Bradygoodz

About a month ago my passenger side converter or resonator started to make a ringing noise after a while it got annoying so I cut it off and bought a 18 inch 2 and a quarter inch pipe and two clamps and some exhaust sealer. I really wanted to get a off road y pipe with simulators but since im in school im short on cash.Well heres my question people have told me that i would trip a code and mess up my motor, but I left the sensor in right after where the cat was.And I havent seen the engine light on so far and my car seems to run smoother without that clogged up cat and it seems to shift alot smoother for some reason.Any info on why that is or if I did something i shouldnt have woulld be greatlt appreciated.Thanks