Should the Opamp behave like a first order filter till unity gain for better stability? Why? Cause second order behaviour is also stable since -180 degrees is only reached at infinite frequency. Thanks.
Look up Barkhausen stability criteria
If negative feedback becomes positive feedback ( due to 3rd order influence) at Av=1 or more , it is unstable. and gain margin is needed such as 10 or 15dB
in real world each stage has Miller capacitance so each stage adds 1 order of effects so 1st order must be much lower.to suppress the higher orders to define the GBW product.
Should the Opamp behave like a first order filter till unity gain for better stability? Why? Cause second order behaviour is also stable since -180 degrees is only reached at infinite frequency. Thanks.
Yes, it`s true - under ideal condtions only (no parasitic pin capacitances and resistive feedback). But the stability margin may be unacceptable small.
On the other hand- you have mentioned "better stability". Of course, the stability is improved for less phase excursions (first order response).