Is there an explicit formulation for n-cascaded RC filters?
The resistor and capacitor values are not necessarily same. Assume that:
$ R_i \neq R_j $ and $ C_i \neq C_j $ for $ i \neq j$ and $ 1 \leq i,j \leq n $.
I built a 5th degree filter with $R_i=1k\Omega$, $C_i=1\mu F$ and $V_{in}=1\sin(2\pi \times 1kHz) \; V$. The output signal was nearly smooth for a $1k\Omega$ lead. And rise of the output signal was visible by eye when the input was a step signal.
I tried to find transfer response of this 5th order filter, but after the 3rd order, the size of A4 paper became insufficient for writing the expressions.
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