Equations describing a low pass filter
The time equation of the low pass filter is:
\[ v_{OUT}(t) = v_{IN}(t) - RC \cdot \frac{dv_{OUT}}{dt} \]
The transfer function of the low pass filter is:
\[ H(s) = \frac{1}{RC \cdot s+1} \]
The discrete equation of the low pass filter is:
\[ v_{OUT}[k] = \alpha v_{IN}[k] + (1 - \alpha) v_{OUT}[k-1] \]
where \( \alpha = \frac{\Delta t}{RC + \Delta t} \)
Electric circuit of a low pass filter
where:
- vIN [V] - input voltage
- vOUT [V] - output voltage
- R [Ω] - resistance
- C [F] - capacitance