commit 0db7b6de9dfd4618fc66b4b6d9cd326cd4794d14
parent c46204202ad64f4923cdb8d5e58e83321cad16bd
Author: Martin Kloeckner <mjkloeckner@gmail.com>
Date: Mon, 24 Nov 2025 12:56:49 -0300
$k_{1,2,3,4}$ Heaviside response coefficients
Diffstat:
1 file changed, 42 insertions(+), 0 deletions(-)
diff --git a/tp/informe/informe.tex b/tp/informe/informe.tex
@@ -745,6 +745,48 @@ como se muestra en \ref{eq-l-f-U-simp}.
\label{eq-l-f-U-simp}
\end{align}
+Para calcular los coeficientes $k_{1,2,3,4}$ se utiliza la ecuacion
+\ref{eq-calculo-ki}.
+
+\begin{align}
+ k_{1} &= \lim_{s\to -500}
+ \dfrac{\left(s + 250\right)}
+ {\left(s^{2} + \dfrac{4000^{2}}{9000}s + 4000^{2}\right)}
+ \cdot
+ \dfrac{1}{s}\; \Rightarrow \boxed{k_{1}\approx -4.05\cdot 10 ^{-3}}
+ \label{eq-calculo-u-k1}
+\end{align}
+
+\vspace{-1em}
+\begin{align}
+ k_{2} &= \lim_{s\to \frac{-8000}{9}+j3900}
+ \dfrac{\left(s + 250\right)}
+ {\left(s + 500\right)
+ \cdot\left(s - \left(\dfrac{-8000}{9}-j3900\right)\right)}
+ \cdot\dfrac{1}{s}\nonumber\\[6pt]
+ &\hspace{2em} \boxed{k_{2}\approx -7.99\cdot 10^{-3} + j493.6\cdot10^{-6}}
+ \label{eq-calculo-u-k2}
+\end{align}
+
+\vspace{-0.5em}
+\begin{align}
+ % k_{3} = k_{2}^{*} \Longrightarrow \boxed{k_{3}\approx -495 - j7849}
+ k_{3} = k_{2}^{*} \Rightarrow \boxed{k_{3} \approx -7.99\cdot 10^{-3} - j493.6\cdot10^{-6}}
+ \label{eq-calculo-u-k3}
+\end{align}
+
+
+\begin{align}
+ k_{4} &= \lim_{s\to 0}\ s
+ \cdot
+ \dfrac{\left(s + 250\right)}{\left(s + 500\right)}
+ \cdot
+ \dfrac{1}
+ {\left(s^{2} + \dfrac{4000^{2}}{9000}s + 4000^{2}\right)}
+ \cdot
+ \dfrac{1}{s}\Rightarrow \boxed{k_{4} \approx -31.3\cdot 10 ^{-9}}
+ \label{eq-calculo-u-k4}
+\end{align}
\pagebreak
\hypertarget{respuesta-a-señal-senoidal}{%
