# Resonant frecuency in high order filters

Discussion in 'General Electronics Chat' started by simo_x, Jun 7, 2015.

1. ### simo_x Thread Starter Member

Dec 23, 2010
200
6
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.

2. ### Papabravo Expert

Feb 24, 2006
11,065
2,152
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.

simo_x likes this.
3. ### simo_x Thread Starter Member

Dec 23, 2010
200
6
Hi papabravo, thank you.

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