commit 4968f411568f321ad876f8ad2f9efbc493d2998a parent c795832288e2e42de47b6954abc5a719cd2a879d Author: Martin Kloeckner <mjkloeckner@gmail.com> Date: Wed, 15 Jul 2026 00:16:56 -0300 Actualizar sección sobre filtro Sallen-Key Diffstat:
41 files changed, 8775 insertions(+), 111 deletions(-) diff --git a/tp/informe/informe.pdf b/tp/informe/informe.pdf Binary files differ. diff --git a/tp/informe/informe.tex b/tp/informe/informe.tex @@ -9,6 +9,10 @@ % \numberwithin{equation}{section} \usepackage{mathtools} +\addto\captionsspanish{ + \renewcommand{\tablename}{Tabla} +} + \usepackage{empheq} \usepackage{graphicx} \usepackage{parskip} @@ -117,6 +121,45 @@ left=0pt, bottom=0pt, right=0pt, colback=gray!25, colframe=white, fontupper={\ttfamily\mystrut}} +\usepackage{listings} +\lstset{ + breaklines=true, + breakatwhitespace=true, + basicstyle=\ttfamily\small, + columns=fixed, + keepspaces=true, +} + +\usepackage{xcolor} + +% tango style +\definecolor{bgcolor}{HTML}{F6F6F6} +\definecolor{keywordcolor}{HTML}{204A87} +\definecolor{commentcolor}{HTML}{8F5902} +\definecolor{stringcolor}{HTML}{4E9A06} +\definecolor{numbercolor}{HTML}{0000CF} +\definecolor{operatorcolor}{HTML}{CE5C00} +\definecolor{identifiercolor}{HTML}{000000} % For general text + +\lstset{ + backgroundcolor=\color{bgcolor}, + basicstyle=\ttfamily\small, + keywordstyle=\color{keywordcolor}\bfseries, + commentstyle=\color{commentcolor}\itshape, + stringstyle=\color{stringcolor}, + identifierstyle=\color{identifiercolor}, + numberstyle=\color{numbercolor}, + emphstyle=\color{operatorcolor}\bfseries, + breaklines=true, + breakatwhitespace=true, + columns=fullflexible, + showstringspaces=true, + frame=none, + framerule=1pt, + xleftmargin=0pt, + moredelim=**[is][\color{operatorcolor}\bfseries]{@}{@}, % allow inline operator styling using @...@ +} + \title{SÃntesis de filtro} % Titulo del trabajo. \author{Klöckner, Martin Javier} \date{\today} % Fecha (automática) @@ -762,7 +805,7 @@ Para la respuesta a una señal senoidal se realiza un procedimiento análogo a l realizados previamente para obtener la respuesta al impulso y al escalón. Se aplica el operador inverso de Laplace a la expresión de la ecuación \eref{eq-y-h-x} con $X(s)$ la transformada de Laplace de la entrada, en este -caso una funcion senoidal, cuya trasnformada para $t\ge 0$ se obtiene de +caso una función senoidal, cuya transformada para $t\ge 0$ se obtiene de tabla\footnotemark[8] y resulta como se muestra a continuación en \eref{eq-l-sin}. Para este caso, se tomará la frecuencia angular $\omega_{0} = 1571\ \text{rad}/\text{s}$ (lo cual corresponde aproximadamente a una frecuencia @@ -873,7 +916,7 @@ Para calcular los coeficientes $k_{1,2,3,4,5}$ se utiliza la ecuación Teniendo el valor de los coeficientes $k_{i}$ y aplicando la antitransformada -termino a termino resulta como en la ecuacion \eref{eq-y-t-sin}. +termino a termino resulta como en la ecuación \eref{eq-y-t-sin}. \vspace{-0.5em} \begin{align} @@ -894,10 +937,10 @@ termino a termino resulta como en la ecuacion \eref{eq-y-t-sin}. \label{eq-y-t-sin} \end{align} -Dado que se tienen dos pares de polos complejos conjugados, se resutiliza el +Dado que se tienen dos pares de polos complejos conjugados, se reutiliza el resultado de la ecuación \eref{eq-comp-conj-comb-res} para reescribir las -exponenciales complejas en terminos de funciones senoidales, resultando la -expresión de la respuesta a una funcion senoidal con frecuencia angular +exponenciales complejas en términos de funciones senoidales, resultando la +expresión de la respuesta a una función senoidal con frecuencia angular $\omega_{0} = 1571\text{rad}/\text{s}$ del sistema en dominio temporal $y(t)$ como se muestra a continuación en la ecuación \eref{eq-y-sin-final}. @@ -957,16 +1000,16 @@ $22.9dB$) y la fase no cambia. En la figura 2 se observa que para frecuencias altas, esto es en la transición en el origen de la función escalón, se comporta similar a la respuesta al impulso, presentando oscilaciones hasta que el sistema se estabiliza. De la -ecuacion \eref{eq-y-U-final} se observa que el transitorio mas lento es el de la -exponencial $e^{-889\cdot t}$ el cual tiene un tiempo caracteristico $\tau = -2$ms; por convencion se toma $5$ veces ese valor, resultando en $10$ms de +ecuación \eref{eq-y-U-final} se observa que el transitorio más lento es el de la +exponencial $e^{-889\cdot t}$ el cual tiene un tiempo caracterÃstico $\tau = +2$ms; por convención se toma $5$ veces ese valor, resultando en $10$ms de tiempo para que el sistema se estabilice por completo, lo cual se ve claramente -en la figura. Cuando la funcion escalon es continua y el sistema se estabiliza +en la figura. Cuando la función escalón es continua y el sistema se estabiliza se observa la ganancia de $6$ (o $15.56 dB$ aproximadamente) propia de la transferencia $H(s)$ para frecuencias bajas, obtenido en la ecuación \eref{eq-tran-to-zero}. -, es por esto que habrá un termino más en la expresion +, es por esto que habrá un termino más en la expresión expandida en fracciones simples, a diferencia de la expansion para la respuesta al impulso de la ecuación \eref{eq-l-f-simp}, como se muestra en \eref{eq-l-f-U-simp}. @@ -977,28 +1020,27 @@ al impulso de la ecuación \eref{eq-l-f-simp}, como se muestra en \hypertarget{circuitos-teoricos}{% \section{Circuitos teóricos}\label{circuitos-teoricos}} -Para la elección del circuito se tiene en cuenta la descomposicion en -transferencias más simples que se muestra en la ecuacion \eref{eq-tran-producto} -y también todo el analisis realizado de cada una de las transferencias, en -particular se sabe que la transferencia $H_{1}(s)$ corresponde con un filtro -pasa altos de primer orden con una diferencia de ganancia entre frecuencias -altas y bajas de $6dB$; mientras que la transferencia $H_{2}(2)$ corresponde con -un filtro pasa bajos de segundo orden. La transferencia total, es decir el -producto de ambas transferencias, debe tener una ganancia de 12 (o $21.6dB$), -este factor de ganancia no esta fijo para la descomposicion de la transferencia -si no que se reparte entre ambas transferencias de acuerdo a como sea mas -conveniente a la hora de implementar el circuito. - -La descomposicion de la transferencia resulta muy util ya que el circuito -resultante sera la cascada de cada unos de los circuitos respectivos a cada -transferencia, es por esto que cada uno de los circutios o ``etapas'' se diseña -por separado y luego se conecta la salida de uno a la entrada de otro, en -``cascada''. +Para la elección del circuito se tiene en cuenta la descomposición en +transferencias más simples que se muestra en la ecuación \eref{eq-tran-producto} +y también todo el análisis realizado de cada una de las transferencias, en +particular se sabe que la transferencia $H_{1}$ corresponde con un filtro pasa +altos de primer orden con una diferencia de ganancia entre frecuencias altas y +bajas de $6dB$; mientras que la transferencia $H_{2}$ corresponde con un filtro +pasa bajos de segundo orden. La transferencia total, es decir el producto de +ambas transferencias, debe tener una ganancia de 12 (o $21.6dB$), este factor de +ganancia no esta fijo para la descomposición de la transferencia si no que se +reparte entre ambas transferencias de acuerdo a como sea más conveniente a la +hora de implementar el circuito. + +La descomposición de la transferencia resulta muy útil ya que el circuito +resultante será la cascada de cada unos de los circuitos respectivos a cada +transferencia, es por esto que cada uno de los circuitos o ``etapas'' se diseña +por separado y luego se conecta la salida de uno a la entrada de otro. \hypertarget{filtro-pasa-altos-de-primer-orden}{% \subsection{Filtro pasa altos de primer orden}\label{filtro-pasa-altos-de-primer-orden}} -La transferencia $H_{1}(s)$ es de la forma de la ecuación +La transferencia $H_{1}$ es de la forma de la ecuación \eref{eq-trans-1gr-generica}, la cual se puede implementar mediante un divisor resistivo con impedancias $\mathbb{Z}_{1}$ y $\mathbb{Z}_{2}$.\footnotemark[9] @@ -1007,30 +1049,30 @@ resistivo con impedancias $\mathbb{Z}_{1}$ y $\mathbb{Z}_{2}$.\footnotemark[9] \label{eq-trans-1gr-generica} \end{align} -Para un divisor resistivo con impedancias no inductivas, como el que se muestra -en la figura \ref{fig-impedance-divider}, la función de transferencia resulta -como se muestra en \eref{eq-trans-res-div}. En la misma ecuacion se muestra la -igualdad utilizando admitancias, que se definen como la inversa de la impedancia +Para un divisor de impedancias no inductivas, como el que se muestra en la +figura \ref{fig-impedance-divider}, la función de transferencia resulta como se +muestra en \eref{eq-trans-res-div}. En la misma ecuación se muestra la igualdad +utilizando admitancias, que se definen como la inversa de la impedancia $\mathbb{Y}=1/\mathbb{Z}$. Se utilizan admitancias porque simplifican las -expresiones de resistores y capactirores en paralelo. +expresiones de resistores y capacitores en paralelo. -\begin{figure}[ht] +\begin{figure}[!ht] \centering - \begin{subfigure}{0.40\textwidth} + \begin{subfigure}{0.44\textwidth} \centering - \includegraphics[width=\textwidth]{sch/complex_resistor_divider.png} + \includegraphics[width=\textwidth]{sch/complex_resistor_divider2.png} \caption{Valores genéricos} \label{fig-impedance-divider} \end{subfigure} \hfill - \begin{subfigure}{0.55\textwidth} + \begin{subfigure}{0.44\textwidth} \centering - \includegraphics[width=\textwidth]{sch/passive_highpass.png} + \includegraphics[width=\textwidth]{sch/passive_highpass2.png} \caption{Valores calculados normalizados} \label{fig-impedance-divider-norm-values} \end{subfigure} - \caption{Circuito pasa altos de primer orden con divisor resistivo} + \caption{Circuito pasa altos de primer orden con divisor de impedancias} \label{fig:circuito-considerado} \end{figure} @@ -1046,13 +1088,13 @@ expresiones de resistores y capactirores en paralelo. \footnotetext[9]{Sección 3.2, ``Realization with Passive Elements'', \cite{schaumann2001}} -Aplicando las expresiones de las admitancias de \eref{eq-trans-res-div} en la -ecuacion \eref{eq-trans-1gr-generica} de la transferencia generica, y con -$\mathbb{G}=1/R$ la conductancia, la transferencia del divisor resistivo resulta -como se muestra en \eref{eq-trans-res-div-comp}. Luego, sacando factor comun -$C_{1}$ en el numerador y $\left(C_{1} + C{2}\right)$ en el denominador se -obtiene una expresión similar a la expresión de la transferencia generica de -\eref{eq-trans-1gr-generica}. +Aplicando las expresiones de las admitancias de la ecuación +\eref{eq-trans-res-div} en la ecuación \eref{eq-trans-1gr-generica}, y denotando +$G=1/R$ a la conductancia, entonces la transferencia del divisor de impedancias +resulta como se muestra en \eref{eq-trans-res-div-comp}. Luego, sacando factor +común $C_{1}$ en el numerador y $\left(C_{1} + C{2}\right)$ en el denominador, +se obtiene una expresión para la transferencia del circuito similar a la +expresión de la transferencia genérica de \eref{eq-trans-1gr-generica}. % Dado que no se utilizarán inductores y que se tienen resistores y capacitores en % paralelo, la expresión de la transferencia en funcion de los resistores y @@ -1068,8 +1110,8 @@ obtiene una expresión similar a la expresión de la transferencia generica de \label{eq-trans-res-div-comp} \end{align} -Igualando la ecuación \eref{eq-trans-res-div-comp} con la expresion generica de -\eref{eq-trans-1gr-generica} resulta como se muestra a continuacion en +Igualando la ecuación \eref{eq-trans-res-div-comp} con la expresión genérica de +\eref{eq-trans-1gr-generica} resulta como se muestra a continuación en \eref{eq-trans-res-div-comp-1}. \begin{align} @@ -1081,47 +1123,48 @@ Igualando la ecuación \eref{eq-trans-res-div-comp} con la expresion generica de \label{eq-trans-res-div-comp-1} \end{align} -De la expresion \eref{eq-trans-res-div-comp-1} se obtiene: +De la expresión \eref{eq-trans-res-div-comp-1} se obtiene: \begin{align} - s &= z_{1} = \dfrac{G_{1}}{C_{1}} = \dfrac{1}{R_{1}\ C_{1}} - \label{eq-trans-res-div-z1}\\[6pt] - s &= p_{1} = \dfrac{G_{1}+G_{1}}{C_{1}+C_{2}} + z_{1} &= \dfrac{G_{1}}{C_{1}} = \dfrac{1}{R_{1}\ C_{1}} + \label{eq-trans-res-div-z1}\\[10pt] + p_{1} &= \dfrac{G_{1}+G_{1}}{C_{1}+C_{2}} = \dfrac{1}{\left(\dfrac{R_{1}\ R_{2}}{R_{1} + R_{2}}\right) \left(C_{1}+C_{2}\right)} - \label{eq-trans-res-div-p1}\\[0pt] - K_{\text{LF}} &= T(0) = \dfrac{G_{1}}{G_{1}+G_{2}} - \label{eq-trans-res-div-dc-gain} \\[0pt] + \label{eq-trans-res-div-p1}\\[8pt] + K_{\text{LF}} &= T(0) = \dfrac{G_{1}}{G_{1}+G_{2}} = \dfrac{R_{2}}{R_{1}+R_{2}} + \label{eq-trans-res-div-dc-gain} \\[8pt] K_{\text{HF}} &= T(\infty) = \dfrac{C_{1}}{C_{1}+C_{2}} \label{eq-trans-res-div-inf-gain} \end{align} -Para el caso de la transferencia $H_{1}(s)$ se tiene que $z_{1} = 250$, $p_{1} = -500$; la ganancia a frecuencias nulas $K=T(0)=0.5$ y para frecuencias muy altas -$K=T(\infty)=1$. Dada la ganancia $K$, entonces de +Para el caso de la transferencia $H_{1}$ se tiene que $z_{1} = 250$, $p_{1} = +500$; la ganancia a frecuencias muy bajas $K_{LF}=T(0)=0.5$ y a frecuencias +muy altas $K_{HF}=T(\infty)=1$. + +Dadas las ganancias $K_{LF}$ y $K_{HF}$, entonces de \eref{eq-trans-res-div-dc-gain} se obtiene $R_{1}=R_{2}$, y de \eref{eq-trans-res-div-inf-gain} resulta que $C_{2}=0$. Imponiendo $C_{1} = -22nF$, entonces de \eref{eq-trans-res-div-z1}: $R_{1} = R_{2} \approx -181818\Omega$ y dado que $181818\Omega$ no es un valor comercial estandarizado -se toma el valor $180k\Omega$, esto último implica un error de aproximadamente -$1\%$. +22nF$, entonces de la ecuación \eref{eq-trans-res-div-z1} resulta $R_{1} = R_{2} +\approx 181818\Omega$ y dado que $181818\Omega$ no es un valor comercial +estandarizado se toma el valor $180k\Omega$, esto último implica un error de +aproximadamente $1\%$ en el valor del resistor elegido. Reemplazando los valores en el circuito de la figura \ref{fig-impedance-divider}, resulta en el circuito de la figura -\ref{fig-impedance-divider-norm-values}. El circuito con los valores +\ref{fig-impedance-divider-norm-values}. Para el circuito con los valores reemplazados se realizó una simulación en LTSpice de manera de comparar el desempeño con la transferencia $H_{1}$. El resultado se muestra en el diagrama de Bode de la figura \ref{fig-pasa-altos-primer-orden}, en la cual se observa que -la diferencia es imperceptible entre la respuesta en frecuencia del circuito -simulado y la transferencia real. +la diferencia es prácticamente nula entre la respuesta en frecuencia del +circuito simulado y la transferencia teórica $H_{1}$. \begin{figure}[!ht] \centering \includegraphics[width=\textwidth]{plot/bode_passive_highpass.png} - \caption{Diagrama de Bode de circuito simulado y teorico para $H_{1}(s)$} + \caption{Diagrama de Bode de circuito pasa altos normalizado y $H_{1}$} \label{fig-pasa-altos-primer-orden} \end{figure} - % circuito pasivo de solo con resistores y capascitores\footnotemark[9] tal como % se muestra en la figura \eref{fig-pasa-bajos-primer-orden-inversor} del cual se % tienen expresiones tabuladas para los componentes en funcion del polo ($p$), @@ -1131,6 +1174,14 @@ simulado y la transferencia real. % que el circuito sea de segundo orden ya que $C_{1}$ y $C_{2}$ comparten el nodo, % por lo que no son linealmente independientes. +La transferencia $H_{1}$ resultante con los valores considerados normalizados se +muestra a continuación en \eref{eq-trans-res-div-compl-values}. + +\begin{align} + \boxed{\boxed{H_{1}(s) \approx \dfrac{s + 252.52}{s + 505.05}}} + \label{eq-trans-res-div-compl-values} +\end{align} + \iffalse La transferencia $H_{1}(s)$ es de la forma de la ecuación @@ -1176,9 +1227,9 @@ funcion de esto, resulta como en \eref{eq-transferencia-lineal-2}. \end{align} Para obtener la mejor relación normalizada de los componentes se utiliza un -script de Python que genera una lista de todas las posbiles combinaciones entre +script de Python que genera una lista de todas las posibles combinaciones entre $R_{1}$, $R_{2}$ y $C$, fijando un valor de $C$ y ajustando $R_{1}$ y $R_{2}$, -luego se ordena en funcion del error porcentual, el mejor resultado con +luego se ordena en función del error porcentual, el mejor resultado con resistores normalizados de tolerancia E24 (esto es $5\%$ de error) y capacitores de tolerancia E6 ($20\%$ de error) es $C_{1} = C_{2} = 22nF$, $R_{1}=180k\Omega$ y $R_{2}=91k\Omega$, de esta forma se tiene un error respecto al valor teórico @@ -1189,18 +1240,178 @@ de $1.00\%$ para $R_{1}$ y $0.10\%$ para $R_{2}$. \hypertarget{filtro-pasa-bajos-de-segundo-orden}{% \subsection{Filtro pasa bajos de segundo orden}\label{filtro-pasa-bajos-de-segundo-orden}} -La transferencia $H_{2}$ corresponde con un circuito Sallen-Key pasa bajos de -segundo orden. Dado que para $H_{1}$ se utilizó un filtro pasivo con ganancia -unitaria, entonces $H_{2}$ debe tener ganancia 12 para que asi sea igual a la -ganancia de $H$. +Para implementar la transferencia $H_{2}$ se elige un circuito Sallen-Key pasa +bajos de segundo orden con ganancia unitaria, ya que este tipo de filtro es +relativamente sencillo con respecto a otros filtros y los cálculos son directos. +La transferencia de un filtro Sallen-Key pasa bajos de segundo orden con +ganancia unitaria se muestra a continuación en la ecuación +\eref{eq-sallen-key-lpf-generic}.\footnotemark[10] + +\footnotetext[10]{\ Esto se obtiene de la sección 4.5.1: ``Sallen-Key Circuits'', +\cite{schaumann2001}. Imponiendo $R_{A}\to\infty$, $R_{B}=0$, logrando asà +ganancia unitaria $K=1$.} + +\begin{align} + T(s) &= \dfrac{\dfrac{1}{R_{1}\ R_{2}\ C_{1}\ C_{2}}} + {s^{2}+\left(\dfrac{R_{1}+R_{2}}{R_{1}\ R_{2}\ + C_{1}}\right)s + \left(\dfrac{1}{R_{1}\ R_{2}\ C_{1}\ C_{2}}\right)} + \label{eq-sallen-key-lpf-generic} +\end{align} + +Igualando la transferencia anterior de la ecuación +\eref{eq-sallen-key-lpf-generic} con la expresión genérica del filtro pasa bajos +de segundo orden mencionado en la ecuación \eref{eq-lpf-2-general} se obtienen +las expresiones para la frecuencia natural $\omega_{0}$ y el factor de calidad +$Q$ que se muestran en las ecuaciones \eref{eq-sallen-key-param-w0} y +\eref{eq-sallen-key-param-Q}. + +\begin{align} + \omega_{0} &= \sqrt{ \dfrac{1}{R_{1}\ R_{2}\ C_{1}\ C_{2}}} + \label{eq-sallen-key-param-w0}\\[8pt] + Q &= \dfrac{\sqrt{\dfrac{1}{R_{1}\ R_{2}\ C_{1}\ C_{2}}}} + {\dfrac{R_{1} + R_{2}}{C_{1}\ R_{1}\ R_{2}}} + \label{eq-sallen-key-param-Q} +\end{align} + +Para obtener valores de los componentes $R_{1}$, $R_{2}$, $C_{1}$ y $C_{2}$ se +sabe que $\omega_{0} = 4000$ y $Q=2.25$, por lo que reemplazando en las +ecuaciones \eref{eq-sallen-key-param-w0} y \eref{eq-sallen-key-param-Q} se +tiene un sistema de dos ecuaciones con 4 incógnitas, por lo que se utiliza un +script de Python que dado una lista de valores normalizados de resistencias y +capacitores se calcula el error de $\omega_{0}$ y $Q$ para cada cuarteto de +valores $R_{1}$, $R_{2}$, $C_{1}$, $C_{2}$ posible, resultando en una lista de +la mejor combinación de valores para minimizar el error de $\omega_{0}$ y $Q$. +En la tabla \ref{tab-sallen-key-componentes} se muestran algunos de los mejores +valores obtenidos mediante el script. En particular se eligió $R_{1} = +20k\Omega$, $R_{2} = 30k\Omega$, $C_{1} = 47nF$ y $C_{2} = 2.20nF$, ya que si +bien no es la opción que mayor minimiza el error, son valores de resistencias +mayores que otras opciones lo cual es deseable, ya que evita cargar etapas +anteriores y disminuye el consumo de corriente y los capacitores tienen valores +fácilmente disponibles comercialmente. De cualquier forma el error de +$\omega_{0}$ y $Q$ permanece por debajo de $1\%$. + +\begin{table}[h] + \centering + \begin{tabular}{|r|r|r|r|r|r|r|r|} + \hline + $R_1$ [$\Omega$] & $R_2$ [$\Omega$] & $C_1$ [nF] & $C_2$ [nF] & $\omega_0$ [rad/s] & $\Delta\omega_0$ [\%] & $Q$ & $\Delta Q$ [\%] \\ + \hline + \hline + 1300 & 15000 & $470$ & $6.80$ & 4005.7 & 0.14 & 2.252 & 0.10 \\ + \hline + 15000 & 1300 & $470$ & $6.80$ & 4005.7 & 0.14 & 2.252 & 0.10 \\ + \hline + 2700 & 4700 & $330$ & $15$ & 3989.9 & 0.25 & 2.258 & 0.35 \\ + \hline + 30000 & 20000 & $47$ & $2.20$ & 4014.8 & 0.37 & 2.264 & 0.64 \\ + \hline + \end{tabular} + \caption{Lista de valores para minimizar $\omega_{0}$ y $Q$.} + \label{tab-sallen-key-componentes} +\end{table} + +Con los valores elegidos, la transferencia $H_{2}$ resulta como se muestra +a continuación en la ecuación \eref{eq-trans-2-val}. + +\begin{align} + % H_{2}(s) = \dfrac{4014.8^{2}}{\left(s^{2} + \dfrac{4014.8^{2}}{9000}s + 4000^{2}\right)} \notag\\ + \boxed{\boxed{H_{2}(s) \approx \dfrac{16118619.04}{s^{2} + 1773.05s + 16118619.04}}} + \label{eq-trans-2-val} +\end{align} + +% \begin{lstlisting} +% R1 R2 C1 C2 w0 dw0 Q dQ +% 1300 15000 4.70e-07 6.80e-09 4005.7 +0.14 2.252 +0.10 +% 15000 1300 4.70e-07 6.80e-09 4005.7 +0.14 2.252 +0.10 +% 2700 4700 3.30e-07 1.50e-08 3989.9 -0.25 2.258 +0.35 +% 30000 20000 4.70e-08 2.20e-09 4014.8 +0.37 2.264 +0.64 +% \end{lstlisting} \begin{figure}[!ht] \centering - \includegraphics[width=0.80\textwidth]{sch/pasa-bajos_activo_segundo_orden_sallen-key.png} - \caption{Pasa bajos segundo orden Sallen-Key para transferencia $H_{2}(s)$} + \includegraphics[width=0.75\textwidth]{sch/pasa-bajos_activo_segundo_orden_sallen-key_script.png} + \caption{Circuito pasa bajos de segundo orden Sallen-Key} \label{fig-pasa-bajos-primer-orden-inversor} \end{figure} +\begin{figure}[!ht] + \centering + \includegraphics[width=\textwidth]{plot/sallen-key_lpf_valores_teoricos_scipt_min_err.png} + \caption{Diagrama de Bode de circuito pasa bajos Sallen-Key normalizado y $H_{2}$} + \label{fig-pasa-altos-primer-orden} +\end{figure} + +\clearpage +\pagebreak +\hypertarget{amplificador-no-inversor}{% +\subsection{Amplificador no inversor}\label{amplificador-no-inversor}} + +Como bien se mencionó la transferencia $H$ se obtiene realizando el producto +entre las transferencias $H_{1}$, $H_{2}$ y un factor de ganancia 12. Dado que +los circuitos correspondientes se diseñaron acorde a las transferencias, se +necesita de una etapa adicional que implemente el factor de ganancia. Para esto +se utiliza un amplificador no inversor con un circuito como el de la figura +\ref{fig-amp-no-inversor}. + +\begin{figure}[!ht] + \centering + \includegraphics[width=0.30\textwidth]{sch/non_invert_amp.png} + \caption{Circuito amplificador no inversor} + \label{fig-amp-no-inversor} +\end{figure} + +La trasferencia del circuito amplificador no inversor de la figura +\ref{fig-amp-no-inversor} resulta como se muestra a continuación en la ecuación +\eref{eq-trans-amp}. + +\begin{align} + T(s)=1+\dfrac{R_{2}}{R_{1}} + \label{eq-trans-amp} +\end{align} + +Dado que se requiere un factor de ganancia de 12, es decir, una transferencia +$T(s)=12$ constante para todas las frecuencias, de \eref{eq-trans-amp} se +obtiene la relación $R_{2}=11\ R_{1}$. Imponiendo $R_{1} = 20k\Omega$, entonces +$R_{2} = 220k\Omega$. + +\pagebreak +\hypertarget{circuito-final}{% +\subsection{Circuito final}\label{circuito-final}} + +El circuito final resulta de la ``cascada'' o conexión en serie de los +diferentes etapas: el filtro pasa altos que implementa la transferencia $H_{1}$, +el filtro pasa bajos Sallen-Key que implementa la transferencia $H_{2}$, y el +amplificador no inversor para ajustar la ganancia. + +Hay que tener en cuenta que la cascada de diferentes circuitos solo es posible +en la práctica si los circuitos no interfieren entre sÃ, en particular esto es +válido cuando la impedancia de salida del primer circuito es mucho menor que la +impedancia de entrada del segundo circuito,\footnotemark[11] teniendo esto en +cuanta se ubica en primer lugar el filtro pasa altos de primer nivel, ya que +este tiene impedancia de entrada y salida baja, luego el amplificador no +inversor ya que este tiene una impedancia infinita debido al amplificador +operacional, por ultimo se ubica el filtro Sallen-Key de segundo orden tal como +se muestra en la figura \ref{fig-pasa-bajos-primer-orden-inversor}. + +\footnotetext[11]{Esto se obtiene de la sección 3.6: ``Cascade Design'', +\cite{schaumann2001}} + + +\begin{figure}[!ht] + \centering + \includegraphics[width=\textwidth]{sch/trans_comp.png} + \caption{Circuito final con valores normalizados} + \label{fig-pasa-bajos-primer-orden-inversor} +\end{figure} + +\begin{figure}[!ht] + \centering + \includegraphics[width=\textwidth]{plot/trans_comp.png} + \caption{Diagrama de Bode de circuito final y $H$} + \label{fig-pasa-bajos-primer-orden-inversor} +\end{figure} + +\pagebreak \hypertarget{diagrama}{% \subsection{Diagrama}\label{diagrama}} diff --git a/tp/informe/plot/bode_passive_highpass.png b/tp/informe/plot/bode_passive_highpass.png Binary files differ. diff --git a/tp/informe/plot/sallen-key_lpf_valores_teoricos.png b/tp/informe/plot/sallen-key_lpf_valores_teoricos.png Binary files differ. diff --git a/tp/informe/plot/sallen-key_lpf_valores_teoricos_scipt_min_err.png b/tp/informe/plot/sallen-key_lpf_valores_teoricos_scipt_min_err.png Binary files differ. diff --git a/tp/informe/plot/trans_comp.png b/tp/informe/plot/trans_comp.png Binary files differ. diff --git a/tp/informe/sch/divisor_resistivo_impedancias_generico.asc b/tp/informe/sch/divisor_resistivo_impedancias_generico.asc @@ -3,53 +3,53 @@ SHEET 1 880 680 WIRE 208 80 192 80 WIRE 304 80 288 80 WIRE 192 112 192 80 -WIRE 192 112 128 112 +WIRE 192 112 144 112 WIRE 304 112 304 80 -WIRE 384 112 304 112 -WIRE 384 128 384 112 -WIRE 384 128 352 128 -WIRE 416 128 384 128 -WIRE 128 144 128 112 +WIRE 368 112 304 112 +WIRE 368 128 368 112 +WIRE 368 128 336 128 +WIRE 400 128 368 128 +WIRE 144 144 144 112 WIRE 192 144 192 112 WIRE 208 144 192 144 WIRE 304 144 304 112 WIRE 304 144 272 144 -WIRE 352 144 352 128 -WIRE 416 144 416 128 -WIRE 352 240 352 208 -WIRE 384 240 352 240 -WIRE 416 240 416 224 -WIRE 416 240 384 240 -WIRE 128 256 128 224 -WIRE 240 256 128 256 -WIRE 384 256 384 240 -WIRE 384 256 240 256 -WIRE 240 272 240 256 -FLAG 240 272 0 -FLAG 384 112 Vout -SYMBOL voltage 128 128 M0 -WINDOW 0 11 4 Left 2 +WIRE 336 144 336 128 +WIRE 400 144 400 128 +WIRE 336 240 336 208 +WIRE 368 240 336 240 +WIRE 400 240 400 224 +WIRE 400 240 368 240 +WIRE 144 256 144 224 +WIRE 368 256 368 240 +WIRE 368 256 144 256 +WIRE 144 272 144 256 +FLAG 144 272 0 +FLAG 368 112 Vout +FLAG 144 112 Vin +SYMBOL voltage 144 128 M0 +WINDOW 0 11 4 Invisible 2 WINDOW 39 0 0 Left 0 SYMATTR InstName Vin SYMATTR Value "" SYMATTR Value2 AC 1 SYMBOL res 304 64 R90 -WINDOW 0 6 25 VBottom 2 +WINDOW 0 9 17 VBottom 2 WINDOW 3 -10 121 Invisible 2 SYMATTR InstName R1 SYMATTR Value 180k SYMBOL cap 272 128 R90 -WINDOW 0 45 -4 VBottom 2 +WINDOW 0 58 32 VBottom 2 WINDOW 3 27 64 Invisible 0 SYMATTR InstName C1 SYMATTR Value 22n -SYMBOL res 400 128 R0 -WINDOW 0 27 93 Left 2 +SYMBOL res 384 128 R0 +WINDOW 0 29 88 Left 2 WINDOW 3 36 76 Invisible 2 SYMATTR InstName R2 SYMATTR Value 180k -SYMBOL cap 368 208 R180 -WINDOW 0 30 10 Left 2 +SYMBOL cap 352 208 R180 +WINDOW 0 30 13 Left 2 WINDOW 3 24 8 Invisible 2 SYMATTR InstName C2 SYMATTR Value 22n diff --git a/tp/informe/sch/passive_highpass_normalized.asc b/tp/informe/sch/passive_highpass_normalized.asc @@ -13,19 +13,18 @@ WIRE 208 176 192 176 WIRE 304 176 304 144 WIRE 304 176 272 176 WIRE 128 256 128 240 -WIRE 240 256 128 256 WIRE 352 256 352 240 -WIRE 352 256 240 256 -WIRE 240 272 240 256 -FLAG 240 272 0 +WIRE 352 256 128 256 +WIRE 128 272 128 256 FLAG 352 144 Vout +FLAG 128 144 Vin +FLAG 128 272 0 SYMBOL voltage 128 144 M0 -WINDOW 0 46 40 Left 2 -WINDOW 123 45 68 Left 2 +WINDOW 0 46 40 Invisible 2 WINDOW 39 0 0 Left 0 SYMATTR InstName Vin -SYMATTR Value "" SYMATTR Value2 AC 1 +SYMATTR Value "" SYMBOL res 304 96 R90 WINDOW 0 11 11 VBottom 2 WINDOW 3 -10 121 VTop 2 @@ -41,4 +40,4 @@ WINDOW 0 41 41 Left 2 WINDOW 3 39 67 Left 2 SYMATTR InstName R2 SYMATTR Value 180k -TEXT 272 280 Left 2 !.ac dec 100 .1 100k +TEXT 168 280 Left 2 !.ac dec 100 .1 100k diff --git a/tp/informe/sch/sallen-key_lpf_valores_teoricos.asc b/tp/informe/sch/sallen-key_lpf_valores_teoricos.asc @@ -0,0 +1,55 @@ +Version 4 +SHEET 1 880 680 +WIRE 128 80 16 80 +WIRE 288 80 192 80 +WIRE -96 128 -144 128 +WIRE 16 128 16 80 +WIRE 16 128 -16 128 +WIRE 32 128 16 128 +WIRE 144 128 112 128 +WIRE 208 128 144 128 +WIRE -144 144 -144 128 +WIRE 288 144 288 80 +WIRE 288 144 272 144 +WIRE 144 160 144 128 +WIRE 208 160 192 160 +WIRE 192 192 192 160 +WIRE 288 192 288 144 +WIRE 288 192 192 192 +WIRE -144 240 -144 224 +WIRE 144 240 144 224 +FLAG -144 240 0 +FLAG 288 80 Vout +FLAG -144 128 Vin +FLAG 144 240 0 +SYMBOL OpAmps\\opamp 240 208 M180 +WINDOW 0 -1 95 Left 2 +SYMATTR InstName U1 +SYMBOL cap 192 64 R90 +WINDOW 0 7 60 VBottom 2 +WINDOW 3 -14 3 VTop 2 +SYMATTR InstName C1 +SYMATTR Value .1µ +SYMBOL cap 160 224 R180 +WINDOW 0 24 56 Left 2 +WINDOW 3 24 8 Left 2 +SYMATTR InstName C2 +SYMATTR Value 4.7n +SYMBOL 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a/tp/informe/sch/sallen-key_lpf_valores_teoricos_scipt_min_err.asc b/tp/informe/sch/sallen-key_lpf_valores_teoricos_scipt_min_err.asc @@ -0,0 +1,55 @@ +Version 4 +SHEET 1 880 680 +WIRE 128 80 16 80 +WIRE 288 80 192 80 +WIRE -96 128 -144 128 +WIRE 16 128 16 80 +WIRE 16 128 -16 128 +WIRE 32 128 16 128 +WIRE 144 128 112 128 +WIRE 208 128 144 128 +WIRE -144 144 -144 128 +WIRE 288 144 288 80 +WIRE 288 144 272 144 +WIRE 144 160 144 128 +WIRE 208 160 192 160 +WIRE 192 192 192 160 +WIRE 288 192 288 144 +WIRE 288 192 192 192 +WIRE -144 240 -144 224 +WIRE 144 240 144 224 +FLAG -144 240 0 +FLAG 288 80 Vout +FLAG -144 128 Vin +FLAG 144 240 0 +SYMBOL OpAmps\\opamp 240 208 M180 +WINDOW 0 -1 95 Left 2 +SYMATTR InstName U1 +SYMBOL cap 192 64 R90 +WINDOW 0 9 63 VBottom 2 +WINDOW 3 -12 -2 VTop 2 +SYMATTR InstName C1 +SYMATTR Value 47n +SYMBOL cap 160 224 R180 +WINDOW 0 24 56 Left 2 +WINDOW 3 24 8 Left 2 +SYMATTR InstName C2 +SYMATTR Value 2.2n +SYMBOL res 0 112 R90 +WINDOW 0 -6 55 VBottom 2 +WINDOW 3 36 56 VTop 2 +SYMATTR InstName R1 +SYMATTR Value 20k +SYMBOL res 128 112 R90 +WINDOW 0 -5 56 VBottom 2 +WINDOW 3 36 55 VTop 2 +SYMATTR InstName R2 +SYMATTR Value 30k +SYMBOL voltage -144 128 M0 +WINDOW 39 0 0 Left 0 +WINDOW 0 24 16 Invisible 2 +SYMATTR InstName V1 +SYMATTR Value2 AC 1 +SYMATTR Value "" +TEXT 176 224 Left 2 !.ac dec 100 .1 100k +TEXT 176 248 Left 2 !.inc opamp.sub diff --git a/tp/informe/sch/sallen-key_lpf_valores_teoricos_scipt_min_err.txt b/tp/informe/sch/sallen-key_lpf_valores_teoricos_scipt_min_err.txt @@ -0,0 +1,602 @@ +Freq. 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Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/bode_mag.png b/tp/scripts/spice_exported_data_plots/bode_mag.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/bode_mag_pha_same_plot.m b/tp/scripts/spice_exported_data_plots/bode_mag_pha_same_plot.m @@ -0,0 +1,129 @@ +clc; clear all; close all; + +%% Figure light theme + +set(0, "defaultAxesColorOrder", [ + 1.0000 0.0000 0.0000; # red + 0.0000 0.0000 1.0000; # blue + 1.0000 0.4980 0.0549; # orange + 0.1725 0.6275 0.1725; # green + 0.5804 0.4039 0.7412; # purple + 0.5490 0.3373 0.2941; # brown + 0.8902 0.4667 0.7608; # pink + 0.4980 0.4980 0.4980; # gray +]); + +set(0, "DefaultFigureColor", [1 1 1]); +set(0, "DefaultAxesColor", [1 1 1]); +set(0, "DefaultAxesXColor", [0 0 0]); +set(0, "DefaultAxesYColor", [0 0 0]); +set(0, "DefaultTextColor", [0 0 0]); + +set(0, "DefaultAxesGridColor", [0 0 0]); +set(0, 'DefaultAxesGridAlpha', 1.00); + +set(0, "DefaultAxesMinorGridColor", [0 0 0]); +set(0, 'DefaultAxesMinorGridAlpha', 0.20); + +set(0, "DefaultLineLinewidth", 3.00); +set(0, "DefaultAxesFontSize", 16); +set(0, "DefaultTextFontSize", 16); +set(0, "DefaultAxesLineWidth", 1.00); + +set(0, "DefaultAxesXGrid", "on"); +set(0, "DefaultAxesYGrid", "on"); +set(0, "DefaultAxesZGrid", "on"); +set(0, "DefaultAxesXMinorGrid", "on"); +set(0, "DefaultAxesYMinorGrid", "on"); +set(0, "DefaultAxesXMinorTick", "on"); +set(0, "DefaultAxesYMinorTick", "on"); + +set(0, 'DefaultAxesGridAlpha', 0.50); + +% exported ltspice data +filename = "passive_highpass_normalized_utf8.txt"; + +fid = fopen(filename, "r"); + +% Skip header +fgetl(fid); + +% Read frequency and complex string +data = textscan(fid, "%f %s", "Delimiter", "\t"); + +fclose(fid); + +freq = data{1}; +response = data{2}; + +N = numel(freq); + +mag = zeros(N,1); +phase = zeros(N,1); + +for k = 1:N + tokens = regexp(response{k}, ... + '\(([-+0-9.eE]+)dB,([-+0-9.eE]+)°\)', ... + 'tokens'); + + mag(k) = str2double(tokens{1}{1}); + phase(k) = str2double(tokens{1}{2}); +end + +figure(1); +grid on; +set(gcf, "paperunits", "inches"); +set(gcf, "papersize", [10 4]); +set(gcf, "paperposition", [0 0 10 6]); +% theorical transfer function + +H1=tf([1 250], [1 500]) +bode(H1) +[mag_the, pha_the, freq] = bode(H1, freq); +max(freq) + +% bode functions returns linear scale y-axis +mag_the = squeeze(mag_the); +pha_the = squeeze(pha_the); +mag_the = 20*log10(mag_the); + +figure; + +% Create common x-axis +freq1 = freq*2*pi; + +[ax, hmag, hphase] = plotyy( ... + freq1, mag, ... + freq1, phase); + +hold(ax(1), "on"); +hold(ax(2), "on"); + +% Theoretical curves +semilogx(ax(1), freq, mag_the, ".", "LineWidth", 2); +semilogx(ax(2), freq, pha_the, ".", "LineWidth", 2); + +% Log frequency axis +set(ax(1), "XScale", "log"); +set(ax(2), "XScale", "log"); + +% Line widths +set(hmag, "LineWidth", 3); +set(hphase, "LineWidth", 3); + +% Limits +xlim(ax(1), [1 1e5]); +xlim(ax(2), [1 1e5]); + +grid(ax(1), "on"); +grid(ax(2), "on"); + +% Labels +xlabel("FRECUENCIA [rad/s]"); +ylabel(ax(1), "MAGNITUD [dB]"); +ylabel(ax(2), "FASE [grados]"); + +legend([hmag, hphase], ... + "Magnitud", "Fase"); + +print("bode_one_plot_passive_highpass.png", "-dpng", "-r500"); diff --git a/tp/scripts/spice_exported_data_plots/bode_one_plot_passive_highpass.png b/tp/scripts/spice_exported_data_plots/bode_one_plot_passive_highpass.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/bode_passive_highpass.png b/tp/scripts/spice_exported_data_plots/bode_passive_highpass.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/bode_pha.png b/tp/scripts/spice_exported_data_plots/bode_pha.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/bode_utf8.txt b/tp/scripts/spice_exported_data_plots/bode_utf8.txt @@ -0,0 +1,402 @@ +Freq. 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0.1725 0.6275 0.1725; # green + 0.5804 0.4039 0.7412; # purple + 0.5490 0.3373 0.2941; # brown + 0.8902 0.4667 0.7608; # pink + 0.4980 0.4980 0.4980; # gray +]); + +set(0, "DefaultFigureColor", [1 1 1]); +set(0, "DefaultAxesColor", [1 1 1]); +set(0, "DefaultAxesXColor", [0 0 0]); +set(0, "DefaultAxesYColor", [0 0 0]); +set(0, "DefaultTextColor", [0 0 0]); + +set(0, "DefaultAxesGridColor", [0 0 0]); +set(0, 'DefaultAxesGridAlpha', 1.00); + +set(0, "DefaultAxesMinorGridColor", [0 0 0]); +set(0, 'DefaultAxesMinorGridAlpha', 0.20); + +set(0, "DefaultLineLinewidth", 3.00); +set(0, "DefaultAxesFontSize", 16); +set(0, "DefaultTextFontSize", 16); +set(0, "DefaultAxesLineWidth", 1.00); + +set(0, "DefaultAxesXGrid", "on"); +set(0, "DefaultAxesYGrid", "on"); +set(0, "DefaultAxesZGrid", "on"); +set(0, "DefaultAxesXMinorGrid", "on"); +set(0, "DefaultAxesYMinorGrid", "on"); +set(0, "DefaultAxesXMinorTick", "on"); +set(0, "DefaultAxesYMinorTick", "on"); + +set(0, 'DefaultAxesGridAlpha', 0.50); + +% exported ltspice data +filename = "passive_highpass_normalized_utf8.txt"; + +fid = fopen(filename, "r"); + +% Skip header +fgetl(fid); + +% Read frequency and complex string +data = textscan(fid, "%f %s", "Delimiter", "\t"); + +fclose(fid); + +freq = data{1}; +response = data{2}; + +N = numel(freq); + +mag = zeros(N,1); +phase = zeros(N,1); + +for k = 1:N + tokens = regexp(response{k}, ... + '\(([-+0-9.eE]+)dB,([-+0-9.eE]+)°\)', ... + 'tokens'); + + mag(k) = str2double(tokens{1}{1}); + phase(k) = str2double(tokens{1}{2}); +end + +figure(1); +grid on; +set(gcf, "paperunits", "inches"); +set(gcf, "papersize", [10 5]); +set(gcf, "paperposition", [0 0 10 5]); +% theorical transfer function + +H1=tf([1 250], [1 500]) +bode(H1); +[mag_the, pha_the, freq] = bode(H1, freq); +max(freq) + +% bode functions returns linear scale y-axis +mag_the = squeeze(mag_the); +pha_the = squeeze(pha_the); +mag_the = 20*log10(mag_the); + +%% Magnitude +ax1 = subplot(2, 1, 1) +y1 = semilogx(freq*2*pi, mag, "LineWidth", 3); +grid on; +hold on; +y2 = semilogx(freq, mag_the, "LineWidth", 2); +ylim([-6.015 0]) +yticks([-6 -3 0]); +xlim([1 1e5]) +% xlabel("Frequency [Hz]"); +ylabel("MAGNITUD [dB]"); +% title("Bode Magnitude"); +% legend("Normalizado", "Teórica", "Location", "southeast"); + +% Remove x tick labels from upper plot +set(ax1, "XTickLabel", []); + +%% Phase +ax2 = subplot(2, 1, 2) +semilogx(freq*2*pi, phase, "LineWidth", 3); +grid on; +hold on; +semilogx(freq, pha_the, "LineWidth", 2); +xlim([1 1e5]) +xlabel('FRECUENCIA [rad/s]'); +ylabel("FASE [grados]"); +% title("Bode Phase"); +% legend("Normalizado", "Teórica", "Location", "northeast"); + +% Create legend on top axes +% lgd = legend(ax1, [y1 y2], ... +% "Respuesta en frecuencia circuito", ... +% 'Transferencia H_{1}(j\omega)') + +% Invisible axes covering the whole figure +axL = axes("Position", [0 0 1 1], ... + "Visible", "off", ... + "Units", "normalized"); + +lgd = legend(axL, [y1 y2], ... + {"Circuito pasa altos\nde primer orden", "Transferencia H_{1}"}); + +% Move legend between plots +set(lgd, "position", [0.58 0.54 -0.50 -0.50]); +set(lgd, "numcolumns", 1); + +% Reduce vertical spacing +set(ax1, "Position", [0.13 0.58 0.80 0.38]); +set(ax2, "Position", [0.13 0.13 0.80 0.38]); + +print("bode_passive_highpass.png", "-dpng", "-r500"); + diff --git a/tp/scripts/spice_exported_data_plots/pasa-bajos_activo_primer_orden_inversor_H1_data.txt b/tp/scripts/spice_exported_data_plots/pasa-bajos_activo_primer_orden_inversor_H1_data.txt @@ -0,0 +1,402 @@ +Freq. 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b/tp/scripts/spice_exported_data_plots/sallen-key_lpf_valores_teoricos.m @@ -0,0 +1,149 @@ +clc; clear all; close all; + +%% Figure light theme + +set(0, "defaultAxesColorOrder", [ + 1.0000 0.0000 0.0000; # red + 0.0000 0.0000 1.0000; # blue + 1.0000 0.4980 0.0549; # orange + 0.1725 0.6275 0.1725; # green + 0.5804 0.4039 0.7412; # purple + 0.5490 0.3373 0.2941; # brown + 0.8902 0.4667 0.7608; # pink + 0.4980 0.4980 0.4980; # gray +]); + +set(0, "DefaultFigureColor", [1 1 1]); +set(0, "DefaultAxesColor", [1 1 1]); +set(0, "DefaultAxesXColor", [0 0 0]); +set(0, "DefaultAxesYColor", [0 0 0]); +set(0, "DefaultTextColor", [0 0 0]); + +set(0, "DefaultAxesGridColor", [0 0 0]); +set(0, 'DefaultAxesGridAlpha', 1.00); + +set(0, "DefaultAxesMinorGridColor", [0 0 0]); +set(0, 'DefaultAxesMinorGridAlpha', 0.20); + +set(0, "DefaultLineLinewidth", 3.00); +set(0, "DefaultAxesFontSize", 16); +set(0, "DefaultTextFontSize", 16); +set(0, "DefaultAxesLineWidth", 1.00); + +set(0, "DefaultAxesXGrid", "on"); +set(0, "DefaultAxesYGrid", "on"); +set(0, "DefaultAxesZGrid", "on"); +set(0, "DefaultAxesXMinorGrid", "on"); +set(0, "DefaultAxesYMinorGrid", "on"); +set(0, "DefaultAxesXMinorTick", "on"); +set(0, "DefaultAxesYMinorTick", "on"); + +set(0, 'DefaultAxesGridAlpha', 0.50); + +set(0, "defaultAxesFontName", "Nimbus Sans"); + +% exported ltspice data +filename = "sallen-key_lpf_valores_teoricos_scipt_min_err_utf8.txt"; + +fid = fopen(filename, "r"); + +% Skip header +fgetl(fid); + +% Read frequency and complex string +data = textscan(fid, "%f %s", "Delimiter", "\t"); + +fclose(fid); + +freq = data{1}; +response = data{2}; + +N = numel(freq); + +mag = zeros(N,1); +phase = zeros(N,1); + +for k = 1:N + tokens = regexp(response{k}, ... + '\(([-+0-9.eE]+)dB,([-+0-9.eE]+)°\)', ... + 'tokens'); + + mag(k) = str2double(tokens{1}{1}); + phase(k) = str2double(tokens{1}{2}); +end + +figure(1); +grid on; +set(gcf, "paperunits", "inches"); +set(gcf, "papersize", [10 5]); +set(gcf, "paperposition", [0 0 10 5]); +% theorical transfer function + +H2=tf([4000^2], [1 4000^2/9000 4000^2]) +bode(H2); +[mag_the, pha_the, freq] = bode(H2, freq); +max(freq) + +% bode functions returns linear scale y-axis +mag_the = squeeze(mag_the); +pha_the = squeeze(pha_the); +mag_the = 20*log10(mag_the); + +%% Magnitude +ax1 = subplot(2, 1, 1) +y1 = semilogx(freq*2*pi, mag, "LineWidth", 3); +grid on; +hold on; +y2 = semilogx(freq, mag_the, "LineWidth", 2); + +ylim([-60 10]) +yticks([-60 -40 -20 0]); +xlim([1 1e5]) + +% xlabel("Frequency [Hz]"); +ylabel("MAGNITUD [dB]"); +% title("Bode Magnitude"); +% legend("Normalizado", "Teórica", "Location", "southeast"); + +% Remove x tick labels from upper plot +set(ax1, "XTickLabel", []); + +%% Phase +ax2 = subplot(2, 1, 2) +semilogx(freq*2*pi, phase, "LineWidth", 3); +grid on; +hold on; +semilogx(freq, pha_the, "LineWidth", 2); + +ylim([-180 0]) +yticks([-180 -90 0]); +xlim([1 1e5]) + +xlabel('FRECUENCIA [rad/s]'); +ylabel("FASE [grados]"); +% title("Bode Phase"); +% legend("Normalizado", "Teórica", "Location", "northeast"); + +% Create legend on top axes +% lgd = legend(ax1, [y1 y2], ... +% "Respuesta en frecuencia circuito", ... +% 'Transferencia H_{1}(j\omega)') + +% Invisible axes covering the whole figure +axL = axes("Position", [0 0 1 1], ... + "Visible", "off", ... + "Units", "normalized"); + +lgd = legend(axL, [y1 y2], ... + {"Circuito pasa bajos Sallen-Key", "Transferencia H_{2}"}); + +% Move legend between plots +set(lgd, "position", [0.15 0.55 -0.50 -0.50]); +set(lgd, "numcolumns", 1); + +% Reduce vertical spacing +set(ax1, "Position", [0.13 0.58 0.80 0.38]); +set(ax2, "Position", [0.13 0.13 0.80 0.38]); + +print("sallen-key_lpf_valores_teoricos_scipt_min_err.png", "-dpng", "-r500"); + diff --git a/tp/scripts/spice_exported_data_plots/sallen-key_lpf_valores_teoricos.png b/tp/scripts/spice_exported_data_plots/sallen-key_lpf_valores_teoricos.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/sallen-key_lpf_valores_teoricos.txt b/tp/scripts/spice_exported_data_plots/sallen-key_lpf_valores_teoricos.txt @@ -0,0 +1,602 @@ +Freq. V(vout) +1.00000000000000e-01 (-8.66603927644977e-05dB,-4.07883304310793e-03°) +1.02329299228075e-01 (-8.66510580432100e-05dB,-4.17384127434661e-03°) +1.04712854805090e-01 (-8.66412833942468e-05dB,-4.27106253191478e-03°) +1.07151930523761e-01 (-8.66310480737547e-05dB,-4.37054836384142e-03°) +1.09647819614319e-01 (-8.66203303822221e-05dB,-4.47235151886511e-03°) +1.12201845430196e-01 (-8.66091075796181e-05dB,-4.57652597440216e-03°) +1.14815362149688e-01 (-8.65973558670699e-05dB,-4.68312696516641e-03°) +1.17489755493953e-01 (-8.65850503068227e-05dB,-4.79221101245550e-03°) +1.20226443461741e-01 (-8.65721648097035e-05dB,-4.90383595411953e-03°) +1.23026877081238e-01 (-8.65586720300086e-05dB,-5.01806097522755e-03°) +1.25892541179417e-01 (-8.65445433587527e-05dB,-5.13494663944859e-03°) +1.28824955169313e-01 (-8.65297488224139e-05dB,-5.25455492116346e-03°) +1.31825673855641e-01 (-8.65142570462891e-05dB,-5.37694923832473e-03°) +1.34896288259165e-01 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a/tp/scripts/spice_exported_data_plots/trans_comp.m b/tp/scripts/spice_exported_data_plots/trans_comp.m @@ -0,0 +1,141 @@ +clc; clear all; close all; + +%% Figure light theme + +set(0, "defaultAxesColorOrder", [ + 1.0000 0.0000 0.0000; # red + 0.0000 0.0000 1.0000; # blue + 1.0000 0.4980 0.0549; # orange + 0.1725 0.6275 0.1725; # green + 0.5804 0.4039 0.7412; # purple + 0.5490 0.3373 0.2941; # brown + 0.8902 0.4667 0.7608; # pink + 0.4980 0.4980 0.4980; # gray +]); + +set(0, "DefaultFigureColor", [1 1 1]); +set(0, "DefaultAxesColor", [1 1 1]); +set(0, "DefaultAxesXColor", [0 0 0]); +set(0, "DefaultAxesYColor", [0 0 0]); +set(0, "DefaultTextColor", [0 0 0]); + +set(0, "DefaultAxesGridColor", [0 0 0]); +set(0, 'DefaultAxesGridAlpha', 1.00); + +set(0, "DefaultAxesMinorGridColor", [0 0 0]); +set(0, 'DefaultAxesMinorGridAlpha', 0.20); + +set(0, "DefaultLineLinewidth", 3.00); +set(0, "DefaultAxesFontSize", 16); +set(0, "DefaultTextFontSize", 16); +set(0, "DefaultAxesLineWidth", 1.00); + +set(0, "DefaultAxesXGrid", "on"); +set(0, "DefaultAxesYGrid", "on"); +set(0, "DefaultAxesZGrid", "on"); +set(0, "DefaultAxesXMinorGrid", "on"); +set(0, "DefaultAxesYMinorGrid", "on"); +set(0, "DefaultAxesXMinorTick", "on"); +set(0, "DefaultAxesYMinorTick", "on"); + +set(0, 'DefaultAxesGridAlpha', 0.50); + +% exported ltspice data +filename = "trans_comp_utf8.txt"; + +fid = fopen(filename, "r"); + +% Skip header +fgetl(fid); + +% Read frequency and complex string +data = textscan(fid, "%f %s", "Delimiter", "\t"); + +fclose(fid); + +freq = data{1}; +response = data{2}; + +N = numel(freq); + +mag = zeros(N,1); +phase = zeros(N,1); + +for k = 1:N + tokens = regexp(response{k}, ... + '\(([-+0-9.eE]+)dB,([-+0-9.eE]+)°\)', ... + 'tokens'); + + mag(k) = str2double(tokens{1}{1}); + phase(k) = str2double(tokens{1}{2}); +end + +figure(1); +grid on; +set(gcf, "paperunits", "inches"); +set(gcf, "papersize", [10 5]); +set(gcf, "paperposition", [0 0 10 5]); +% theorical transfer function + +H1=tf([1 250], [1 500]) +H2=tf([4000^2], [1 4000^2/9000 4000^2]) +H=12*H1*H2 +bode(H) +[mag_the, pha_the, freq] = bode(H, freq); + +% bode functions returns linear scale y-axis +mag_the = squeeze(mag_the); +pha_the = squeeze(pha_the); +mag_the = 20*log10(mag_the); + +%% Magnitude +ax1 = subplot(2, 1, 1) +y1 = semilogx(freq*2*pi, mag, "LineWidth", 3); +grid on; +hold on; +y2 = semilogx(freq, mag_the, "LineWidth", 2); +ylim([-35 31]) +yticks([-20 0 20]); +xlim([1 1e5]) +% xlabel("Frequency [Hz]"); +ylabel("MAGNITUD [dB]"); +% title("Bode Magnitude"); +% legend("Normalizado", "Teórica", "Location", "southeast"); + +% Remove x tick labels from upper plot +set(ax1, "XTickLabel", []); + +%% Phase +ax2 = subplot(2, 1, 2) +semilogx(freq*2*pi, phase, "LineWidth", 3); +grid on; +hold on; +semilogx(freq, pha_the, "LineWidth", 2); + +ylim([-180 45]) +yticks([-180 -90 0]); +xlim([1 1e5]) +xlabel("FRECUENCIA [rad/s]"); +ylabel("FASE [grados]"); +% title("Bode Phase"); +% legend("Normalizado", "Teórica", "Location", "northeast"); + +% Invisible axes covering the whole figure +axL = axes("Position", [0 0 1 1], ... + "Visible", "off", ... + "Units", "normalized"); + +% Create legend on top axes +lgd = legend(axL, [y1 y2], ... + {"Resp. frecuencia circuito final", "Transferencia H"}); + +% Move legend between plots +set(lgd, "position", [0.25 0.54 0.10 0.05]); +set(lgd, "numcolumns", 1); + +% Reduce vertical spacing +set(ax1, "Position", [0.13 0.58 0.80 0.38]); +set(ax2, "Position", [0.13 0.13 0.80 0.38]); + +print("trans_comp.png", "-dpng", "-r500"); + diff --git a/tp/scripts/spice_exported_data_plots/trans_comp.png b/tp/scripts/spice_exported_data_plots/trans_comp.png Binary files differ. diff --git a/tp/scripts/spice_exported_data_plots/trans_comp.txt b/tp/scripts/spice_exported_data_plots/trans_comp.txt @@ -0,0 +1,642 @@ +Freq. 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(-7.87368134939450e+01dB,-1.65486300250693e+02°) +2.04173794466949e+05 (-7.91480066013832e+01dB,-1.65155793934375e+02°) +2.08929613085400e+05 (-7.95596966807254e+01dB,-1.64818490682810e+02°) +2.13796208950219e+05 (-7.99719044282087e+01dB,-1.64474282954376e+02°) +2.18776162394951e+05 (-8.03846512749498e+01dB,-1.64123064024312e+02°) +2.23872113856829e+05 (-8.07979594017792e+01dB,-1.63764728180246e+02°) +2.29086765276772e+05 (-8.12118517532945e+01dB,-1.63399170929198e+02°) +2.34422881531987e+05 (-8.16263520510048e+01dB,-1.63026289216281e+02°) +2.39883291901944e+05 (-8.20414848054338e+01dB,-1.62645981655262e+02°) +2.45470891568498e+05 (-8.24572753270379e+01dB,-1.62258148771122e+02°) +2.50000000000000e+05 (-8.27878991339887e+01dB,-1.61944784818410e+02°) diff --git a/tp/scripts/valores.py b/tp/scripts/valores.py @@ -11,7 +11,7 @@ E24_R = [ E24_R_custom = [ 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, - 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1 + 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2 ] # resistencias de 2% de error diff --git a/tp/scripts/valores_normalizados_H1.py b/tp/scripts/valores_normalizados_H1.py @@ -0,0 +1,68 @@ +import itertools + +# Capacitores +E6_C = [1.0, 1.5, 2.2, 3.3, 4.7, 6.8] + +# resistencias de 5% de error +E24_R = [ + 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, + 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1 +] + +E24_R_custom = [ + 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, + 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2 +] + +# resistencias de 2% de error +E48_R = [ + 1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40, 1.47, 1.54, 1.62, 1.69, + 1.78, 1.87, 1.96, 2.05, 2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01, + 3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42, 4.64, 4.87, 5.11, 5.36, + 5.62, 5.90, 6.19, 6.49, 6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53 +] + +# resistencias de 1% de error +E96_R = [ + 1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, + 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, + 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, + 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, + 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, + 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, + 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, + 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76 +] + +SERIE_R = E24_R_custom +SERIE_C = E6_C + +# décadas +DECADAS_R = [1, 10, 100, 1_000, 10_000, 100_000] +DECADAS_C = [1e-9, 10e-9, 100e-9, 1e-6] # pF–uF + +# lista de resistencias y capacitores disponibles +resistencias = [v * d for v, d in itertools.product(SERIE_R, DECADAS_R)] +capacitores = [v * d for v, d in itertools.product(SERIE_C, DECADAS_C)] + +# a = 1/(RC) +def find_lower_error(a, res_list=resistencias, cap_list=capacitores): + resultados = [] + + for R in resistencias: + C_ideal = 1/(250*R) + + for C in capacitores: + err = abs((C - C_ideal)/C_ideal)*100 + resultados.append((err, R, C, C_ideal)) + + resultados.sort(key=lambda x: x[0]) + + return resultados + +if __name__ == "__main__": + resultados = find_lower_error(250) + + print(" R [Ω] C [F] Cideal [F] Error [%]") + for err, R, C, Cideal in resultados[:20]: + print(f"{R:9.0f} {C:9.2e} {Cideal:9.2e} {err:6.2f}") diff --git a/tp/scripts/valores_sallen-key.py b/tp/scripts/valores_sallen-key.py @@ -0,0 +1,103 @@ +import itertools +from math import sqrt + +# Capacitores +E6_C = [1.0, 1.5, 2.2, 3.3, 4.7, 6.8] + +# resistencias de 5% de error +E24_R = [ + 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, + 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1 +] + +E24_R_custom = [ + 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, + 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2 +] + +# resistencias de 2% de error +E48_R = [ + 1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40, 1.47, 1.54, 1.62, 1.69, + 1.78, 1.87, 1.96, 2.05, 2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01, + 3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42, 4.64, 4.87, 5.11, 5.36, + 5.62, 5.90, 6.19, 6.49, 6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53 +] + +# resistencias de 1% de error +E96_R = [ + 1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, + 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, + 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, + 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, + 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, + 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, + 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, + 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76 +] + + +OMEGA0_OBJ = 4000.0 +Q_OBJ = 2.25 + +SERIE_R = E24_R_custom +SERIE_C = E6_C + +DECADAS_R = [1e3, 1e4, 1e5] +DECADAS_C = [1e-9, 10e-9, 100e-9, 1e-6] + +resistencias = [v*d for v, d in itertools.product(SERIE_R, DECADAS_R)] +capacitores = [v*d for v, d in itertools.product(SERIE_C, DECADAS_C)] + +def calc_params(R1, R2, C1, C2): + omega0 = sqrt(1/(R1*R2*C1*C2)) + Q = omega0 / ((R1 + R2) / (C1*R1*R2)) + + return omega0, Q + +def cost(omega, Q): + err_w = (omega - OMEGA0_OBJ) / OMEGA0_OBJ + err_q = (Q - Q_OBJ) / Q_OBJ + + return err_w**2 + err_q**2 + +resultados = [] + +for R1, R2, C1, C2 in itertools.product( + resistencias, + resistencias, + capacitores, + capacitores): + + omega, Q = calc_params(R1, R2, C1, C2) + + E = cost(omega,Q) + + resultados.append(( + E, + omega, + Q, + R1, + R2, + C1, + C2 + )) + +resultados.sort(key=lambda x: x[0]) + +print(f" R1 [Ω] R2 [Ω] C1 [F] C2 [F] w0 dw0 [%] Q dQ [%] cost") +for E, omega, Q, R1, R2, C1, C2 in resultados[:20]: + + errw = 100 * (omega - OMEGA0_OBJ)/OMEGA0_OBJ + errq = 100 * (Q - Q_OBJ)/Q_OBJ + + print( + f"{R1:8.0f} " + f"{R2:6.0f} " + f"{C1:8.2e} " + f"{C2:8.2e} " + f"{omega:6.1f} " + f"{errw:+7.2f} " + f"{Q:6.3f} " + f"{errq:+6.2f} " + f"{E:.3e}" + )
