{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from sympy import Matrix, symbols, sin, cos, trigsimp, init_printing, I, \\\n", " simplify, Eq, solve, expand, lambdify, diff, solveset, exp, factor\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from scipy import optimize\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import os\n", "from functools import partial\n", "init_printing()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "attachments": { "lm35.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "![lm35.png](attachment:lm35.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The object of this exercise is to maximise the change in current through i3 as a result in change in Voltage signal from Vout when Vout is in the millivolt range. The ultimate goal is to replace the diode with an NPN transistor to amplify the current. The 0.6V is an attempt to model the switch on voltage of that transistor." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "r1, r2, r3, i1, i2, i3, vo, vbe, n, vd, vt, Is = symbols(\"r_1 r_2 r_3 i_1 i_2 i_3 Vout V_{BE} n V_D V_T I_S\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$ 5 - V_{out} = R_1 * i_1 + R_2 * i_2 $ \\\n", "\n", "$ 5 - V_{BE} = 4.4 = R_1 * i_1 + R_3 * i_3 = R_1 * i_1 + R_3 * (i_1 - i_2) = (R_1 +R_3) * i_1 - R_3 * i_2 $ \n", "\n", "Because i1 is entering the junction and i2 is leaving the junction then because of conservation of charge the current going through R3 must be i1 - i2" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}r_{1} & r_{2}\\\\r_{1} + r_{3} & - r_{3}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ r₁ r₂ ⎤\n", "⎢ ⎥\n", "⎣r₁ + r₃ -r₃⎦" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = Matrix([[r1, r2], [r1+r3, -r3]]); m" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{r_{3}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} & \\frac{r_{2}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}}\\\\\\frac{r_{1} + r_{3}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} & - \\frac{r_{1}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ r₃ r₂ ⎤\n", "⎢───────────────────── ─────────────────────⎥\n", "⎢r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃⎥\n", "⎢ ⎥\n", "⎢ r₁ + r₃ -r₁ ⎥\n", "⎢───────────────────── ─────────────────────⎥\n", "⎣r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃⎦" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "minv = m**-1; minv" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}5 - Vout\\\\5 - V_{BE}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 5 - Vout ⎤\n", "⎢ ⎥\n", "⎣5 - V_{BE}⎦" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = Matrix([5-vo, 5-vbe]); b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now try to calculate the currents i1 and i2 by multiplying the matrix inverse by vector b" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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3YZQHSP+l9CuX6v90Tl/l3Dg2I8w5UgwzdsL9GteXWro+TaLYnHMwZEhfpLGFcFYe2zVplqsscY0WPbvB0NfBZ4hWpiLnfEIdl+QDftwmeQ58vdl7SeXsH/ZAeU2HbaiymkMCDrbjix6XK0lImHSUJ5vx7KeqB6LDMKgjBbwmEhoKDucX0YR5KbqaPFuOoMxw9hjTYnzs09EueIzse0bliZjuPxYeM8VrXc7olb715XFAv/lsbREgPnHOPKQZDaJfuj6tb7HT4d1K9u5CRwWuszVkozgOkTRxA7YpmNED6Dy2zZ6OS/JRGbij7yUYOBSG2lQ5s1b4os83uuy+CZvq9TEsyMUvcgULz8cASs6ihn1mVggsBkbZa5W5BwOK40hSM6qYbjCtejBqDDMcyXt0wqFvO4WdAStuo7jN9EIaRnym/CxjcYrOMJTOORBmgq2yC9tvjdNf1+fGihapz6hPyJ7tDbMtnqLGtnAlHPTJ4GV2ji5Dh8iKhteiyKeOW4UhpHSck4+1EdLPHS+2qf7UHJiR6mOR78ti6UILJQwU3+qA2BdgttQzNm84vbwpxaD6ew8YEnUzU+vNWFG+8rhCg98pn5EvzPtZeYyK5HfOUnEHysfIdgr3yu4wVv27VH12QvVyz83QHZ5wGIjCwSiMGw46T9Yj+pyOc/KZ4l5yfNX+iMdsm57/4oEZhT4WWVjrzK7YKQmD2Q4jI/ttzNL2ZkTKw6EwfU/N7or1z1UoXnBSGCV8MfrbDIA89hE7J6U4fSJ/5/Ho7xvF3ytk9tBzmOAJzODvUif06/u7KH3ek3iTOh4rH9EN3kuJfnZ2migrZqm9WyFgv9iybc3wZRH5Bsk+WmEuvNdTT3JMHTNfQkRwbACHwjwmC0dpS/1jycNSJuUEj8JDqhHxg9Nm2dJ7mpzCrclTPWehz5Qs1PdBHa9dPjV9jGUjGnfqyUnO7OLOltISxGxL1lK791DGEndRjm4OGZyRPlPiG9TxCchnsI8pwZA3OLOTcNgD+K8uwlrgaWO4l7RT+mMt8Ya3TglIx9kXr1XGpjrL9Bjs1Z6buEBpXnko7s1udpWQ2hlmDdiem9kNOrszlNvW5SNKQEY66TL2iKxvTa1EArKxbRm7El1tbG4S2CQwgQTOfs9uAhluVWwS2CSwAgmctbPT9JZ9pFXBGnlelYBnYnaNelsjzyX1nbWzk2CelISz0LI18rxQUR6VrTXqbY08Z5V6mS2ZoUAjBZvRfObBZ008heMJL18U8B3o4IuIrfRq5yBoba+V/iBmPXJLmy20Y3idk6a1L630h/attb1W+kP5Bb+lzRbaMbxCczGWcCQdDo43/PkAGmHxIukzXU9JV0ArfUUTPZTW9lrpe8xUJlrabKGtZG8PjZe5uaaG1r600h/an9b2WukP5Rf8ljZbaMfwujvazE6O7ak45KVW3rXiTX5OFwGqDt2soRcOdTNbZPrNjJHjmka9SFvTnurfCY+22Ptzx9KQB9TQexycPZA7pPCutOK3ss2kjCpp0eFk/NIltTtKPyVx1PTFt92iu6QcS3zlyo7E76S6q+FZOEkZVdJOyi+yv8wpYOp8ddC9ZKyQZew7q9/ySStOBzFArh4YnsIsvQhwbu50XoU4Pd6vcS+6Ko1DiuttOmRQdbbyy6dN2UMK5+BZ7SVlpLYG9SPaIr8qXwTU9GUC3SXliABU92Zrd5aQlFGNfkQ+ua0dzdnd9d394u2TT0G9ELIHBfo6svQqZ3ZkgGPrlkeqe++UCOU1HTI4Ab/FQwrn4FkyycrIC64k3yK/JvgFhdm+TKC7rBzn0NsE/BZ1NwfPS7O1i2MapgSKA+JkilFLlyF6lYcPORgZip8aDfV9qL1WetV/69vgpuRzqQ9DdQ6VD/Gs8qyMKmgn53eoP2PLh/oyVO8QfUmOQ3WnyofaS9GEeUP0Kp9cdxVtLsrWjurspByWlnvnc4VKG4hX0UsJzBxZHo5yqgEPVe0F+HG0SI+x6LL9S5zzH0pD0wLFNq1itZOSUZF2Jn6NpanDYl8qGquiz8ixovo9lKr29qj+n1Gkn0l3xTaNtYyMirRz8HtpDB0jVAfYFxo926qhF46t9RnJOA9u9NFBNe2V5FaiVxnKLh5SWKo7V1Zq02iEk5RRiXYufo2nqcNSX2raqqEXTlKONfXHODXtxTRhukSvss3WJKxFHQQgpbDhz5LuWhdPa39XXvVMULj8oQ11GDBryp4MrDL+om1vL8+Ih0LRtvLL+WMAxvhcF/wUZ6MT8HyQjGDOQG0fzK/RLi2cQHcHyXECvW22NnBv5GxMsu+fepJALDqKBP6WtUlgk8AmgXuVgBxbPAgZP69YxrIpzuscMbBhvsEmgU0CmwTWJIErMfsowfCH/wE6Z1CJCT+J6AAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{r_{2} \\left(5 - V_{BE}\\right)}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} + \\frac{r_{3} \\left(5 - Vout\\right)}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}}\\\\- \\frac{r_{1} \\left(5 - V_{BE}\\right)}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} + \\frac{\\left(5 - Vout\\right) \\left(r_{1} + r_{3}\\right)}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ r₂⋅(5 - V_{BE}) r₃⋅(5 - Vout) ⎤\n", "⎢ ───────────────────── + ───────────────────── ⎥\n", "⎢ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ ⎥\n", "⎢ ⎥\n", "⎢ r₁⋅(5 - V_{BE}) (5 - Vout)⋅(r₁ + r₃)⎥\n", "⎢- ───────────────────── + ─────────────────────⎥\n", "⎣ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃⎦" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b2 = minv*b; b2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The current through R3 then $ i_3 = i_1 - i_2 $ is the current through R3 due to the conservation of charge law." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{- V_{BE} r_{1} - V_{BE} r_{2} + Vout r_{1} + 5 r_{2}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} = i_{3}$" ], "text/plain": [ "-V_{BE}⋅r₁ - V_{BE}⋅r₂ + Vout⋅r₁ + 5⋅r₂ \n", "─────────────────────────────────────── = i₃\n", " r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr1 = Eq(simplify(b2[0]-b2[1]), i3); expr1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we just plug in some values to make sure the calculations look right" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - \\frac{11700.0 r_{1}}{r_{1} - 87900.0}$" ], "text/plain": [ "-11700.0⋅r₁ \n", "────────────\n", "r₁ - 87900.0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e1 = solve(expr1.subs(((vbe, 0.6), (vo,0.020), (i3,0.00005), (r3,100))), r2)[0]; e1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we want to produce some graphs to see what resistance values are likely to make this work if we are thinking we want a $V_{out}$ of 20mV should produce a current of 50$\\mu$A." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "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(2, 10, 1000)\n", "f1 = lambdify(r1, e1, \"numpy\")\n", "ax.set_ylabel(\"$ R_2 $\")\n", "ax.set_xlabel(\"$ R_1 $\")\n", "ax.set_title(\"Possible values of R1 and R2\")\n", "ax.plot(x, f1(x))\n", "ax.grid()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That looks reasonable so now we try for different values of R3 and see if R3 is really necessary." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "from matplotlib import ticker\n", "def plotR2s(milliVolts, microAmps, lin=None, vbeval=0.6, r3codes=[(1000,'b'), (500, 'b:'), (200, 'b--'), (100, 'b-.')] ):\n", " if lin:\n", " x = np.linspace(*lin)\n", " else:\n", " x = np.linspace(0, 10000, 1000)\n", " plt.figure(figsize=(7,7))\n", " lines = []\n", " legends = []\n", " for r, c in r3codes:\n", " expr2 = solve(expr1.subs(((vo, milliVolts/1000),(r3,r),(i3, microAmps/1000000), (vbe, vbeval))), r2)\n", " f2 = lambdify(r1, expr2, \"numpy\")\n", " line2d, = plt.plot(x, f2(x)[0], c)\n", " currax = plt.gca()\n", " currax.xaxis.set_major_formatter(ticker.FuncFormatter(lambda x, pos: \"{:.1f} K\".format(x/1000)))\n", " currax.yaxis.set_major_formatter(ticker.FuncFormatter(lambda x, pos: \"{:.1f} K\".format(x/1000)))\n", " lines.append(line2d)\n", " legends.append(\"R3 = {:1.2f} K\".format((r/1000)))\n", "\n", " plt.grid()\n", "\n", " plt.xlabel(\"R1\")\n", " plt.ylabel(\"R2\")\n", " plt.legend(lines, legends)\n", " plt.title(\"R1 vs R2 where $V_{{out}} = {} mV $ and $ i_3 $ = {} $ \\mu $ A\".format(milliVolts, microAmps,))\n", " return plt" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plotR2s(250, 40, (0,10000, 1000), r3codes=[(100,'b'), (50, 'b:'), (10, 'b--'), (0, 'b-.')] )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So a good match looks like R1 = 8K, R2 = 1K and R3 = 100 ohms (or less)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We've currently been modelling this as a linear equation but let's see what happens if we treat the diode as non-linear." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{- V_{BE} r_{1} - V_{BE} r_{2} + Vout r_{1} + 5 r_{2}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} = i_{3}$" ], "text/plain": [ "-V_{BE}⋅r₁ - V_{BE}⋅r₂ + Vout⋅r₁ + 5⋅r₂ \n", "─────────────────────────────────────── = i₃\n", " r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ " ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apprently n = 1 for germanium and n = 2 for silicon and $ V_T $ is about 27mV at room temperature. (For me it seems more like 16mV.)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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"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": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr2 = Is * (exp(vbe/(n*vt))-1); expr2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now invert this equation so that we can solve for $V_{BE}$ and make the diode current the subject of the equation." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle V_{T} n \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)}$" ], "text/plain": [ " ⎛I_S + i₃⎞\n", "V_T⋅n⋅log⎜────────⎟\n", " ⎝ I_S ⎠" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr3 = solve(Eq(expr2,i3), vbe)[0]; expr3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now plug in some realistic values for $n \\cdot V_{T}$ and $I_S$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle 1.6 \\cdot 10^{-12} e^{31.073040452191 V_{BE}} - 1.6 \\cdot 10^{-12}$" ], "text/plain": [ " 31.073040452191⋅V_{BE} \n", "1.6e-12⋅ℯ - 1.6e-12" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e2 = expr2.subs(((n*vt,0.0321822385401455), (Is, 1.6e-12))); e2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now plot the diodes V-I characteristic" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "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, 1, 1000)\n", "f1 = lambdify(vbe, e2, \"numpy\")\n", "ax.set_ylabel(\"base-emiiter current (Amps)\")\n", "ax.set_xlabel(\"base-emitter voltage\")\n", "ax.set_title ('Diode V-I characteristic')\n", "ax.plot(x, f1(x))\n", "ax.grid()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we want to add this result into our previous linear equation for the entire circuit. (Of course now it will be non-linear)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 0.0160911192700727$" ], "text/plain": [ "0.01609111927007275" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vtval = 0.0321822385401455/2; vtval" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{- V_{BE} r_{1} - V_{BE} r_{2} + Vout r_{1} + 5 r_{2}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} = I_{S} \\left(e^{\\frac{V_{BE}}{V_{T} n}} - 1\\right)$" ], "text/plain": [ " ⎛ V_{BE} ⎞\n", " ⎜ ────── ⎟\n", "-V_{BE}⋅r₁ - V_{BE}⋅r₂ + Vout⋅r₁ + 5⋅r₂ ⎜ V_T⋅n ⎟\n", "─────────────────────────────────────── = I_S⋅⎝ℯ - 1⎠\n", " r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr4 = Eq(expr1.args[0], expr2); expr4" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\frac{- V_{T} n r_{1} \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} - V_{T} n r_{2} \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + Vout r_{1} + 5 r_{2}}{r_{1} r_{2} + r_{1} r_{3} + r_{2} r_{3}} = i_{3}$" ], "text/plain": [ " ⎛I_S + i₃⎞ ⎛I_S + i₃⎞ \n", "- V_T⋅n⋅r₁⋅log⎜────────⎟ - V_T⋅n⋅r₂⋅log⎜────────⎟ + Vout⋅r₁ + 5⋅r₂ \n", " ⎝ I_S ⎠ ⎝ I_S ⎠ \n", "────────────────────────────────────────────────────────────────── = i₃\n", " r₁⋅r₂ + r₁⋅r₃ + r₂⋅r₃ " ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr5 = expr1.subs(vbe, expr3); expr5" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\frac{V_{T} n r_{2} \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + i_{3} r_{2} r_{3} + r_{1} \\left(V_{T} n \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + i_{3} r_{2} + i_{3} r_{3}\\right) - 5 r_{2}}{r_{1}}$" ], "text/plain": [ " ⎛I_S + i₃⎞ ⎛ ⎛I_S + i₃⎞ ⎞ \n", "V_T⋅n⋅r₂⋅log⎜────────⎟ + i₃⋅r₂⋅r₃ + r₁⋅⎜V_T⋅n⋅log⎜────────⎟ + i₃⋅r₂ + i₃⋅r₃⎟ -\n", " ⎝ I_S ⎠ ⎝ ⎝ I_S ⎠ ⎠ \n", "──────────────────────────────────────────────────────────────────────────────\n", " r₁ \n", "\n", " \n", " 5⋅r₂\n", " \n", "─────\n", " " ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr6 = solve(expr5, vo)[0]; expr6" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle - Vout + \\frac{V_{T} n r_{2} \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + r_{1} \\left(V_{T} n \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + i_{3} r_{2}\\right) - 5 r_{2}}{r_{1}}$" ], "text/plain": [ " ⎛I_S + i₃⎞ ⎛ ⎛I_S + i₃⎞ ⎞ \n", " V_T⋅n⋅r₂⋅log⎜────────⎟ + r₁⋅⎜V_T⋅n⋅log⎜────────⎟ + i₃⋅r₂⎟ - 5⋅r₂\n", " ⎝ I_S ⎠ ⎝ ⎝ I_S ⎠ ⎠ \n", "-Vout + ────────────────────────────────────────────────────────────────\n", " r₁ " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr7 = simplify(expr6.subs(r3,0))-vo; expr7" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\frac{r_{1} \\left(- V_{T} n \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + Vout\\right)}{V_{T} n \\log{\\left(\\frac{I_{S} + i_{3}}{I_{S}} \\right)} + i_{3} r_{1} - 5}$" ], "text/plain": [ " ⎛ ⎛I_S + i₃⎞ ⎞\n", "r₁⋅⎜- V_T⋅n⋅log⎜────────⎟ + Vout⎟\n", " ⎝ ⎝ I_S ⎠ ⎠\n", "─────────────────────────────────\n", " ⎛I_S + i₃⎞ \n", " V_T⋅n⋅log⎜────────⎟ + i₃⋅r₁ - 5 \n", " ⎝ I_S ⎠ " ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e7 = solve(expr7, r2)[0]; e7" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle - \\frac{0.535385945984242 r_{1}}{5.0 \\cdot 10^{-5} r_{1} - 4.44461405401576}$" ], "text/plain": [ " -0.535385945984242⋅r₁ \n", "────────────────────────────\n", "5.0e-5⋅r₁ - 4.44461405401576" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e8 = e7.subs(((Is, 1.6e-12),(n,2),(vt,vtval), (i3, 0.000050),(vo,0.020))); e8" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "f1 = lambdify(r1, e8, \"numpy\")" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\frac{0.533453240832388 r_{1}}{5.5 \\cdot 10^{-5} r_{1} - 4.44154675916761}$" ], "text/plain": [ " -0.533453240832388⋅r₁ \n", "────────────────────────────\n", "5.5e-5⋅r₁ - 4.44154675916761" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e9 = e7.subs(((Is, 1.6e-12),(n,2),(vt,vtval), (i3, 0.000055),(vo,0.025))); e9" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "f2 = lambdify(r1, e9, \"numpy\")" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "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(0, 10, 1000)\n", "ax.set_ylabel(\"$ R_{2} $\")\n", "ax.set_xlabel(\"$ R_1 $\")\n", "ax.set_title(\"R1 vs R2\")\n", "ax.plot(x, f1(x), label=\"Vout = 20mV, i3 = 50 $ \\mu $A\")\n", "ax.plot(x, f2(x), label=\"Vout = 25mV, i3 = 55 $\\mu$A\")\n", "ax.grid()\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So R1 = 8K and R2 = 1K look like a good starting candidate." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 2 }