If we have a transfer function that shows no peaking in the magnitude bode plot (Starting from a flatline and then rolling off). Does this mean that there is no resonant frequency? Or do we consider the point at which the curve begins to roll off the resonant frequency?
I understand that resonant frequency is the location at which we have the maximum value so I'm assuming that there isn't a resonant frequency in this case but I wanted to be sure.
Best Answer
My answer applies to higher-than-1st-order systems.
There will always be a resonant point even if you can't see it. You need to understand how "poles" work. Take a look at this: -
Even if there doesn't appear to be a resonance in the bode plot there will be a "pole" that is present and this pole represents the resonant frequency even though the "dampening" is causing it not to appear in the bode plot. Here is what a 2nd order low pass filter looks like with varying degrees of Q (where Q = \$\dfrac{1}{2\zeta}\$): -
If you could determine the phase angle where the output shifted by 90 degrees from the input you would find the resonant frequency even if it doesn't appear to have a "peak" in the bode plot.