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Ejercicio 4.25 Hambley (Amplificacion, emisor comun, Zi, Zo)

Solapas principales

Enviado por pichu en Jue, 07/26/2012 - 13:26

Solucion:

Zi

$\begin{displaymath}Z_{i}=\frac{v_{in}}{i_{in}}\end{displaymath}$

$\begin{displaymath}i_{in}=i_{b}+i_{R_{B}}\end{displaymath}$

$\begin{displaymath}v_{in}=r_{\pi}\,i_{b}\end{displaymath}$

$\begin{displaymath}v_{in}=v_{o}+R_{B}\,i_{R_{B}}\end{displaymath}$

Utilizando una ecuacion del problema anterior.

$\begin{displaymath}v_{o}=(-\beta\,v_{i}\,R_{B}+r_{\pi}\,v_{i})\,\frac{R'_{L}}{(R'_{L}+R_{B})\,r_{\pi}}\end{displaymath}$

$\begin{displaymath}v_{in}=v_{o}+R_{B}\,i_{R_{B}}=(-\beta\,v_{i}\,R_{B}+r_{\pi}\,v_{i})\,\frac{R'_{L}}{(R'_{L}+R_{B})\,r_{\pi}}+R_{B}\,i_{R_{B}}\end{displaymath}$

$\begin{displaymath}v_{in}\,(1-(-\beta\,R_{B}+r_{\pi})\,\frac{R'_{L}}{(R'_{L}+R_{B})\,r_{\pi}})=R_{B}\,i_{R_{B}}\end{displaymath}$

$\begin{displaymath}Z_{i}=\frac{v_{in}}{i_{in}}=\frac{(R'_{L}+R_{B})\,r_{\pi}}{(R'_{L}+R_{B}+r_{\pi}+\beta\,R'_{L})}\end{displaymath}$
Zo

$\begin{displaymath}Z_{o}=\frac{v_{o}}{i_{o}}\end{displaymath}$

$\begin{displaymath}v_{o}=R_{B}\,(i_{b}+\frac{r_{\pi}\,i_{b}}{R_{S}})+r_{\pi}\,i_{b}\end{displaymath}$

$\begin{displaymath}i_{b}=\frac{R_{s}\,v_{o}}{(R_{B}\,R_{S}+r_{\pi}(R_{B}+R_{S}))}\end{displaymath}$

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