Lugovtsov/3.3.4-semiconductor-hall-effect/processing.ipynb

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{
"cells": [
{
"cell_type": "code",
2022-10-17 00:13:23 +03:00
"execution_count": 102,
"id": "1dd847b1-0ad5-4f0f-b22b-8c68142dcbe3",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
"from scipy.optimize import curve_fit"
]
},
{
"cell_type": "code",
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"execution_count": 103,
"id": "657cc2c7-920b-46e0-a7a8-ef65146ddf4e",
"metadata": {},
"outputs": [],
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"source": [
"I_names = np.array([13, 24, 35, 46, 57, 68, 79, 90, 101])\n",
"I_values = I_names * 1.5 / 155# ток в мА"
]
},
{
"cell_type": "code",
"execution_count": 124,
"id": "61022dfd-06b7-43cb-ac1f-2128f46ff7ee",
"metadata": {},
"outputs": [],
"source": [
"colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:brown', 'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan']"
]
},
{
"cell_type": "markdown",
"id": "cab0ae39-aeb0-425a-a38a-8491552135fe",
"metadata": {
"tags": []
},
"source": [
"### График зависимости индукции от силы тока в обмотках магнита $B = f(I_\\text{М})$"
]
},
{
"cell_type": "code",
"execution_count": 105,
"id": "4c853de8-c61e-4ce0-b796-ffaa6e697b12",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"df = pd.read_csv(rf'data/induction_on_amperage.csv')\n",
"\n",
"B = np.array(df['Ind[mT]'])\n",
"I_m = np.array(df['I[mA]'])"
]
},
{
"cell_type": "code",
"execution_count": 131,
"id": "576974ec-5d4d-42c1-9280-7a7f9b74a6be",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1800x1200 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 4), dpi=300)\n",
"\n",
"# plt.minorticks_on()\n",
"# plt.grid(which='minor', linestyle=':', color='0.9')\n",
"plt.grid(which='major', linestyle='-', color='0.8', lw=0.3)\n",
"\n",
"plt.errorbar(I_m, B, xerr=5+0.003*I_m, yerr=0.5+0.003*B, lw=1, ls='', marker='.', markersize=8, label=r\"$B = f(I_М)$\", ds='default')\n",
" \n",
"plt.xlabel(r\"$I_М$, мА\")\n",
"plt.ylabel(r\"$B$, мТл\")\n",
"\n",
"plt.legend()\n",
"plt.savefig(rf\"images/BonI.png\", facecolor=\"white\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c9e18b07-8656-49b4-bf8e-1c2371bee3e5",
"metadata": {},
"source": [
"### Семейство характеристик $\\varepsilon_\\text{х} = f(B)$"
]
},
{
"cell_type": "code",
"execution_count": 108,
"id": "fadcfd44-216a-4449-9e75-398c8d3c740c",
"metadata": {},
"outputs": [],
"source": [
"def B_approx(x):\n",
" for i, xi in enumerate(I_m):\n",
" if xi >= x:\n",
" x1 = I_m[i - 1]\n",
" x2 = I_m[i]\n",
" y1 = B[i - 1]\n",
" y2 = B[i]\n",
" return y1 + (y2-y1)/(x2-x1)*(x-x1)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"id": "e6741806-03fb-487f-8366-bbb6c825c49b",
"metadata": {},
"outputs": [],
"source": [
"def line(x, arg1, arg2):\n",
" return x * arg1 + arg2"
]
},
{
"cell_type": "code",
"execution_count": 176,
"id": "08c7f31f-1c40-4904-b619-91c227f7a6b3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1800x1200 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 4), dpi=300)\n",
"plt.grid(which='major', linestyle='-', color='0.8', lw=0.3)\n",
"\n",
"dE_dB = []\n",
"\n",
"for i, I_name in enumerate(I_names):\n",
" df = pd.read_csv(rf\"data/VoA_{I_name}.csv\")\n",
" \n",
" U_ = df[\"U_34[mV]\"]\n",
" U0 = U_[0]\n",
" U = 1000*(U0 - U_)\n",
" \n",
" I_ = df[\"I_m[mA]\"]\n",
" B_ = np.array([B_approx(x) for x in I_], dtype=np.float64)\n",
" \n",
" popt, pcov = curve_fit(line, B_, U)\n",
" \n",
" # print(f\"k = {popt[0]:.4f} \\t \")\n",
" dE_dB.append(popt[0]/1000)\n",
" \n",
" plt.errorbar(B_, U, xerr=1+0.003*B_, yerr=1+0.003*U, ls='', marker='.', markersize=4, label=r\"$I_{||} = $\"+rf\"${I_values[i]:.2f}\\pm{1.5/155:.2f}$ мА\", ds='default', color=colors[i])\n",
" plt.plot(B_, line(B_, popt[0], popt[1]), color=colors[i], lw=1)\n",
"\n",
"dE_dB = np.array(dE_dB) * 1000\n",
" \n",
"plt.xlabel(r\"$B$, мТл\")\n",
"plt.ylabel(r\"$\\varepsilon_x$, мкВ\")\n",
"\n",
"plt.legend()\n",
"plt.savefig(rf\"images/UonB.png\", facecolor=\"white\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ed4c8024-e86f-4672-bd64-1d5d8e596592",
"metadata": {},
"source": [
"### Зависимость $k = f(I)$"
]
},
{
"cell_type": "code",
"execution_count": 179,
"id": "0d76d070-47ce-4f4f-9342-566a1107abab",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1800x1200 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 4), dpi=300)\n",
"\n",
"plt.grid(which='major', linestyle='-', color='0.8', lw=0.3)\n",
"\n",
"popt, pcov = curve_fit(line, I_values, dE_dB)\n",
"\n",
"k = popt[0]\n",
"\n",
"plt.errorbar(I_values, dE_dB, xerr=0.01, yerr=3.15e-03, color=colors[0], lw=1, ls='', marker='.', markersize=4, label=r\"$\\dfrac{d\\varepsilon_x}{dB} = f(I_{||})$\", ds='default')\n",
"plt.plot(I_values, line(I_values, popt[0], popt[1]), color=colors[0], lw=1)\n",
"\n",
"plt.xlabel(r\"$I_М$, мА\")\n",
"plt.ylabel(r\"$d\\varepsilon_x/dB$, мВ/Тл\")\n",
"\n",
"plt.legend()\n",
"plt.savefig(rf\"images/KonI.png\", facecolor=\"white\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 180,
"id": "2d140d8b-b9fb-48b7-88fd-ccd862fc794f",
"metadata": {},
"outputs": [],
"source": [
"h = 2.2e-3"
]
},
{
"cell_type": "code",
"execution_count": 189,
"id": "deb90002-f303-4b6b-ad90-e3c83d3ab41b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0004318927697950297"
]
},
"execution_count": 189,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R_h = k*h\n",
"R_h"
]
},
{
"cell_type": "code",
"execution_count": 190,
"id": "8731ed11-0b5c-4304-9ab3-eb563dbe33e3",
"metadata": {},
"outputs": [],
"source": [
"q = 1.6e-19"
]
},
{
"cell_type": "code",
"execution_count": 191,
"id": "048587bd-6a59-449c-a65c-86f810f3ce4c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.44711846020626e+22"
]
},
"execution_count": 191,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 1 / (R_h * q)\n",
"n"
]
},
{
"cell_type": "code",
2022-10-18 11:37:28 +03:00
"execution_count": 204,
2022-10-17 00:13:23 +03:00
"id": "8f61c6e8-356b-4a4c-b797-dd5e8d0331eb",
"metadata": {},
2022-10-18 11:37:28 +03:00
"outputs": [],
"source": [
"a = 2.2e-3\n",
"L35 = 3e-3\n",
"l = 2.5e-3"
]
},
{
"cell_type": "code",
"execution_count": 207,
"id": "1f153f00-d44c-41e5-8bab-ad09bd8e5896",
"metadata": {},
2022-10-17 00:13:23 +03:00
"outputs": [
{
"data": {
"text/plain": [
2022-10-18 11:37:28 +03:00
"274.0977615349475"
2022-10-17 00:13:23 +03:00
]
},
2022-10-18 11:37:28 +03:00
"execution_count": 207,
2022-10-17 00:13:23 +03:00
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
2022-10-18 11:37:28 +03:00
"sigma = 1 * L35/(1.99 * a * l)\n",
2022-10-17 00:13:23 +03:00
"sigma"
]
},
{
"cell_type": "code",
2022-10-18 11:37:28 +03:00
"execution_count": 208,
2022-10-17 00:13:23 +03:00
"id": "cf5b7366-16f9-434f-969f-74b61fed23ca",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
2022-10-18 11:37:28 +03:00
"1183.8084142394603"
2022-10-17 00:13:23 +03:00
]
},
2022-10-18 11:37:28 +03:00
"execution_count": 208,
2022-10-17 00:13:23 +03:00
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = sigma * R_h\n",
"b*10000"
]
}
],
"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": "3.10.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}