15 lines
712 B
TeX
15 lines
712 B
TeX
\begin{align}
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H &= \frac{V_{ut}}{V_{inn}} \label{eq:frekvensresponsStart}\\
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|H| &= \sqrt{\text{Re}\left(H\right)^2 + \text{Im}\left(H\right)^2} \label{eq:amplituderesponsStart}
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\end{align}
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Vi kan bare regne ut $H$ direkte, fordi vi bare deler vekk $V_{inn}$
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\begin{align}
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H &= \frac{-j\frac{1}{\omega C} + j\omega L}{R-j\frac{1}{\omega C} + j\omega L} \nonumber\\
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&\phantom{1}\vdots \qquad\text{Regner ut og forenkler uttrykket} \nonumber\\
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H &= \frac{\left(\omega L - \frac{1}{\omega C}\right)^2}{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2} + j\frac{R\left(\omega L - \frac{1}{\omega C}\right)}{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2}
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\end{align}
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Finner deretter amplituderesponsen
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