Regarding phase margin adjustments using a capacitor and resistor connected to the ITH pin, if the resistor is increased from the normal value of 9.1 kΩ to for example 27 kΩ, what happens to the phase and gain margins?
Both the phase margin and the gain margin will tend to be worse. When the resistance is increased, the feedback loop zero point moves to lower frequencies. The zero point raises the gain, and so movement of the zero point to lower frequencies causes the crossover frequency to move to higher frequencies. The phase lags as the frequency moves higher, and consequently, due to broadening of crossover frequencies and the phase lag at higher frequencies, both the phase margin and the gain margin are worsened.