Hi all, I have a doubt about RLC filter networks of order \(n \geq 3\).
If we consider the canonical form of the denominator of a transfer function:

\(s^2 + 2\zeta\omega_0s + \omega_0^2 = s^2 + {\omega_0 \over Q}s+ \omega_0^2\)

Solving for \(\omega_0\) is straightforward.
But what about high order networks ? How to determine it ? Given \(n\) the order of the network, will just be:

\(\sqrt[n]{\omega_0\omega_1\omega_2\ _{...}\ \omega_n}\)

The question arise from calculating the central resonant frequency of high order bandpass and highpass filters.

I think I am missing some important mathematical theorem, but I am not certain of it.

Thank you in advance.

 

In higher order filters of odd order there is a single pole on the real axis and the remaining poles are complex conjugate pairs.
In higher order filters of even order there are n/2 complex conjugate poles.
Usually the addition of poles will steepen the rolloff of the filter without changing the corner frequency. At least that has been my experience.
From the pole locations and a knowledge of Complex Analysis you can determine everything you need to know about a filter.

 

Hi papabravo, thank you.

I have to do more self tests with high order networks, but after your response I thought ... No real poles ?