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
    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.
  2. Papabravo


    Feb 24, 2006
    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
    Hi papabravo, thank you.

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