# Improve the performance of Buck Converter Loop Stability

The following are the specifications of my Buck Converter.

Input Voltage Range : 6V to 16V

Output Voltage : 5V

Switching Freq : 2.1MHz

Output Inductor : 22uH

I have output capacitors of 2 qty of 10uF (25V 1206 package) and one Feedforward capacitor of 10pF (0603 package).

Added feedforward capacitor to improve the loop stability performance based on the recommendations given by this AppNote

I'm using Omicron Bode 100 to perform and view the loop stability analysis.

Since my switching frequency is 2.1MHz, My crossover frequency should be atleast 1/10 or 1/20 of my switching frequency. Which happens to be around 105kHz. But from testing, I am observing the gain crossover frequency of less than 105kHz at the mentioned voltage ranges and minimum to maximum load currents.

Could you please provide the reasons why this is happening and provide me a solution to improve the crossover frequency to meet the criteria.

• Is that your actual circuit - as per LMR14020 data sheet front page? Or ...? Feb 25 '20 at 3:32
• The specification details I have provided is my circuit. The schematic circuit provided in the front page is not mine. Feb 25 '20 at 7:48
• Since all is internal, there is not much you can do to shape the compensation differently. Adding the extra capacitor is a possible patch but one major concern that arises when one wants to extend $f_c$ is the lack of open-loop gain and the low frequency pole location of the op-amp. Unfortunately, there is not much information about the internal op-amp. Feb 25 '20 at 7:59
• Ok. How to come up with the capacitor value that needs to be added? Any suggestions or calculations you can help me with? Feb 25 '20 at 8:01
• The specification details are NOT your circuit. Often enough (actually, far too often) people insiste that there circuits are obvious or contained in a word description or ...., and it is in due course found that the circuit is not what anyone but them expected. Feb 25 '20 at 11:51

The addition of a capacitor across the upper-side resistor is not as straightforward as what the TI application note implies. First off, you need to make sure that there is no virtual ground at the FB pin meaning that the compensator is an operational transconductance amplifier or OTA. This is important to verify because if this is an op-amp, then the virtual ground at the FB pin excludes the low-side resistor which does not play a role in the ac analysis. Adding the single capacitor in this case will produce a single zero without a pole. If you want a pole for proper gain roll-off at higher frequencies, then a series resistance needs to be added to the added capacitor and you have a type 3. Anyway, assuming the internal compensator in the TI part is an OTA, the equivalent circuit is this one:

The transfer function including the capacitor has been derived in the book I wrote on loop control:

So you see that you add a zero and pole whose distance is fixed and given by $$\R_{upper}\$$ and $$\R_{lower}\$$. What TI proposes is to determine the capacitor value so that you center the geometric mean at the selected (or measured) crossover frequency $$\f_c\$$ where the phase boost is maximum between the added pole and zero. However, doing so will add gain and the original $$\f_c\$$ may go up significantly. In the below graph, I have designed the type 2 OTA-based compensator to boost the phase by 50° and provide a 20-dB gain at 1 kHz.

In the example I have chosen, the formula given by TI recommends a capacitor of 9.2 nF to be paralleled with $$\R_{upper}\$$. When I do that, the curve at 1 kHz shifts up by 6.8 dB and you will now surely crossover at a farther 0-dB point. Unfortunately, as the phase boost peaks at 1 kHz, it can happen that at the next crossover point reached via the addition of $$\C_3\$$ the phase boost is even lower than the original value (beyond 4 kHz on the graph). I think this is what the author observes in one of the application note. Besides, if the power stage lags more at the next crossover, you may end-up in a completely unstable converter.

As a conclusion, be cautious when adding the capacitor so that the new crossover frequency coincides with a sufficiently-high boost to gain in stability while the crossover has extended.

• Thank you for the answer. What solution would you recommend to improve my cross-over frequency? Mar 3 '20 at 4:26
• What solution would you recommend Mar 3 '20 at 9:52
• It is difficult to recommend anything without looking at the loop gain and the original control-to-output transfer function of the power stage. One way perhaps could be to reduce a bit the output capacitor value as it should reduce the attenuation at the current crossover but the ripple will increase so it has to be carefully considered. When the compensation is inside a part, you are pretty much stuck! What current crossover do you have with what phase margin? Mar 3 '20 at 10:02
• Thank you. Give me sometime. I will do the changes and come back Mar 3 '20 at 11:06