Monday 22 September 2014

low pass - What is the transfer function of n-cascaded RC filters?


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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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