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Low Pass Filter#

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

Click on the values to change them! E.g. change "10k" to "20k". All equations and figures in the step response will adjust immediately!

10k 100n C R U(0) 5
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:#

t [ms] 5.00 3.16 0 Vout [V] 0 1.0 2.0 3.0 4.0

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