If there are multiple points across 0dB in the open loop transfer function bode plot, which one should I take as the cutoff frequency to calculate the phase margin?
In Matlab, it seems that the last point that crosses 0dB from top to bottom is taken as the cutoff frequency to calculate the phase margin.
Any answer is a great help to me, thank you!
Cutoff Frequency – Choosing the Right Point for Cutoff Frequency
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Best Answer
What you see on this Bode plot is the effect of a crossover frequency \$f_c\$ that is selected too close to the resonating peak. You should normally select a crossover value that is at least 3-5 times beyond the resonance. This is to make sure the system has gain at resonance and can effectively reject oscillations.
In the below circuit, I have simulated a voltage-mode-controlled boost converter featuring a 100-µF output capacitance. The RHPZ is evaluated at 14.5 kHz in worst-case which suggests a maximum crossover of 20% of this value, i.e. 2.9 kHz:
If you run the simulation in this mode, compensating the converter for a 2-kHz crossover, you see below the multiple crossover points occurring as in your plot:
This is because of the zeroes placed before crossover which affect the loop gain in the 200-400-Hz region. To improve the situation and respect the 3-5 times relationship between the peak and crossover, the easiest way is to move the peak to a lower frequency. Increasing the inductance value is a bad option as it will affect the RHPZ and bring it even lower. The fastest and simplest way - if cost and size permit of course - is to increase the output capacitance. In the below example, increasing the capacitance to 680 µF while resizing the compensator does the job with a single crossover point around 2 kHz:
These examples can be downloaded from my webpage and are part of the free 60+ ready-made simulation templates working with the demo version of SIMPLIS that I recently released.