I would like to draw Bode plot for a complex pole as below. Let's assume that for now regardless that the single complex pole doesn't exist. This is the function:
$$H = \frac{1}{s - (a + jb)}$$ where \$a\$ and \$b\$ are real numbers.
Now I would like to draw Bode plot of this transfer function. First, substitute \$s\$ by \$j\omega\$ and we have:
$$H(j\omega) = \frac{1}{-a + j(\omega -b)}$$
From this I can calculate the magnitude and phase and draw Bode diagram.
I want to calculate break frequency (the frequency where the gain is 0.707 value of DC gain).
My questions are:
Is that method correct to draw Bode plot of a single complex pole?
Is my method of break frequency calculation correct?
Assume that I have a second order transfer function as under-damped system. The transfer function has two complex poles. Does this mean it has two break frequencies?
Can I draw Bode plot of the under-damped system by plot Bode diagram of each single complex pole separately and then sum or subtract them?