{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cuadripolos elementales y sus matrices asociadas\n", " \n", "\n", "#### Por Mariano Llamedo Soria" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Resumen \n", "En este documento se presentan algunas de las capacidades que posee el módulo PyTC2 para operar con cuadripolos. Se muestran ejemplos de cómo definir redes y sus modelos Z, Y y $T_{ABCD}$ asociados, como también algunas redes que implementan dichos modelos.\n", "\n", "* Funciones de dibujo de redes: [dibujar_Pi](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/dibujar/index.html#pytc2.dibujar.dibujar_Pi), [dibujar_Tee](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/dibujar/index.html#pytc2.dibujar.dibujar_Tee), [dibujar_lattice](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/dibujar/index.html#pytc2.dibujar.dibujar_lattice)\n", "* Funciones de conversión y definición de cuadripolos: [Z2Tabcd_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/cuadripolos/index.html#pytc2.cuadripolos.Z2Tabcd_s), [Y2Tabcd_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/cuadripolos/index.html#pytc2.cuadripolos.Y2Tabcd_s), [TabcdY_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/cuadripolos/index.html#pytc2.cuadripolos.TabcdY_s), [TabcdZ_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/cuadripolos/index.html#pytc2.cuadripolos.TabcdZ_s), [TabcdLZY_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/cuadripolos/index.html#pytc2.cuadripolos.TabcdLZY_s), \n", "* De presentación algebraica: [print_latex](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/general/index.html#pytc2.general.print_latex), [a_equal_b_latex_s](https://pytc2.readthedocs.io/en/latest/autoapi/pytc2/general/index.html#pytc2.general.a_equal_b_latex_s)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introducción\n", "\n", "A lo largo del curso se presentó una metodología sistemática para arribar a una función transferencia $T(s)$ a partir de restricciones de la función de módulo $\\vert T(j\\omega) \\vert $ o retardo $ \\tau(\\omega) $. Si bien en primera instancia arribamos a una $T_{LP}(s)$ pasabajos, es posible mediante núcleos de transformación el pasaje a otro tipo de transferencias (pasa-alto, pasabanda, etc).\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Ahora importamos las funciones de PyTC2\n", "\n", "from pytc2.dibujar import dibujar_Pi, dibujar_Tee, dibujar_lattice\n", "from pytc2.general import print_latex, print_subtitle, a_equal_b_latex_s\n", "import sympy as sp\n", "from IPython.display import display, Markdown\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Impedancia serie\n", "\n", "La matriz de parámetros Z para un cuadripolo constituido por una impedancia en serie **no está definida**. Esto se debe a que bajo las condiciones de medición de corriente nula (circuito abierto), ninguno de los parámetros $Z_{ii}$ está definido. Sin embargo, sí se puede calcular la matriz de parámetros Y\n", "\n", "$$ \n", "Y_Z = \\begin{pmatrix}\n", "\\frac{1}{Z} & -\\frac{1}{Z} \\\\\n", "-\\frac{1}{Z} & \\frac{1}{Z} \\\\\n", "\\end{pmatrix} = \\frac{1}{Z} . \\begin{pmatrix} 1 & -1 \\\\ -1 & 1 \\\\ \\end{pmatrix}\n", "$$\n", "\n", "Veremos cómo podemos proceder para el análisis simbólico.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Impedancia en serie" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_Z=\\left[\\begin{matrix}\\frac{1}{Z} & - \\frac{1}{Z}\\\\- \\frac{1}{Z} & \\frac{1}{Z}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:30:57.412003\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Definimos la matriz Yz\n", "\n", "Y, Z = sp.symbols('Y, Z', complex=True)\n", "\n", "Yz = 1/Z * sp.Matrix([[1, -1], [-1, 1]])\n", "\n", "print_subtitle('Impedancia en serie')\n", "print_latex(a_equal_b_latex_s('Y_Z', Yz))\n", "\n", "print_subtitle('Red equivalente')\n", "dibujar_Pi(Yz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Admitancia (Y) en derivación\n", "\n", "La matriz de parámetros Y para un cuadripolo constituido por una admitancia en derivación **no existe**, dado que para las condiciones de medición de tensión nula, ninguno de los parámetros está definido. Sería la condición dual de la *Z-serie* para los parámetros Z. Es decir que la matríz Z de la *Y-en-derivación* será\n", "\n", "$$ \n", "Z_Y = \\begin{pmatrix}\n", "\\frac{1}{Y} & \\frac{1}{Y} \\\\\n", "\\frac{1}{Y} & \\frac{1}{Y} \\\\\n", "\\end{pmatrix} = \\frac{1}{Y} . \\begin{pmatrix} 1 & 1 \\\\ 1 & 1 \\\\ \\end{pmatrix}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Admitancia en derivación" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_Y=\\left[\\begin{matrix}\\frac{1}{Y} & \\frac{1}{Y}\\\\\\frac{1}{Y} & \\frac{1}{Y}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:30:58.527039\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Definimos la matriz Yz\n", "\n", "Zy = 1/Y * sp.Matrix([[1, 1], [1, 1]])\n", "\n", "print_subtitle('Admitancia en derivación')\n", "print_latex(a_equal_b_latex_s('Z_Y', Zy))\n", "\n", "print_subtitle('Red equivalente')\n", "dibujar_Tee(Zy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Redes Pi y T (Tee)\n", "\n", "La red T, o *Tee* por su denominación en inglés, está naturalmente asociada a los parámetros Z de cuadripolo, mientras que la Pi ($\\pi$) se asocia a los parámetros Y.\n", "\n", "$$ \n", "Z_T = \\begin{pmatrix}\n", "Z_a + Z_b & Z_b \\\\\n", "Z_b & Z_c + Z_b \\\\\n", "\\end{pmatrix} \n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red Tee" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_T=\\left[\\begin{matrix}Za + Zb & Zb\\\\Zb & Zb + Zc\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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Zc = sp.symbols('Za, Zb, Zc', complex=True)\n", "\n", "Zt = sp.Matrix([[Za+Zb, Zb], [Zb, Zc+Zb]])\n", "\n", "print_subtitle('Red Tee')\n", "print_latex(a_equal_b_latex_s('Z_T', Zt))\n", "print_subtitle('Red equivalente')\n", "dibujar_Tee(Zt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "del mismo modo la red pi\n", "\n", "$$ \n", "Y_{\\pi} = \\begin{pmatrix}\n", "Y_a + Y_b & -Y_b \\\\\n", "-Y_b & Y_c + Y_b \\\\\n", "\\end{pmatrix} \n", "$$\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red Pi" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{\\pi}=\\left[\\begin{matrix}Ya + Yb & - Yb\\\\- Yb & Yb + Yc\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"metadata": {}, "output_type": "display_data" } ], "source": [ "Ya, Yb, Yc = sp.symbols('Ya, Yb, Yc', complex=True)\n", "\n", "Ypi = sp.Matrix([[Ya+Yb, -Yb], [-Yb, Yc+Yb]])\n", "\n", "print_subtitle('Red Pi')\n", "print_latex(a_equal_b_latex_s('Y_{\\pi}', Ypi))\n", "\n", "print_subtitle('Red equivalente')\n", "dibujar_Pi(Ypi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Conversión de parámetros de cuadripolos\n", "\n", "Los modelos de cuadripolos pueden convertirse mediante álgebra convencional, respetando las condiciones de medición de cada parámetro. En los siguientes ejemplos se muestran las funciones que permiten la conversión de parámetros de cuadripolo\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "## Conversión Z - Y" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red Tee original" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_T=\\left[\\begin{matrix}Za + Zb & Zb\\\\Zb & Zb + Zc\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/markdown": [ "#### Conversión a Pi ([T. Kennelly](https://es.wikipedia.org/wiki/Teorema_de_Kennelly))" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_T=\\left[\\begin{matrix}\\frac{Zb + Zc}{Za Zb + Za Zc + Zb Zc} & - \\frac{Zb}{Za Zb + Za Zc + Zb Zc}\\\\- \\frac{Zb}{Za Zb + Za Zc + Zb Zc} & \\frac{Za + Zb}{Za Zb + Za Zc + Zb Zc}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:03.657430\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "para mayor claridad, si se trabaja un poco más las expresiones de los componentes quedan" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{At}=\\frac{Zc}{Za Zb + Za Zc + Zb Zc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{Bt}=\\frac{Zb}{Za Zb + Za Zc + Zb Zc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{Ct}=\\frac{Za}{Za Zb + Za Zc + Zb Zc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pytc2.cuadripolos import Z2Tabcd_s, Y2Tabcd_s, Tabcd2Z_s, Tabcd2Y_s\n", "\n", "display(Markdown('## Conversión Z - Y'))\n", "\n", "print_subtitle('Red Tee original')\n", "\n", "print_latex(a_equal_b_latex_s('Z_T', Zt))\n", "\n", "dibujar_Tee(Zt)\n", "\n", "print_subtitle('Conversión a Pi ([T. Kennelly](https://es.wikipedia.org/wiki/Teorema_de_Kennelly))')\n", "\n", "print_latex(a_equal_b_latex_s('Y_T', Zt**-1))\n", "\n", "print_subtitle('Red equivalente')\n", "\n", "Yt_a, Yt_b, Yt_c = dibujar_Pi(Zt**-1, return_components = True)\n", "\n", "display(Markdown('para mayor claridad, si se trabaja un poco más las expresiones de los componentes quedan'))\n", "\n", "print_latex(a_equal_b_latex_s('Y_{At}', sp.simplify(sp.expand(Yt_a)) ))\n", "\n", "print_latex(a_equal_b_latex_s('Y_{Bt}', sp.simplify(sp.expand(Yt_b)) ))\n", "\n", "print_latex(a_equal_b_latex_s('Y_{Ct}', sp.simplify(sp.expand(Yt_c)) ))\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "## Conversión Y - Z" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red Pi original" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{\\pi}=\\left[\\begin{matrix}Ya + Yb & - Yb\\\\- Yb & Yb + Yc\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Conversión a Tee (T. Kennelly)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{\\pi}=\\left[\\begin{matrix}\\frac{Yb + Yc}{Ya Yb + Ya Yc + Yb Yc} & \\frac{Yb}{Ya Yb + Ya Yc + Yb Yc}\\\\\\frac{Yb}{Ya Yb + Ya Yc + Yb Yc} & \\frac{Ya + Yb}{Ya Yb + Ya Yc + Yb Yc}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red equivalente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:06.238969\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "para mayor claridad, si se trabaja un poco más las expresiones de los componentes quedan" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{A\\pi}=\\frac{Yc}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{B\\pi}=\\frac{Yb}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{C\\pi}=\\frac{Ya}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "la similitud en las expresiones es evidente:" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{At}=\\frac{Zc}{Za Zb + Za Zc + Zb Zc} \\qquad Z_{A\\pi}=\\frac{Yc}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{Bt}=\\frac{Zb}{Za Zb + Za Zc + Zb Zc} \\qquad Z_{B\\pi}=\\frac{Yb}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{Ct}=\\frac{Za}{Za Zb + Za Zc + Zb Zc} \\qquad Z_{C\\pi}=\\frac{Ya}{Ya Yb + Ya Yc + Yb Yc}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "display(Markdown('## Conversión Y - Z'))\n", "\n", "print_subtitle('Red Pi original')\n", "\n", "print_latex(a_equal_b_latex_s('Y_{\\pi}', Ypi))\n", "\n", "dibujar_Pi(Ypi)\n", "\n", "print_subtitle('Conversión a Tee (T. Kennelly)')\n", "\n", "Zpi = Ypi**-1\n", "print_latex(a_equal_b_latex_s('Z_{\\pi}', Zpi))\n", "\n", "print_subtitle('Red equivalente')\n", "\n", "Zpi_a, Zpi_b, Zpi_c = dibujar_Tee(Zpi, return_components = True)\n", "\n", "display(Markdown('para mayor claridad, si se trabaja un poco más las expresiones de los componentes quedan'))\n", "\n", "print_latex(a_equal_b_latex_s('Z_{A\\pi}', sp.simplify(sp.expand(Zpi_a)) ))\n", "\n", "print_latex(a_equal_b_latex_s('Z_{B\\pi}', sp.simplify(sp.expand(Zpi_b)) ))\n", "\n", "print_latex(a_equal_b_latex_s('Z_{C\\pi}', sp.simplify(sp.expand(Zpi_c)) ))\n", "\n", "\n", "display(Markdown('la similitud en las expresiones es evidente:'))\n", "\n", "\n", "print_latex( '$' + a_equal_b_latex_s('Y_{At}', sp.simplify(sp.expand(Yt_a)))[1:-1] \n", " + ' \\qquad ' + \n", " a_equal_b_latex_s('Z_{A\\pi}', sp.simplify(sp.expand(Zpi_a)))[1:-1] \n", " + '$')\n", "\n", "print_latex( '$' + a_equal_b_latex_s('Y_{Bt}', sp.simplify(sp.expand(Yt_b)))[1:-1] \n", " + ' \\qquad ' + \n", " a_equal_b_latex_s('Z_{B\\pi}', sp.simplify(sp.expand(Zpi_b)))[1:-1] \n", " + '$')\n", "\n", "print_latex( '$' + a_equal_b_latex_s('Y_{Ct}', sp.simplify(sp.expand(Yt_c)))[1:-1] \n", " + ' \\qquad ' + \n", " a_equal_b_latex_s('Z_{C\\pi}', sp.simplify(sp.expand(Zpi_c)))[1:-1] \n", " + '$')\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "## Conversión Z/Y a $T_{ABCD}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Redes sencillas Z-serie Y-derivación" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Tomamos como referencia las matrices $Y_Z$ y $Z_Y$ definidas más arriba, luego su matriz $T_{ABCD}$ será para la Y-derivación" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_Z=\\left[\\begin{matrix}\\frac{1}{Z} & - \\frac{1}{Z}\\\\- \\frac{1}{Z} & \\frac{1}{Z}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_Z=\\left[\\begin{matrix}1 & Z\\\\0 & 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "mientras que para la Z-serie " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_Y=\\left[\\begin{matrix}\\frac{1}{Y} & \\frac{1}{Y}\\\\\\frac{1}{Y} & \\frac{1}{Y}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_Y=\\left[\\begin{matrix}1 & 0\\\\Y & 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "display(Markdown('## Conversión Z/Y a $T_{ABCD}$'))\n", "\n", "print_subtitle('Redes sencillas Z-serie Y-derivación')\n", "\n", "display(Markdown('Tomamos como referencia las matrices $Y_Z$ y $Z_Y$ definidas más arriba, luego su matriz $T_{ABCD}$ será para la Y-derivación'))\n", "\n", "print_latex(a_equal_b_latex_s('Y_Z', Yz ))\n", "print_latex(a_equal_b_latex_s('T_Z', Y2Tabcd_s(Yz)))\n", "\n", "display(Markdown('mientras que para la Z-serie '))\n", "\n", "print_latex(a_equal_b_latex_s('Z_Y', Zy ))\n", "print_latex(a_equal_b_latex_s('T_Y', Z2Tabcd_s(Zy)))\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dado que se trata de redes elementales, que mediante interconexión podrían conformar redes de complejidad arbitrariamente grande, existen otras formas más directas de definirlas" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "## Generación de matrices T de redes elementales (Z, Y, L)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Z-serie" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_Z=\\left[\\begin{matrix}1 & Za\\\\0 & 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Y-derivación" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_Y=\\left[\\begin{matrix}1 & 0\\\\Ya & 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red L (Y-Z)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_{Lyz}=\\left[\\begin{matrix}1 & Za\\\\Ya & Ya Za + 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "por supuesto que se podría convertir la matriz T a Z y representar la red L" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{Lyz}=\\left[\\begin{matrix}\\frac{1}{Ya} & \\frac{1}{Ya}\\\\\\frac{1}{Ya} & Za + \\frac{1}{Ya}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AMIc4AQDMIU4AAHOIEwDAHOIEADCHOAEAzCFOAABziBMAwBziBAAwhzgBAMz5H2ecLb76Oct5AAAAAElFTkSuQmCC", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:08.948304\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "aunque no es la única manera de lograrlo, por ejemplo convirtiendo a Pi mediante la matriz Y" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{Lyz}=\\left[\\begin{matrix}Ya + \\frac{1}{Za} & - \\frac{1}{Za}\\\\- \\frac{1}{Za} & \\frac{1}{Za}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:10.162040\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pytc2.cuadripolos import TabcdZ_s, TabcdY_s, TabcdLYZ_s, TabcdLZY_s\n", "\n", "display(Markdown('## Generación de matrices T de redes elementales (Z, Y, L)'))\n", "\n", "print_subtitle('Z-serie')\n", "\n", "print_latex(a_equal_b_latex_s('T_Z', TabcdZ_s(Za)))\n", "\n", "print_subtitle('Y-derivación')\n", "\n", "print_latex(a_equal_b_latex_s('T_Y', TabcdY_s(Ya)))\n", "\n", "print_subtitle('Red L (Y-Z)')\n", "\n", "TLyz = TabcdLYZ_s(Ya,Za)\n", "\n", "print_latex(a_equal_b_latex_s('T_{Lyz}', TLyz ))\n", "\n", "display(Markdown('por supuesto que se podría convertir la matriz T a Z y representar la red L'))\n", "\n", "ZLyz = Tabcd2Z_s(TLyz)\n", "\n", "print_latex(a_equal_b_latex_s('Z_{Lyz}', ZLyz ))\n", "\n", "dibujar_Tee(ZLyz)\n", "\n", "display(Markdown('aunque no es la única manera de lograrlo, por ejemplo convirtiendo a Pi mediante la matriz Y'))\n", "\n", "YLyz = Tabcd2Y_s(TLyz)\n", "\n", "print_latex(a_equal_b_latex_s('Y_{Lyz}', YLyz ))\n", "\n", "dibujar_Pi(YLyz)\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red L invertida (Z-Y)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_{Lzy}=\\left[\\begin{matrix}Ya Za + 1 & Za\\\\Ya & 1\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "convirtiendo a Z se obtiene" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{Lzy}=\\left[\\begin{matrix}Za + \\frac{1}{Ya} & \\frac{1}{Ya}\\\\\\frac{1}{Ya} & \\frac{1}{Ya}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:11.132263\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print_subtitle('Red L invertida (Z-Y)')\n", "\n", "TLzy = TabcdLZY_s(Za,Ya)\n", "\n", "print_latex(a_equal_b_latex_s('T_{Lzy}', TLzy ))\n", "\n", "display(Markdown('convirtiendo a Z se obtiene'))\n", "\n", "ZLzy = Tabcd2Z_s(TLzy)\n", "\n", "print_latex(a_equal_b_latex_s('Z_{Lzy}', ZLzy ))\n", "\n", "dibujar_Tee(ZLzy)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interconexión de cuadripolos\n", "\n", "Una vez que la red se encuentra modelizada por algún juego de parámetros (Z, Y, $T_{ABCD}$, etc.) se puede proceder a la interconexión mediante las operaciones básicas del álgebra matricial:\n", "\n", "* Conexión en cascada. Equivale a la multiplicación matricial de matrices $T_{ABCD}$.\n", "* Conexión en serie. Suma de matrices Z.\n", "* Conexión en paralelo. Suma de matrices Y.\n", "\n", "Presentaremos algunos ejemplos para hallar los modelos de redes más complejas, a partir del conocimiento de las redes elementales y el concepto de interconexión.\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red T puenteada (bridged tee)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Matrix $T_{ABCD}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_{TP}=\\left[\\begin{matrix}\\frac{Za Zb Zd + Za Zc Zd + Za + Zb Zc Zd + Zb}{Za Zb Zd + Za Zc Zd + Zb Zc Zd + Zb} & \\frac{Za Zb + Za Zc + Zb Zc}{Zb + Zd \\left(Za Zb + Za Zc + Zb Zc\\right)}\\\\\\frac{Za Zd + Zc Zd + 1}{Zb + Zd \\left(Za Zb + Za Zc + Zb Zc\\right)} & \\frac{Za Zb Zd + Za Zc Zd + Za + Zb Zc Zd + Zb}{Za Zb Zd + Za Zc Zd + Zb Zc Zd + Zb}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pytc2.dibujar import dibujar_puerto_salida, dibujar_puerto_entrada\n", "from schemdraw import Drawing\n", "from schemdraw.elements import ResistorIEC, Line, Resistor, Capacitor\n", "\n", "print_subtitle('Red T puenteada (bridged tee)')\n", "\n", "Zd, Ze, Zf = sp.symbols('Zd, Ze, Zf', complex=True)\n", "\n", "Ttp = Y2Tabcd_s( Tabcd2Y_s(TabcdZ_s(1/Zd)) + Zt**-1 )\n", "\n", "# dibujamos la red T-puenteada\n", "with Drawing() as d:\n", " d.config(fontsize=16, unit=4)\n", " d = dibujar_puerto_entrada(d, port_name = '' )\n", " d.push()\n", " d += (line_start_aux := Line().length(d.unit*.4).up())\n", " d.pop()\n", " d += ResistorIEC().right().label('Za').dot().idot()\n", " d.push()\n", " d += ResistorIEC().right().label('Zc').dot()\n", " d.push()\n", " d += (line_end_aux := Line().length(d.unit*.4).up())\n", " d.pop()\n", " d = dibujar_puerto_salida(d, port_name = '' )\n", " d.pop()\n", " d += ResistorIEC().down().label('Zb').dot()\n", " y_down = d.here[1]\n", " d += Line().endpoints( [line_start_aux.end[0], y_down ], [line_end_aux.end[0], y_down ])\n", " d += ResistorIEC().down().label('Zd').endpoints(line_start_aux.end, line_end_aux.end)\n", "\n", "print_subtitle('Matrix $T_{ABCD}$')\n", "\n", "print_latex(a_equal_b_latex_s('T_{TP}', Ttp ))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red doble T (twin tee - notch RC)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Matrix $T_{ABCD}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle T_{TT}=\\left[\\begin{matrix}\\frac{\\frac{Za^{2}}{4} + 2 Za Zb + Zb^{2}}{Za Zb \\left(Za + 2 Zb\\right)} & \\frac{- \\frac{Za^{2}}{4} - Zb^{2}}{Za Zb \\left(Za + 2 Zb\\right)}\\\\\\frac{- Za^{2} - 4 Zb^{2}}{4 Za Zb \\left(Za + 2 Zb\\right)} & \\frac{\\frac{Za^{2}}{4} + 2 Za Zb + Zb^{2}}{Za Zb \\left(Za + 2 Zb\\right)}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print_subtitle('Red doble T (twin tee - notch RC)')\n", "\n", "Zt2 = sp.Matrix([[2*Zb+Za/2, Za/2], [Za/2, 2*Zb+Za/2]])\n", "\n", "# dibujamos la red T-puenteada\n", "with Drawing() as d:\n", " d.config(fontsize=16, unit=4)\n", " d = dibujar_puerto_entrada(d, port_name = '' )\n", " d.push()\n", " d += Line().length(d.unit*.4).up().idot()\n", " d += (zb_up := ResistorIEC().right().label('2Zb').dot())\n", " d += ResistorIEC().right().label('2Zb') \n", " d += Line().length(d.unit*.4).down().dot()\n", " d.pop()\n", " d += Line().length(d.unit*.2).right()\n", " d += ResistorIEC().right().label('Za').dot()\n", " d.push()\n", " d += (za_down := ResistorIEC().right().label('Za'))\n", " d = dibujar_puerto_salida(d, port_name = '' )\n", " d.pop()\n", " d += ResistorIEC().label('Zb', loc='bottom').down().dot()\n", " y_down = d.here[1]\n", " d += ResistorIEC().down().label('Za/2').idot().dot().endpoints( zb_up.end, [zb_up.end[0], y_down ])\n", " d += Line().endpoints( [zb_up.start[0], y_down ], [za_down.end[0], y_down ])\n", " \n", "\n", "Ttt = Y2Tabcd_s( Tabcd2Y_s(Zt2**-1 + Zt.subs(Zc, Za) **-1) )\n", "\n", "print_subtitle('Matrix $T_{ABCD}$')\n", "\n", "print_latex(a_equal_b_latex_s('T_{TT}', Ttt ))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "# Redes desbalanceadas convertidas a balanceadas" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red desbalanceada original" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2024-08-13T08:31:19.537783\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.7.3, https://matplotlib.org/\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Matrix $Z_{t3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Z_{t3}=\\left[\\begin{matrix}Zd + Ze & Ze\\\\Ze & Zd + Ze\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red lattice simétrica (balanceada)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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"source": [ "display(Markdown('# Redes desbalanceadas convertidas a balanceadas'))\n", "\n", "print_subtitle('Red desbalanceada original')\n", "\n", "# fuerzo la red Tee simétrica Za = Zc\n", "Zt3 = sp.Matrix([[Zd+Ze, Ze], [Ze, Zd+Ze]])\n", "\n", "dibujar_Tee(Zt3)\n", "\n", "print_subtitle('Matrix $Z_{t3}$')\n", "\n", "print_latex(a_equal_b_latex_s('Z_{t3}', Zt3 ))\n", "\n", "print_subtitle('Red lattice simétrica (balanceada)')\n", "\n", "dibujar_lattice(Zt3)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Red desbalanceada original" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AYArBBAAw5X+0FrRarBBZyQAAAABJRU5ErkJggg==", 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"output_type": "display_data" }, { "data": { "text/markdown": [ "#### Matrix $Y_{\\pi}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Y_{\\pi}=\\left[\\begin{matrix}Yb + Yc & - Yb\\\\- Yb & Yb + Yc\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red lattice simétrica (balanceada)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"display_data" }, { "data": { "text/markdown": [ "la conversión a una red balanceada puede realizarse sin problemas, tanto desde una red Tee como de una red Pi. Veremos si lo recíproco se cumple también." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ypi2 = sp.Matrix([[Yc+Yb, -Yb], [-Yb, Yc+Yb]])\n", "\n", "print_subtitle('Red desbalanceada original')\n", "\n", "dibujar_Pi(Ypi2)\n", "\n", "print_subtitle('Matrix $Y_{\\pi}$')\n", "\n", "print_latex(a_equal_b_latex_s('Y_{\\\\pi}', Ypi2 ))\n", "\n", "print_subtitle('Red lattice simétrica (balanceada)')\n", "\n", "dibujar_lattice(Ypi2**-1)\n", "\n", "display(Markdown('la conversión a una red balanceada puede realizarse sin problemas, tanto desde una red Tee como de una red Pi. Veremos si lo recíproco se cumple también.'))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "# Redes balanceadas convertidas a desbalanceadas" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "#### Red lattice simétrica (balanceada)" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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T_{lat}=\\left[\\begin{matrix}\\frac{Za}{2} + \\frac{Zb}{2} & - \\frac{Za}{2} + \\frac{Zb}{2}\\\\- \\frac{Za}{2} + \\frac{Zb}{2} & \\frac{Za}{2} + \\frac{Zb}{2}\\end{matrix}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "si implementamos una red balanceada como desbalanceada se obtiene una red Tee como la siguiente" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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[ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "notar que la conversión a desbalanceado **NO SIEMPRE** puede realizarse por la diferencia entre inmitancias" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(Markdown('# Redes balanceadas convertidas a desbalanceadas'))\n", "\n", "print_subtitle('Red lattice simétrica (balanceada)')\n", "\n", "Zlat = sp.Matrix([[(Za+Zb)/2, (Zb-Za)/2], [(Zb-Za)/2, (Za+Zb)/2]])\n", "\n", "dibujar_lattice(Zlat)\n", "\n", "print_latex(a_equal_b_latex_s('T_{lat}', Zlat ))\n", "\n", "display(Markdown('si implementamos una red balanceada como desbalanceada se obtiene una red Tee como la siguiente'))\n", "\n", "dibujar_Tee(Zlat)\n", "\n", "display(Markdown('o una Pi'))\n", "\n", "dibujar_Pi(Zlat**-1)\n", "\n", "display(Markdown('notar que la conversión a desbalanceado **NO SIEMPRE** puede realizarse por la diferencia entre inmitancias'))\n", "\n" ] } ], "metadata": { 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