Calculo teorico del amplificador multietapa, Av, fl, fh, Zi, Zo

Enunciado de la Practica
Calculo teorico del amplificador multietapa, Av, fl, fh, Zi, Zo

Frecuencias medias
La primera etapa es un amplificador emisor comun.

$\begin{displaymath}\beta=290\end{displaymath}$

$\begin{displaymath}r_{\pi_{1}}=\frac{V_{T}}{I_{B_{1}}}=\frac{26\,10^{-3}}{19.61\,10^{-6}}=1325.85\,\Omega\end{displaymath}$

$\begin{displaymath}R_{i_{1}}=R_{1}\vert\vert R_{2}\vert\vert(r_{\pi})=1309\,\Omega\end{displaymath}$

$\begin{displaymath}R'_{L}=R_{i_{2}}\vert\vert R_{C_{1}}\end{displaymath}$

$\begin{displaymath}R_{o}=R_{C_{1}}=1\,k\Omega\end{displaymath}$

$\begin{displaymath}A_{v_{1}}=-\frac{\beta \,R'_{L_{1}}}{r_{\pi}+0}\end{displaymath}$

La segunda etapa es un amplificador seguidor de emisor.

$\begin{displaymath}\beta=190\end{displaymath}$

$\begin{displaymath}r_{\pi_{2}}=\frac{V_{T}}{I_{B_{1}}}=\frac{26\,10^3}{6.66\,10^{-6}}=3903.9\,\Omega\end{displaymath}$

$\begin{displaymath}A_{v_{2}}=\frac{(\beta+1)\,R'_{L_{2}}}{r_{\pi}+(\beta+1)\,R'_{L_{2}}}=0.99\end{displaymath}$

$\begin{displaymath}R'_{L_{2}}=R_{E_{2}}\vert\vert R_{L_{2}}=R_{E_{2}}=3.3\,k\Omega\end{displaymath}$

$\begin{displaymath}R_{o_{2}}=R_{E_{2}}\vert\vert\frac{r_{\pi}+R'_{S_{2}}}{\beta+... ...0^3\vert\vert 330\,10^3\vert\vert 330\,10^3}{191}=25.45\,\Omega\end{displaymath}$

$\begin{displaymath}R_{i_{2}}=R_{B}\vert\vert(r_{\pi}+(\beta+1)\,R'_{L_{2}})=130.78\,k\Omega\end{displaymath}$

$\begin{displaymath}R'_{L_{1}}=130.78\,10^3\vert\vert 1\,10^3=992.41\,\Omega\end{displaymath}$

$\begin{displaymath}A_{v_{1}}=\frac{\beta\,R'_{L_{1}}}{r_{\pi}+0}=\frac{290\cdot 992.41}{1325.85+0}=217.15\end{displaymath}$

$\begin{displaymath}A_{v}=A_{v_{1}}\,A_{v_{2}}=-214.97\end{displaymath}$

$\begin{displaymath}R_{i}=1309\,\Omega\end{displaymath}$

$\begin{displaymath}R_{0}=25.45\,\Omega\end{displaymath}$

Frecuencias bajas

$\begin{displaymath}f_{L_{1}}=\frac{1}{2\,\pi\,(R_{i}+R_{s})\,C_{1}}=\frac{1}{2\cdot\pi\cdot (1309+50)\cdot 100\,10^{-9}}=1.17\,kHz\end{displaymath}$

$\begin{displaymath}f_{L_{2}}=\frac{1}{2\,\pi\,(R_{o_{1}+R_{i_{2}}})\,C_{2}}=\fra... ...{2\cdot\pi\cdot(1\,10^3+130.78\,10^3)\cdot 100\,10^{-9}}=12\,Hz\end{displaymath}$

$\begin{displaymath}f_{L_{3}}=\frac{1}{2\,\pi\,R'_{E_{1}}\,C_{E}}=\frac{1}{2\,\pi... ...ert\vert 150\,10^3\vert\vert 50}{291}))\,4.7\,10^{-6}}=7.3\,kHz\end{displaymath}$

$\begin{displaymath}f_{L}=7.3\,kHz\end{displaymath}$

Frecuencias altas

$\begin{displaymath}f_{T}=100\,MHz\end{displaymath}$

$\begin{displaymath}C_{\mu_{1}}=1.5\,pF\end{displaymath}$

$\begin{displaymath}C_{\pi_{1}}=\frac{\beta_{1}}{2\,\pi\,r_{\pi_{1}}\,f_{T_{1}}}-... ...{1}}=\frac{290}{2\,\pi\,1325.85\,100\,10^{6}}-C_{\mu}=346.6\,pF\end{displaymath}$

$\begin{displaymath}R'_{S_{1}}=r_{\pi_{1}}\vert\vert(r_{x_{1}}+(R_{1}\vert\vert R... ...(0+(330\,10^3\vert\vert 150\,10^3\vert\vert 50))=48.16\,\Omega \end{displaymath}$

$\begin{displaymath}R'_{L_{1}}=R_{i_{2}}\vert\vert R_{L_{1}}=130.78\,10^3\vert\vert 1\,10^3=992.41\,\Omega\end{displaymath}$

$\begin{displaymath}g_{m_{1}}=\frac{\beta}{r_{\pi}}=\frac{290}{1325.85}=0.22\end{displaymath}$

$\begin{displaymath}C_{T_{1}}=C_{\pi}+C_{\mu}\,(1+g_{m}\,R'_{L})=346.6\,10^{-12}+328\,10^{-12}=675.2\,pF\end{displaymath}$

$\begin{displaymath}f_{H_{1}}=\frac{1}{2\,\pi\,R'_{S}\,C_{T}}=4.89\,MHz\end{displaymath}$

$\begin{displaymath}f_{T}=250\,MHz\end{displaymath}$

$\begin{displaymath}C_{\mu_{1}}=4.5\,pF\end{displaymath}$

$\begin{displaymath}C_{\pi_{2}}=\frac{\beta_{1}}{2\,\pi\,r_{\pi_{2}}\,f_{T_{2}}}-... ..._{2}}=\frac{190}{2\,\pi\,3903.9\,250\,10^{6}}-C_{\mu}=26.48\,pF\end{displaymath}$

$\begin{displaymath}R'_{S_{2}}=(r_{x_{2}}+(R_{3}\vert\vert R_{4}\vert\vert R_{o_{1}}))=(0+(330\,10^3\vert\vert 330\,10^3\vert\vert 1\,10^3))=993.97\end{displaymath}$

$\begin{displaymath}R'_{L_{2}}=R_{E_{2}}\vert\vert R_{L_{2}}=3.3\,k\Omega\end{displaymath}$

$\begin{displaymath}g_{m_{2}}=\frac{\beta}{r_{\pi}}=\frac{190}{3903.9}=0.05\end{displaymath}$

$\begin{displaymath}C_{T_{2}}=C_{\mu}+\frac{C_{\pi}}{1+g_{m}\,R'_{L}}=4.5\,10^{-12}+\frac{26.48\,10^{-12}}{1+0.05\cdot 3.3\,10^3}=4.65\,pF\end{displaymath}$

$\begin{displaymath}R_{T_{2}}=R'_{S}\vert\vert(r_{\pi}+(1+g_{m}\,R'_{L}))=993.97\vert\vert(3903.8+(1+0.05\cdot 3.3\,10^3))=798.86\,\Omega\end{displaymath}$

$\begin{displaymath}f_{H_{2}}=\frac{1}{2\,\pi\,R'_{T}\,C_{T}}=\frac{1}{2\cdot \pi\cdot 798.86\cdot 4.65\,pF}=42.78\,MHz\end{displaymath}$

$\begin{displaymath}f_{H}=4.89\,MHz\end{displaymath}$