The AMS1117 is a linear voltage regulator. Reading the datasheet of AMS1117, it says this:
The circuit design used in the AMS1117 series requires the use of an output capacitor as part of the device frequency compensation. The addition of 22μF solid tantalum on the output will ensure stability for all operating conditions.
I have recently learnt that linear voltage regulators use a negative feedback loop to keep the output voltage stable. I then realized that this means that there exists a transfer function and logically a bode plot with gain and phase margin. These details are obviously not given.
A linear time invariant control system becomes unstable mainly if the gain is more than 1 when the phase shift is -180. Basically this causes the system to become positive feedback rather than negative feedback.
How does using a tantalum capacitor specifically make the voltage regulator control loop stable? Is it possible for a user to observe oscillation or even instability of voltage regulator output when not using an output capacitor?