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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: fc=12πRC=f_c = \frac{1}{2\pi R C} = 159 Hz
Time-Constant τ\tau =RC=12πfC== RC = \frac{1}{2\pi f_C} = 6.28ms
Amplitude at fcf_c is U(fc)=U(0)2=U(f_c)=\frac{U(0)}{\sqrt{2}} = 3.54 V
Dynamic: IC=CU̇CI_C = C \cdot \dot U_C

Filter Response:

Vout=Vmax(1exp(t/τ))V_{\mathrm{out}} = V_{\mathrm{max}} \left( 1 - \exp( - t/\tau) \right)
VoutV_{\mathrm{out}} will reach VmaxV_{\mathrm{max}} after 3 to 4τ4 \tau.