# Low Pass Filter#

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

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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 $$4 \tau$$.