User:DX-MON/DACS ACD

Formulae
$$\frac{1.3}{4\times10^{-3}} = 325\Omega$$

$$ \begin{align} \frac{15}{8.4\times10^{-3}} &\approx 1786\Omega\\ 1786 - 330 &= 1456\Omega \approx 1.5\text{k}\Omega \end{align} $$

$$ \begin{align} \tau &= 2\pi\\ f_c &= \frac{1}{\tau RC}\text{Hz}\\ C &= 10\text{nF}\\ R &= 1\text{k}\Omega\\ \mu &= RC\\ &= \left ( 10\times10^{-9} \right ) \times \left ( 1\times10^{3} \right ) \\ &= 10\times10^{-6}\\ f_c &= \frac{1}{\tau\mu}\\ &= 15915.45709 \text{ (to 5 decimal places)}\\ &\approx 15915\text{Hz} \end{align} $$

$$ \begin{align} \tau &= 2\pi\\ f_c &= \frac{1}{\tau RC}\text{Hz}\\ C &= 10\text{nF}\\ R &= 10\text{k}\Omega\\ \mu &= RC\\ &= \left ( 10\times10^{-9} \right ) \times \left ( 10\times10^{3} \right ) \\ &= 10\times10^{-4}\\ f_c &= \frac{1}{\tau\mu}\\ &= 1591.54571 \text{ (to 5 decimal places)}\\ &\approx 1592\text{Hz} \end{align} $$

Results
$$ \begin{align} V_1 &= 4.98\\ V_2 &= 2.60 \end{align} $$

$$ \begin{align} V_1 &= 4.96\\ V_2 &= 4.30 \end{align} $$

$$ \begin{align} V_\text{in} &= 105\text{mV}\\ V_\text{out} &= 524\text{mV}\\ \text{gain} &= \frac{V_\text{out}}{V_\text{in}} \approx 5 \end{align} $$

$$ \begin{align} V_{ds} &= 7\text{V}\\ V_{gs} &= 1.3\text{V}\\ \text{gain} &= \frac{V_{ds}}{V_{gs}} \approx 5.38 \end{align} $$