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Definition

A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a certain cutoff frequency.

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Circuit of low-pass filter

Cut-Off Frequency: $f_c = \frac{1}{2\pi R C} =$ 159 Hz
Time-Constant $\tau$ $= RC = \frac{1}{2\pi f_C} =$ 6.28ms
Amplitude at $f_c$ is $U(f_c)=\frac{U(0)}{\sqrt{2}} =$ 3.54 V
Dynamic: $I_C = C \cdot \dot U_C$

Filter Response:

$V_{\mathrm{out}} = V_{\mathrm{max}} \left( 1 - \exp( - t/\tau) \right)$
$V_{\mathrm{out}}$ will reach $V_{\mathrm{max}}$ after 3 to $4 \tau$.

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