyzY67PHRPFZkmg8ilE0TwVLjIoaBSVYMBYUsYFIUQERYQFB+u7Om5ldcKmuOzvMv5f7naM7s8te/t2PmX/unVsQRYAEEjoAQgWID1gQH7AgPmBBfMACog9ZcWGJjH6USoWOpO4B56P4wd7V08bNWhcYE/fTfaGDqXuA+SgKm9h3+V8x8Y8Ch9jbdUwUOpy6B5aPpJl2Yx/Iz1Jpw9HQfKHjqXtA+bje03BBTtlOiPkqoeMRAEg+rvwLTS7XQaX2OCZ0QAIAyEesG+qmlDFyfOphOgfkI28iMjmktJ+7Uyx0SAIAx8dxc/R5ltK+NE8mdEgCAMbHmy+QaK/QQQgPGB9hVqjNU6GDEB4wPtYg5FUkdBDCA8VH/jCEfhQ6CABA8ZHeDRkcFjoIAEDxkeiMzEOFDgIAUHw8a4sahgkdBACg+Mjqg0zPCh0EAKD4kMxGOtuFDgIAUHxQ5yzQ6AKlfXGO2kVpM2B8vB2HbM69232594XQEQkCGB/UQ3fULbpsJ2H3A6HjEQY4Pqj7Iww7BWZKKaroxal99fBWLQsgH1T2wWGdBs1c4bd1e/hboWMRCkg+6CMj6eqZC3fSSoSOQzhg+SAQH7AgPmBBfMCC+IAF8QEL4gMWxAcsQPhIibwTmVbpudRqnqsHgPCxysjMeEul59bSz20SOrC6B4SPpQihDZWeW04/t17owOoe4gMWxAcsiA9YEB+wID5gQXzA4p0P2YNzRwKDAo/9FUfv5IcFBR4OvFBHI5Rw8PHq4onAwMCgMzeL6a/y/rHAwEN/xqpRjJKP1NvT9JHZ2rvp9E7xzUHIfNb1OrqNjYOPN493N0FoRHiShP4qn68U6fY/rk7zQoXz1X17NPiNYnuNjX+dDcfAwQdFFY5CjW8otq9Ze6eqVUgFH48c0SLFoL1Uzy2ldfZJ8PBRNAp1fCnflK4coWbbWwUfN2zRVvmWZMM8VSZHkOXERMZxH3epNT5kuU8iY3Jq+Lx5A1E/xdnlyvCHav6GCj7OmugGyLdCxj9X4c3JGz2aWtv3/zWD48fkz0d+/P2nmkuCr3f0s7du2tMvpdpXM9zLRtyleZ9U91dU8HFA1+g0u5E4LlyF917uriNq7uKgr/85x5H7fPkoOPKFo4Xj4EANzYNyz1Nf39GluUjX42p1Lz9rj2awc68Ur9mg9rm+go+fkM0/zOPbhTtUmHoquj3qfexZevw+V9RLlaOpZnjy8XaZKWIwWZTLrSA5SR6oy/749KQjvVCH6noXRzdBK9iNI1PUP2FU8LESOT6mH2S7fd+8/50F49BI+YEb2wst4TR1GE8+thoiOSI/DUwtIF2I+jxht5KHo4mFVX/gsjn6mXm853VH/d+i7EPig9owvfyvfvNEhXdet3KKUmyGWLTgNHScHx9JbVEZzhoY2f6kmeVFxeYdB5ubVX/glLFhEP0gnnLoQ4qthLKPwmGoWyZFpYwPVuWdP6NJEsXm24E626Ii1SbKuwYfM+6pX2hk1CZRuQ/9HzmEpyhui87nZeOFSsejHVW/kAB9s1D6Nb8VhZT6KPvI6ctMAVa4fJNK2Wgh2li+PROZWnPAuAYfJlwKtTZB7+BWEosp8i0P7ge0tOoXsgHZ3KKo4AkpFAeUfaR1Qd6l1P+mlrdaleTXct5dir4v25RNRU6dXdWmc+MafDThUKhrZwclH/ZcSpIX54i+Kw9uDfpP1S9kHnKKpWJHX6W4oOwjrgWaR0V+GVW2X7zui1qqNXvQqLIGlaweBkcy09VG7FuDj2Vi9QtNzzxkXK7DcD+H8BTFHdbvma2IrXA42lfl+yidhDqn5c7Yze3SQdnHLRu0IWNSUPl+Tn+jUzW/876DdYhi83fDTpwOUn7yebp7uY+uLzmVxJLc0agsUf9l6VT1D7VgGOqXtX1uHrffouwj1Ex/9w8r37Uiyq7sy675naWLULfb7DS5Ia31tnEKgqfr3aPWCh2WGpmJY7Ne24vMZb3sZle0RFLlZXEPNPLM6AQVCoqvxZmyj6OGJhMmqv6XlDwANV99KfL8Ajs0Nkvld1UHTz5K9zrKk4e/RppGxV6oycILkZdWNUOfVXM6eNEG9fnyggrl5KxMrvlFZR+/6qION99b3DviJ5giYytDZDmHY0dCvtpLpHeWtkbOi29raJ7rl7MtkKGVMTL1ru4oiHFEDbdIVCjmkEctTfHKPlYis98qvlrI/mEVlVKyvOoutd6enuLh2ts3jOuNEh7bd1ehpZqb9q/w4uxPXXtODa62hfKmLfomu+JTkpysYoppBc/MypVRRZlZOaWU5HzLto/EBTX9CiUfsllohnLLW2nczjFRlOT5gXH/vN7o0f9Yde6lOem53D8vjz7WoZXcC1H6jnLTc2o42s6ZuDyu+N3cWOvzlffRfKokfFFHrxwqdVffHpHU3wNEDYd5nanpFyj5KPbyeKb8Uuxq24bXqCQ/B1P/db7fNbK/rskPVgHt8VELAY3/qLAv/X3AiVfxi60X5FLUvSZd6Epd4RizcCo/tl3rh5mqHB9vJodULDDH0+waJS0Yq7fgqUy24V31T+Ng4WP7qorDtG+13Ez/nztatIPO9c6daR/SaeaXKep1h/a1XDMp+Sh6VGncd9GoBtfoQ3SuMXN0nRHN4G3+VSx8JFbsjCOZbcneTD9l/ElamY+pch/tVPNRhdIxjA/pXBPmuLlsPoW35Tiw8FGJV10bsXXGhNYW14mPcgTzEdfSlp0dR9zd9CLxUY5gPlI+NmXng8zu1fheuQ86nxMffEVdO0UT0DrmMfXjwW9oH66ZdEqZbHD2A/J5FUq8GkQw+Zz1ccV8KvHxIYTafsz0vA1tfoyiMt0+uksVh/fSDaSoDNcWCaUJNVXka/PxZqAR7bPIS58uhToh+rqA4gksfZT+Yj3ynvi21/oipn+cXrdls/eNR54nCorG6Hv/WOPUtrX4SN7eve20a+kBvdt4n8++4NOml386T6Fj6YMqPuc99Nvlwezd2/SlnT4PKvhh8jk6jdwc1nO3KvXByhSmZ2SmZxe9pv/PLKH/ZaQX8xQ5nj7oE744s6xprzQ7n6Ly5RW8glqamECM/9ji3LaVf6XnttHP7eJetKA+1ACEj/yMjIwCFZ5TA+IDFsQHLIgPWBAfsCA+YEF8wIL4gAXxAQviAxbEByyID1gQH7AgPmBBfMCC+IAF8QEL4gMW3xMfkJDNRz5atbAk5j5SP0am/X55WndTeXEFcx8ZvRFCeq3mXtHQFD+8g7kP6tHCdga0Eqshvyfz1r1Sk+Dug5Ik/tqnATMlgMvqKL76j2kQ7H3QZJ/71l4HIZ0m35zIFDqW91EffFBUSfRSG3ZaGQ9/4Cux1g8f+VenWzI+zD0PAU/s9cCHLOXAUGbmDL3m00JUmPdOWLD3URy1xoW5wjLu/t9YVWZPEBjMfWQGT/xIl07ldl7HX/M2PFiT4OxDEr+9FzPDqMG/lt7iModeXYKvj7xw31b6tA2LQb+90IITlQJMfchSDwyxYnP4d6EamXy3rsDSR3HUWldm7l1j982x2tOUyIKhD/Fp74+Y6njjr4+la0UOVwY7H4W/dWdnCW+44K625HBlsPNRfGhgQ8aH2XdXgTeNVAt2PijqTehUJ12mjX3ooTRyvoJA6ePNHszku4auq+9qQRu7Mlj6oEk/+lUjJqk7eJ/JFjqWDwFXHxRVdGtZB6bhyrT39qekPggBadKezyyY1Q3azNOa3I6zD5q8sOny3D7k4EutyO2Y+6Cokoeb3JncbtR1Lbl/DoPXR79sRBvR+WgS/NxeH3xQVEHkHLbSbvppAPBKez3xcUvuo0GvAN4mVdMM9cCH7FXgKBu6LqLr+O25bKGDeR/Y+yh+sNHNiM3n66NLuBfHN5j7eBPi48Bc71qPCKrclpUfGX7lyuWwS3/fSwdUXcTZhyRx1wCmrVe/3YKIqvXB/MtjTQwtx8ydOsDV5xqYvr34+ii8saQ9c/+8Qd8dCdV/3Q8dkGsKJUmapmt/VOhoy8DUhywtaJQtk8OdJtWcw5NaoklMSkn+BHVKFDpiBVj6KH28ic3hhp2/f1BLnTzcUpedRVM6FRkdETpmBRj6yDnvw7ZZ2YwMfFVrm9UmZHeb3ZiP5CsBAwA7H0UH+5uz989nRbyn63TBCOTBrtlR6o1EXNYA1iTY+Sjc/2kD1se89/VJjGuF5rPHz7NOqFWM0HErwM4HRWWd/Zapc+g0+jroVW0/d9zIkJmYnipdry/aCOWCF0MfFFVy/4euTH84o24bHtVYJ5ctQC1i6ce8nyyM5oAZE42lD+Z69+AIZkSUntOUv2r4rsWfItfTl8P8hzdy28Nx0VkNgqkPihkTNa81Ux808/R/Vl2DyK1Guj4bpzugnqEZQoeqBL4+KEqSsLMfk9sN2i26UTW379Sx/YcqGou6cFzsVbPg7IMmK1ie2xuPPlqpL2/xeNQjk6IC9E2DhQ5SGcx9MLl9fVcRm9v9Hin3dX/eAc2hDcW0QPOhXFsxYO+Dzu0vDw63Ztqymk0PeZfbg03Zq93CMegTDSxWrzHqgQ+a/IhZbCdr8/6/l92vXY4c2fUa9+ibnRc6PCXqh4+iyIXs+HNTD3+Fj5yBaDB7lfuwGVoCqGdWffAhPjnWjunLa/fNyfI1Zu82lS8PSBV8idz5WqdMDbD3Ufpki4cJfWiIXCr0dd+ma3hCvrVTzwTM3SjsfeSFzXDWo21Y/vvAC+XLqAR3ZKiwEO2A+jwVOs5ycPYhTd43mEnjes6+lyvcP4857NXUzm7IgXhm5+1426ZD9sQLHawCfH0URq7oJGL7wG2NqTTINiMuLiEh4enTLPlefEJcXJbQ4SrA1UfmyTGN5Tn8NJSvWiWw9FEas6Un0z9U1GlVJPD+upXB0Efe3zNbyHN4QDKgmoVqYOejKMjTgh3vPO0qnLsaqoOfj33uJmzTyMLoIu6l1TnY+aBT+alxTZjhN03GnBBzL62OwdAH01y1woW5f27aaxuZTwYEspSAQUxVULelr9ZMTc2CqQ+a3L992aYSK/oyC9Idp9rB1wdFSWK3stNmiFxWacPQWhacfdCnrcw/x7FzYTUd+wekXiQ1g7cPisntyzoy02aYfPpzHKBxUDWBvQ+mmTdgEFNF1GsxKxx8FbEe+KDJDZvCdrK2/HcQ8Epi/fBR8vA/7P1zo86/kvHngpN1ZpI92+G9Sqc4eGDvQ5K4k12PxaD9kn+0oO0dcx/5l33bMJ2qG3rueq4VlUKcfUjTDo9kBh3oOvmcBzPA4z3g66Mkel1ndlCOm99j7WlUxNVH1jl5x3bbr468gp7DlcHShzRxB5vD9dsvvq4FOVwZDH28vTqvLbvQhKd/klbkcGWw81F4fJgVe7924kWtWmhCAXY+3u7qxrSxI9sVWpTF34GdD0qmmL5S12kq/OXUqoCfD5rCW8s7MF1FzQfueaFlGQRLH/QV1rO9bBu7qOPyWKFj+SAw9UGTe0neTbHPa6Ej+RDw9SHvxmuCOqUKHceHgLMPGvEU5KtN1XPcfVDfo5VCh/BB4O5jHfEBCuIDFsQHLIgPWBAfsCA+YEF8wIL4gAXxAQviAxbEByyID1gQH7AgPmBBfMCC+IAF8QEL4gMWxAcsiA9YEB+wID5gQXzAgviABfEBC+IDFsQHLIgPWNQzH7I8cT7o/vwa9iHLF+fx+nk5+SgI8e3v/tmSCMCTRa5GyzVXWPG1xZ7u/eeE8jiHFhcfz6aYI0NzA2SzBOiQMOmDte1Rm9XRGhrTmb7IGhmYi5D5tOe8hczBx8vByGHx2YiTM2x0JoGcPkd6sKUOMxS9+QGNTGSZPUHHduapiLOL7NEQ3tZYVd+HZBlyjWD+8kqDWxhs5ys+Lvxpi+RYH9NEcT/rO59lxEqvuqAVfA2jVt/HIyeLs4rNvaLOkNa4VJDhgcpwe8W9uBQXw/2KzeCGzWN4Clp9H3vRiLK5c8Ruoj9yxMDIOWJS7sPoEOfwco4Z9Chb+ahgKNqv7tfGm49ligUVaWRTkHN3d2B0b47e0YxzeN1bounlV7qr0QpwPhYiv/LtWci4ITiMlHwYaqK4OeWf90e0BJyPbWhyWVIr+EzH70YEMG6sNyjXob+Gc3g3NqDBZedniTf6BZyPaxbN7ys2w6yaPeEpPg7Etyr30UID4cU4WocrNu81s7rOU9Dq+8j3Ql7yhXjj+6H5AKeql/mVHSD66zXQxiGZgwYmsltpX6GxfFXROdQH77TW8TydKn5+2A11T+QpPE7kzjeWX135aqS6Gu+G3INeiFNODdBpG8VXzFzaS0K76Bi3dWsp0usbyVd43Hh7YECTBnb9AjS0qsHtProiZ/c2RjpdL/EWMqf2xMTVXW3MG3ts4a31gDO5j2890twkcS8392hsbvvJ2iT+AubW3i7NvBfxMBt0g7tGkWU/iIjO5HPKOdzvR2kbxAcsiA9YEB+wID5gQXzAgviABfEBC+IDFsQHLIgPWBAfsCA+YEF8wIL4gAXxAQviAxbEByyID1gQH7AgPmBBfMCC+IAF8QEL4gMW/wdG6Kpl6cpCgwAAACV0RVh0ZGF0ZTpjcmVhdGUAMjAyMC0xMS0yMVQwOTo1OToxMy0wNTowMNJfWPYAAAAldEVYdGRhdGU6bW9kaWZ5ADIwMjAtMTEtMjFUMDk6NTk6MTMtMDU6MDCjAuBKAAAAAElFTkSuQmCC)\n","\n","\n","\n","$\\frac{Vin(\\omega)}{Vout(\\omega)} = \\frac{R}{R+X_c}$\n"]},{"cell_type":"code","metadata":{"id":"uk8vI60S7Pfd","outputId":"d607b31c-9973-4374-d65f-c762ec45a760"},"source":["hp  = r./(r+xc);        % high-pass filter transfer function\n","MgH = abs(hp);          % Magnitude response\n","PhH = angle(hp)*180/pi; % Phase response in degree\n","\n","figure();\n","subplot(211);semilogx(f,MgH);grid on; title('High-pass filter: Magnitude response')\n","subplot(212);semilogx(f,PhH);grid on; title('High-pass filter: Phase response')"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAJMmlDQ1BkZWZhdWx0X3JnYi5pY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpTNDAsAAAAJcEhZcwAACxMAAAsTAQCanBgAAAAddEVYdFNvZnR3YXJlAEdQTCBHaG9zdHNjcmlwdCA5LjUw/rJdRQAAIABJREFUeJzt3bFvWmm6x/GHq22vbVLnWLKjCwVU8TSwXexIppjGSoK7xdKANc2muHbsYn2L0NjGTarIuHFpk5GbSEskmOkCjX2bPRS2FI/EGel2S/A/wC3e2TMsYExs4H3P4fspIniB44fHgZ+fc45xoNVqCQAAuv2H7gIAABAhkAAAhiCQAABGIJAAAEYgkAAARiCQAABGIJAAAEYgkAAARiCQAABGIJAAAEYgkPBQ5XI5EAhsbW2pq1tbW4FAoFwuq/VyudznUbfdOiIvX75Upbpfvb0MtX6/LavtBAKBDx8+iEij0VBX3bbce5vfWpvq/72/KKARgYRRWVhYKJVKCwsLugv5w08//ZROp9fX13vWtr+/XyqVHvglzs/PReTi4mJmZuaBm2ovcii1AYYjkDAqFxcXz58/v7i4EJF8Ph8IBObn5zOZzNLSknufQqEQDAaDwWA+n29/rBoO1EDj3tpoNJaWltTksbS01Gg0Bllxt6mGFTUVtdfWfuuHDx/Uopoz3BHHnQKDwaC6tf1ZuF68eKEe3p52PUvqboj6EplMRt0zn8+7RbbX1jE2ucOQuhwMBq+vr9ufVM9BrfvptN+tu+Ce3w71wGAwqJ6IeuLdz6Ln07+tMEy6FvAwPX9yL5VKar1UKqmhIZ1OFwoFEVlcXHQftbi4WCqV5ubmZmZmurf59OnTUqn09OnTmZmZf/7zn7u7uyJSKBTUdg4PDztWdnd3u1fcbbplfPnyxa2tu8juL7S7u6vuNjc39+bNm1artbi42PHaUXd48+aNWl9cXFSX37x50112n4a8ePFCPWVVVXdt7mKr1XK/3OHhofpahUJBTWatVqtPK9qfziA97PntUIvpdNpd7Pksvul7hAnHhIThUG9MpVIpnU533KTed/b29l6+fPnixYv2m7a3t5eWll6+fPn161c1diwtLbmDy97e3tLS0vb29tevX9WgcH5+fn5+rt5/v3z54v6Af35+XigU2n/kd1fcr6VGlmAwOD8/312/e2swGFQZqb7WzMyMm7h7e3t7e3siUi6XW73+bsvz58/VrWq4UYvdZfdpyPr6umrCbbX1bL6qU23w5cuXavG2Z+FST6f7brf1sOPboTaYz+fdRfcoV/uz6N7anYVhYhFIGI5gMKjeg25701TrPcPgzi2rC3t7e999952IrK+vq5VMJlMqlZaWlvL5/KtXr7a2trpX7vl8/iWTybx69aqjkj4WFxcLhcLXr1/dUOkuu31r92hIt0aj4dbWs8j2Z9FRQPfd+vdwkCZ0bLPP1noWholFIGHknjx5IiJ7e3vX19cdx4ra7e3tqQM87tEXdx+X/OsI/9zc3Pb2tnuYZGtr6/DwcG9vr9FozM3NXV9fd6/co+CFhYVGo7G9va2+VvuBKCWfz/eMukajsbCw8OHDB7W3Sukue8CG9HFxcXF9fa3O6BOR77777tdff/3w4UP74p3P4ra73dbDjm+HehaqfrWrsOcJLN1bG7AwTCACCSOXyWSePn26vb395MmTbxoILi4uAoHATz/9dHh4GAwG19fXf/3110ePHrk7eV69elUulx89ehQIBBqNxvr6evfK4F9uZmZmf3+/XC5vb2/Pz88/evTo0aNH19fXmUym456FQmF/f797C8Fg8Lvvvmsfj0Sku+x7NMStbWFhYWZmpuOxaoOvXr168uSJO8Hc+Sxuu9ttPez4dmQyGXXKolrc29vrOTx1b23AwjCBAj13hQNDdH19rX4QXlhY2N3dvb6+vvNXasrl8vPnz9U7+Pz8vPvO626n484isrCw4L4hdq8MotFoXFxcuI8ql8vBYHAop613lH2PhrTXpi63t0Upl8s9Fwd5Ft13a+/hbd8OEbm4uFBPpH+re36PhtVe+Ifusyrgf1++fJmZmZmbm1PnOxweHt75kPZzyfznHg3Ry9/fDpjjT3rjEJNgfn5eHdtoNBpfvnwZZCfV/Pz8mzdvhnLA30D3aIhe/v52wBzssgMAGIGTGgAARiCQAABGIJAAAEYgkAAARvB2IDWbTcdxdFcBABgCbwdSoVA4OTnRXQUAYAg8HEgrKysHBwe6qwAADIeHA+ns7OyHH37QXQUAYDh8+0kN4XBYdwkAYJbLy0vdJfTj20AS41s/BoEAn8RBE0T+vQmBjV+Gss3WwbOhbGc8+G8gXvgx3c+BBEymHpHz3z+3L3orSzA5CCTAw24bdzoih/kAnuDtQNrc3NRdAjBW3QnEuAPf8HYgob9QKKS7BP180ISOELpHAvmgCQ9EBzyBQAIMxVEfTBoCCTALOYSJRSABRiCHAAIJ0MyNInIIE45AArQhioB2BBKggYoicghoRyABY0UUAbchkIDxCWz8QhQBtyGQgHFgMALuRCABI8dgBAyCQAJGiMEIGByBBIwKgxHwTTz8J8wBk5FGwLdiQgKGjN10wP0QSMAwMRgB98YuO2BoSCPgIQgkYDhII+CBCCRgCEgj4OEIJOChSCNgKLwRSLZtN5vNwdeBsSGNgGHxQCClUqnT09O1tbVKpeIuNpvNlZWV09NT9a/G8jDJSCNgiEwPpGKxaFlWNpt99+5dPp931z99+hSLxbLZ7NnZWbFY1FghJhZpBAyX6b+HZNt2NBoVEcuyqtWqux6JRE5PTyuVSq1Wi0Qi+grEhCKNgKEzPZBExLIsdSEWi7UvTk1NFYvFWq2WTCZ7PjAQCLRfDYVCoyvSWOFwWHcJ+g29CVffvw99/DH8cbhbHS3+J0xmB66urtzL5r8HeiCQHMdRF9onpHw+n0gkVBQtLi72zKRWqzWeCo0VDocvLy91V6HZ0Jvw+2x04KXG8j+BDogXItn0Y0jRaLRer4uI4zjsmoN27KkDRsf0CSmRSBwdHeVyuWq1mk6nK5XK2tra5eXl6upqKpWq1+u1Wm15eVl3mZgI6lNTAYyI6YEkImdnZ5VKZXV1VR1MUnO3ZVk///xz+zowBoxHwOh4IJBEJB6Pf9M6MHTsrANGzfRjSIAJSCNgDAgk4A6kETAeBBLQD2kEjA2BBAAwAoEE3IrxCBgnAgnojTQCxoxAAnogjYDxI5AAAEYgkIBOjEeAFgQS8G9II0AXAgn4A2kEaEQgAQCMQCABv2M8AvQikAAR0ggwAIEEADACgQQwHgFGIJAw6UgjwBAEEiYaaQSYg0ACABjBG4Fk23az2exedxzHcZzx1wN/YDwCjPIn3QXcLZVKWZZVq9U2Njbi8bi7vrOzIyKO4yQSiWQyqa9AeBJpBJjG9AmpWCxalpXNZt+9e5fP5931SqUiImpdXQYAeJrpE5Jt29FoVEQsy6pWq+7658+fZ2dnT09PReTdu3fa6oM3MR4BBjI9kETEsix1IRaLta+fnJxkMpl6vZ5KpY6Pj7sfGAgE2q+GQqGR1WiucDisuwT9Oppw9f370Mcfwx91laMH/xMmswNXV1fuZfPfAz0QSO5pC+0TkogsLy+rQ0crKys9H9hqtUZdm+HC4fDl5aXuKjTrbkJg45dJawv/E+iAeCGSTT+GFI1G6/W6iDiOE4lE3PXZ2Vn3cs8T8ICe2FkHGMv0QEokEtVqNZfLvX79Op1OVyoVFfLJZFKtp1KpTCaju0x4A2kEmMwDu+zOzs4qlcrq6qo6mOTO3R3rAABP80AgiUj7rx8Nsg50YzwCDGf6LjtgKEgjwHwEEgDACAQS/I/xCPAEAgk+d/X9e9II8AQCCQBgBAIJfhbY+CX08UfdVQAYCIEE3+LQEeAtBBL8iTQCPIdAAgAYgUCCDzEeAV5EIMFvSCPAowgkAIARCCT4CuMR4F0EEvyDNAI8jUACABiBQIJPMB4BXkcgwQ9II8AHCCR4HmkE+IM3Asm27Waz2fMmx3FuuwkA4CEeCKRUKnV6erq2tlapVDpuajabKysr09PTWgqDCRiPAN8wPZCKxaJlWdls9t27d/l8vuPWg4ODqakpJqSJRRoBfmJ6INm2HY1GRcSyrGq12n7T0dHR7OysZVlMSJOJNAJ8xvRAEhHLstSFWCzmLtq2bdt2Op3WVBQAYMj+pLuAuzmOoy60T0hHR0ePHz/O5XKO4+zs7GQyGTe3XIFAoP1qKBQadakGCofDuksYiavv34c+/hj+ONCd/dqEb0ITJrMDV1dX7mXz3wNND6RoNGrbtog4jhOJRNz1dDp9c3MjItVqNZFITE1NdT+21WqNrU4zhcPhy8tL3VUM3+876w4Gemp+bcI3oQl0QLwQyaYHUiKRODo6yuVy1Wo1nU5XKpW1tbXLy0t1YElEpqam4vG43iIxThw6AvzK9EASkbOzs0qlsrq6qnbKdfyYc3x8rKcs6EAaAT7mgUASEWYgAPA9D5xlByiMR4C/EUjwBtII8D0CCR5AGgGTgECC6UgjYEIQSDAaaQRMDgIJ5iKNgIlCIAEAjEAgwVCMR8CkIZBgItIImEAEEoxDGgGTiUCCWUgjYGIRSDAIaQRMMgIJpiCNgAlHIMEIpBEAAgn6kUYAhECCdqQRAMUbf6APvhTY+EVESCMACoEEPRiMAHRglx00II0AdPNGINm23Ww2e647jjP+evAQpBGAnjywyy6VSlmWVavVNjY24vG4Wmw2m2tra5FIxHGcSCSyubmpt0gMiDQCcBvTA6lYLFqWlc1mHcfZ2dlxA6lQKMRiMZVDi4uLBJL5OIUBQH+mB5Jt29FoVEQsy6pWq+768vKyutBzVx5Mw2AE4E6mB5KIWJalLsRisY7FSqVycHCQyWR6PjAQCLRfDYVCI6vRXOFwWHcJcvX9+9DHH8MftRVgQhO0owmT2YGrqyv3svnvgR4IJPe0hfYJSURyudxvv/327t07N7E6tFqtkRdntnA4fHl5qbGAP3bTHWgrQ3sTTEAT6IB4IZJND6RoNGrbtoiokxfc9dPTU5VG+krDHdhNB+CbmB5IiUTi6Ogol8tVq9V0Ol2pVNbW1i4vL9UJ36lUSt3t+PhYZ5X4d5y/AOAeTA8kETk7O6tUKqurq2rXnJq7s9ms7rrQG4MRgPvxQCCJiHu2N0zGYATgIbwRSDAfgxGAByKQ8FAMRgCGgkDC/RFFAIaIQMJ9EEUAho5AwrchigCMCIGEQRFFAEaKQMLdiCIAY0AgoR+iCMDYEEjoQeWQEEUAxohAwh/IIQAaEUgghwAYgUCaXOQQAKMQSBOHHAJgJgJpIrghJOQQAFMRSL4V2PhFvn/PedsAvIJA8o/2MUhEWgfPwuGw+nuGAGA+AsnDuhNIVyUA8HAEkmd0xI+QQAD8hUAyUXf2CPEDwO+8HUi2bVuWNT09rbuQ++iZOsqwsufq6moo2/E0miA0gQ54hIcDKZVKWZZVq9U2Njbi8bjucv5Nn7BxMfEAQDuvBlKxWLQsK5vNOo6zs7MzukAaJFq6ETYA8K28Gki2bUejURGxLKtarfa8z/2ypAPRAgDjEWi1WrpruI9cLvfnP/9ZDUapVOr4+LjjDuFwWENZAGAww38x0asTkog4jqMu9JyQDO87AKDDf+gu4J6i0Wi9XhcRx3EikYjucgAAD+XVXXYisrKyEovFqtVqOp1OJBK6ywEAPIiHA0lEKpWKZVmWZfW/W7PZPDg4EJF4PD6x0aWacHNzk06n1fkgE+v09DQSiUxmE2zbVq+FSCSyubmpuxxtcrncb7/9try8PLFvCLlcrlarqcsbGxumvBxaEyCfz//9739vtVp/+ctfdNeizf7+/j/+8Y9Wq/XXv/5Vdy061ev1Z8+eff78WXchenz+/Pnk5ER3FZqdnJzk8/lWq7W/v6+7Fs2+fv36t7/9TXcVf/DwSQ2DW15eVlPUzc2N7lq02dzcbDabxWLx8ePHumvRKZ/PLy8v665Cm1qtZtt2pVJJJpOm/Tr52NTr9dnZ2Vwut7q6qrsWzfL5fCaT0V3FH7x6UkO3ZrPpnnen2LbdbDZFxLKsSqWSSqXevn2rqbox6WiC2wHXzc2N71O5TxNyuVwymdRU1/j0eS1EIpF0Ov327Vu1487H+jShVqvV6/XV1dWdnR1N1Y1JnyaIiOM4Nzc3dx7yGCf/BFKhUDg5OXGvplKp09PTtbW1SqVSLBaLxeLx8bEp+0lHpr0J7R0QkVwuNz09nUwmO/6D+k+fJszOzhaLxVqtViwWtdY4Wn1eC47jRKPR6enpqakpjRWOQZ8mRCKR1dVVo96IR6RPE0Tk06dPpv185pNddisrK7Va7YcfflBXOz5YaHp6utlsplIpEen+FVrfaG9C90crRaPR169fP3782N+vw/5NUC8/9VvVuisdlf6vhWQyqf4b+PuXJfo3IZvNHhwcTNRrQXq9HD5//pxOp/UW2cEngXR2dpbL5dyrHR8sNCG/JNvehO6PVkokEtFotNls+ntM7N8Exd9nl/V/LRwfH8fjcTUn6atx5Po3wbKst2/fTngTxMifzn0SSN3cn31isZjeSnTp7sAgp8j7DP8NpKsJ09PTHv2LLQ9BE8QLLwf/HEPq0P+DhSYBHRCaICI0QURogoh4oQn+DCQ+WIgOCE0QEZogIjRBRDzSBH/uskskEkdHR7lcTn2wkO5yNKADQhNEhCaICE0QEY80wdsfHdTfgB8s5GN0QGiCiNAEEaEJImJ8E/wcSAAAD/HnMSQAgOcQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIGLlyuRwIBLa2ttTVra2tQCBQLpfVerlc7vOo224dkZcvX6pS3a/eXoZav9+W1XZc8/PzFxcXWp4jYCwCCdosLCyUSqWFhQXdhfzhp59+SqfT6+vrPWvb398vlUoP2X46nS6VSru7u41GI5PJPKxYwG8IJGhzcXHx/Pnzi4sLEcnn82puyGQyS0tL7n0KhUIwGAwGg/l8vv2xarZQA417a6PRWFpaUiPI0tJSo9EYZMXdpprh1FTUXlv7rR8+fFCLas5zJz93CgwGg+rW9mfhCgaDS0tLW1tbCwsL//u//9vzOQ5Yc0cBHZ1xK+m+Z/fWejZTPTAYDHbMc5lMRj32tmr71AbcoQWMWM+polQqqfVSqXR+fi4i6XS6UCiIyOLiovuoxcXFUqk0Nzc3MzPTvc2nT5+WSqWnT5/OzMz885//3N3dFZFCoaC2c3h42LGyu7vbveJu0y3jy5cvbm3dRXZ/od3dXXW3ubm5N2/etFqtxcXFjheXuoOakAqFwszMjCq++zk+8Fl0VDLIY3s2s71gtahWXrx4oVbUE/ym2oD+mJAwJuqtrVQqpdPpjpvUO9fe3t7Lly9fvHjRftP29vbS0tLLly+/fv0q/5o8lpaWrq6u1EOWlpa2t7e/fv16cXGxtbV1fn5+fn5+eHgoIl++fHHnlfPz80Kh0D7BuCvu11I76ILB4Pz8fHf97q3BYFDlh/pa7ju1qmdvb09EyuVyq9Xq3sjR0dHz589fvXolIu4g0v0c73wWtxXgcivpvudtHehoptpmPp93F9VIt76+rr4F6lH3qA24DYGEMVF7q5aWltxdSd13EJGeYXDnltWFvb297777TkTW19fVSiaTKZVKS0tL+Xz+1atXW1tb3Sv3fD7/kslkVMC0V3Iblcrn5+eNRuO2g2eDPIvbCnD1rETds//W7nwK3dv81tqA2xBI0O/Jkycisre3d3193XGsqMPe3p46xhMKheRfo5WaJNRpCHNzc9vb29fX1+r+W1tbh4eHe3t7jUZjbm7u+vq6e+UeBS8sLDQaje3tbfW12g9EKfl8vmfUqVTufx7HIM/izgL6lHpbBzqaqb4p6tuh9jH+13/9V/f2H1Ib0IFAgn6ZTObp06fb29tPnjz5pgnp4uIiEAj89NNPh4eHwWBwfX39119/ffTokbub6NWrV+Vy+dGjR4FAoNForK+vd68M/uVmZmb29/fL5fL29vb8/PyjR48ePXp0fX3dfb5coVDY398ffMvtBnkWdxbg6r7nbR3oaGYmk1EnHKrFvb29//zP/+ze/kNqAzoEeu7pBsbp+vpa/Si9sLCwu7t7fX1956/mlMvl58+fq7fs+fl5N8bc7XTcWUQWFhbc/VHdK4NoNBoXFxfuo8rlcjAYHMVp64M/iwEL6L5n+9Zua6aIXFxcqEr6N+ohtQEuAgn6qf08anfW0dHR4eHhnT9Wu++hPc+uxjehmTDEn3QXAMj8/Pz19fWHDx8ajcaXL18G2Ws3Pz//5s2be5wBgW40E4ZgQgIAGIGTGgAARiCQAABGIJAAAEYgkAAARjA6kJrNpuM47Su2bTebzduuAgC8y+hAKhQKJycn7tVUKnV6erq2tlapVLqvAgA8zdzfQ1pZWanVaj/88IO6WiwWLcvKZrOO4+zs7DSbzfar8Xhcb7UAgAcyd0I6Oztz00hEbNuORqMiYllWtVrtuKqtSgDAkJg7IXWzLEtdiMVi3Vc7hMPhsRUGAJ5weXmpu4R+vBRI7gkO1Wo1Eom0X+15f8NbPwaBAJ/EQRNEaAIdEBEv/Jhu7i67DtFotF6vi4jjOJFIpOOq7uoAAA/lmQkpkUgcHR3lcrlqtZpOpzuu6q4OAPBQHhtjK5WKZVnu0aOOq+3C4TC77NhNITRBRGgCHRARL7wremZCUjpO7+ZsbwDwDc8cQ8I9hEIh3SXoRxOEJtABjyCQAABGIJAAAEYgkAAARiCQAABGIJAAAEYgkAAARiCQAABGIJAAAEbw2Cc1fJPAxi/3eFTr4NnQKwEA3MnPgXS/aLlfjA2CqAOAPvwcSPczuti4R9SRYQAmB4E0PvdIlzszjMQC4BsEktHuzJvbEougAuA5BJK33RY8vwfV9+/bE4uUAmAyAsmfVPZ0/D2u7nGKiAJgDgJpgnTHT0dEkU8ANCKQJlpHApFPADQikPCHPvlEOAEYNY8Fkm3blmVNT0/3vIrhag8hwgnAqHkmkJrN5traWiQSqVQqmUwmmUymUinLsmq12sbGRjwe112gz/UMJ5IJwBB5JpA+ffoUi8U2Nzebzebr16+npqYsy8pms47j7OzsEEjj5OYQyQRgiDwTSJFI5PT0tFKp1Gq1SCRi23Y0GhURy7Kq1aru6iYUyQRgiDwTSJZlTU1NFYvFWq2WTCbr9bplWeqmWCzW8yGBQKD9aigUGnmV5gmHw2P4Km5nA/L+95WPP47h6w5oPE0wHE2YzA5cXV25l81/D/RMIOXz+UQikUwmRWRxcXF5edlxHHXTbRNSq9UaX31G6vjF2HFSyWTCwKSxCeagCXRAvBDJngmkDtFo1LZtEXEcJxKJ6C4HnVQUsSsPwOA8E0irq6upVKper9dqteXl5UQicXR0lMvlqtVqOp3WXR166zjIRCwB6MMzgWRZ1s8//1ypVFZXV9XRo7Ozs/arMFn7wEQsAejJM4GkdJzezdne3kIsAejDY4EEHyCWAPREIEEPYglABwIJOhFLAFz/obsAQFoHz1oHz277c+wAJgSBBFOoTCKWgIlFIMEgjErAJCOQYBxGJWAyEUgwEaMSMIEIJJiLUQmYKAQSjMaoBEwOAgkewKgETAICCd7AqAT4HoEELyGTAB8jkOAx7L4D/IpAgvew+w7wJQIJXkUmAT5DIMHDyCTATwgkeBuZBPgGgQTPI5MAf/BYIDmO4ziOe9W27WazqbEeGIJT7wAf8NJfjN3Z2RERx3ESiUQymUylUpZl1Wq1jY2NeDyuuzpo5v7xWf7yLOBRngmkSqUiItlsttls/s///M/U1JRlWdls1nGcnZ0dAgmKGpXIJMCLPLPL7vPnz7Ozs6enp58+fXr37p1t29FoVEQsy6pWq7qrg0E4pAR4lGcmJBE5OTnJZDL1ej2VSkUiEcuy1HosFut5/0Ag0H41FAqNvETzhMNh3SVoEBIJyPvQxx/V1clsQgeaMJkduLq6ci+b/x7opUBaXl5OJpMisrKyIiLu2Q23TUitVmtstZkpHA5fXl7qrkKbgLxvHTyb8CYoNIEOiBci2TO77GZnZ93LzWYzGo3W63URcRwnEonoqwvmYt8d4C2emZCSyeTKykoul6vVaplMJpFIHB0d5XK5arWaTqd1VwdDtQ6eBeS97ioADMQzgSQiZ2dnlUpldXVVHT3quAr0FPr4o9p3p7sQAHfwzC47JR6Pt8dPx1WgJ/bdAZ7gsUAC7odMAsxHIGFSkEmA4QgkTBAyCTAZgYTJQiYBxiKQMHHIJMBMBBImEZkEGIhAwoQikwDTEEiYXGQSYBQCCRONTALMQSABAIxAIGHSMSQBhiCQADIJMAKBBIiQSYABCCTgd2QSoBeBBPyBTAI0IpCAf0MmAboQSEAnMgnQgkACeiCTgPHzXiA5jtNsNtVl27bdy8BwkUnAmHkskJrN5srKyvT0tIikUqnT09O1tbVKpaK7LvgTmQSMk8cC6eDgYGpqqtlsFotFy7Ky2ey7d+/y+bzuuuBbZBIwNl4KpKOjo9nZWcuypqenbduORqMiYllWtVrVXRoA4KE8E0i2bdu2nU6n3RXLstSFWCymqShMBIYkYDwCrVZLdw0Def369ePHj0Xk06dP8Xg8EAhEIpFkMiki4XD48vKy4/7hcPjq6qp9JRQKja1a+M/V9+9DH3/UXQXwbdrfBkOhUPdbpVH+pLuAQaXT6ZubGxGpVquJROL//u//rq+vRcRxnEgk0vMhXsna0ekZ1ZNmiE0IyPvWwbOhbGrM+J9AB0QkHA7rLuEOngkkdcRIRKampuLxuIisrKzkcrlqtdq+Hw8YHbXvzqOZBJjPM4HkOj4+VhfOzs4qlcrq6qp7MAkYNTIJGB3PnNTQUzweJ40wZpzjAIyItwMJ0IJMAkaBQALug0wCho5AAu6JTAKGi0AC7o9MAoaIQAIehEwChoVAAh6KTAKGgkAChoBMAh6OQAKGg0wCHohAAoaGTALjSdnHAAAHSUlEQVQegkACholMAu6NQAKGjEwC7odAAoaPTALugUACRoJMAr4VgQSMCpkEfBMCCRghlUnEEjAIAgkYrdbBM0YlYBAEEjAOZBJwJwIJGBMyCeiPQALGh0wC+vBYINm27ThO+9Vms6mxHuBbcZoDcJs/6S5gUM1mc21tLRKJOI4TiUQ2NzdTqZRlWbVabWNjIx6P6y4QGFTr4JmIBDZ+URcAKJ4JpEKhEIvFNjc3RWRxcTEajVqWlc1mHcfZ2dkhkOA5alQikwCXZwJpeXlZXVD76GzbjkajImJZVrVa1VkZcF/uISViCRAPHUOyLMuyrEqlsra2lslk1Iq6KRaLaS0NuD9+SwlweWZCEpFcLvfbb7+9e/fOsqxcLuee3XDbhBQIBNqvhkKhkZdonnA4rLsE/cxvQkgkIO9DH38c3ZcwvwmjNpkduLq6ci+b/x7omUA6PT1VaaSuRqNR27ZFRJ3j0PMhrVZrfPUZKRwOX15e6q5CMw81ISDvZTS77zzUhBGhA+KFSPZMIKkTvlOplLp6fHx8dHSUy+Wq1Wo6ndZaGjAc7tl3wlElTCTPBFI2m+1YOTs7q1Qqq6ur7sEkwAfcX1QikzBpPBNIPXG2N3yJUQmTyduBBPgYsYRJ45nTvoHJ1B5LgL8xIQGmY1TChCCQAG8gluB7BBLgJcQSfIxjSID3uLHEX7KAnzAhAZ7kjkduJjEwweuYkABvUx/PKm3JBHgUExLgB92ZxMAEzyGQAP9gPx48jUACfKhzYPr+veaCgAEQSIBvdQ9MwswEgxFIgP+FPv6o/hpQx4kPhBOMQiABE6Q9gRibYBoCCZhQHeF0203A2BBIAG6dnIRwwhgRSAD+TZ9wEvIJo0QgAbhVR/z0/DAIIgrDQiABGFR39tz2eUWkFO4h0Gq1dNdwf7ZtW5Y1PT3dfVM4HFbnuU6yQMDb39+hoAky9ib0/0g9LVnFfwPxwruihyekVCplWVatVtvY2IjH47rLAfC7PpEz4CfAMmBNJq8GUrFYtCwrm806jrOzs0MgAZ4wSNLc42PLCTB/8Gog2bYdjUZFxLKsarWquxwAQ/Ot6TJQgP33z/f72xxE3Th5NZBExLIsdSEWi/W8QzgcHmM5JgqFQjSBJojfmxAa5cbDH0e5dfw7DweS4zjqQs8JyfBjdwCADl79i7HRaLRer4uI4ziRSER3OQCAh/LwqZArKyuxWKxarabT6UQiobscAMCDeDiQRKRSqViW5R5Muk2z2Tw4OBCReDw+sdGlmnBzc5NOp9X5IBPr9PQ0EolMZhNs21avhUgksrm5qbscbXK53G+//ba8vDyxbwi5XK5Wq6nLGxsbprwcWhMgn8///e9/b7Vaf/nLX3TXos3+/v4//vGPVqv117/+VXctOtXr9WfPnn3+/Fl3IXp8/vz55OREdxWanZyc5PP5Vqu1v7+vuxbNvn79+re//U13FX/w8EkNg1teXlZT1M3Nje5atNnc3Gw2m8Vi8fHjx7pr0Smfzy8vL+uuQptarWbbdqVSSSaTE/vbe/V6fXZ2NpfLra6u6q5Fs3w+n8lkdFfxB6+e1NCt2Wy6590ptm03m00RsSyrUqmkUqm3b99qqm5MOprgdsB1c3Pj+1Tu04RcLpdMJjXVNT59XguRSCSdTr99+1btuPOxPk2o1Wr1en11dXVnZ0dTdWPSpwki4jjOzc3NnYc8xsk/gVQoFE5OTtyrqVTq9PR0bW2tUqkUi8VisXh8fGzKftKRaW9CewdEJJfLTU9PJ5PJjv+g/tOnCbOzs8VisVarFYtFrTWOVp/XguM40Wh0enp6ampKY4Vj0KcJkUhkdXXVqDfiEenTBBH59OmTaT+f+WSX3crKSq1W++GHH9TVjg8Wmp6ebjabqVRKRI6PjzXWOVLtTej+aKVoNPr69evHjx/7+3XYvwnq5ZfL5f785z/rrnRU+r8Wksmk+m/g71+W6N+EbDZ7cHAwUa8F6fVy+Pz5czqd1ltkB58E0tnZWS6Xc692fLDQhPySbHsTuj9aKZFIRKPRZrPp7zGxfxMUf59d1v+1cHx8HI/H1Zykr8aR698Ey7Levn074U0QI38690kgdbvzg4V8r7sDg5wi7zP8N5CuJkxPT/f8iy3+RhPECy8H/xxD6tD/g4UmAR0QmiAiNEFEaIKIeKEJ/gwkPliIDghNEBGaICI0QUQ80gR/7rJLJBJHR0e5XE59sJDucjSgA0ITRIQmiAhNEBGPNMHbHx3U34AfLORjdEBogojQBBGhCSJifBP8HEgAAA/x5zEkAIDnEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAIxBIAAAjEEgAACMQSAAAI/w/j2Q6NljyMfYAAAAASUVORK5CYII=","text/plain":["<IPython.core.display.Image 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)\n","\n","\n","$\\frac{Vin(\\omega)}{Vout(\\omega)} = \\frac{R}{R+X_c+X_l}$"]},{"cell_type":"code","metadata":{"id":"bYsCPWsu7Pfm","outputId":"5258e70d-e89d-42b4-d7e0-3b5753bb0c95"},"source":["bp  = r./(r+xc+xl);     % band-pass filter transfer function\n","MgB = abs(bp);          % Magnitude response\n","PhB = angle(bp)*180/pi; % Phase response in degree\n","\n","figure();\n","subplot(211);semilogx(f,MgB);grid on; title('Band-pass filter: Magnitude response')\n","subplot(212);semilogx(f,PhB);grid on; title('Band-pass filter: Phase response')"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":3}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"V6JB3GIfgo8Q"},"source":["## Phase  Measurement by Lissajous Patterns\n","The oscilloscope may be used to compare simultaneously two separate waveforms. When two signals of the same frequency are impressed on the oscilloscope, one on the vertical and one on the horizontal plates, an elliptic pattern results on the screen. The width of this pattern is dependent on the phase difference between the input signals, if they are in phase or 180° out of phase: a straight line will be displayed. An ellipse is obtained for other phase angles. The phase difference can be calculated by taking the ratio of the vertical intercept to the maximum vertical deflection. The phase shift is now calculated $\\phi = \\sin^{-1} (a / b)$\n","\n","![lissajous.png](data:image/png;base64,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)"]},{"cell_type":"code","metadata":{"id":"oHR8Mwkago8Q","outputId":"4444942c-32d5-4c29-fce6-77fe43e037f7"},"source":["fs   =  1e2;\n","t    =  0 : 1/fs : 1;\n","vin  =  sin(2*pi*t);\n","vout =  sin(2*pi*t+pi/4);\n","\n","plot(vin,vout);grid on;"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":38}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"n2TJw_smgo8Q"},"source":["----\n","\n","### Filter Design in Matlab\n","\n","Filters can be designed using different ways. In the textbook, Butterworth filters were introduced.\n","\n","$|H(f)| = \\frac{1}{\\sqrt{1+(\\frac{f}{B})^{2n}}}$\n","\n","![butter.png](data:image/png;base64,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)\n","\n","Here, we will design analog filters using ``` matlab command: butter ```\n","\n","In ```Octave, butter ``` is a built-in function from ``` signal package```\n"]},{"cell_type":"code","metadata":{"id":"YgGMN6Sygo8Q"},"source":["pkg load signal % loading signal package\n","help butter"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"VVtuEYvGgo8Q"},"source":["```\n"," Low pass filter with cutoff 'pi*Wc' radians:\n","\n","          [b, a] = butter (n, Wc)\n","\n","     High pass filter with cutoff 'pi*Wc' radians:\n","\n","          [b, a] = butter (n, Wc, \"high\")\n","\n","     Band pass filter with edges 'pi*Wl' and 'pi*Wh' radians:\n","\n","          [b, a] = butter (n, [Wl, Wh])\n","\n","     Band reject filter with edges 'pi*Wl' and 'pi*Wh' radians:\n","\n","          [b, a] = butter (n, [Wl, Wh], \"stop\")\n","```"]},{"cell_type":"code","metadata":{"id":"KRTR6W3Bgo8Q","outputId":"b3b45f6a-3778-4b09-80d2-4349cb9f3b85"},"source":["fc     = 300;                  % cutoff frequency\n","fs     = 1000;                 % sampling frequency\n","n      = 3;                    % filter order\n","\n","[b, a] = butter (n, fc/fs/2);  % Low pass filter with cutoff fc radians\n","freqz(b,a)                     % Plots the magnitude and phase response of b/a filter"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"code","metadata":{"id":"sOpZ1fI2go8Q","outputId":"60f1f995-6345-48de-c0a7-e1b3d585da4c"},"source":["fc     = 300;                        % cutoff frequency\n","fs     = 1000;                       % sampling frequency\n","n      = 3;                          % filter order\n","\n","[b, a] = butter (n, fc/fs/2, \"high\"); % High pass filter with cutoff fs\n","freqz(b,a)                            % Plots the magnitude and phase response of b/a filter"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":14}]},{"cell_type":"code","metadata":{"id":"1bdTt7nogo8R","outputId":"6aafd98e-da36-4033-b12d-18dc546341f3"},"source":["fc1    = 300;                           % first cutoff frequency\n","fc2    = 500;                           % first cutoff frequency\n","fs     = 1000;                          % sampling frequency\n","n      = 3;                             % filter order\n","\n","[b, a] = butter (n, [fc/fs/2, fc2/fs/2]); % Band pass filter with edges fc1 and fc2 radians\n","freqz(b,a)                                % Plots the magnitude and phase response of b/a filter"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"Owysf9kAgo8R"},"source":["---\n","\n","### Filtering a Signal from High Frequency Noise"]},{"cell_type":"code","metadata":{"id":"PT7XFMx1xkpg","outputId":"0df36494-72d7-4fce-e807-28bc798e208b"},"source":["warning(\"off\")\n","pkg load signal\n","\n","fs    = 1e4;\n","t     = 0:1/fs:1;\n","f     = 100;\n","x     = cos( 2*pi*f*t )+ 0.5*randn( size(t) );\n","[b a] = butter(5,10*f/fs/2);\n","X     = filter(b,a,x);\n","\n","figure();\n","subplot(211);plot(t(1:300),x(1:300));title('Signal + Noise')\n","subplot(212);plot(t(1:300),X(1:300));title('Filtered Signal')\n"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":27}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"eFKymXbjgo8R"},"source":["---\n","\n","### Filtering a Square Wave to a Sinusoidal Signal"]},{"cell_type":"code","metadata":{"id":"MF8ArVOpgo8R","outputId":"30846098-220b-4680-d80f-5105824811e1"},"source":["fs    = 1e2;\n","t     = 0:1/fs:4*pi;\n","x     = square(t);\n","[b a] = butter(5,1/fs/2);\n","X     = filter(b,a,x);\n","\n","figure();\n","subplot(211);plot(t,x);title('Signal + Noise')\n","subplot(212);plot(t,X);title('Filtered Signal')"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"image/png":"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","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":37}]},{"cell_type":"markdown","metadata":{"collapsed":false,"id":"idji9X0d7Pft"},"source":["---\n","\n","## Discussion\n","- What is cutoff frequency of a filter? Determine cutoff frequency for above filters?\n","- What is the resonance frequency in Bandpass circuit? Determine the phase shift at resonance frequency?\n","- What is the normalized frequency? ( x$\\pi$ rad/sample )\n"]}]}