sgsawant said:
Thanks for your reply. But the cases where 2 * zeta * omega is valid - for those that I have seen - have omega squared in the numerator and also as the constant in the quadratic of s in the denominator. Thus omega can be usually simply calculated (either by taking the root of the numerator or that of the constant term in the denominator).
Yes, that's the case for a second order
lowpass system (or a second order lowpass
section of a more complex system).
The transfer function of a second order lowpass system
H(
s) takes the form
H_{LP}(s) = A_0 \frac{\omega_0^2}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}
Note that at low frequencies (frequencies can be seen by replacing
s with
jω),
H(
jω) approaches
A0. But at high frequencies,
H(
jω) approaches 0; meaning only the low frequencies get through.
But there are other types of second order systems. A second order
highpass system takes the form
H_{HP}(s) = A_0 \frac{s^2}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}.
Here, only the high frequencies make it through.
Similarly for a bandpass we have:
H_{BP}(s) = A_0 \frac{2 \zeta \omega_0 s}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}.
And bandstop,
H_{BS}(s) = A_0 \frac{s^2 + \omega_0^2}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}.
Note that the denominator is the same in all types.
What method would you advice in this case to calculate omega - and then eventually zeta?
The numerator (i.e. zeros) of your transfer function doesn't seem to quite fit with any of the standard second order systems. But if I remember correctly, both the the resonant (natural) frequency and the damping factor are functions of the pole locations, not the zeros.
