{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "confused-thriller", "metadata": {}, "outputs": [], "source": [ "from sympy import Matrix, symbols, sin, cos, trigsimp, init_printing, I, \\\n", " simplify, Eq, solve, expand, lambdify, diff, solveset, exp\n", "from scipy import optimize\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import os\n", "init_printing()" ] }, { "cell_type": "code", "execution_count": 2, "id": "prostate-tanzania", "metadata": {}, "outputs": [], "source": [ "i, vo, vbe, n, vd, vt, Is, k = symbols(\"i Vout V_{BE} n V_D V_T I_S k\")" ] }, { "cell_type": "markdown", "id": "opponent-gibson", "metadata": {}, "source": [ "Formula for a shockley diode basically taken from wikipedia. I started this to see if I could estimate values of $ n V_T $ and $ I_S $ from the data sheet. It has been a little less than straight forward but this notebook is about this attempt." ] }, { "cell_type": "code", "execution_count": 3, "id": "waiting-rugby", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_png function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_rgba function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_mask function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The MathtextBackendBitmap class was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n" ] }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle I_{S} \\left(e^{\\frac{V_{BE}}{V_{T} n}} - 1\\right)$" ], "text/plain": [ " ⎛ V_{BE} ⎞\n", " ⎜ ────── ⎟\n", " ⎜ V_T⋅n ⎟\n", "I_S⋅⎝ℯ - 1⎠" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr1 = Is * (exp(vbe/(n*vt))-1); expr1" ] }, { "cell_type": "markdown", "id": "practical-easter", "metadata": {}, "source": [ "Because I don't care about constituents of $ n V_T $ I replace it with k." ] }, { "cell_type": "code", "execution_count": 4, "id": "parallel-sodium", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHYAAAAbCAYAAACpzXuVAAAFQ0lEQVR4nO3aeaxdQxwH8M9ra6naS0gEJZTIw7XvO5VI0NiC2CKWWGpfUkEaO3+oXZEIUbE+sUbsUtrQKs8ram+tjSXEWrHVH7857rzbe99y72t61f0mJ3NmfjPnzD3f+S3zm9s2btw4LSx6GLSwJ9BEuALPLOxJDBSamdg3cVUN2XGYi7UafMcEXJPuS+hs8HlNg2YmtgvtVdqXwyWC9FkNPL8N++DhVC/hjQae11RYEMTeia8xrMHn1CL2QvwqTGcj2AJL4GWsilWUNXYY7sXrGNHgexYkNsM8HFMpqEbs06nzrnW8aAscLj76L3WMz9GF1bFs1jYSY3CmMMWNYDSewJ9CW+fiPayHqal9O8xu8D39xQG4Hi/hR8HFxBp9pwuLczGWzgXViC1WwfQ6JnVpmszNdYytRFcqc629GpPQkepn4HOhabNwY9Y3l3UKM7tMJt9XdzM8Q5A9BbfhMI0vnnpwPk5Oc/qiD/0vFxbnlLyxkti1sSI+xA/9nNBI7I77DcwHmYNvsWGq75muU7M+7alewgY4Snnl5rISNsFPSbaO+K1PpXoJ6+J27KccUC0MnC6+5bI4oQ/9p+JdHC/js5LYzVP5Wh0TOloEJPf10m9/PClI+x0f4DwMrtK38LNDMB434O1M3q7sF0v4CD9XkVViNJ5TdhclPITFxMJemHhBfJN5/RhzL9bAHkXDQBK7O/7CKzXkg3EPHhQa8wBuwt/ChN9eZUxB7EkYjnGZrE34ww68j0eEf6qUdaZrr2xsboaXEtp6C47FXdi055/adJicyn+JHVLRoV5ih4lVP1PtoOlaHCwCqwtEcAJn40UcgSvxTjamS5jXjUXAlLuHtdL7tk7184UZOyHJ3sVWVeaxchpTLIKNhHa8hWlYH49hS33zcc2AaancsWjINbZNrNS/RZjfH6wmNHJODflWOFFo1VhlUuEPsUUq+uXowvLCNN1RIWsXUWyBGWLLUsjerzGXvcWH+CrVS+n5RVxwodCAR4U2/xfwA34T5hjdNXZdsfmfqeyn+orhqfy+hnyMWDi/6m5OCxSRb6VrmJ7GVUNO7GAcIvxmIatFbG6GiezThKw+DwfVGFuJ2Vizj33hbhFtLwh8p7ywuxFbywyvJoKbUWJf+ZPQjrF4NfUpVvuSNV46KpWH9DK5T3qR52jH9jhQkPGk8jarHTuIQI1YcLuk+8nC1w8EPhKa0ld8OUDvrYahst1Ib8SuKczWFOHrvhBE7ysi2gJfp3K4+bGk8GuTsFP9854Ph9Ypq5V/rge7DeCzGsEg4bL+TbH2RuwpItLdP5WE+ZmsO+bgGxGJVqIwpSvVMeEW+ob1xHfuLBoGZeUmgrw8Eb4CFtd7vnSe0MiVxFYmx1wRBG0gNv/VsL3q+9gW+oZiZ/BC0VBo7PoiYzND96zRdcI3fSBWw/Mib9lZ5eEdQrP3FJmrHGeLvGwHnhVEDxJmfTORGFhDC0TyZHS6XzWV2yjvCr7FWRVjRgmlfKRoKIitFTh1Cg3cVmx+DxB7xaOVtygFOoSvPUL3nC1xsLAtzhXaubMI0ecIou+v8gP/ryjhyIq2tdNFBJg5scuJhfA4Pisa2/r515jBYuM/W5blyDAWl4n98CJzttnkGCMs6w7iCBL9P49tE1HuNzXk4/EpLqpjgi30H0OFMnXISGX+lGKOiSJZ8ZwwmSNwjlD9Wofcv4nz2F1EmrHRM9kWesYI3Gr+rFyPxE4XPvU0cY75mYi6Svi4h3GT0tXCgsdM1TN5PRI7Pl0t/AfRzH9ma6EBtIhdRNEidhHFPxEcHcNy9CdvAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle I_{S} \\left(e^{\\frac{V_{BE}}{k}} - 1\\right)$" ], "text/plain": [ " ⎛ V_{BE} ⎞\n", " ⎜ ────── ⎟\n", " ⎜ k ⎟\n", "I_S⋅⎝ℯ - 1⎠" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr2 = expr1.subs(vt*n, k); expr2\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "surface-gross", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{i}{e^{\\frac{V_{BE}}{k}} - 1}$" ], "text/plain": [ " i \n", "───────────\n", " V_{BE} \n", " ────── \n", " k \n", "ℯ - 1" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr3 = solve(expr2-i, Is)[0]; expr3" ] }, { "cell_type": "markdown", "id": "classical-parameter", "metadata": {}, "source": [ "Because my datasheet says that at 0.6V the current = 200 $ \\mu A $ and at 0.8V the current = 100 mA then I try to find the relationship between $ I_S $ and k." ] }, { "cell_type": "code", "execution_count": 6, "id": "baking-powell", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{0.0002}{e^{\\frac{0.6}{k}} - 1}$" ], "text/plain": [ " 0.0002 \n", "────────\n", " 0.6 \n", " ─── \n", " k \n", "ℯ - 1" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e3 = expr3.subs(((vbe, 0.6), (i, 0.0002))); e3" ] }, { "cell_type": "code", "execution_count": 7, "id": "level-deadline", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{0.1}{e^{\\frac{0.8}{k}} - 1}$" ], "text/plain": [ " 0.1 \n", "────────\n", " 0.8 \n", " ─── \n", " k \n", "ℯ - 1" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e4 = expr3.subs(((vbe, 0.8), (i, 0.1))); e4" ] }, { "cell_type": "code", "execution_count": 8, "id": "charitable-smoke", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ 0.0321822385401455, \\ -4.56149019945187 \\cdot 10^{-5} - 0.0954666886406207 i, \\ -4.56149019945187 \\cdot 10^{-5} + 0.0954666886406207 i\\right]$" ], "text/plain": [ "[0.0321822385401455, -4.56149019945187e-5 - 0.0954666886406207⋅ⅈ, -4.56149019945187e-5 + 0.0954666886406207⋅ⅈ]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ks = solve(Eq(e3, e4), k); ks" ] }, { "cell_type": "code", "execution_count": 9, "id": "every-celebration", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 1.6000000511232 \\cdot 10^{-12}$" ], "text/plain": [ "1.60000005112320e-12" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_val = e4.subs(k, ks[0]); is_val" ] }, { "cell_type": "code", "execution_count": 10, "id": "blank-stage", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "x = np.linspace(.030, 0.034, 1000)\n", "f1 = lambdify(k, e3, \"numpy\")\n", "f2 = lambdify(k, e4, \"numpy\")\n", "ax.plot(x, f1(x), label=\"$ V_{BE} $ = 0.6 and i = 0.2mA\")\n", "ax.plot(x, f2(x), label=\"$ V_{BE} $ = 0.8 and i = 100mA\")\n", "\n", "ax.set_title(\"Possible values of K and $ I_S $\")\n", "ax.set_xlabel('k')\n", "ax.set_ylabel(\"$ I_s $\")\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": 11, "id": "lovely-gravity", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_png function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_rgba function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The to_mask function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n", "/home/splat/.local/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n", "The MathtextBackendBitmap class was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n", " mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n" ] }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle 1.6000000511232 \\cdot 10^{-12} e^{31.073040452191 V_{BE}} - 1.6000000511232 \\cdot 10^{-12}$" ], "text/plain": [ " 31.073040452191⋅V_{BE} \n", "1.6000000511232e-12⋅ℯ - 1.6000000511232e-12" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e2 = expr2.subs(((Is, is_val),(k, ks[0]))); e2" ] }, { "cell_type": "code", "execution_count": 12, "id": "infinite-festival", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "x = np.linspace(0.5, 0.8, 1000)\n", "f1 = lambdify(vbe, e2, \"numpy\")\n", "ax.plot(x, f1(x))\n", "ax.set_title(\"V-I characteristic of diode\")\n", "ax.set_xlabel('V')\n", "ax.set_ylabel(\"$ I_e $\")\n", "ax.set_yscale(\"log\")\n", "ax.grid(which=\"both\", axis='both')\n" ] }, { "cell_type": "code", "execution_count": null, "id": "narrative-aircraft", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }