Improve the performance of Buck Converter Loop Stability
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.