# About choosing the right point to be the cutoff frequency

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!

• Matlab is correct in selecting this point. However, how did you obtain this compensated transfer function? It looks like that of a buck converter operated in voltage-mode control? If this is the case, then the crossover frequency is not selected far enough from the resonating peak. It should be at least 3-5 times this value. It looks to me that you have placed zeroes in the low-frequency part and it can explain why you have the multiple crossover points. By shifting crossover to higher values, the zeroes will go up and should let the magnitude curve fly well above the 0-dB axis before $f_c$. Apr 6, 2022 at 11:19
• Thanks for your answer! !In fact, I'm trying to design a compensation loop for boost in voltage-mode control, and I can't set the cutoff frequency too high because of the inherent right-half-plane zero of boost. It is mentioned in some literature that the cutoff frequency should be set to within 1/3 of the right half plane zero to ensure sufficient stability margin . The open-loop gain obtained after the design is the one above. Could you please explain in detail why the phase margin is not calculated by taking the first point passing through 0dB? Looking forward to your answer！
– T L
Apr 6, 2022 at 12:27
• I see, in this case, if you are stuck with the RHP zero of the boost, then increase the output capacitance to shift the resonance at a lower value - this will not affect the RHP zero - and you should be able to place the zeroes differently, usually at the resonance or so. Reduce $f_c$ to 20% of the lowest RHPZ as 30% can lead to marginal results. What matter is a loop gain with a magnitude of 1 so the point where the margin is critical in your example is after the peak as it is very large before. If time permits, I will try to write an answer tonight. Apr 6, 2022 at 13:17
• Thank you! I will try to improve my compensator design by changing the resonant frequency by changing the value of the output capacitor as you suggested. Thanks again for your selfless help!
– T L
Apr 7, 2022 at 0:42

## 1 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.

• Thanks！Learn a lot！Maybe I should read your book carefully before asking questions. I have bought your Designing Control Loops for Linear and Switching Power Supplies: a Tutorial Guide. Ashamed that I started trying to design the circuit before I even started watching the book.
– T L
Apr 8, 2022 at 2:59
• You now have some material to study and I wish you luck with your design! Apr 8, 2022 at 5:15